An Empirical Comparison of Multiple Linear Regression and …downloads.hindawi.com/journals/mpe/2019/7620948.pdf · is paper studies the application characteristics and eects of the

Research ArticleAn Empirical Comparison of Multiple LinearRegression and Artificial Neural Network forConcrete Dam Deformation Modelling

Mingjun Li and JunxingWang

State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Wuhan 430072 China

Correspondence should be addressed to JunxingWang jxwangwhueducn

Received 12 January 2019 Revised 6 March 2019 Accepted 24 March 2019 Published 17 April 2019

Academic Editor Łukasz Jankowski

Copyright copy 2019 Mingjun Li and Junxing Wang This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Deformation predicting models are essential for evaluating the health status of concrete dams Nevertheless the application ofthe conventional multiple linear regression model has been limited due to the particular structure random loading and strongnonlinear deformation of concrete dams Conversely the artificial neural network (ANN) model shows good adaptability tocomplex and highly nonlinear behaviors This paper aims to evaluate the specific performance of the multiple linear regression(MLR) and artificial neural network (ANN)model in characterizing concrete dam deformation under environmental loads In thisstudy four models namely the multiple linear regression (MLR) stepwise regression (SR) backpropagation (BP) neural networkand extreme learning machine (ELM) model are employed to simulate dam deformation from two aspects single measurementpoint and multiple measurement points approximately 11 years of historical dam operation records Results showed that theprediction accuracy of the multipoint model was higher than that of the single point model except the MLR model Moreoverthe prediction accuracy of the ELM model was always higher than the other three models All discussions would be conducted inconjunction with a gravity dam study

1 Introduction

Deformation modelling is an important component of damsafety systems both for the daily operation and for long-term behavior evaluation [1] They are built to calculatethe dam response under safe conditions for a given loadcombination which is compared to actual measurements ofdam performance with the aim of detecting anomalies andpreventing failures Current predictive models for simulatingdam deformation can be classified as three types determin-istic models statistical models and hybrid models [2] ie amixture of the first two

Deterministic models based on physical laws such asload material properties and stress-strain relationships areoften used to design dams and function throughout the lifeof concrete dams [3] Anomalies in the operation of con-crete dams can be fundamentally explained by deterministic

models whose parameters have specific physical meaningsuncertainties existing in geological conditions and inmaterialproperties of rock base and concrete hinder the implementa-tion of deterministic models

Statistical models are mathematical equation that quan-titatively describe the variation law of dam monitoringvalues and are the abstraction and simplification of theactual working state of the dam [4] Without regard to thespecific physical mechanism of dam operation the statisticalmodel is essentially an empirical model based on dammeasurement data over years As the most widely usedmodel for characterizing concrete dam deformation thestatistical model usually consists of three parts tempera-ture component hydrostatic pressure component and agingcomponent The statistical model assumes that the compo-nents are completely independent and may not match theactual situation [5] At present the most common statistical

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 7620948 13 pageshttpsdoiorg10115520197620948

2 Mathematical Problems in Engineering

models are based on regression methods such as the mul-tiple linear regression (MLR) [6] stepwise regression (SR)[7] principal component regression (PCR) [8] and partialleast squares regression (PLSR) [9] By gradually screeningregression factors of MLR models SR models obtain regres-sion coefficients at a certain significance level results moreaccurate than those obtained by the general least squaremethod

In recent years more and more scholars have begun toapply machine learning algorithms or intelligent algorithmsto dam safety effect prediction or dam safety diagnosis analy-sis [2 10 11] Mata [12] found that ANNmodels can be a verypowerful tool in evaluating dam behavior by comparing themultiple linear regression model with the multilayer percep-tronmodel for the horizontal displacement of a concrete archdam F Salazar [2] assessed the potential of some state-of-the-art machine learning techniques including random forestsboosted regression trees neural networks and multivariateadaptive regression splines to build models for the predictionof dam behavior in the field of displacement and leakage Kao[13] studied the feasibility of ANN-based approaches for damhealth monitoring and set an early warning threshold levelof the Fei-Tsui dam based on the analysis results But theartificial neural network based on gradient descent methodis still relatively slow and easily gets stuck Su [14] proposeda dam safety monitoring model based on support vectormachine which could overcome the disadvantages of theabove artificial neural network but the selection of kernelfunction parameters is a difficult point The extreme learningmachine (ELM) is a new method training single hiddenlayer feedforward neural networks proposed by Huang etal [15 16] The extreme learning machine first randomlygenerates the hidden layer deviation and weight of theconnected input and the hidden layer and then directlydetermines theweight value between the hidden layer and theoutput layer by Moore-Penrose generalized inverse methodWhile overcoming the shortcomings of the gradient descentlearning method the ELM greatly improves the learningspeed of artificial neural networks and ensures good gener-alization ability Kang [17] proposed an ELM-based gravitydam deformation prediction model and explored the appli-cation of ELM algorithm from the perspective of predictionaccuracy However the adaptability of the ELM model tothe interpretation of dam deformation has not yet beenelucidated

The dam deformation monitoring model can be dividedinto two types the single point deformation monitoringmodel and the multipoint deformation monitoring modelThe current research mainly focuses on single point moni-toring deformation model which cannot reflect the spatialdistribution of deformation And themultipoint deformationmonitoring model can better reflect the mutual relationshipbetween the deformation points of the dam body which ismore reasonable than the single point model As a kind ofstatically indeterminate shell structure the concrete arch damis obviously affected by the spatial integrity of the concretearch dam

This paper studies the application characteristics andeffects of the multiple linear regression (MLR) stepwiseregression (SR) backpropagation (BP) neural networkand extreme learning machine (ELM) on concrete damdeformation modelling based on the monitoring data ofthe Dongjiang arch dam The similarities and differencesbetween the single point model and the one-dimensionalmultipoint model are discussed The work focuses on pre-diction accuracy and the suitability for interpreting dambehavior All discussions will be carried out in conjunctionwith the results of a gravity dam [17] study

2 Statistical Model

Statistical models are established by the correlation betweenobserved effect quantities and environmental variables Withthe environment treated as an independent variable thestructural response of the dam is affected by three effects thereversible effect of the hydrostatic load the reversible thermalinfluence of the temperature and the irreversible term due tothe evolution of the dam response over time [4 18] Accord-ing to the influencing factors the displacement 120575119911 of thearbitrary point 119896(119909 119910 119911) in the 119911 direction can be expressedas 120575 = 119891 119892 (119867119879 120579) 119897 (119911)= 1198911 1198921 (119867) 1198971 (119911) + 1198912 1198922 (119879) 1198972 (119911)+ 1198913 1198923 (120579) 1198973 (119911) (1)

where 1198921(119867) 1198922(119879) 1198923(120579) represent the hydraulic displace-ment component temperature displacement component andaging displacement component respectively 119897119894(119909 119910 119911) indi-cates the deformed surface of the dam fixed point 119896(119909 119910 119911)under the action of water pressure (119894 = 1) temperature (119894 =2) and aging (119894 = 3) alone where 119897(119911) is approximated bymultiple power series and

119897 (119911) = 3sum119899

119886119899119911119899 (2)

And the hydraulic displacement component 1198921(119867) tem-perature displacement component 1198922(119879) and aging displace-ment component 1198923(120579) can expressed as follows [19]

1198921 (119867) = 4sum119894=1

119886119894119867119894 (3)

1198922 (119879) = 1198981sum119895=1

119887119895119879119901119895minus119902119895 (4)

or 1198922 (119879) = 2sum119894=1

(1198871119894 sin 2120587119894119905365 + 1198872119894 cos 2120587119894119905365 ) (5)1198923 (120579) = 1198881120579 + 1198882119868119899120579 (6)

Mathematical Problems in Engineering 3

where 119867 is the upstream and downstream water leveldifference 119894 represents the period 119894 = 1 represents theannual period and 119894 = 2 represents the half-year periodin (4) 1198981 is the number of days since the initial date 119879119901minus119902is the average temperature from 119901 to 119902 days before theobservation day 120579 = (119905 minus 1199050)100 119905 is the measured dateand 1199050 is the initial date 119886119894 1198871119894 1198872119894 119887119895 1198881 1198882 are the regressioncoefficients

More attention should be placed on the choice of twocalculation methods for temperature displacement (see (4)and (5)) When the temperature data is complete and contin-uous (4) is adopted to consider the influence of the actualtemperature When the temperature data is incomplete ordiscontinuous (5) is used

Substituting (2) (3) (4) (6) or (2) (3) (5) and (6)into (1) using Taylor series expansion omitting high-orderterms and combining similar items we can obtain the space-time distribution model of the fixed point 119896(119909 119910 119911) in the 119911direction that is the one-dimensional multipoint statisticaldeformation model

120575 = 4sum119896=0

3sum119901=0

119860119896119901119867119896119911119901 + 1198981sum119896119895=1

3sum119901=0

119861119896119901119879119901119895minus119902119895119911119901+ 1sum119896119895=0

3sum119901=0

119862119896119895119901120579119896 ln 120579119895119911119901 (7)

or 120575 = 4sum119896=0

3sum119901=0

119860119896119901119867119896119911119901+ 1sum119896119895=0

3sum119901=0

119861119896119895119901 sin 2120587119896119905365 cos2120587119895119905365 119911119901

+ 1sum119896119895=0

3sum119901=0

119862119896119895119901120579119896 ln 120579119895119911119901(8)

When the 119911 coordinate of measuring point remainsunchanged a displacement statistical model of the singlemeasuring point is obtained120575 = 1198860 + 4sum

119894=1

119886119894119867119894 + 1198981sum119896119895=1

119861119896119895119879119901119895minus119902119895 + 1198881120579 + 1198882 ln 120579 (9)

or 120575 = 1198860 + 4sum119894=1

119886119894119867119894 + 2sum119894=1

(1198871119894 sin 2120587119894119905365 + 1198872119894 cos 2120587119894119905365 )+ 1198881120579 + 1198882 ln 120579 (10)

According to the reasons mentioned above this paperchooses (7) and (9) to study the deformation monitoringmodel of concrete dams Therefore the input variable ofthe single point deformation prediction model is 119883 =(1198671198672 1198673 1198674 1198791-10 11987911-30 11987931-60 11987961-100 120579 119868119899120579) the inputvariable of the one-dimensional multipoint deformationprediction model is

119883 = ( 119867119867211986731198674 119911 1199112 1199113 1198791-10 11987911-30 11987931-60 11987961-100 120579 119868119899120579119911119867 1199111198672 1199111198673 1199111198674 1199112119867 11991121198672 11991121198673 11991121198674 1199113119867 11991131198672 11991131198673 119911311986741199111198791-10 11991111987911-30 11991111987931-60 11991111987961-100 11991121198791-10 119911211987911-30 119911211987931-60 119911211987961-100 11991131198791-10 119911311987911-30 119911311987931-60 119911311987961-100119911120579 119911119868119899120579 1199112120579 1199112119868119899120579 1199113120579 1199113119868119899120579 ) (11)

and the output variable is the radial displacement of themeasuring point

3 Methodology

31 Multiple Linear Regression Multiple linear regression(MLR) models are based on the linear correlation betweendam effect quantities and environmental variables Whenconsidering the relationship between the 119896 independentvariables (1198831 1198832 1198833 sdot sdot sdot 119883119896) and the dependent variable 119884 aregression equation is established 119884119894 = 1205730 + 12057311198831198941 + 12057321198831198942 +sdot sdot sdot + 120573119896119883119894119896 + 119906119894 where 1205730 1205731 1205732 sdot sdot sdot 120573119896 are the regressioncoefficients to be estimated 119894 = 1 2 sdot sdot sdot 119899 (119899 is the samplesize) 119906119894 is the random error [20]

Assuming that the random errors are generally normaldistributed 119873(0 1205902) and independent of each other themultiple linear regression equation is represented by amatrixY = X120573 + 119906 where Y is the vector of observations 120573 is theparameter vector X is the constant vector 119906 is the random

error vector There is a set of parameter estimates 120573 such thatthe residual sum of squares 119876 = sum119899119894=1 1199061198942 = 119906119879119906 = (Y minusX120573)119879(Y minusX120573) is the smallest that is the system of equations120597119876120597120573 = 0 is solved Therefore the overall parameter ofthe least squares estimation is 120573 = (X119879X)minus1X119879Y the fittedmodel is Y = X120573 and the vector of the residuals is denotedby = Y minus Y The ultimate goal of the overall model isto minimize the sum of the squared deviations between themodel predictions and the observations

32 Stepwise Regression For the MLR method the moreindependent variables the smaller the residual square sum119876 the better the regression equation effect and the higherthe prediction accuracy In the optimal regression equation itis always desirable to include as many independent variablesas possible especially the independent variables that have asignificant influence on the dependent variable Nonethelesstoo many independent variables may also result in some


Ｒ1

Ｒ2

Ｒm

y1

y2

yn

Input layer Hidden layer Output layer

Figure 1 Structure of a typical single hidden layer feedforwardneural network

disadvantages of the regression equation Firstly if moreindependent variables are required many quantities must bemeasured and calculations are inconvenient Secondly if theregression equation includes an independent variable thathas no effect on the dependent variable or has a very smalleffect then the residual square sum 119876 will not decrease thusaffecting the accuracy of the regression equation Thirdly theexistence of independent variables that have no significantinfluence on the dependent variable affects the stability ofthe regression equation and reduces the prediction accuracyThus in the optimal regression equation it is desirable toexclude independent variables that have no significant effecton the dependent variable

Stepwise regression (SR) is a method for a linear regres-sion model to select independent variables [21] The basicidea is to introduce variables one by one with the con-dition that its partial regression squared and experienceare significant According to the above principle stepwiseregression can be used to screen and eliminate the variablescausing multicollinearity The specific steps are as followsfirst use119884 tomake a simple regression for each119883119894 consideredand then gradually introduce the remaining 119883119894minus1 basedon the regression equation corresponding to the 119883119894 thatcontributes the most to 119884 After a stepwise regression 119883119894that is finally retained in the model is both important andnot heavily multicollinear The effect of stepwise regressionon the improvement of multiple linear regression is stillcontroversial which is also a focus of this paper

33 Backpropagation Neural Network Artificial neural net-works are often divided into two categories one is a recursivenetwork that generates loops through feedback connectionsand the other is a feedforward neural network [22] in whichthe network structure has no loopsThe typical single hiddenlayer feedforward neural network structure is shown inFigure 1 Both the ELM and BP neural network belong tothe feedforward neural network except that the learningmethods of the two are different The BP neural network isa learning method that uses backpropagation by the gradientdescent method which requires constant iteration to updatethe weights and thresholds while the ELM randomly deter-mines the initial weights and thresholds without adjustment

The traditional BP neural network adopts the errorbackpropagation algorithm whose guiding idea is that theweight and threshold should be adjusted along the direction

of negative gradient which is the fastest descending errorfunction Supervised BP neural network learning algorithmusually consists of three stages [10]

The first stage is to feed the data forward and thecomputed output of the 119894th node in the output layer is asfollows119910119894 = 119892(119873ℎsum

119895=1

(119908119894119895119892(119873119894sum119896=1

V119895119896119909119896 + 120579V119895) + 120579119908119894))119894 = 1 2 119873119900 (12)

where 119908119894119895 is the connective weight between nodes in thehidden layer and those in the output layer V119895119896 representsthe connective weight between the nodes in the input layerand those in the hidden layer 120579119908119894 (or 120579V119895) are bias terms thatrepresent the threshold of the transfer function 119892 119909119896 is theinput to the 119896th node in the input layer 119873119894 119873ℎ and 119873119900 arethe number of nodes in the input hidden layer and outputlayer respectively

The second stage is the backpropagation of the error Thelearning process of error backpropagation is the process ofpropagating errors from the output layer to the input layerand correcting the corresponding network parameters Thegoal of learning is to minimize or reduce the total error of thenetwork

The third and final stage is to adjust the weights andthresholds The training is performed using a gradientdescent method with a learning ratio in the standard BPalgorithm and is defined as follows

119882(119903+1) =119882(119903) + Δ119882(119903) (13)

where 119882 = (V11V12 sdot sdot sdot V119895119896 sdot sdot sdot V119873ℎ119873119894120579v1120579v2 sdot sdot sdot 120579v119873ℎ times 1199081111990812sdot sdot sdot 119908119894119895 sdot sdot sdot 119908119873ℎ119873119894120579w1120579w2 sdot sdot sdot 120579w119873119900) 119882 is the parameter vectorto be determined in the BP neural network The weight isadjusted as follows Δ119882(119903) = minus120578120597119864 (119882)120597119882(119903) (14)

where 120578 is the learning ratio the superscript (119903) refers to the119903th learning iteration and 119864(119882) is the system error functionThe convergence speed of BP neural network depends onthe learning speed For computational efficiency Levenberg-Marquardt [23] algorithm is applied to obtain 119908119894119895 V119895119896 120579119908119894and 120579V119895 by minimizing the system error function

34 Extreme Learning Machine Extreme learning machineis an algorithm for single hidden layer feedforward neuralnetwork Suppose there are 119873 arbitrary samples where119883119894 =[1199091198941 1199091198942 sdot sdot sdot 119909119894119873] and 119905119894 = [1199051198941 1199051198942 sdot sdot sdot 119905119894119898]119879 isin 119877119898 Theoutput of a standard single hidden layer neural network with119871 hidden nodes can be mathematically described as follows

119900119895 = 119871sum119894=1

120573119894119892 (119882119895 sdot119883119895 + 119887119894) 119895 = 1 2 sdot sdot sdot 119873 (15)

where 119900119895 is the output vector relative to the input 119883119895 119892(119909) isthe activation function119882119894 = [1199081198941 1199081198942 sdot sdot sdot 119908119894119899]119879 is the input


weight vector 120573119894 = [1205731198941 1205731198942 sdot sdot sdot 120573119894119898]119879 isin 119877119898 is the outputweight vector 119887119894 is the offset of the 119894th hidden layer119882119894 sdot 119883119895is the inner product of119882119894 and 119883119895

The learning goal of single hidden layer neural networkis to minimize the output errors which can be expressed asfollows

119871sum119895=1

10038171003817100381710038171003817119900119895 minus 11990510038171003817100381710038171003817 = 0 (16)

That is there exist specific 120573119894119882119894 and 119887119894 such that119871sum119894=1

120573119894119892 (119882119895 sdot119883119895 + 119887119894) = 119905119895 119895 = 1 2 sdot sdot sdot 119873 (17)

Equation (17) can be simplified as119867120573 = 119879 (18)

where Τ is the target matrix of training samples

119867 (1198821 sdot sdot sdot 119882119871 1198871 sdot sdot sdot 1198871198711198831 sdot sdot sdot 119883119871)= [[[[[

119892 (1198821 sdot1198831 + 1198871) sdot sdot sdot 119892 (119882119871 sdot1198831 + 119887119871) sdot sdot sdot 119892 (1198821 sdot119883119873 + 119887119894) sdot sdot sdot 119892 (119882119871 sdot119883119873 + 119887119871)]]]]]119873times119871

(19)

120573 = [[[[[1205731198791120573119879119871

]]]]]119871times119898 119879 = [[[[[1198791198791119879119879119873

]]]]]119873times119898(20)

There are 120573119894 119894 and 119894 such that10038171003817100381710038171003817119867 (119894 119894) 119894 minus 11987910038171003817100381710038171003817 = min119882119887120573

10038171003817100381710038171003817119867 (119894 119894) 119894 minus 11987910038171003817100381710038171003817 (21)

where 119894 = 1 2 sdot sdot sdot 119871 (21) is equivalent to the followingminimization loss function119864 = 119873sum

119895=1

( 119871sum119894=1

120573119894119892 (119882119895 sdot119883119895 + 119887119894) minus 119905119895)2119895 = 1 2 sdot sdot sdot 119873 (22)

Conventional gradient-based learning algorithms requireadjustment of all parameters over multiple iterations In theELM algorithm once the input weights 119882119894 and the hiddenlayer offsets 119887119894 are randomly determined the output matrixof the hidden layer is uniquely determined [15] The trainingsingle hidden layer neural network can be transformed intosolving a linear system119867 = 119879 And the output weight canbe determined

= 119867119879119879 (23)

where119867119879 is the Moore-Penrose generalized inverse of119867

4 Data and Processing

41 Case Dam and Operation Data The Dongjiang (DJ)dam is located in Zixing City Hunan Province China Itis a variable center double-curved concrete arch dam witha maximum height of 157m and a center arc length of438m Its left and right shores are basically symmetrical Thedesigned normal storage level is 285m above the sea levelcorresponding to a storage capacity of 812 billion m3 Thefirst water impounding began in 1986 and has been goingon for more than 20 years now The DJ dam is equippedwith monitoring items such as deformation and seepage Thedeformation monitoring items include forward intersectioninverted perpendicular vertical displacement and cross-river length monitoring system The layout of dam verticalmonitoring system is shown in Figure 3 There are 5 sets ofvertical lines namely L1 L3 L5 L7 and L9 and each verticalline has a vertical reversal lineThe vertical line monitoring isavailable in both manual and automated monitoring

The observation data of the measuring point L5-205 fromFebruary 2003 toDecember 2013 is the basis of this studyThedata includes temperature upstream and downstream waterlevels and the radial deformation of measuring points Theposition of the L5-205Zmeasuring point is shown in Figure 2

Kang [17] has initially discussed the application of ELMin deformation prediction of Fengman (FM) concrete gravitydam which will be presented here to be a reference for theresearch of this paper Table 1 shows the basic parameters ofthe two dams and Figure 3 shows a cross-sectional view ofthe two dams

Figure 4 shows the time history curve of environmen-tal variables and corresponding radial horizontal displace-ment of the L5-205Z measuring point and the verticaldotted line marks the division between training and pre-dicted sets In Figure 4 sign (+) denotes the displacementtowards the upstream and sign (-) indicates the displace-ment towards the downstream The radial displacement ofthe measuring point changes periodically with tempera-ture that is the temperature rises the measuring pointdeforms upstream the temperature drops and themeasuringpoint deforms downstream The change in displacementlags significantly behind the change in temperature Thehighest temperature generally occurs between July and Octo-ber and the lowest temperature occurs between Januaryand March However the displacement generally reachesa maximum value (maximum to the downstream) fromApril to June and reaches a minimum value (maximumto the upstream) from October to December The radialdisplacement of the L5-205Z measuring point is in accor-dance with the general law of the arch dam deformationwhich also proves the validity of the data samples from theside

As shown in Figure 5 [17] the water level of the FMdam also changes periodically with the season Unlike theDJ dam the FM dam has hardly observed the hysteresisof the displacement change with respect to the temperaturechange The existence of correlation among water levelchanges temperature changes and time changes may affectthe prediction accuracy of conventional linear equations


294Right

TS5 TS6

TS5-294DTS5-291D

TS5-274DL1-250D L1-250Z

L15-162D

TS2-287D TS2-287Z

L3-175D

L5-205Z

L5-250Z

DT-281Z

DT-250Z

DT-217Z

DT-205Z

DT-162Z

ElevatorL1 L3 L5 L7 L9

L3-205Z

L5-175D L5-175Z

L7-250Z

L7-205Z

L7-175Z

L9-250D L9-250Z

TS6-294D

TS1-286D TS1-286Z

145

175

TS6-294ZLeft

250

205

L12-162DL7-175D

L5-145D

L3-175Z

L3-250D

Figure 2 Distribution of vertical lines of the Dongjiang dam

294

250

205

145

107

L5

V-perpendicular line

The intersection of the perpendicularand the inverted vertical lines

Inverted vertical line

(a)

2689

26350

22750

22600

22000

19911

139

580

26400

90 140 160

6400

20430

19900

(b)

Figure 3 Cross section of dam (unit m) (a) the DJ dam (b) the FM dam

42 Parameter Settings For the BPneural network the initialweights and thresholds were obtained by the most widelyused Levenberg-Marquardt The optimal number of hiddenneurons and the optimal learning rate were determined bytrial and error while the transfer functions of the hiddenlayer and the output layer respectively selected the sigmoidfunction and the linear function The number of trainingepochs was set as 103 and the training goal for the MSE wasset as 10minus3The activation function of the ELMmodel was alsoa sigmoid function Compared with the BP model the ELMmodel only needs to determine the number of hidden nodesto obtain satisfactory results

Because the weights are randomly initialized differentresults can be achieved by separate runs In order to enhance

the reliability of calculation results both the ELM and BPneural network are continuously trained 20 times the resultof a calculation with a small difference between the MSE ofthe training set and the predicting set will be the final resultKang [17] used the average of 5 calculations as the final resultand this paper believes that 5 times may not be sufficient toprove the reliability of the results

Figures 6 and 7 show the effect of the number of hiddenlayer neurons to the predictive performance of ANN modelsfor the DJ dam For the single point deformation monitoringmodel the training and predicting errors of the BPmodel arerelatively small when the number of hidden nodes is 16 Andfor the ELM model when the number of hidden nodes is 17the error of training and predicting is relatively small For


Table 1 Dimensional parameters of the dam considered

Dam Typology Height Top elevation Impact factors Output(m) (m absea level)

Dongjiang(DJ) ARC 157 294 HT t H T t z RADFengman [17] (FM) GRA 91 2689 H T t RADTypology ARC= arch GRA= gravity outputs RAD= radial displacement H= water level T= air temperature t= time z= Z coordinate

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

minus12minus10

minus8minus6minus4minus2

02

Disp

lace

men

t (m

m)

105110115120125130135140

Wat

er le

vel d

iffer

ence

(m)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus505

101520253035

Air

tem

pera

ture

()

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

∘C

Figure 4 Time series of environmental variables and responsedisplacements at theDJ dam site From top to bottommean daily airtemperature upper and lower water level difference and measuredhorizontal displacementsThe vertical dotted linemarks the divisionbetween training and predicting periods

the FM dam Kang [17] determined the optimal number ofhidden nodes of the BP neural network model is 15 and theELMmodel is 22 For themultipoint deformationmonitoringmodel in the BP network and ELM models the numbers ofhidden nodes are set as 15 and 14 respectively

43 Performance Evaluation It is important to appropri-ately estimate the prediction error of a model since (a) itprovides insight into its accuracy (b) it allows comparisonof different models and (c) it is used to define warningthresholds [24 25] In order to facilitate the analysis offinal calculation results different performance evaluationfunctions are adopted in this paper that is mean absoluteerror (MAE) mean square error (MSE) maximum absoluteerror (S) and correlation coefficient (R) as shown below[17] 119872119860119864 = 1119873 119873sum119894=1 1003816100381610038161003816119910119863 (119894) minus 119910 (119894)1003816100381610038161003816 (24)

minus12minus10


024

Disp

lace

men

t (m

m)

Wat

er le

vel d

iffer

ence

(m)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

70

65

60

55

50

45

0

10

20

30

minus10

minus20

Air

tem

pera

ture

()

∘C

Figure 5 Time series of environmental variables and responsedisplacements at the FM dam site (Kang F et al 2017) From topto bottom mean daily air temperature upper and lower water leveldifference and measured horizontal displacements The verticaldotted line marks the division between training and predictingperiods

119872119878119864 = 1119873 119873sum119894=1 (119910119863 (119894) minus 119910 (119894))2 (25)119878 = max 1003816100381610038161003816119910119863 (119894) minus 119910 (119894)1003816100381610038161003816 119894 = 1 2 sdot sdot sdot 119873 (26)119877 = sum119873119894=1 (119910119863 (119894) minus 119910119863) (119910 (119894) minus 119910)radicsum119873119894=1 (119910119863 (119894) minus 119910119863)2sum119873119894=1 (119910 (119894) minus 119910)2 (27)

where 119910119863 and 119910119863 are simulation values and simulationaverages 119910 and 119910 are observed values and observed averagevalues respectively 119873 is the number of measured samples

To estimate the uncertainty associated with model sim-ulations the residuals of predicting sets are computed andanalyzed [26] The independence analysis heteroscedasticanalysis and normality analysis of residuals are performed byplotting graphs of residual autocorrelation residual variationrelative to observed values and residual probability distri-butions If the residual sequence is autocorrelated then the


TrainedPredicted

191713 1815 16 2010 1211 14Number of hidden nodes

0

05

1

15

2

25M

SE

(a) Back propagation

Trained

Predicted

05

1

15

2

25

MSE

1816 2010 12 14Number of hidden nodes

(b) Extreme learning machine

Figure 6 Effects of hidden nodes on model performance for the single point model

TrainedPredicted

0

05

1

15

2

25

MSE



Trained

Predicted

0

05

1

15

2

25M

SE



Figure 7 Effects of hidden nodes on model performance for the one-dimensional multipoint model

model fails to fully explain the variation rule of the variableOn the other hand low residual heteroscedasticity and a closeapproximation to the normal distribution indicate the modelis closer to unbiased estimation and has low uncertainty Inthis paper the standardized residual of the model is shown in119903119904 = 119890119894120590 = 119910 minus 119910119863120590 (28)

where 119910 represents observed values 119910119863 represents predictedvalues 119903119904 represents standardized residuals and 120590 representsthe standard deviation 119890119894 = 119910minus119910119863 and 119890119894 represents residuals5 Results and Discussion

51 Comparison of Simulation Results In this section theobserved DJ dam deformations are compared with simulatedresults based on the four different models ie the MLR SR

BP neural network and ELMmodelThe specific calculationresults for both the DJ arch dam and the FM gravity dam ofthe fourmodels are shown inTables 2-3 and Figures 8ndash10Thecalculation results show that in the single point deformationmonitoring model the best MAE MSE S and R values areobtained by the ELMmodels for both theDJ arch damand theFM gravity dam And the best results are highlighted in blackbold According to the comparison among different modelsthe best accuracy ranking for the DJ dam is the ELM modelgt BP neural network gt SR gtMLR while for the FM dam theranking is the ELMmodel gt BP neural network gtMLR gt SRThe stepwise regression does not always play a positive rolein the improvement of multiple linear regression and shouldbe analyzed in specific situations

It can be seen from Figure 8 that except for themultimeasurement MLR model the fitting and predicteddisplacements of all the models are consistent with the trend


Table 2 Statistical performance of the MLR SR BP and ELM single-point models

DAM model MAE MSE S R Time(s)Training Predicting Training Predicting Training Predicting Training Predicting

DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265

MAE = mean absolute error MSE = mean square error S = maximum absolute error R = the correlation coefficient MLR = multiple linear regression SR =stepwise regression BP = backpropagation ELM = extreme learning machine DJ = the Dongjiang arch dam FM = the Fengman gravity dam

Table 3 Statistical performance of the MLR SR BP and ELM multipoint models

model MAE MSE S R TimeTraining Predicting Training Predicting Training Predicting Training Predicting (s)

MLR 03586 11977 03510 22516 35438 40139 07621 07541 14200SR 05224 04225 04729 04777 32501 32718 09517 09188 16910BP 05609 05824 03609 04542 27205 28618 09759 09543 30750ELM 03571 04117 03073 04016 17774 25375 09792 09558 17010MAE = mean absolute error MSE = mean square error S = maximum absolute error R = the correlation coefficient MLR = multiple linear regression SR =stepwise regression BP = backpropagation ELM = extreme learning machine

of the measured displacement In June 2004 all modelsshowed similarly large errors The reason is that the hightemperature generated by the high voltage line affects themeasurement accuracy

With respect to the multipoint deformation monitoringmodel the best MAE MSE S and R values are also obtainedby the ELM models for the DJ arch dam And the bestaccuracy ranking is the same as the point deformationmonitoring model which is the ELM model gt BP neuralnetwork gt SR gt MLR Nonetheless in the multipoint defor-mation monitoring model the prediction accuracy of theMLR model drops sharply due to the inclusion of too manyredundant independent variables And the SR BP and ELMperform better in the multipoint deformation modelling andthe prediction accuracy is higher which indicates that themultipoint model is more reasonable than the single pointmodel

In addition to the simulation accuracy the calculationspeed is also an important index to measure the performanceof a model In this paper the time consumption is usedas an evaluation index to compare the calculation speedof the four models In general the time consumption isranked as the BP neural network gt ELM gt SR gt MLRmodel among the different models and as the multipointdeformation model gt the single point deformation modelamong the different measuring points It should be noted thatthe BP neural network is the longest-running model and thetime consumption of the ELM model is significantly lowerthan that of the BP neural network Table 2 (FM dam) is Table5 in [Kang et al 2017]

52 Residuals Analysis As shown in Figures 11-12 to evaluatethe uncertainty of the models residual analysis is performedon the statistical results of the fourmodels In the single pointdeformation monitoring models the experimental resultsshow that the autocorrelation of 119903119904 is almost not found in allfour models and the ACF lies mainly in the 95 confidenceinterval (Figures 11(a)ndash11(d)) Figures 11(e)ndash11(h) show thescatter points of 119903119904 as a function of observed deformationsIt is clear that the 119903119904 values do not appear to be randomlydistributed over the deformation interval except for the ELMmodel And the 119903119904 of the other threemodels show adecreasingtrend with an increase in deformation Figures 11(i)ndash11(l)display the probability density distribution of 119903119904 for all thefour models The results show that the probability densitydistribution curve of 119903119904 for all four models is unimodalwithout considering the influence of two abnormal pointsand the values of 119903119904 are mainly distributed between minus2 and2 (Figures 11(e)ndash11(h)) The existence of two abnormal pointswas caused by the measurement anomaly in December 2013when the vertical line was being overhauled

In the multipoint deformation monitoring models theexperimental results show that the autocorrelation of 119903119904 isalmost not found in the SR BP and ELMmodels whereas the119903119904 values of the MLRmodel show remarkable autocorrelation(Figures 12(a)ndash12(d)) The 119903119904 values of the MLR modelexhibit heteroscedasticity as the observed outflow changesCompared with the MLR SR and BP neural network thespatial distribution of 119903119904 with observed deformation for theELM model is relatively uniform (Figures 12(e)ndash12(h)) Theprobability density of 119903119904 for the MLR displays a multimodal


Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)

Figure 8 Performance of the MLR (a) SR (b) BP (c) and ELM (d) single point models for the DJ dam fitting of measured values andsimulated values The vertical dotted line marks the division between training and predicting periods

210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10

minus1minus2minus3minus4Re

sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)

Figure 9 Performance of the MLR (a) SR (b) BP (c) and ELM (d) single point models for the FM dam [17] fitting of measured values andsimulated values (above) and residual error (below) The vertical dotted line marks the division between training and predicting periods


MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)

Figure 10 Performance of the MLR (a) SR (b) BP (c) and ELM (d) multipoint models for the DJ dam fitting of measured values andsimulated values The vertical dotted line marks the division between training and predicting periods

MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals

minus8 minus6 0minus10 minus4 minus2

Observed deformation (mm)

(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty

minus3 0 3minus1minus4 1 2minus2 4 5minus5

Standardised residuals

(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)

Figure 11 Investigation of residuals ofMLR (a e i) SR (b f j) BP neural network (c g k) and ELM (d h l) for the single pointmodel (andashd)Autocorrelation function (ACF) plots of 119903119904 at with 95 significance levels (endashh) 119903119904 as a function of the observed deformation (indashl) Fitted(solid line) and actual (bars) probability density function (PDF) of 119903119904


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty

3minus3 0 5minus5 1 2minus2 4minus4 minus1


(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)

Figure 12 Investigation of residuals of MLR (a e i) SR (b f j) BP neural network (c g k) and ELM (d h l) for the one-dimensionalmultipoint model (andashd) Autocorrelation function (ACF) plots of 119903119904 at with 95 significance levels (endashh) 119903119904 as a function of the observeddeformation (indashl) Fitted (solid line) and actual (bars) probability density function (PDF) of the 119903119904distribution with four peaks (one high and three low)distributed at minus14 041 and 22 respectively (Figure 12(i))The 119903119904 of the ELM model presents a unimodal distributionwith a sharp peak without considering the influence of twoabnormal points and 119903119904 is mainly distributed between minus15and 12 (Figure 12(l))

6 Conclusion

This paper investigated the usefulness of two traditionalmultiple regression models (MLR and SR) and two artificialneural networkmodels (ELMand BP neural network) in pre-dicting dam deformation All the four models presented herehave the advantages of simple operation and fast applicationwhich increases the confidence in using these models

The artificial neural networks (ELM and BP) can signifi-cantly improve the accuracy of conventional statistical meth-ods (MLR and SR) for predicting the behavior of concretedams and have good adaptability and generalization abilityfor deformation predicting of concrete dams Comparedwith the BP model the ELM model has fewer adjustmentparameters faster learning and higher efficiency If there isa high accuracy requirement for concrete dam deformationprediction the ELMmodel would be optimal

The one-dimensional deformation multipoint monitor-ingmodel can reflect the deformation distribution in the one-dimensional direction of the arch dam with clear physical

concepts and spatial characteristics Compared with thesingle point model it has better anti-interference ability andhigher prediction accuracy In general for the single pointdeformation monitoring model the four models mentionedin this paper can meet the engineering needs Nonethelessartificial neural networks are a better choice when consid-ering the interaction of measuring points Among themthe ELM model can effectively solve the time consumptionproblem associated with the BP neural network and it hassuperior performances over other three models in simulatingdam deformation

Obviously artificial neural network-based models aremore suitable for reproducing nonlinear effects and complexinteractions between input variables and dam responsesNonetheless the determination of the number of hiddennodes is the key and difficult point that artificial neuralnetworks are difficult to avoid In order to overcome theerror caused by randomness and improve the generalizationability model based on ELM evolutionary algorithms suchartificial bee colony (ABC) algorithm [27] or particle swarmalgorithm can be used to optimize the ELM model which isthe next research goal

Data Availability

(1) The initial observation data of Dongjiang dam used tosupport the findings of this study were supplied by Hunan


Electric Power Company Science Research Institute underlicense and so cannot be made freely available Requestsfor access to these data should be made to Tianhaiping329971674qqcom (2) The calculated data used to supportthe findings of this study are included within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] F Salazar R Moran M A Toledo and E Onate ldquoData-basedmodels for the prediction of dam behaviour a review andsome methodological considerationsrdquo Archives of Computa-tional Methods in Engineering State-of-the-Art Reviews vol 24no 1 2017

[2] F Salazar M A Toledo E Onate and R Moran ldquoAn empiricalcomparison of machine learning techniques for dam behaviourmodellingrdquo Structural Safety vol 56 pp 9ndash17 2015

[3] G Liang Y Hu andQ Li ldquoSafetymonitoring of high arch damsin initial operation period using vector error correctionmodelrdquoRock Mechanics and Rock Engineering vol 51 no 8 pp 2469ndash2481 2018

[4] Q B Li G H Liang Y Hu and Z Zuo ldquoNumerical analysison temperature rise of a concrete arch dam after sealing basedon measured datardquo Mathematical Problems in Engineering vol2014 Article ID 602818 12 pages 2014

[5] J Mata A Tavares de Castro and J Sa da Costa ldquoConstructingstatistical models for arch dam deformationrdquo Structural Controland Health Monitoring vol 21 no 3 pp 423ndash427 2014

[6] A Bayer M BachmannAMuller and H Kaufmann ldquoA Com-parison of feature-based MLR and PLS regression techniquesfor the prediction of three soil constituents in a degraded SouthAfrican ecosystemrdquoApplied and Environmental Soil Science vol2012 Article ID 971252 20 pages 2012

[7] M O Akinwande H G Dikko and A Samson ldquoVarianceinflation factor as a condition for the inclusion of suppressorvariable(s) in regression analysisrdquoOpen Journal of Statistics vol05 no 07 pp 754ndash767 2015

[8] A G Mulat and S A Moges ldquoAssessment of the impact of thegrand ethiopian renaissance dam on the performance of thehigh aswan damrdquo Journal of Water Resource and Protection vol06 no 06 pp 583ndash598 2014

[9] M H Ali M R Alam M N Haque and M J AlamldquoComparison of design and analysis of concrete gravity damrdquoNatural Resources vol 03 no 01 pp 18ndash28 2012

[10] C H Chen ldquoStructural identification from field measurementdata using a neural networkrdquo Smart Materials and Structuresvol 14 no 3 pp S104ndashS115 2005

[11] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Soware vol 65 pp 182ndash190 2013

[12] J Mata ldquoInterpretation of concrete dam behaviour with arti-ficial neural network and multiple linear regression modelsrdquoEngineering Structures vol 33 no 3 pp 903ndash910 2011

[13] C Y Kao and C H Loh ldquoMonitoring of long-term staticdeformation data of Fei-Tsui arch dam using artificial neu-ral network-based approachesrdquo Structural Control and HealthMonitoring vol 20 no 3 pp 282ndash303 2013

[14] H Su Z Chen and Z Wen ldquoPerformance improvementmethod of support vector machine-based model monitoringdam safetyrdquo Structural Control and Health Monitoring vol 23no 2 pp 252ndash266 2016

[15] G Huang S Song and K You ldquoTrends in extreme learningmachinesrdquoNeural Networks vol 61 pp 32ndash48 2015

[16] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006

[17] F Kang J Liu J Li and S Li ldquoConcrete dam deformationprediction model for health monitoring based on extremelearning machinerdquo Structural Control and Health Monitoringvol 24 no 10 2017

[18] M A Hariri-Ardebili and H Mirzabozorg ldquoFeasibility studyof dez arch dam heightening based on nonlinear numericalanalysis of existing damrdquo Archives of Civil Engineering vol 59no 1 pp 21ndash49 2013

[19] B Dai C Gu E Zhao and X Qin ldquoStatistical model optimizedrandom forest regression model for concrete dam deformationmonitoringrdquo Structural Control and Health Monitoring vol 25no 6 2018

[20] V Rankovic A Novakovic N Grujovic D Divac and NMilivojevic ldquoPredicting piezometric water level in dams viaartificial neural networksrdquo Neural Computing and Applicationsvol 24 no 5 pp 1115ndash1121 2014

[21] Z Pengfei andL Zeyu ldquoPrediction of urbanwater consumptionbased on SPSS multiple linear regression modelrdquoWater Scienceand Technology and Economy vol 05 pp 6ndash10 2018

[22] A Zeroual A Fourar and M Djeddou ldquoPredictive modelingof static and seismic stability of small homogeneous earth damsusing artificial neural networkrdquo Arabian Journal of Geosciencesvol 12 no 2 2019

[23] A K Singh B Tyagi and V Kumar ldquoANN controller for binarydistillation column - A Marquardt-Levenberg approachrdquo inProceedings of the 2011 Nirma University International Confer-ence on Engineering Current Trends in Technology NUiCONE2011 India December 2011

[24] F Salazar M A Toledo J M Gonzalez and E Onate ldquoEarlydetection of anomalies in dam performance A methodologybased on boosted regression treesrdquo Structural Control andHealth Monitoring vol 24 no 11 2017

[25] A Swanepoel S Barnard F Recknagel andHCao ldquoEvaluationof models generated via hybrid evolutionary algorithms forthe prediction of Microcystis concentrations in the Vaal DamSouth AfricardquoWater SA vol 42 no 2 pp 243ndash252 2016

[26] D Zhang J Lin Q Peng et al ldquoModeling and simulatingof reservoir operation using the artificial neural networksupport vector regression deep learning algorithmrdquo Journal ofHydrology vol 565 pp 720ndash736 2018

[27] B Yilmaz E Aras S Nacar and M Kankal ldquoEstimatingsuspended sediment load with multivariate adaptive regressionspline teaching-learning based optimization and artificial beecolony modelsrdquo Science of the Total Environment vol 639 pp826ndash840 2018

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


models are based on regression methods such as the mul-tiple linear regression (MLR) [6] stepwise regression (SR)[7] principal component regression (PCR) [8] and partialleast squares regression (PLSR) [9] By gradually screeningregression factors of MLR models SR models obtain regres-sion coefficients at a certain significance level results moreaccurate than those obtained by the general least squaremethod

In recent years more and more scholars have begun toapply machine learning algorithms or intelligent algorithmsto dam safety effect prediction or dam safety diagnosis analy-sis [2 10 11] Mata [12] found that ANNmodels can be a verypowerful tool in evaluating dam behavior by comparing themultiple linear regression model with the multilayer percep-tronmodel for the horizontal displacement of a concrete archdam F Salazar [2] assessed the potential of some state-of-the-art machine learning techniques including random forestsboosted regression trees neural networks and multivariateadaptive regression splines to build models for the predictionof dam behavior in the field of displacement and leakage Kao[13] studied the feasibility of ANN-based approaches for damhealth monitoring and set an early warning threshold levelof the Fei-Tsui dam based on the analysis results But theartificial neural network based on gradient descent methodis still relatively slow and easily gets stuck Su [14] proposeda dam safety monitoring model based on support vectormachine which could overcome the disadvantages of theabove artificial neural network but the selection of kernelfunction parameters is a difficult point The extreme learningmachine (ELM) is a new method training single hiddenlayer feedforward neural networks proposed by Huang etal [15 16] The extreme learning machine first randomlygenerates the hidden layer deviation and weight of theconnected input and the hidden layer and then directlydetermines theweight value between the hidden layer and theoutput layer by Moore-Penrose generalized inverse methodWhile overcoming the shortcomings of the gradient descentlearning method the ELM greatly improves the learningspeed of artificial neural networks and ensures good gener-alization ability Kang [17] proposed an ELM-based gravitydam deformation prediction model and explored the appli-cation of ELM algorithm from the perspective of predictionaccuracy However the adaptability of the ELM model tothe interpretation of dam deformation has not yet beenelucidated

The dam deformation monitoring model can be dividedinto two types the single point deformation monitoringmodel and the multipoint deformation monitoring modelThe current research mainly focuses on single point moni-toring deformation model which cannot reflect the spatialdistribution of deformation And themultipoint deformationmonitoring model can better reflect the mutual relationshipbetween the deformation points of the dam body which ismore reasonable than the single point model As a kind ofstatically indeterminate shell structure the concrete arch damis obviously affected by the spatial integrity of the concretearch dam

This paper studies the application characteristics andeffects of the multiple linear regression (MLR) stepwiseregression (SR) backpropagation (BP) neural networkand extreme learning machine (ELM) on concrete damdeformation modelling based on the monitoring data ofthe Dongjiang arch dam The similarities and differencesbetween the single point model and the one-dimensionalmultipoint model are discussed The work focuses on pre-diction accuracy and the suitability for interpreting dambehavior All discussions will be carried out in conjunctionwith the results of a gravity dam [17] study

2 Statistical Model

Statistical models are established by the correlation betweenobserved effect quantities and environmental variables Withthe environment treated as an independent variable thestructural response of the dam is affected by three effects thereversible effect of the hydrostatic load the reversible thermalinfluence of the temperature and the irreversible term due tothe evolution of the dam response over time [4 18] Accord-ing to the influencing factors the displacement 120575119911 of thearbitrary point 119896(119909 119910 119911) in the 119911 direction can be expressedas 120575 = 119891 119892 (119867119879 120579) 119897 (119911)= 1198911 1198921 (119867) 1198971 (119911) + 1198912 1198922 (119879) 1198972 (119911)+ 1198913 1198923 (120579) 1198973 (119911) (1)

where 1198921(119867) 1198922(119879) 1198923(120579) represent the hydraulic displace-ment component temperature displacement component andaging displacement component respectively 119897119894(119909 119910 119911) indi-cates the deformed surface of the dam fixed point 119896(119909 119910 119911)under the action of water pressure (119894 = 1) temperature (119894 =2) and aging (119894 = 3) alone where 119897(119911) is approximated bymultiple power series and

119897 (119911) = 3sum119899

119886119899119911119899 (2)

And the hydraulic displacement component 1198921(119867) tem-perature displacement component 1198922(119879) and aging displace-ment component 1198923(120579) can expressed as follows [19]

1198921 (119867) = 4sum119894=1

119886119894119867119894 (3)

1198922 (119879) = 1198981sum119895=1

119887119895119879119901119895minus119902119895 (4)

or 1198922 (119879) = 2sum119894=1

(1198871119894 sin 2120587119894119905365 + 1198872119894 cos 2120587119894119905365 ) (5)1198923 (120579) = 1198881120579 + 1198882119868119899120579 (6)





120575 = 4sum119896=0

3sum119901=0

119860119896119901119867119896119911119901 + 1198981sum119896119895=1

3sum119901=0

119861119896119901119879119901119895minus119902119895119911119901+ 1sum119896119895=0

3sum119901=0

119862119896119895119901120579119896 ln 120579119895119911119901 (7)

or 120575 = 4sum119896=0

3sum119901=0

119860119896119901119867119896119911119901+ 1sum119896119895=0

3sum119901=0

119861119896119895119901 sin 2120587119896119905365 cos2120587119895119905365 119911119901

+ 1sum119896119895=0

3sum119901=0

119862119896119895119901120579119896 ln 120579119895119911119901(8)


119894=1

119886119894119867119894 + 1198981sum119896119895=1

119861119896119895119879119901119895minus119902119895 + 1198881120579 + 1198882 ln 120579 (9)

or 120575 = 1198860 + 4sum119894=1

119886119894119867119894 + 2sum119894=1

(1198871119894 sin 2120587119894119905365 + 1198872119894 cos 2120587119894119905365 )+ 1198881120579 + 1198882 ln 120579 (10)


119883 = ( 119867119867211986731198674 119911 1199112 1199113 1198791-10 11987911-30 11987931-60 11987961-100 120579 119868119899120579119911119867 1199111198672 1199111198673 1199111198674 1199112119867 11991121198672 11991121198673 11991121198674 1199113119867 11991131198672 11991131198673 119911311986741199111198791-10 11991111987911-30 11991111987931-60 11991111987961-100 11991121198791-10 119911211987911-30 119911211987931-60 119911211987961-100 11991131198791-10 119911311987911-30 119911311987931-60 119911311987961-100119911120579 119911119868119899120579 1199112120579 1199112119868119899120579 1199113120579 1199113119868119899120579 ) (11)


3 Methodology






Ｒ1

Ｒ2

Ｒm

y1

y2

yn









119895=1

(119908119894119895119892(119873119894sum119896=1

V119895119896119909119896 + 120579V119895) + 120579119908119894))119894 = 1 2 119873119900 (12)




119882(119903+1) =119882(119903) + Δ119882(119903) (13)




119900119895 = 119871sum119894=1






119871sum119895=1

10038171003817100381710038171003817119900119895 minus 11990510038171003817100381710038171003817 = 0 (16)







(19)

120573 = [[[[[1205731198791120573119879119871

]]]]]119871times119898 119879 = [[[[[1198791198791119879119879119873

]]]]]119873times119898(20)


10038171003817100381710038171003817119867 (119894 119894) 119894 minus 11987910038171003817100381710038171003817 (21)


119895=1

( 119871sum119894=1



= 119867119879119879 (23)









294Right

TS5 TS6

TS5-294DTS5-291D

TS5-274DL1-250D L1-250Z

L15-162D

TS2-287D TS2-287Z

L3-175D

L5-205Z

L5-250Z

DT-281Z

DT-250Z

DT-217Z

DT-205Z

DT-162Z


L3-205Z

L5-175D L5-175Z

L7-250Z

L7-205Z

L7-175Z

L9-250D L9-250Z

TS6-294D

TS1-286D TS1-286Z

145

175

TS6-294ZLeft

250

205

L12-162DL7-175D

L5-145D

L3-175Z

L3-250D


294

250

205

145

107

L5




(a)

2689

26350

22750

22600

22000

19911

139

580

26400

90 140 160

6400

20430

19900

(b)










2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Disp

lace

men

t (m

m)

105110115120125130135140

Wat

er le

vel d

iffer

ence

(m)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus505

101520253035

Air

tem

pera

ture

()

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

∘C




minus12minus10


024

Disp

lace

men

t (m

m)

Wat

er le

vel d

iffer

ence

(m)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

70

65

60

55

50

45

0

10

20

30

minus10

minus20

Air

tem

pera

ture

()

∘C






TrainedPredicted


0

05

1

15

2

25M

SE


Trained

Predicted

05

1

15

2

25

MSE




TrainedPredicted

0

05

1

15

2

25

MSE



Trained

Predicted

0

05

1

15

2

25M

SE












DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265











Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018












120575 = 4sum119896=0

3sum119901=0

119860119896119901119867119896119911119901 + 1198981sum119896119895=1

3sum119901=0

119861119896119901119879119901119895minus119902119895119911119901+ 1sum119896119895=0

3sum119901=0

119862119896119895119901120579119896 ln 120579119895119911119901 (7)

or 120575 = 4sum119896=0

3sum119901=0

119860119896119901119867119896119911119901+ 1sum119896119895=0

3sum119901=0

119861119896119895119901 sin 2120587119896119905365 cos2120587119895119905365 119911119901

+ 1sum119896119895=0

3sum119901=0

119862119896119895119901120579119896 ln 120579119895119911119901(8)


119894=1

119886119894119867119894 + 1198981sum119896119895=1

119861119896119895119879119901119895minus119902119895 + 1198881120579 + 1198882 ln 120579 (9)

or 120575 = 1198860 + 4sum119894=1

119886119894119867119894 + 2sum119894=1

(1198871119894 sin 2120587119894119905365 + 1198872119894 cos 2120587119894119905365 )+ 1198881120579 + 1198882 ln 120579 (10)


119883 = ( 119867119867211986731198674 119911 1199112 1199113 1198791-10 11987911-30 11987931-60 11987961-100 120579 119868119899120579119911119867 1199111198672 1199111198673 1199111198674 1199112119867 11991121198672 11991121198673 11991121198674 1199113119867 11991131198672 11991131198673 119911311986741199111198791-10 11991111987911-30 11991111987931-60 11991111987961-100 11991121198791-10 119911211987911-30 119911211987931-60 119911211987961-100 11991131198791-10 119911311987911-30 119911311987931-60 119911311987961-100119911120579 119911119868119899120579 1199112120579 1199112119868119899120579 1199113120579 1199113119868119899120579 ) (11)


3 Methodology






Ｒ1

Ｒ2

Ｒm

y1

y2

yn









119895=1

(119908119894119895119892(119873119894sum119896=1

V119895119896119909119896 + 120579V119895) + 120579119908119894))119894 = 1 2 119873119900 (12)




119882(119903+1) =119882(119903) + Δ119882(119903) (13)




119900119895 = 119871sum119894=1






119871sum119895=1

10038171003817100381710038171003817119900119895 minus 11990510038171003817100381710038171003817 = 0 (16)







(19)

120573 = [[[[[1205731198791120573119879119871

]]]]]119871times119898 119879 = [[[[[1198791198791119879119879119873

]]]]]119873times119898(20)


10038171003817100381710038171003817119867 (119894 119894) 119894 minus 11987910038171003817100381710038171003817 (21)


119895=1

( 119871sum119894=1



= 119867119879119879 (23)









294Right

TS5 TS6

TS5-294DTS5-291D

TS5-274DL1-250D L1-250Z

L15-162D

TS2-287D TS2-287Z

L3-175D

L5-205Z

L5-250Z

DT-281Z

DT-250Z

DT-217Z

DT-205Z

DT-162Z


L3-205Z

L5-175D L5-175Z

L7-250Z

L7-205Z

L7-175Z

L9-250D L9-250Z

TS6-294D

TS1-286D TS1-286Z

145

175

TS6-294ZLeft

250

205

L12-162DL7-175D

L5-145D

L3-175Z

L3-250D


294

250

205

145

107

L5




(a)

2689

26350

22750

22600

22000

19911

139

580

26400

90 140 160

6400

20430

19900

(b)










2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Disp

lace

men

t (m

m)

105110115120125130135140

Wat

er le

vel d

iffer

ence

(m)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus505

101520253035

Air

tem

pera

ture

()

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

∘C




minus12minus10


024

Disp

lace

men

t (m

m)

Wat

er le

vel d

iffer

ence

(m)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

70

65

60

55

50

45

0

10

20

30

minus10

minus20

Air

tem

pera

ture

()

∘C






TrainedPredicted


0

05

1

15

2

25M

SE


Trained

Predicted

05

1

15

2

25

MSE




TrainedPredicted

0

05

1

15

2

25

MSE



Trained

Predicted

0

05

1

15

2

25M

SE












DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265











Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018









Ｒ1

Ｒ2

Ｒm

y1

y2

yn









119895=1

(119908119894119895119892(119873119894sum119896=1

V119895119896119909119896 + 120579V119895) + 120579119908119894))119894 = 1 2 119873119900 (12)




119882(119903+1) =119882(119903) + Δ119882(119903) (13)




119900119895 = 119871sum119894=1






119871sum119895=1

10038171003817100381710038171003817119900119895 minus 11990510038171003817100381710038171003817 = 0 (16)







(19)

120573 = [[[[[1205731198791120573119879119871

]]]]]119871times119898 119879 = [[[[[1198791198791119879119879119873

]]]]]119873times119898(20)


10038171003817100381710038171003817119867 (119894 119894) 119894 minus 11987910038171003817100381710038171003817 (21)


119895=1

( 119871sum119894=1



= 119867119879119879 (23)









294Right

TS5 TS6

TS5-294DTS5-291D

TS5-274DL1-250D L1-250Z

L15-162D

TS2-287D TS2-287Z

L3-175D

L5-205Z

L5-250Z

DT-281Z

DT-250Z

DT-217Z

DT-205Z

DT-162Z


L3-205Z

L5-175D L5-175Z

L7-250Z

L7-205Z

L7-175Z

L9-250D L9-250Z

TS6-294D

TS1-286D TS1-286Z

145

175

TS6-294ZLeft

250

205

L12-162DL7-175D

L5-145D

L3-175Z

L3-250D


294

250

205

145

107

L5




(a)

2689

26350

22750

22600

22000

19911

139

580

26400

90 140 160

6400

20430

19900

(b)










2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Disp

lace

men

t (m

m)

105110115120125130135140

Wat

er le

vel d

iffer

ence

(m)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus505

101520253035

Air

tem

pera

ture

()

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

∘C




minus12minus10


024

Disp

lace

men

t (m

m)

Wat

er le

vel d

iffer

ence

(m)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

70

65

60

55

50

45

0

10

20

30

minus10

minus20

Air

tem

pera

ture

()

∘C






TrainedPredicted


0

05

1

15

2

25M

SE


Trained

Predicted

05

1

15

2

25

MSE




TrainedPredicted

0

05

1

15

2

25

MSE



Trained

Predicted

0

05

1

15

2

25M

SE












DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265











Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018











119871sum119895=1

10038171003817100381710038171003817119900119895 minus 11990510038171003817100381710038171003817 = 0 (16)







(19)

120573 = [[[[[1205731198791120573119879119871

]]]]]119871times119898 119879 = [[[[[1198791198791119879119879119873

]]]]]119873times119898(20)


10038171003817100381710038171003817119867 (119894 119894) 119894 minus 11987910038171003817100381710038171003817 (21)


119895=1

( 119871sum119894=1



= 119867119879119879 (23)









294Right

TS5 TS6

TS5-294DTS5-291D

TS5-274DL1-250D L1-250Z

L15-162D

TS2-287D TS2-287Z

L3-175D

L5-205Z

L5-250Z

DT-281Z

DT-250Z

DT-217Z

DT-205Z

DT-162Z


L3-205Z

L5-175D L5-175Z

L7-250Z

L7-205Z

L7-175Z

L9-250D L9-250Z

TS6-294D

TS1-286D TS1-286Z

145

175

TS6-294ZLeft

250

205

L12-162DL7-175D

L5-145D

L3-175Z

L3-250D


294

250

205

145

107

L5




(a)

2689

26350

22750

22600

22000

19911

139

580

26400

90 140 160

6400

20430

19900

(b)










2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Disp

lace

men

t (m

m)

105110115120125130135140

Wat

er le

vel d

iffer

ence

(m)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus505

101520253035

Air

tem

pera

ture

()

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

∘C




minus12minus10


024

Disp

lace

men

t (m

m)

Wat

er le

vel d

iffer

ence

(m)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

70

65

60

55

50

45

0

10

20

30

minus10

minus20

Air

tem

pera

ture

()

∘C






TrainedPredicted


0

05

1

15

2

25M

SE


Trained

Predicted

05

1

15

2

25

MSE




TrainedPredicted

0

05

1

15

2

25

MSE



Trained

Predicted

0

05

1

15

2

25M

SE












DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265











Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018









294Right

TS5 TS6

TS5-294DTS5-291D

TS5-274DL1-250D L1-250Z

L15-162D

TS2-287D TS2-287Z

L3-175D

L5-205Z

L5-250Z

DT-281Z

DT-250Z

DT-217Z

DT-205Z

DT-162Z


L3-205Z

L5-175D L5-175Z

L7-250Z

L7-205Z

L7-175Z

L9-250D L9-250Z

TS6-294D

TS1-286D TS1-286Z

145

175

TS6-294ZLeft

250

205

L12-162DL7-175D

L5-145D

L3-175Z

L3-250D


294

250

205

145

107

L5




(a)

2689

26350

22750

22600

22000

19911

139

580

26400

90 140 160

6400

20430

19900

(b)










2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Disp

lace

men

t (m

m)

105110115120125130135140

Wat

er le

vel d

iffer

ence

(m)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus505

101520253035

Air

tem

pera

ture

()

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

∘C




minus12minus10


024

Disp

lace

men

t (m

m)

Wat

er le

vel d

iffer

ence

(m)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

70

65

60

55

50

45

0

10

20

30

minus10

minus20

Air

tem

pera

ture

()

∘C






TrainedPredicted


0

05

1

15

2

25M

SE


Trained

Predicted

05

1

15

2

25

MSE




TrainedPredicted

0

05

1

15

2

25

MSE



Trained

Predicted

0

05

1

15

2

25M

SE












DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265











Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018












2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Disp

lace

men

t (m

m)

105110115120125130135140

Wat

er le

vel d

iffer

ence

(m)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus505

101520253035

Air

tem

pera

ture

()

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

∘C




minus12minus10


024

Disp

lace

men

t (m

m)

Wat

er le

vel d

iffer

ence

(m)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Time (year)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Time (year)

70

65

60

55

50

45

0

10

20

30

minus10

minus20

Air

tem

pera

ture

()

∘C






TrainedPredicted


0

05

1

15

2

25M

SE


Trained

Predicted

05

1

15

2

25

MSE




TrainedPredicted

0

05

1

15

2

25

MSE



Trained

Predicted

0

05

1

15

2

25M

SE












DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265











Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018









TrainedPredicted


0

05

1

15

2

25M

SE


Trained

Predicted

05

1

15

2

25

MSE




TrainedPredicted

0

05

1

15

2

25

MSE



Trained

Predicted

0

05

1

15

2

25M

SE












DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265











Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018











DJ

MLR 05194 04962 04710 05599 33345 32524 09519 09054 13800SR 05210 06517 04999 06951 34872 31291 09489 09143 13910BP 04325 05889 03595 07087 37087 34262 09649 09360 24140ELM 04240 04555 03504 05005 33246 24620 09652 09420 14360

FM [17]

MLR 08355 10673 09947 17170 20376 28455 09388 09190 21619SR 09097 10959 11750 16609 25263 23165 09361 09099 27656BP 04270 08491 03505 11311 22703 23678 09824 09466 53310ELM 03978 07020 02653 08929 16336 22076 09840 09564 29265











Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018









Time (year)2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014Va

lue o

f disp

lace

men

t (m

m)

minus12minus10


02

MeasuredModeled

(a)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(b)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(c)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(d)


210


Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

valu

e of d

ispla

cem

ent (

mm

)

(a)

234

10


sidua

l err

or (m

m)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

420


minus10minus12

Valu

e of d

ispla

cem

ent (

mm

)

(b)

2

1

0

minus1

minus2

minus3

minus4

Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(c)

2

3

4

1

0

minus1

minus2Resid

ual e

rror

(mm

)

1991 1992 1993 1994 1995

Time (year)

1996 1997 1998 1999 2000 2001

MeasuredModeled

4

2

0

minus2

minus4

minus6

minus8

minus10

minus12

Valu

e of d

ispla

cem

ent (

mm

)

(d)



MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018









MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20142003Time (year)

(a)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

(b)

2007 200920062004 20082005 2010 2011 2012 2013 20142003Time (year)

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)

MeasuredModeled

(c)

MeasuredModeled

minus12minus10


02

Valu

e of d

ispla

cem

ent (

mm

)2007 200920062004 20082005 2010 2011 2012 2013 20142003

Time (year)

(d)


MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(b)

BP

1510 200 5

Lag

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR

minus5

minus25

0

25

5

Stan

dard

resid

uals



(e)

SR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(f)

BP

minus5

minus25

0

25

5

Stan

dard

resid

uals



(g)

ELM



minus5

minus25

0

25

5

Stan

dard

resid

uals

(h)

MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)



MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018









MLR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(a)

SR

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(b)

BP

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(c)

ELM

minus1

minus05

0

05

1

Sam

ple A

utoc

orre

latio

n

1510 200 5

Lag

(d)MLR



minus5

minus25

0

25

5

Stan

dard

resid

uals

(e)

SR

minus5

minus25

0

25

5St

anda

rd re

sidua

ls



(f)

BP



minus5

minus25

0

25

5

Stan

dard

resid

uals

(g)

ELM

minus5

minus25

0

25

5

Stan

dard

resid

uals



(h)MLR

0

01

02

03

04

05

Prob

abili

ty



(i)

SR

0

01

02

03

04

05

Prob

abili

ty



(j)

BP

0

01

02

03

04

05

Prob

abili

ty



(k)

ELM

0

01

02

03

04

05

Prob

abili

ty



(l)


6 Conclusion






Data Availability






References



































Journal of












Journal of







Volume 2018






Volume 2018












References



































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

An Empirical Comparison of Multiple Linear Regression and …downloads.hindawi.com/journals/mpe/2019/7620948.pdf · is paper studies the application characteristics and eects of the