Research ArticleWater Pollution Detection Based on Hypothesis Testingin Sensor Networks

Xu Luo1 and Jun Yang2

1Department of Information Engineering Zunyi Medical University Zunyi 563000 China2School of Information Science and Engineering Wuhan University of Science and Technology Wuhan 430081 China

Correspondence should be addressed to Jun Yang yangjunwusteducn

Received 17 October 2016 Revised 10 December 2016 Accepted 15 December 2016 Published 16 January 2017

Academic Editor Andrea Cusano

Copyright copy 2017 Xu Luo and Jun YangThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Water pollution detection is of great importance in water conservation In this paper the water pollution detection problems ofthe network and of the node in sensor networks are discussed The detection problems in both cases of the distribution of themonitoring noise being normal and nonnormal are consideredThe pollution detection problems are analyzed based on hypothesistesting theory firstly then the specific detection algorithms are given Finally two implementation examples are given to illustratehow the proposed detection methods are used in the water pollution detection in sensor networks and prove the effectiveness ofthe proposed detection methods

1 Introduction

Water is the most important material to humanrsquos survival andvaluable resource to industrial and agricultural productionWith the development of economy and industry more kindsof pollution materials are discharged into the water envi-ronment such as rivers and lakes and more water pollutiondisasters have happened Detecting the pollution timely isimportant for water conservation and is the precondition tolocate and find the pollution source

In most pollution monitoring and pollution source local-ization applications by using sensor networks the criteriaof the pollution detecting are that the nodes have pollutionconcentration values and the concentration values are largerthan a given threshold such as the works about the pollutionmonitoring [1ndash8] and the works about the pollution sourcelocalization [9ndash12]

Since there is an initial pollution concentration of normalproduction and life in water when the sensor nodes havemonitored relevant information it cannot be deduced thatthere exists pollution generated by a pollution source Atthe same time in the water environment there are planktongarbage aquatic animals plants and so forth which inter-vene in water pollution monitoring and bring disturbances

to the monitoring data The decision threshold to determinewhether there is pollution is difficult to be given properly inthe simple source detection method

In this paper hypothesis testing is adopted to solve thewater pollution detection problems Firstly a brief descrip-tion of the monitoring sensor network and what problemsthere are in the pollution detection are given Secondly theo-retical approaches to solve the detection problems are ana-lyzed based on hypothesis testing Thirdly the specific detec-tion algorithms are given Finally implementation examplesare given to illustrate the proposed pollution detectionmethods

2 Problem Statement

21 Network Deployment The self-organizing sensor net-work is used in the water pollutionmonitoring 119869 (gt5) sensornodes are deployed in the monitoring area uniformly and thedetail information of the pollutant to be monitored is knownpreviously The detection sensors which are stretched intowater are identified The locations of the nodes are fixed Thesensor nodes know their own positions and all static nodesin the network sample and store the concentration values

HindawiJournal of SensorsVolume 2017 Article ID 3829894 8 pageshttpsdoiorg10115520173829894

2 Journal of Sensors

A The pollutionsource

The processing

The sensor node

The sink nodecenter

B

CD

E

Figure 1 The sensor network for pollution detection

synchronously with the same time interval The backgroundinformation such as the diffusion coefficient the water depthand the interval of sampling time is known previouslyThe monitoring information is routed to the sink nodeand processed by the data processing center The networkdeployment is as shown in Figure 1

22TheDetection Problems Thepollution detection problemof the network is to detect whether the sensor networkfinds the pollution More specifically that is 119869 static nodessample and store the concentrations uniformly with a timeinterval119879 At the sampling time 119905119897 based on the samples (119909119894119910119894 119905119897) 119894 = 1 2 3 119869 of the 119869 nodes determine whe-ther there is pollution at a given significance level 120572 inhypothesis testing

The purpose of the pollution detection of the network isto detect the pollution timely

The pollution detection problem of the node is that eachnode in the network determineswhether it has accessed to theconcentration information about the pollution source Morespecifically that is all static nodes in the network sample andstore the concentrations synchronously with a time interval119879 At a given significance level 120572 in hypothesis testing it isdetermined whether the node (119909119894 119910119894) has found the waterpollution at 119905119871 based on the known samples (119909119894 119910119894 119905119897) 119897 =1 2 3 119871

The change of the diffusion in the concentration field isslowWhen the network finds the pollution it is not that eachsensor node has detected the pollution With time passingthe sensor nodes having detected the pollution will be moreand more In the pollution source localization a node can beused in the localization only when the node has detected thepollution

3 Pollution Detection Based onHypothesis Testing

In [13] a simple discussion about the water pollution detec-tion is given by the present authors under the assumption thatthe distribution of themonitoring noise is normal and knownpreviously In this paper the pollution detection problems arediscussed in more general cases

Assume that the initial pollutant concentration (thepollution concentration of normal production and livingsewage) in water is 1198620 If there is no diffusion source(119909119894 119910119894 119905119897) = 1198620 + 119890 119894 = 1 2 3 119869 If there is somenode (119909119894 119910119894) having detected the pollution (119909119894 119910119894 119905119897) =119862(119909119894 119910119894 119905119897)+1198620+119890 where 119890 is themeasurement noise of sensornodes and 119862(119909119894 119910119894 119905119897) is the theoretical concentration valuerelated to the pollution source

Remark 1 The concentration 119862(119909119894 119910119894 119905119897) changes over timeand at different locations The specific forms of water pollu-tion diffusion can be seen in literature [14]

31 Distribution Test Under different statistical distributionsof samples the specific hypothesis testing problems aredifferent In the water pollution detection the first is todetermine whether the distribution of the observation noiseis normal

In the initial state there are only a few nodes perceivingthe pollution or there is no node perceiving the pollutionWhen there is no pollution (119909119894 119910119894 1199051) = 1198620 + 119890 and if thedistribution of (119909119894 119910119894 1199051) is normal 119890 is a normal variable

In order to save cost the number of sampling nodes isoften limited in practical applications The Shapiro-Wilk 119882

Journal of Sensors 3

Table 1 The two groups of independent samples in the detection of the network

Sample 1 (1199091 1199101 119905119897) (1199092 1199102 119905119897) (1199093 1199103 119905119897) sdot sdot sdot (119909lfloor1198692rfloor 119910lfloor1198692rfloor 119905119897)Sample 2 (119909lfloor1198692rfloor+1 119910lfloor1198692rfloor+1 119905119897) (119909lfloor1198692rfloor+2 119910lfloor1198692rfloor+2 119905119897) (119909lfloor1198692rfloor+3 119910lfloor1198692rfloor+3 119905119897) sdot sdot sdot (119909119869 119910119869 119905119897)

test [15] method in the case of small samples can be used asthe distribution test method here

Step 1 Remark the monitoring values of the 119869 nodes at 1199051 as119894 119894 = 1 2 3 119869 Order the values as follows[1 2 3 119869] (1 le 2 le 3 le sdot sdot sdot le 119869) (1)

Step 2 The test statistic119882 is calculated as

119882 = (sum119869119894=1 119886119894119894)2sum119869119894=1 (119894 minus 119862)2

(2)

where 119862 = (1119869)sum119869119894=1 119894Step 3 At a given significance level of hypothesis testing 120572if 119882 ⩽ 119882120572 the distribution is nonnormal otherwise thedistribution is normal

In the above steps the values of 119886119894 and119882120572 can be obtainedby the method of table lookup [16]

The specific detection problems when the distribution ofthe sensing values is normal are different from the detectionproblems when the distribution is nonnormal The detectionmethods in the two cases are discussed in the following

32 The Pollution Detection of the Network

Case 1 (hypothesis testing under normal distribution)According to the nature of the normal distribution if thenode has detected no pollution at 119905119897 it can be deduced that(1) (119909119894 119910119894 119905119897) sim 119873(1198620 + 120583 1205752) the noise 119890 sim (120583 1205752) (2) if1 = min(119909119894 119910119894 119905119897) 119894 = 1 2 3 119869 ((119909119894 119910119894 119905119897) minus 1) sim119873(0 21205752)

Investigate the mean value 120583119896 of 119862(119909119894 119910119894 119905119897) minus 1 119894 =1 2 3 4 119869 The hypotheses are given by

119867(1)0 120583120581 = 0119867(1)1 120583120581 = 0 (3)

As 120575 is unknown the test statistic is1198661 = 119862120581(119878120581radic119869) (4)

where 119862120581 = (1119869)sum119869119894=1((119909119894 119910119894 119905119897) minus 1) and 1198782120581 = (1(119869 minus1))sum119869119894=1(((119909119894 119910119894 119905119897) minus 1) minus 119862120581)2

At the significance level 120572 [17] if100381610038161003816100381611986611003816100381610038161003816 ge 1199051205722 (119869 minus 1) (5)

that is when 119875(1198661 ge 1199051205722(119869 minus 1)) = 120572 reject 119867(1)0 it isdeduced that there is a pollution source Note that 1199051205722 is the1205722 quantile of 119905-distribution [17 18]

Case 2 (hypothesis testing under nonnormal distribution)While the sample distribution is nonnormal it is difficult toverify what the specifying distribution of the values is In thiscase the Wilcoxon rank sum test is used directly [17]

Our test problem is to determine whether there is sig-nificant difference between the two groups of independentsamples in Table 1 The hypotheses are

119867(1)0 1205831198781 = 1205831198782119867(1)1 1205831198781 = 1205831198782

(6)

List the data in ascending order and allocate the ranks 119904119895according to the order The significance level of hypothesistesting is 120572 and 1198771 is the sum of ranks of Sample 1

When

1198771 le 119862119871 (1205722 )or 1198771 ge 119862119880 (1205722 )

(7)

reject 1198670 there is a pollution source in the monitoring area119862119880(1205722) and 119862119871(1205722) are the upper tail value and lower tailvalue of the two-tailed rank sum test [17 18]

33 The Pollution Source Detection of the Node Based onthe monitoring values (119909119894 119910119894 119905119897) 119897 = 1 2 3 119871 ofnode (119909119894 119910119894) determine whether the node has detected thepollution source

Case 1 (hypothesis testing under normal distribution) If thesample noise 119890 is normal when the node does not detect thepollution at 119905119897 there is ((119909119894 119910119894 119905119897)minus(119909119894 119910119894 1199051)) sim 119873(0 21205752)

Let 1205831015840 be the average value of (119909119894 119910119894 119905119897) minus (119909119894 119910119894 1199051)119897 = 2 3 119871 The hypotheses are given by

119867(3)0 1205831015840 = 0119867(3)1 1205831015840 = 0 (8)

The test statistic is

1198662 = 1198621015840(1198781015840radic119871 minus 1) (9)

where 1198621015840 = (1(119871 minus 1))sum119871119897=2((119909119894 119910119894 119905119897) minus (119909119894 119910119894 1199051)) and11987810158402 = (1(119871 minus 2))sum119871119897=2((119909119894 119910119894 119905119897) minus (119909119894 119910119894 1199051) minus 1198621015840)2If

100381610038161003816100381611986621003816100381610038161003816 ge 1199051205722 (119871 minus 2) (10)

that is when 119875(|1198662| ge 1199051205722(119871 minus 2)) = 120572 reject 119867(3)0 and it isdeduced that the node has detected the pollution Here 1199051205722

4 Journal of Sensors

Table 2The two groups of independent samples in the detection ofthe node

Sample 3 (119909119894 119910119894 1199051) (119909119894 119910119894 1199052) sdot sdot sdot (119909119894 119910119894 119905lfloor1198712rfloor)Sample 4 (119909119894 119910119894 119905lfloor1198712rfloor+1) (119909119894 119910119894 119905lfloor1198712rfloor+2) sdot sdot sdot (119909119894 119910119894 119905119871)

is the 1205722 quantile of 119905-distribution and 120572 is the significancelevel of hypothesis testing [17 18]

Case 2 (hypothesis testing under nonnormal distribution)The Wilcoxon rank sum test is used Our test problem is todetermine whether there is significant difference between thetwo groups of independent samples in Table 2

The hypotheses are

119867(4)0 1205831198783 = 1205831198784119867(4)1 1205831198783 = 1205831198784

(11)

The same solving method as hypothesis testing problem (6)can be used in (11)

34 Sample Size Requirements in Detection

341 Basic Requirements According to the basic samplenumber requirements of the hypothesis testing methods [1718] the basic sample size requirements in our detectionmethods are given as follows In the distribution test thenumber of samples 119869 should be 3 le 119869 le 50 When thedistribution of the sample noise is normal there should beat least 4 samples in the pollution detection of the networkand the pollution detection of the node so 119869 ge 4 and 119871 ge 5When the distribution is not normal there should be at least6 samples in the pollution detection of the network and inthe pollution detection of the node so the sample numbersshould satisfy 119869 ge 6 and 119871 ge 6342 The Power of Tests

(A) 119905 Test In hypotheses test under the normal distributionthe OC function of 119905 test of (3) and (8) is

120573 (120583) = 119875120583 (accept 1198670)= 119875120583 (minus1199051205722 (119899 minus 1) lt 119862

(119904sqrt (119899)) lt 1199051205722 (119899 minus 1)) (12)

where 119862(119904sqrt(119899)) = ((119862minus120583)(120575sqrt(119899)) + 120583(120575sqrt(119899)))(119904120575) 119862 is 119862120581 in (4) and 1198621015840 in (9) respectively 119904 is 119878119896 in (4)and 1198781015840 in (9) respectively and 119899 = 119869 in (4) and 119899 = 119871 minus 1 in(9) 120583 is 120583119896 in (3) and 1205831015840 in (8) respectively

In the pollution detection of the network to reduce thecost the number of nodes is always given previously So thereis a precondition that is the number of the sensor nodesis 119899 le 1198731 where 1198731 is a given number For the purposeof participating in the pollution source localization timelythere also should not bemany sampling times in the pollution

detection of the node and themaximum sampling number isalso often given

To reduce the probability of false alarm under giventhresholds 120573 120579 gt 0 in the hypothesis testing problems (3)and (8) the significance level 120572 should satisfy

119875120583 (accept 1198670)= 119875120583 (minus1199051205722 (119899 minus 1) lt 119862

(119904sqrt (119899)) lt 1199051205722 (119899 minus 1))le 120573

(13)

when 120583 isin 1198671 and |120583120575| ge 120579(B)The Nonparametric TestThere are no explicit expressionsof the test power in nonparametric testsWhen themaximumnumber of samples is given if we want to reduce thepossibility of the I type error in the test the possibility of the IItype error often increases [19] so an appropriate significancelevel is necessary In nonparametric tests 120572 = 005 is oftenadopted

4 The Detection Algorithms

Based on the theoretical research above there are pollutionsource detection algorithms as follows

Algorithm 1 (the pollution detection of the network)

Preconditions The number of providing samples 119869 is largeenough and known The samples at the first sampling time1199051 and the detection time 119905119897 are knownThe parameters 120573 and120579 which are related to the test power are given

Step 1 Use Shapiro-Wilk119882 test to test the distribution of thesample noise according to (2) at the first sampling time 1199051Step 2 If the distribution is normal get the value range of thesignificance level according to (13) choose an any significancelevel 120572 in the range calculate the test statistic as (4) and goto Step 3 If the distribution is nonnormal go to Step 4

Step 3 When the test statistic satisfies the test criterion (5)there is pollution otherwise there is no pollution

Step 4 List the data in ascending order and allocate the ranksaccording to the order Calculate 1198771 which is the sum ofranks of Samples 1 in Table 1 Look up the table to get thetail values in the rank sum test When the sum 1198771 satisfiesthe test criterion (7) there is pollution otherwise there is nopollution

At time 119905119897 if the network does not detect the pollutionthe pollution detection of the network will be made at 119905119897+1Algorithm 2 (the pollution detection of the node (119909119894 119910119894))Preconditions The number of samples 119871 is large enough andknown The samples at the first sampling time 1199051 are knownThe samples of the detection node (119909119894 119910119894) are known The

Journal of Sensors 5

parameters 120573 and 120579 which are related to the test power aregiven

Step 1 Use Shapiro-Wilk119882 test to test the distribution of thesample noise according to (2) at the first sampling time 1199051Step 2 If the distribution is normal get the value range of thesignificance level according to (13) choose an any significancelevel 120572 in the range calculate the test statistic as (9) and go toStep 3 If the distribution is nonnormal go to Step 4

Step 3 When the test statistic satisfies the test criterion (10)the node detects the pollution otherwise the node fails todetect the pollution

Step 4 List the data in ascending order and allocate the ranksaccording to the order Calculate1198773 which is the sum of ranksof Samples 3 in Table 2 Look up the table to get the tailvalues in the rank sum test When the sum 1198773 satisfies thetest criterion (7) the node detects the pollution otherwisethe node fails to detect the pollution

5 Implementation Examples

Experiment 1 A simulation is carried out to test the proposeddetection algorithmsThedistribution ofmonitoring noises isnormal

BackgroundThesize of the static shallowwater is 10mtimes 10mand the average depth of the water is 119891 = 10m Apart fromthe coast of impervious 119884 there is a continuous source at(1199090 1199100) = (105 555) (m) Starting from time 1199050 = 0 h thesolution with pollutant is injected into the water The mass ofthe pollutant is119872 = 100 kg The diffusion coefficient is 119863 =01m2hThe nodes in the network sample the concentrationuniformly with interval 119879 = 005 h The diffusion can bedepicted by the model

119862 (119909 119910 1199090 1199100)= ( 119872

(4120587119863 (119905 minus 1199050))) 119890minus[((119909minus1199090)

2+(119910minus1199100)2)4119863(119905minus1199050)] (14)

where 119905 is the current time The locations of the monitoringnodes are (205 555) (105 455) (005 555) (105 655)(055 605) (155 605) (055 505) (155 505) (005 625)and (105 705) The monitoring values in the experiment arethe simulation values of (14) adding the noise with a normaldistribution 119873(0 1205752) The given parameters are 120573 = 05 and120579 = 1 and there are 10 nodes 119899 = 1198731 = 10(A) The Pollution Detection of the Network According toconstraint (13) and the sample size table of 119905 test in [18] itis can be deduced that 120572 gt 0025 under the given parameters120573 120579 and 120575 in Table 3

For different 120575 values and significance levels detect thepollution at the initial observation time 001 h and theresults are shown in Table 3The hypothesis testing detectionmethod under the normal distribution is used and in the

Table 3 The detection results of the network

120575 Significance levels Detection results001 003 100100001 005 100100001 01 10010001 003 10010001 005 9910001 01 10010005 003 9910005 005 10010005 01 100100

table ldquo119883100rdquo represents that in the 100 experiments thepollution is detected successfully119883 times

The results show that the pollution can be detected by thenetwork soon

(B) The Pollution Detection of the Node Detect whether thenode has detected the pollution source based on the observeddata of the node (105 705) The monitoring data is as shownin Table 4 Compare with the simple detection method inwhich the criterion of whether the pollution source has beendetected is that the monitoring value is larger than a giventhreshold and the results are shown in Table 5

In Table 5 ldquomdashrdquo represents no result Comparing theresults in the table it can be seen that the detection methodusing hypothesis testing is more stable if an appropriatesignificance level is chosen and in the simple detection todetect the pollution source timely the threshold should be assmall as possible But apparently if the noise in the practicalapplications is considered small thresholds may bring aboutlarge false alarm rates

Experiment 2 Apractical experiment is carried out to test theproposed detection algorithms

Background In water of which the size is 200 cm times 200 cmthe average depth119891 = 100 cmThere is a continuous source atthe boundary Starting from 1199050 = 0 s the solution of MgSO4is discharged to the water continuallyThe nodes deploymentis depicted by Figure 2 The monitoring values of differentsensor nodes in the experiment are shown in Table 6

DistributionVerificationBoth at time 5 s and 10 s for differentsignificance levels 120572 = 001 120572 = 005 and 120572 = 01 thedetection results all show that the distribution of monitoringdata is not normal So the detection methods based on theWilcoxon rank sum tests are used

(A) The Pollution Detection of the NetworkThe given signifi-cance level is 120572 = 005 and the network detects the pollutionat 30 s

(B)The Pollution Detection of the NodeThe significance levelis 120572 = 005 and the time when nodes 0 1 2 3 4 5 6 and 7

6 Journal of Sensors

Table 4 The monitoring values of node (105 705) in Experiment 1

Time(s) 119879 2119879 3119879 4119879 5119879 6119879 7119879 8119879 9119879 10119879Observations (gL) 0008 0009 0010 0015 0017 0019 0081 0217 0423 0748

Table 5 The detection results comparing with the simple detection method

Significance levels Detection time of 119905 test Threshold (gL) Detection time of the simple detection method003 mdash 003 7119879005 6119879 005 711987901 5119879 01 8119879015 5119879 015 811987902 5119879 02 811987905 4119879 05 10119879

Table 6 The monitoring values in Experiment 2

Time(s) Node 0 (gL) Node 1 (gL) Node 2 (gL) Node 3 (gL) Node 4 (gL) Node 5 (gL) Node 6 (gL) Node 7 (gL)5 000000 000000 000032 000000 000016 000000 000000 00000010 000000 000000 000242 000000 000548 000000 000000 00000015 000000 000000 000581 000000 001210 000000 000000 00000020 000000 000000 000790 000000 001726 000000 000000 00000025 000000 000000 001161 000000 003532 000000 000000 00000030 000210 000000 001661 000050 004532 000000 000033 00000035 001726 000000 005686 000415 006284 000242 001561 00000040 005686 000000 008422 001445 009608 003048 003206 00000045 006216 000000 010429 001877 012071 004081 005216 00000050 008441 000000 012990 005186 013163 007324 006912 00000055 009333 000000 014969 006784 015386 009186 008118 00000060 011235 000000 016957 008324 017286 010673 009559 00000065 012439 000000 018557 009804 017557 011449 011316 00000070 012959 000016 019014 011694 017957 012418 012663 00000075 013449 000129 019457 012245 018786 013122 013010 00008180 013673 000177 020385 012561 019957 013449 013449 00025885 014204 000242 020846 012888 020846 013990 013684 00029090 014643 000403 021135 013224 021019 014122 013847 00043595 014878 000516 021692 013786 021154 014714 014327 000613100 015114 000532 021808 014133 021346 015071 015200 000694105 015386 000726 022423 014776 021481 015343 015814 000823110 015686 000790 022885 015300 021558 015714 016043 000790115 016000 000839 023115 015829 021962 016214 016643 000839120 016329 001000 023462 016343 022154 016543 016814 001097125 016557 001194 023558 016986 022288 016814 017000 001161130 016757 001339 023885 017214 022365 017386 017114 001403135 016814 001484 023923 017329 022404 017414 017186 001597140 016857 001516 023942 017386 022500 017429 017229 001613145 016914 001613 023962 017414 022519 017457 017286 001694150 016929 001774 024000 017457 022519 017457 017300 001774155 016971 001887 024058 017486 022558 017471 017314 001887160 017014 001919 024077 017514 022577 017486 017357 002871165 017086 001935 024096 017543 022615 017514 017371 002968170 017114 002048 024115 017571 022635 017529 017414 003000175 017157 002065 024154 017614 022654 017557 017429 003016180 017171 002097 024173 017629 022712 017571 017457 003065

Journal of Sensors 7

Table 7 The detection time of different nodes in Experiment 2

Significance level Node 0 (s) Node 1 (s) Node 2 (s) Node 3 (s) Node 4 (s) Node 5 (s) Node 6 (s) Node 7 (s)005 50 95 40 50 40 50 50 100

200 cm

200 cm

7 5 3 1

6 4 2 0

(minus60 60) (minus20 60) (20 60) (60 60)

(minus60 20) (minus20 20) (20 20) (60 20)(0 0)

The source

Figure 2 The nodes deployment in Experiment 2

find the pollution is shown in Table 7 The detection methodis as (11)

The results show that the pollution can be detected bythe nodes only when there are some increasing concentrationsamples

From the results of the experiments above it can beenseen that in the simple detection method an appropriatedecision threshold is hard to be given so the pollution sourcedetection by using hypothesis testing is more preferableWhether the distribution of the sample noise is normal or notthe corresponding detection algorithms are available

6 Conclusions

Water pollution detection is important in the water environ-ment monitoring The pollution source detection problemsof the network and of the node are discussed based onhypothesis testing The sample size requirements in differentdetection problems are also analyzed In implementationexamples the proposed pollution detection algorithms aretestedThe effectiveness of the detection algorithms is provedThisworkmainly focuses on theoretical detection approachesbased on hypothesis testing In the future work moreproblems in the practical applications will be studied whenthe proposed detection algorithms are adopted such as theoptimized detection methods of the node related to largeor small concentration variations and the influences of theconcentration variations on the statistical distribution in thedistribution test step

Disclosure

The founding sponsors had no role in the design of the studythe collection analyses or interpretation of data the writingof the manuscript and the decision to publish the results

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this article

Acknowledgments

The research is sponsored by National Natural Science Foun-dation (NNSF) ofChina underGrant nos 61463053 61501337and 61471275 and Natural Science Foundation of GuizhouProvince in China under Grant LH[2015]7549 The authorswould like to thank Dr Li Chai in Wuhan University ofScience and Technology for the helpful suggestions

References

[1] J Wang X Wang X Ren and Y Shen A Water PollutionDetective System Based on Wireless Sensor Network Addison-Wesley Harlow UK 3rd edition 1999

[2] P Jiang H Xia Z He and ZWang ldquoDesign of a water environ-ment monitoring system based on wireless sensor networksrdquoSensors vol 9 no 8 pp 6411ndash6434 2009

[3] E V Hatzikos N Bassiliades L Asmanis and I VlahavasldquoMonitoring water quality through a telematic sensor networkand a fuzzy expert systemrdquo Expert Systems vol 24 no 3 pp143ndash161 2007

[4] B OrsquoFlynn R Martinez-Catala S Harte et al ldquoSmartCoasta wireless sensor network for water quality monitoringrdquo inProceedings of the 32nd IEEE Conference on Local ComputerNetworks (LCN rsquo07) pp 815ndash816 Dublin Ireland October 2007

[5] J HeidemannM Stojanovic andMZorzi ldquoUnderwater sensornetworks applications advances and challengesrdquo PhilosophicalTransactions of the Royal Society A Mathematical Physical andEngineering Sciences vol 370 no 1958 pp 158ndash175 2012

[6] J X He J Li and HW Yan ldquoAn architecture of geospatial sen-sor network for water quality monitoringrdquo Journal of Jilin Uni-versity (Earth Science Edition) vol 41 no 4 pp 1262ndash1266 2011

[7] N Harris A Cranny M Rivers K Smettem and E G Barrett-Lennard ldquoApplication of distributedwireless chloride sensors toenvironmentalmonitoring initial resultsrdquo IEEETransactions onInstrumentation and Measurement vol 65 no 4 pp 736ndash7432016

[8] Y Derbew andM Libsie ldquoAwireless sensor network frameworkfor large-scale industrial water pollution monitoringrdquo in Pro-ceedings of the IST-Africa Conference and Exhibition (IST-Africarsquo14) pp 1ndash8 Mauritius May 2014

8 Journal of Sensors

[9] J Yang L Chai and X Luo ldquoPollution source localization inlake environment based on wireless sensor networksrdquo in Pro-ceedings of the 31st Chinese Control Conference pp 6649ndash6654Hefei China July 2012

[10] X Luo L Chai and J Yang ldquoMobile diffusion source trackingin wireless sensor networksrdquo Control Theory and Applicationsvol 24 no 3 pp 143ndash161 2007

[11] X Luo L Chai and J Yang ldquoOffshore pollution source locali-zation in static water using wireless sensor networksrdquo ActaAutomatica Sinica vol 40 no 5 pp 849ndash861 2014

[12] J Yang X Luo and L Chai ldquoThe localization of pollution sou-rce in steady diffusion state in river based on wireless sensornetworksrdquo Chinese Journal of Sensors and Actuators vol 27 no10 pp 1423ndash1430 2014

[13] X Luo J Yang and L Chai ldquoWater pollution source detectionin wireless sensor networksrdquo in Proceedings of the IEEE Interna-tional Conference on Information andAutomation (ICIA rsquo15)mdashInconjunction with IEEE International Conference on Automationand Logistics pp 2311ndash2315 IEEE Lijiang China August 2015

[14] Z Peng T Yang and X LiangTheWater Environment Mathe-matical Model and Its Application Chemical Industry PressBeijing China 2007

[15] S S Shapiro and M B Wilk ldquoAn analysis of variance test fornormality (complete samples)rdquo Biometrika vol 52 no 3-4 pp591ndash611 1965

[16] B Thomas Serious Stats A Guide to Advanced Statistics for theBehavioral Sciences Palgrave Macmillan Press London UK2012

[17] R E Walpole R H Myers S L Myers and K Ye Probabilityand Statistics for Engineers and Scientists Pearson Prentice HallUpper Saddle River NJ USA 8th edition 2007

[18] Z Shen S Xie and C Pan Probability and Mathematical Sta-tistics High Education Press Beijing China 2005

[19] Sample size for nonparametric January 2016 httpswwwgra-phpadcomguidesprism6statisticsindexhtmstat samplesize for nonparametric htm

Journal of Sensors 3

Table 1 The two groups of independent samples in the detection of the network

Sample 1 (1199091 1199101 119905119897) (1199092 1199102 119905119897) (1199093 1199103 119905119897) sdot sdot sdot (119909lfloor1198692rfloor 119910lfloor1198692rfloor 119905119897)Sample 2 (119909lfloor1198692rfloor+1 119910lfloor1198692rfloor+1 119905119897) (119909lfloor1198692rfloor+2 119910lfloor1198692rfloor+2 119905119897) (119909lfloor1198692rfloor+3 119910lfloor1198692rfloor+3 119905119897) sdot sdot sdot (119909119869 119910119869 119905119897)

test [15] method in the case of small samples can be used asthe distribution test method here

Step 1 Remark the monitoring values of the 119869 nodes at 1199051 as119894 119894 = 1 2 3 119869 Order the values as follows[1 2 3 119869] (1 le 2 le 3 le sdot sdot sdot le 119869) (1)

Step 2 The test statistic119882 is calculated as

119882 = (sum119869119894=1 119886119894119894)2sum119869119894=1 (119894 minus 119862)2

(2)

where 119862 = (1119869)sum119869119894=1 119894Step 3 At a given significance level of hypothesis testing 120572if 119882 ⩽ 119882120572 the distribution is nonnormal otherwise thedistribution is normal

In the above steps the values of 119886119894 and119882120572 can be obtainedby the method of table lookup [16]

The specific detection problems when the distribution ofthe sensing values is normal are different from the detectionproblems when the distribution is nonnormal The detectionmethods in the two cases are discussed in the following

32 The Pollution Detection of the Network

Case 1 (hypothesis testing under normal distribution)According to the nature of the normal distribution if thenode has detected no pollution at 119905119897 it can be deduced that(1) (119909119894 119910119894 119905119897) sim 119873(1198620 + 120583 1205752) the noise 119890 sim (120583 1205752) (2) if1 = min(119909119894 119910119894 119905119897) 119894 = 1 2 3 119869 ((119909119894 119910119894 119905119897) minus 1) sim119873(0 21205752)

Investigate the mean value 120583119896 of 119862(119909119894 119910119894 119905119897) minus 1 119894 =1 2 3 4 119869 The hypotheses are given by

119867(1)0 120583120581 = 0119867(1)1 120583120581 = 0 (3)

As 120575 is unknown the test statistic is1198661 = 119862120581(119878120581radic119869) (4)

where 119862120581 = (1119869)sum119869119894=1((119909119894 119910119894 119905119897) minus 1) and 1198782120581 = (1(119869 minus1))sum119869119894=1(((119909119894 119910119894 119905119897) minus 1) minus 119862120581)2

At the significance level 120572 [17] if100381610038161003816100381611986611003816100381610038161003816 ge 1199051205722 (119869 minus 1) (5)

that is when 119875(1198661 ge 1199051205722(119869 minus 1)) = 120572 reject 119867(1)0 it isdeduced that there is a pollution source Note that 1199051205722 is the1205722 quantile of 119905-distribution [17 18]

Case 2 (hypothesis testing under nonnormal distribution)While the sample distribution is nonnormal it is difficult toverify what the specifying distribution of the values is In thiscase the Wilcoxon rank sum test is used directly [17]

Our test problem is to determine whether there is sig-nificant difference between the two groups of independentsamples in Table 1 The hypotheses are

119867(1)0 1205831198781 = 1205831198782119867(1)1 1205831198781 = 1205831198782

(6)

List the data in ascending order and allocate the ranks 119904119895according to the order The significance level of hypothesistesting is 120572 and 1198771 is the sum of ranks of Sample 1

When

1198771 le 119862119871 (1205722 )or 1198771 ge 119862119880 (1205722 )

(7)

reject 1198670 there is a pollution source in the monitoring area119862119880(1205722) and 119862119871(1205722) are the upper tail value and lower tailvalue of the two-tailed rank sum test [17 18]

33 The Pollution Source Detection of the Node Based onthe monitoring values (119909119894 119910119894 119905119897) 119897 = 1 2 3 119871 ofnode (119909119894 119910119894) determine whether the node has detected thepollution source

Case 1 (hypothesis testing under normal distribution) If thesample noise 119890 is normal when the node does not detect thepollution at 119905119897 there is ((119909119894 119910119894 119905119897)minus(119909119894 119910119894 1199051)) sim 119873(0 21205752)

Let 1205831015840 be the average value of (119909119894 119910119894 119905119897) minus (119909119894 119910119894 1199051)119897 = 2 3 119871 The hypotheses are given by

119867(3)0 1205831015840 = 0119867(3)1 1205831015840 = 0 (8)

The test statistic is

1198662 = 1198621015840(1198781015840radic119871 minus 1) (9)

where 1198621015840 = (1(119871 minus 1))sum119871119897=2((119909119894 119910119894 119905119897) minus (119909119894 119910119894 1199051)) and11987810158402 = (1(119871 minus 2))sum119871119897=2((119909119894 119910119894 119905119897) minus (119909119894 119910119894 1199051) minus 1198621015840)2If

100381610038161003816100381611986621003816100381610038161003816 ge 1199051205722 (119871 minus 2) (10)

that is when 119875(|1198662| ge 1199051205722(119871 minus 2)) = 120572 reject 119867(3)0 and it isdeduced that the node has detected the pollution Here 1199051205722

4 Journal of Sensors

Table 2The two groups of independent samples in the detection ofthe node

Sample 3 (119909119894 119910119894 1199051) (119909119894 119910119894 1199052) sdot sdot sdot (119909119894 119910119894 119905lfloor1198712rfloor)Sample 4 (119909119894 119910119894 119905lfloor1198712rfloor+1) (119909119894 119910119894 119905lfloor1198712rfloor+2) sdot sdot sdot (119909119894 119910119894 119905119871)

is the 1205722 quantile of 119905-distribution and 120572 is the significancelevel of hypothesis testing [17 18]

Case 2 (hypothesis testing under nonnormal distribution)The Wilcoxon rank sum test is used Our test problem is todetermine whether there is significant difference between thetwo groups of independent samples in Table 2

The hypotheses are

119867(4)0 1205831198783 = 1205831198784119867(4)1 1205831198783 = 1205831198784

(11)

The same solving method as hypothesis testing problem (6)can be used in (11)

34 Sample Size Requirements in Detection

341 Basic Requirements According to the basic samplenumber requirements of the hypothesis testing methods [1718] the basic sample size requirements in our detectionmethods are given as follows In the distribution test thenumber of samples 119869 should be 3 le 119869 le 50 When thedistribution of the sample noise is normal there should beat least 4 samples in the pollution detection of the networkand the pollution detection of the node so 119869 ge 4 and 119871 ge 5When the distribution is not normal there should be at least6 samples in the pollution detection of the network and inthe pollution detection of the node so the sample numbersshould satisfy 119869 ge 6 and 119871 ge 6342 The Power of Tests

(A) 119905 Test In hypotheses test under the normal distributionthe OC function of 119905 test of (3) and (8) is

120573 (120583) = 119875120583 (accept 1198670)= 119875120583 (minus1199051205722 (119899 minus 1) lt 119862

(119904sqrt (119899)) lt 1199051205722 (119899 minus 1)) (12)

where 119862(119904sqrt(119899)) = ((119862minus120583)(120575sqrt(119899)) + 120583(120575sqrt(119899)))(119904120575) 119862 is 119862120581 in (4) and 1198621015840 in (9) respectively 119904 is 119878119896 in (4)and 1198781015840 in (9) respectively and 119899 = 119869 in (4) and 119899 = 119871 minus 1 in(9) 120583 is 120583119896 in (3) and 1205831015840 in (8) respectively

In the pollution detection of the network to reduce thecost the number of nodes is always given previously So thereis a precondition that is the number of the sensor nodesis 119899 le 1198731 where 1198731 is a given number For the purposeof participating in the pollution source localization timelythere also should not bemany sampling times in the pollution

detection of the node and themaximum sampling number isalso often given

To reduce the probability of false alarm under giventhresholds 120573 120579 gt 0 in the hypothesis testing problems (3)and (8) the significance level 120572 should satisfy

119875120583 (accept 1198670)= 119875120583 (minus1199051205722 (119899 minus 1) lt 119862

(119904sqrt (119899)) lt 1199051205722 (119899 minus 1))le 120573

(13)

when 120583 isin 1198671 and |120583120575| ge 120579(B)The Nonparametric TestThere are no explicit expressionsof the test power in nonparametric testsWhen themaximumnumber of samples is given if we want to reduce thepossibility of the I type error in the test the possibility of the IItype error often increases [19] so an appropriate significancelevel is necessary In nonparametric tests 120572 = 005 is oftenadopted

4 The Detection Algorithms

Based on the theoretical research above there are pollutionsource detection algorithms as follows

Algorithm 1 (the pollution detection of the network)

Preconditions The number of providing samples 119869 is largeenough and known The samples at the first sampling time1199051 and the detection time 119905119897 are knownThe parameters 120573 and120579 which are related to the test power are given

Step 1 Use Shapiro-Wilk119882 test to test the distribution of thesample noise according to (2) at the first sampling time 1199051Step 2 If the distribution is normal get the value range of thesignificance level according to (13) choose an any significancelevel 120572 in the range calculate the test statistic as (4) and goto Step 3 If the distribution is nonnormal go to Step 4

Step 3 When the test statistic satisfies the test criterion (5)there is pollution otherwise there is no pollution

Step 4 List the data in ascending order and allocate the ranksaccording to the order Calculate 1198771 which is the sum ofranks of Samples 1 in Table 1 Look up the table to get thetail values in the rank sum test When the sum 1198771 satisfiesthe test criterion (7) there is pollution otherwise there is nopollution

At time 119905119897 if the network does not detect the pollutionthe pollution detection of the network will be made at 119905119897+1Algorithm 2 (the pollution detection of the node (119909119894 119910119894))Preconditions The number of samples 119871 is large enough andknown The samples at the first sampling time 1199051 are knownThe samples of the detection node (119909119894 119910119894) are known The

Journal of Sensors 5

parameters 120573 and 120579 which are related to the test power aregiven

Step 1 Use Shapiro-Wilk119882 test to test the distribution of thesample noise according to (2) at the first sampling time 1199051Step 2 If the distribution is normal get the value range of thesignificance level according to (13) choose an any significancelevel 120572 in the range calculate the test statistic as (9) and go toStep 3 If the distribution is nonnormal go to Step 4

Step 3 When the test statistic satisfies the test criterion (10)the node detects the pollution otherwise the node fails todetect the pollution

Step 4 List the data in ascending order and allocate the ranksaccording to the order Calculate1198773 which is the sum of ranksof Samples 3 in Table 2 Look up the table to get the tailvalues in the rank sum test When the sum 1198773 satisfies thetest criterion (7) the node detects the pollution otherwisethe node fails to detect the pollution

5 Implementation Examples

Experiment 1 A simulation is carried out to test the proposeddetection algorithmsThedistribution ofmonitoring noises isnormal

BackgroundThesize of the static shallowwater is 10mtimes 10mand the average depth of the water is 119891 = 10m Apart fromthe coast of impervious 119884 there is a continuous source at(1199090 1199100) = (105 555) (m) Starting from time 1199050 = 0 h thesolution with pollutant is injected into the water The mass ofthe pollutant is119872 = 100 kg The diffusion coefficient is 119863 =01m2hThe nodes in the network sample the concentrationuniformly with interval 119879 = 005 h The diffusion can bedepicted by the model

119862 (119909 119910 1199090 1199100)= ( 119872

(4120587119863 (119905 minus 1199050))) 119890minus[((119909minus1199090)

2+(119910minus1199100)2)4119863(119905minus1199050)] (14)

where 119905 is the current time The locations of the monitoringnodes are (205 555) (105 455) (005 555) (105 655)(055 605) (155 605) (055 505) (155 505) (005 625)and (105 705) The monitoring values in the experiment arethe simulation values of (14) adding the noise with a normaldistribution 119873(0 1205752) The given parameters are 120573 = 05 and120579 = 1 and there are 10 nodes 119899 = 1198731 = 10(A) The Pollution Detection of the Network According toconstraint (13) and the sample size table of 119905 test in [18] itis can be deduced that 120572 gt 0025 under the given parameters120573 120579 and 120575 in Table 3

For different 120575 values and significance levels detect thepollution at the initial observation time 001 h and theresults are shown in Table 3The hypothesis testing detectionmethod under the normal distribution is used and in the

Table 3 The detection results of the network

120575 Significance levels Detection results001 003 100100001 005 100100001 01 10010001 003 10010001 005 9910001 01 10010005 003 9910005 005 10010005 01 100100

table ldquo119883100rdquo represents that in the 100 experiments thepollution is detected successfully119883 times

The results show that the pollution can be detected by thenetwork soon

(B) The Pollution Detection of the Node Detect whether thenode has detected the pollution source based on the observeddata of the node (105 705) The monitoring data is as shownin Table 4 Compare with the simple detection method inwhich the criterion of whether the pollution source has beendetected is that the monitoring value is larger than a giventhreshold and the results are shown in Table 5

In Table 5 ldquomdashrdquo represents no result Comparing theresults in the table it can be seen that the detection methodusing hypothesis testing is more stable if an appropriatesignificance level is chosen and in the simple detection todetect the pollution source timely the threshold should be assmall as possible But apparently if the noise in the practicalapplications is considered small thresholds may bring aboutlarge false alarm rates

Experiment 2 Apractical experiment is carried out to test theproposed detection algorithms

Background In water of which the size is 200 cm times 200 cmthe average depth119891 = 100 cmThere is a continuous source atthe boundary Starting from 1199050 = 0 s the solution of MgSO4is discharged to the water continuallyThe nodes deploymentis depicted by Figure 2 The monitoring values of differentsensor nodes in the experiment are shown in Table 6

DistributionVerificationBoth at time 5 s and 10 s for differentsignificance levels 120572 = 001 120572 = 005 and 120572 = 01 thedetection results all show that the distribution of monitoringdata is not normal So the detection methods based on theWilcoxon rank sum tests are used

(A) The Pollution Detection of the NetworkThe given signifi-cance level is 120572 = 005 and the network detects the pollutionat 30 s

(B)The Pollution Detection of the NodeThe significance levelis 120572 = 005 and the time when nodes 0 1 2 3 4 5 6 and 7

6 Journal of Sensors

Table 4 The monitoring values of node (105 705) in Experiment 1

Time(s) 119879 2119879 3119879 4119879 5119879 6119879 7119879 8119879 9119879 10119879Observations (gL) 0008 0009 0010 0015 0017 0019 0081 0217 0423 0748

Table 5 The detection results comparing with the simple detection method

Significance levels Detection time of 119905 test Threshold (gL) Detection time of the simple detection method003 mdash 003 7119879005 6119879 005 711987901 5119879 01 8119879015 5119879 015 811987902 5119879 02 811987905 4119879 05 10119879

Table 6 The monitoring values in Experiment 2

Time(s) Node 0 (gL) Node 1 (gL) Node 2 (gL) Node 3 (gL) Node 4 (gL) Node 5 (gL) Node 6 (gL) Node 7 (gL)5 000000 000000 000032 000000 000016 000000 000000 00000010 000000 000000 000242 000000 000548 000000 000000 00000015 000000 000000 000581 000000 001210 000000 000000 00000020 000000 000000 000790 000000 001726 000000 000000 00000025 000000 000000 001161 000000 003532 000000 000000 00000030 000210 000000 001661 000050 004532 000000 000033 00000035 001726 000000 005686 000415 006284 000242 001561 00000040 005686 000000 008422 001445 009608 003048 003206 00000045 006216 000000 010429 001877 012071 004081 005216 00000050 008441 000000 012990 005186 013163 007324 006912 00000055 009333 000000 014969 006784 015386 009186 008118 00000060 011235 000000 016957 008324 017286 010673 009559 00000065 012439 000000 018557 009804 017557 011449 011316 00000070 012959 000016 019014 011694 017957 012418 012663 00000075 013449 000129 019457 012245 018786 013122 013010 00008180 013673 000177 020385 012561 019957 013449 013449 00025885 014204 000242 020846 012888 020846 013990 013684 00029090 014643 000403 021135 013224 021019 014122 013847 00043595 014878 000516 021692 013786 021154 014714 014327 000613100 015114 000532 021808 014133 021346 015071 015200 000694105 015386 000726 022423 014776 021481 015343 015814 000823110 015686 000790 022885 015300 021558 015714 016043 000790115 016000 000839 023115 015829 021962 016214 016643 000839120 016329 001000 023462 016343 022154 016543 016814 001097125 016557 001194 023558 016986 022288 016814 017000 001161130 016757 001339 023885 017214 022365 017386 017114 001403135 016814 001484 023923 017329 022404 017414 017186 001597140 016857 001516 023942 017386 022500 017429 017229 001613145 016914 001613 023962 017414 022519 017457 017286 001694150 016929 001774 024000 017457 022519 017457 017300 001774155 016971 001887 024058 017486 022558 017471 017314 001887160 017014 001919 024077 017514 022577 017486 017357 002871165 017086 001935 024096 017543 022615 017514 017371 002968170 017114 002048 024115 017571 022635 017529 017414 003000175 017157 002065 024154 017614 022654 017557 017429 003016180 017171 002097 024173 017629 022712 017571 017457 003065

Journal of Sensors 7

Table 7 The detection time of different nodes in Experiment 2

Significance level Node 0 (s) Node 1 (s) Node 2 (s) Node 3 (s) Node 4 (s) Node 5 (s) Node 6 (s) Node 7 (s)005 50 95 40 50 40 50 50 100

200 cm

200 cm

7 5 3 1

6 4 2 0

(minus60 60) (minus20 60) (20 60) (60 60)

(minus60 20) (minus20 20) (20 20) (60 20)(0 0)

The source

Figure 2 The nodes deployment in Experiment 2

find the pollution is shown in Table 7 The detection methodis as (11)

The results show that the pollution can be detected bythe nodes only when there are some increasing concentrationsamples

From the results of the experiments above it can beenseen that in the simple detection method an appropriatedecision threshold is hard to be given so the pollution sourcedetection by using hypothesis testing is more preferableWhether the distribution of the sample noise is normal or notthe corresponding detection algorithms are available

6 Conclusions

Water pollution detection is important in the water environ-ment monitoring The pollution source detection problemsof the network and of the node are discussed based onhypothesis testing The sample size requirements in differentdetection problems are also analyzed In implementationexamples the proposed pollution detection algorithms aretestedThe effectiveness of the detection algorithms is provedThisworkmainly focuses on theoretical detection approachesbased on hypothesis testing In the future work moreproblems in the practical applications will be studied whenthe proposed detection algorithms are adopted such as theoptimized detection methods of the node related to largeor small concentration variations and the influences of theconcentration variations on the statistical distribution in thedistribution test step

Disclosure

The founding sponsors had no role in the design of the studythe collection analyses or interpretation of data the writingof the manuscript and the decision to publish the results

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this article

Acknowledgments

The research is sponsored by National Natural Science Foun-dation (NNSF) ofChina underGrant nos 61463053 61501337and 61471275 and Natural Science Foundation of GuizhouProvince in China under Grant LH[2015]7549 The authorswould like to thank Dr Li Chai in Wuhan University ofScience and Technology for the helpful suggestions

References

[1] J Wang X Wang X Ren and Y Shen A Water PollutionDetective System Based on Wireless Sensor Network Addison-Wesley Harlow UK 3rd edition 1999

[2] P Jiang H Xia Z He and ZWang ldquoDesign of a water environ-ment monitoring system based on wireless sensor networksrdquoSensors vol 9 no 8 pp 6411ndash6434 2009

[3] E V Hatzikos N Bassiliades L Asmanis and I VlahavasldquoMonitoring water quality through a telematic sensor networkand a fuzzy expert systemrdquo Expert Systems vol 24 no 3 pp143ndash161 2007

[4] B OrsquoFlynn R Martinez-Catala S Harte et al ldquoSmartCoasta wireless sensor network for water quality monitoringrdquo inProceedings of the 32nd IEEE Conference on Local ComputerNetworks (LCN rsquo07) pp 815ndash816 Dublin Ireland October 2007

[5] J HeidemannM Stojanovic andMZorzi ldquoUnderwater sensornetworks applications advances and challengesrdquo PhilosophicalTransactions of the Royal Society A Mathematical Physical andEngineering Sciences vol 370 no 1958 pp 158ndash175 2012

[6] J X He J Li and HW Yan ldquoAn architecture of geospatial sen-sor network for water quality monitoringrdquo Journal of Jilin Uni-versity (Earth Science Edition) vol 41 no 4 pp 1262ndash1266 2011

[7] N Harris A Cranny M Rivers K Smettem and E G Barrett-Lennard ldquoApplication of distributedwireless chloride sensors toenvironmentalmonitoring initial resultsrdquo IEEETransactions onInstrumentation and Measurement vol 65 no 4 pp 736ndash7432016

[8] Y Derbew andM Libsie ldquoAwireless sensor network frameworkfor large-scale industrial water pollution monitoringrdquo in Pro-ceedings of the IST-Africa Conference and Exhibition (IST-Africarsquo14) pp 1ndash8 Mauritius May 2014

8 Journal of Sensors

[9] J Yang L Chai and X Luo ldquoPollution source localization inlake environment based on wireless sensor networksrdquo in Pro-ceedings of the 31st Chinese Control Conference pp 6649ndash6654Hefei China July 2012

[10] X Luo L Chai and J Yang ldquoMobile diffusion source trackingin wireless sensor networksrdquo Control Theory and Applicationsvol 24 no 3 pp 143ndash161 2007

[11] X Luo L Chai and J Yang ldquoOffshore pollution source locali-zation in static water using wireless sensor networksrdquo ActaAutomatica Sinica vol 40 no 5 pp 849ndash861 2014

[12] J Yang X Luo and L Chai ldquoThe localization of pollution sou-rce in steady diffusion state in river based on wireless sensornetworksrdquo Chinese Journal of Sensors and Actuators vol 27 no10 pp 1423ndash1430 2014

[13] X Luo J Yang and L Chai ldquoWater pollution source detectionin wireless sensor networksrdquo in Proceedings of the IEEE Interna-tional Conference on Information andAutomation (ICIA rsquo15)mdashInconjunction with IEEE International Conference on Automationand Logistics pp 2311ndash2315 IEEE Lijiang China August 2015

[14] Z Peng T Yang and X LiangTheWater Environment Mathe-matical Model and Its Application Chemical Industry PressBeijing China 2007

[15] S S Shapiro and M B Wilk ldquoAn analysis of variance test fornormality (complete samples)rdquo Biometrika vol 52 no 3-4 pp591ndash611 1965

[16] B Thomas Serious Stats A Guide to Advanced Statistics for theBehavioral Sciences Palgrave Macmillan Press London UK2012

[17] R E Walpole R H Myers S L Myers and K Ye Probabilityand Statistics for Engineers and Scientists Pearson Prentice HallUpper Saddle River NJ USA 8th edition 2007

[18] Z Shen S Xie and C Pan Probability and Mathematical Sta-tistics High Education Press Beijing China 2005

[19] Sample size for nonparametric January 2016 httpswwwgra-phpadcomguidesprism6statisticsindexhtmstat samplesize for nonparametric htm

4 Journal of Sensors

Table 2The two groups of independent samples in the detection ofthe node

Sample 3 (119909119894 119910119894 1199051) (119909119894 119910119894 1199052) sdot sdot sdot (119909119894 119910119894 119905lfloor1198712rfloor)Sample 4 (119909119894 119910119894 119905lfloor1198712rfloor+1) (119909119894 119910119894 119905lfloor1198712rfloor+2) sdot sdot sdot (119909119894 119910119894 119905119871)

is the 1205722 quantile of 119905-distribution and 120572 is the significancelevel of hypothesis testing [17 18]

Case 2 (hypothesis testing under nonnormal distribution)The Wilcoxon rank sum test is used Our test problem is todetermine whether there is significant difference between thetwo groups of independent samples in Table 2

The hypotheses are

119867(4)0 1205831198783 = 1205831198784119867(4)1 1205831198783 = 1205831198784

(11)

The same solving method as hypothesis testing problem (6)can be used in (11)

34 Sample Size Requirements in Detection

341 Basic Requirements According to the basic samplenumber requirements of the hypothesis testing methods [1718] the basic sample size requirements in our detectionmethods are given as follows In the distribution test thenumber of samples 119869 should be 3 le 119869 le 50 When thedistribution of the sample noise is normal there should beat least 4 samples in the pollution detection of the networkand the pollution detection of the node so 119869 ge 4 and 119871 ge 5When the distribution is not normal there should be at least6 samples in the pollution detection of the network and inthe pollution detection of the node so the sample numbersshould satisfy 119869 ge 6 and 119871 ge 6342 The Power of Tests

(A) 119905 Test In hypotheses test under the normal distributionthe OC function of 119905 test of (3) and (8) is

120573 (120583) = 119875120583 (accept 1198670)= 119875120583 (minus1199051205722 (119899 minus 1) lt 119862

(119904sqrt (119899)) lt 1199051205722 (119899 minus 1)) (12)

where 119862(119904sqrt(119899)) = ((119862minus120583)(120575sqrt(119899)) + 120583(120575sqrt(119899)))(119904120575) 119862 is 119862120581 in (4) and 1198621015840 in (9) respectively 119904 is 119878119896 in (4)and 1198781015840 in (9) respectively and 119899 = 119869 in (4) and 119899 = 119871 minus 1 in(9) 120583 is 120583119896 in (3) and 1205831015840 in (8) respectively

In the pollution detection of the network to reduce thecost the number of nodes is always given previously So thereis a precondition that is the number of the sensor nodesis 119899 le 1198731 where 1198731 is a given number For the purposeof participating in the pollution source localization timelythere also should not bemany sampling times in the pollution

detection of the node and themaximum sampling number isalso often given

To reduce the probability of false alarm under giventhresholds 120573 120579 gt 0 in the hypothesis testing problems (3)and (8) the significance level 120572 should satisfy

119875120583 (accept 1198670)= 119875120583 (minus1199051205722 (119899 minus 1) lt 119862

(119904sqrt (119899)) lt 1199051205722 (119899 minus 1))le 120573

(13)

when 120583 isin 1198671 and |120583120575| ge 120579(B)The Nonparametric TestThere are no explicit expressionsof the test power in nonparametric testsWhen themaximumnumber of samples is given if we want to reduce thepossibility of the I type error in the test the possibility of the IItype error often increases [19] so an appropriate significancelevel is necessary In nonparametric tests 120572 = 005 is oftenadopted

4 The Detection Algorithms

Based on the theoretical research above there are pollutionsource detection algorithms as follows

Algorithm 1 (the pollution detection of the network)

Preconditions The number of providing samples 119869 is largeenough and known The samples at the first sampling time1199051 and the detection time 119905119897 are knownThe parameters 120573 and120579 which are related to the test power are given

Step 1 Use Shapiro-Wilk119882 test to test the distribution of thesample noise according to (2) at the first sampling time 1199051Step 2 If the distribution is normal get the value range of thesignificance level according to (13) choose an any significancelevel 120572 in the range calculate the test statistic as (4) and goto Step 3 If the distribution is nonnormal go to Step 4

Step 3 When the test statistic satisfies the test criterion (5)there is pollution otherwise there is no pollution

Step 4 List the data in ascending order and allocate the ranksaccording to the order Calculate 1198771 which is the sum ofranks of Samples 1 in Table 1 Look up the table to get thetail values in the rank sum test When the sum 1198771 satisfiesthe test criterion (7) there is pollution otherwise there is nopollution

At time 119905119897 if the network does not detect the pollutionthe pollution detection of the network will be made at 119905119897+1Algorithm 2 (the pollution detection of the node (119909119894 119910119894))Preconditions The number of samples 119871 is large enough andknown The samples at the first sampling time 1199051 are knownThe samples of the detection node (119909119894 119910119894) are known The

Journal of Sensors 5

parameters 120573 and 120579 which are related to the test power aregiven

Step 1 Use Shapiro-Wilk119882 test to test the distribution of thesample noise according to (2) at the first sampling time 1199051Step 2 If the distribution is normal get the value range of thesignificance level according to (13) choose an any significancelevel 120572 in the range calculate the test statistic as (9) and go toStep 3 If the distribution is nonnormal go to Step 4

Step 3 When the test statistic satisfies the test criterion (10)the node detects the pollution otherwise the node fails todetect the pollution

Step 4 List the data in ascending order and allocate the ranksaccording to the order Calculate1198773 which is the sum of ranksof Samples 3 in Table 2 Look up the table to get the tailvalues in the rank sum test When the sum 1198773 satisfies thetest criterion (7) the node detects the pollution otherwisethe node fails to detect the pollution

5 Implementation Examples

Experiment 1 A simulation is carried out to test the proposeddetection algorithmsThedistribution ofmonitoring noises isnormal

BackgroundThesize of the static shallowwater is 10mtimes 10mand the average depth of the water is 119891 = 10m Apart fromthe coast of impervious 119884 there is a continuous source at(1199090 1199100) = (105 555) (m) Starting from time 1199050 = 0 h thesolution with pollutant is injected into the water The mass ofthe pollutant is119872 = 100 kg The diffusion coefficient is 119863 =01m2hThe nodes in the network sample the concentrationuniformly with interval 119879 = 005 h The diffusion can bedepicted by the model

119862 (119909 119910 1199090 1199100)= ( 119872

(4120587119863 (119905 minus 1199050))) 119890minus[((119909minus1199090)

2+(119910minus1199100)2)4119863(119905minus1199050)] (14)

where 119905 is the current time The locations of the monitoringnodes are (205 555) (105 455) (005 555) (105 655)(055 605) (155 605) (055 505) (155 505) (005 625)and (105 705) The monitoring values in the experiment arethe simulation values of (14) adding the noise with a normaldistribution 119873(0 1205752) The given parameters are 120573 = 05 and120579 = 1 and there are 10 nodes 119899 = 1198731 = 10(A) The Pollution Detection of the Network According toconstraint (13) and the sample size table of 119905 test in [18] itis can be deduced that 120572 gt 0025 under the given parameters120573 120579 and 120575 in Table 3

For different 120575 values and significance levels detect thepollution at the initial observation time 001 h and theresults are shown in Table 3The hypothesis testing detectionmethod under the normal distribution is used and in the

Table 3 The detection results of the network

120575 Significance levels Detection results001 003 100100001 005 100100001 01 10010001 003 10010001 005 9910001 01 10010005 003 9910005 005 10010005 01 100100

table ldquo119883100rdquo represents that in the 100 experiments thepollution is detected successfully119883 times

The results show that the pollution can be detected by thenetwork soon

(B) The Pollution Detection of the Node Detect whether thenode has detected the pollution source based on the observeddata of the node (105 705) The monitoring data is as shownin Table 4 Compare with the simple detection method inwhich the criterion of whether the pollution source has beendetected is that the monitoring value is larger than a giventhreshold and the results are shown in Table 5

In Table 5 ldquomdashrdquo represents no result Comparing theresults in the table it can be seen that the detection methodusing hypothesis testing is more stable if an appropriatesignificance level is chosen and in the simple detection todetect the pollution source timely the threshold should be assmall as possible But apparently if the noise in the practicalapplications is considered small thresholds may bring aboutlarge false alarm rates

Experiment 2 Apractical experiment is carried out to test theproposed detection algorithms

Background In water of which the size is 200 cm times 200 cmthe average depth119891 = 100 cmThere is a continuous source atthe boundary Starting from 1199050 = 0 s the solution of MgSO4is discharged to the water continuallyThe nodes deploymentis depicted by Figure 2 The monitoring values of differentsensor nodes in the experiment are shown in Table 6

DistributionVerificationBoth at time 5 s and 10 s for differentsignificance levels 120572 = 001 120572 = 005 and 120572 = 01 thedetection results all show that the distribution of monitoringdata is not normal So the detection methods based on theWilcoxon rank sum tests are used

(A) The Pollution Detection of the NetworkThe given signifi-cance level is 120572 = 005 and the network detects the pollutionat 30 s

(B)The Pollution Detection of the NodeThe significance levelis 120572 = 005 and the time when nodes 0 1 2 3 4 5 6 and 7

6 Journal of Sensors

Table 4 The monitoring values of node (105 705) in Experiment 1

Time(s) 119879 2119879 3119879 4119879 5119879 6119879 7119879 8119879 9119879 10119879Observations (gL) 0008 0009 0010 0015 0017 0019 0081 0217 0423 0748

Table 5 The detection results comparing with the simple detection method

Significance levels Detection time of 119905 test Threshold (gL) Detection time of the simple detection method003 mdash 003 7119879005 6119879 005 711987901 5119879 01 8119879015 5119879 015 811987902 5119879 02 811987905 4119879 05 10119879

Table 6 The monitoring values in Experiment 2

Time(s) Node 0 (gL) Node 1 (gL) Node 2 (gL) Node 3 (gL) Node 4 (gL) Node 5 (gL) Node 6 (gL) Node 7 (gL)5 000000 000000 000032 000000 000016 000000 000000 00000010 000000 000000 000242 000000 000548 000000 000000 00000015 000000 000000 000581 000000 001210 000000 000000 00000020 000000 000000 000790 000000 001726 000000 000000 00000025 000000 000000 001161 000000 003532 000000 000000 00000030 000210 000000 001661 000050 004532 000000 000033 00000035 001726 000000 005686 000415 006284 000242 001561 00000040 005686 000000 008422 001445 009608 003048 003206 00000045 006216 000000 010429 001877 012071 004081 005216 00000050 008441 000000 012990 005186 013163 007324 006912 00000055 009333 000000 014969 006784 015386 009186 008118 00000060 011235 000000 016957 008324 017286 010673 009559 00000065 012439 000000 018557 009804 017557 011449 011316 00000070 012959 000016 019014 011694 017957 012418 012663 00000075 013449 000129 019457 012245 018786 013122 013010 00008180 013673 000177 020385 012561 019957 013449 013449 00025885 014204 000242 020846 012888 020846 013990 013684 00029090 014643 000403 021135 013224 021019 014122 013847 00043595 014878 000516 021692 013786 021154 014714 014327 000613100 015114 000532 021808 014133 021346 015071 015200 000694105 015386 000726 022423 014776 021481 015343 015814 000823110 015686 000790 022885 015300 021558 015714 016043 000790115 016000 000839 023115 015829 021962 016214 016643 000839120 016329 001000 023462 016343 022154 016543 016814 001097125 016557 001194 023558 016986 022288 016814 017000 001161130 016757 001339 023885 017214 022365 017386 017114 001403135 016814 001484 023923 017329 022404 017414 017186 001597140 016857 001516 023942 017386 022500 017429 017229 001613145 016914 001613 023962 017414 022519 017457 017286 001694150 016929 001774 024000 017457 022519 017457 017300 001774155 016971 001887 024058 017486 022558 017471 017314 001887160 017014 001919 024077 017514 022577 017486 017357 002871165 017086 001935 024096 017543 022615 017514 017371 002968170 017114 002048 024115 017571 022635 017529 017414 003000175 017157 002065 024154 017614 022654 017557 017429 003016180 017171 002097 024173 017629 022712 017571 017457 003065

Journal of Sensors 7

Table 7 The detection time of different nodes in Experiment 2

Significance level Node 0 (s) Node 1 (s) Node 2 (s) Node 3 (s) Node 4 (s) Node 5 (s) Node 6 (s) Node 7 (s)005 50 95 40 50 40 50 50 100

200 cm

200 cm

7 5 3 1

6 4 2 0

(minus60 60) (minus20 60) (20 60) (60 60)

(minus60 20) (minus20 20) (20 20) (60 20)(0 0)

The source

Figure 2 The nodes deployment in Experiment 2

find the pollution is shown in Table 7 The detection methodis as (11)

The results show that the pollution can be detected bythe nodes only when there are some increasing concentrationsamples

From the results of the experiments above it can beenseen that in the simple detection method an appropriatedecision threshold is hard to be given so the pollution sourcedetection by using hypothesis testing is more preferableWhether the distribution of the sample noise is normal or notthe corresponding detection algorithms are available

6 Conclusions

Water pollution detection is important in the water environ-ment monitoring The pollution source detection problemsof the network and of the node are discussed based onhypothesis testing The sample size requirements in differentdetection problems are also analyzed In implementationexamples the proposed pollution detection algorithms aretestedThe effectiveness of the detection algorithms is provedThisworkmainly focuses on theoretical detection approachesbased on hypothesis testing In the future work moreproblems in the practical applications will be studied whenthe proposed detection algorithms are adopted such as theoptimized detection methods of the node related to largeor small concentration variations and the influences of theconcentration variations on the statistical distribution in thedistribution test step

Disclosure

The founding sponsors had no role in the design of the studythe collection analyses or interpretation of data the writingof the manuscript and the decision to publish the results

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this article

Acknowledgments

The research is sponsored by National Natural Science Foun-dation (NNSF) ofChina underGrant nos 61463053 61501337and 61471275 and Natural Science Foundation of GuizhouProvince in China under Grant LH[2015]7549 The authorswould like to thank Dr Li Chai in Wuhan University ofScience and Technology for the helpful suggestions

References

[1] J Wang X Wang X Ren and Y Shen A Water PollutionDetective System Based on Wireless Sensor Network Addison-Wesley Harlow UK 3rd edition 1999

[2] P Jiang H Xia Z He and ZWang ldquoDesign of a water environ-ment monitoring system based on wireless sensor networksrdquoSensors vol 9 no 8 pp 6411ndash6434 2009

[3] E V Hatzikos N Bassiliades L Asmanis and I VlahavasldquoMonitoring water quality through a telematic sensor networkand a fuzzy expert systemrdquo Expert Systems vol 24 no 3 pp143ndash161 2007

[4] B OrsquoFlynn R Martinez-Catala S Harte et al ldquoSmartCoasta wireless sensor network for water quality monitoringrdquo inProceedings of the 32nd IEEE Conference on Local ComputerNetworks (LCN rsquo07) pp 815ndash816 Dublin Ireland October 2007

[5] J HeidemannM Stojanovic andMZorzi ldquoUnderwater sensornetworks applications advances and challengesrdquo PhilosophicalTransactions of the Royal Society A Mathematical Physical andEngineering Sciences vol 370 no 1958 pp 158ndash175 2012

[6] J X He J Li and HW Yan ldquoAn architecture of geospatial sen-sor network for water quality monitoringrdquo Journal of Jilin Uni-versity (Earth Science Edition) vol 41 no 4 pp 1262ndash1266 2011

[7] N Harris A Cranny M Rivers K Smettem and E G Barrett-Lennard ldquoApplication of distributedwireless chloride sensors toenvironmentalmonitoring initial resultsrdquo IEEETransactions onInstrumentation and Measurement vol 65 no 4 pp 736ndash7432016

[8] Y Derbew andM Libsie ldquoAwireless sensor network frameworkfor large-scale industrial water pollution monitoringrdquo in Pro-ceedings of the IST-Africa Conference and Exhibition (IST-Africarsquo14) pp 1ndash8 Mauritius May 2014

8 Journal of Sensors

[9] J Yang L Chai and X Luo ldquoPollution source localization inlake environment based on wireless sensor networksrdquo in Pro-ceedings of the 31st Chinese Control Conference pp 6649ndash6654Hefei China July 2012

[10] X Luo L Chai and J Yang ldquoMobile diffusion source trackingin wireless sensor networksrdquo Control Theory and Applicationsvol 24 no 3 pp 143ndash161 2007

[11] X Luo L Chai and J Yang ldquoOffshore pollution source locali-zation in static water using wireless sensor networksrdquo ActaAutomatica Sinica vol 40 no 5 pp 849ndash861 2014

[12] J Yang X Luo and L Chai ldquoThe localization of pollution sou-rce in steady diffusion state in river based on wireless sensornetworksrdquo Chinese Journal of Sensors and Actuators vol 27 no10 pp 1423ndash1430 2014

[13] X Luo J Yang and L Chai ldquoWater pollution source detectionin wireless sensor networksrdquo in Proceedings of the IEEE Interna-tional Conference on Information andAutomation (ICIA rsquo15)mdashInconjunction with IEEE International Conference on Automationand Logistics pp 2311ndash2315 IEEE Lijiang China August 2015

[14] Z Peng T Yang and X LiangTheWater Environment Mathe-matical Model and Its Application Chemical Industry PressBeijing China 2007

[15] S S Shapiro and M B Wilk ldquoAn analysis of variance test fornormality (complete samples)rdquo Biometrika vol 52 no 3-4 pp591ndash611 1965

[16] B Thomas Serious Stats A Guide to Advanced Statistics for theBehavioral Sciences Palgrave Macmillan Press London UK2012

[17] R E Walpole R H Myers S L Myers and K Ye Probabilityand Statistics for Engineers and Scientists Pearson Prentice HallUpper Saddle River NJ USA 8th edition 2007

[18] Z Shen S Xie and C Pan Probability and Mathematical Sta-tistics High Education Press Beijing China 2005

[19] Sample size for nonparametric January 2016 httpswwwgra-phpadcomguidesprism6statisticsindexhtmstat samplesize for nonparametric htm

Journal of Sensors 5

parameters 120573 and 120579 which are related to the test power aregiven

Step 1 Use Shapiro-Wilk119882 test to test the distribution of thesample noise according to (2) at the first sampling time 1199051Step 2 If the distribution is normal get the value range of thesignificance level according to (13) choose an any significancelevel 120572 in the range calculate the test statistic as (9) and go toStep 3 If the distribution is nonnormal go to Step 4

Step 3 When the test statistic satisfies the test criterion (10)the node detects the pollution otherwise the node fails todetect the pollution

Step 4 List the data in ascending order and allocate the ranksaccording to the order Calculate1198773 which is the sum of ranksof Samples 3 in Table 2 Look up the table to get the tailvalues in the rank sum test When the sum 1198773 satisfies thetest criterion (7) the node detects the pollution otherwisethe node fails to detect the pollution

5 Implementation Examples

Experiment 1 A simulation is carried out to test the proposeddetection algorithmsThedistribution ofmonitoring noises isnormal

BackgroundThesize of the static shallowwater is 10mtimes 10mand the average depth of the water is 119891 = 10m Apart fromthe coast of impervious 119884 there is a continuous source at(1199090 1199100) = (105 555) (m) Starting from time 1199050 = 0 h thesolution with pollutant is injected into the water The mass ofthe pollutant is119872 = 100 kg The diffusion coefficient is 119863 =01m2hThe nodes in the network sample the concentrationuniformly with interval 119879 = 005 h The diffusion can bedepicted by the model

119862 (119909 119910 1199090 1199100)= ( 119872

(4120587119863 (119905 minus 1199050))) 119890minus[((119909minus1199090)

2+(119910minus1199100)2)4119863(119905minus1199050)] (14)

where 119905 is the current time The locations of the monitoringnodes are (205 555) (105 455) (005 555) (105 655)(055 605) (155 605) (055 505) (155 505) (005 625)and (105 705) The monitoring values in the experiment arethe simulation values of (14) adding the noise with a normaldistribution 119873(0 1205752) The given parameters are 120573 = 05 and120579 = 1 and there are 10 nodes 119899 = 1198731 = 10(A) The Pollution Detection of the Network According toconstraint (13) and the sample size table of 119905 test in [18] itis can be deduced that 120572 gt 0025 under the given parameters120573 120579 and 120575 in Table 3

For different 120575 values and significance levels detect thepollution at the initial observation time 001 h and theresults are shown in Table 3The hypothesis testing detectionmethod under the normal distribution is used and in the

Table 3 The detection results of the network

120575 Significance levels Detection results001 003 100100001 005 100100001 01 10010001 003 10010001 005 9910001 01 10010005 003 9910005 005 10010005 01 100100

table ldquo119883100rdquo represents that in the 100 experiments thepollution is detected successfully119883 times

The results show that the pollution can be detected by thenetwork soon

(B) The Pollution Detection of the Node Detect whether thenode has detected the pollution source based on the observeddata of the node (105 705) The monitoring data is as shownin Table 4 Compare with the simple detection method inwhich the criterion of whether the pollution source has beendetected is that the monitoring value is larger than a giventhreshold and the results are shown in Table 5

In Table 5 ldquomdashrdquo represents no result Comparing theresults in the table it can be seen that the detection methodusing hypothesis testing is more stable if an appropriatesignificance level is chosen and in the simple detection todetect the pollution source timely the threshold should be assmall as possible But apparently if the noise in the practicalapplications is considered small thresholds may bring aboutlarge false alarm rates

Experiment 2 Apractical experiment is carried out to test theproposed detection algorithms

Background In water of which the size is 200 cm times 200 cmthe average depth119891 = 100 cmThere is a continuous source atthe boundary Starting from 1199050 = 0 s the solution of MgSO4is discharged to the water continuallyThe nodes deploymentis depicted by Figure 2 The monitoring values of differentsensor nodes in the experiment are shown in Table 6

DistributionVerificationBoth at time 5 s and 10 s for differentsignificance levels 120572 = 001 120572 = 005 and 120572 = 01 thedetection results all show that the distribution of monitoringdata is not normal So the detection methods based on theWilcoxon rank sum tests are used

(A) The Pollution Detection of the NetworkThe given signifi-cance level is 120572 = 005 and the network detects the pollutionat 30 s

(B)The Pollution Detection of the NodeThe significance levelis 120572 = 005 and the time when nodes 0 1 2 3 4 5 6 and 7

6 Journal of Sensors

Table 4 The monitoring values of node (105 705) in Experiment 1

Time(s) 119879 2119879 3119879 4119879 5119879 6119879 7119879 8119879 9119879 10119879Observations (gL) 0008 0009 0010 0015 0017 0019 0081 0217 0423 0748

Table 5 The detection results comparing with the simple detection method

Significance levels Detection time of 119905 test Threshold (gL) Detection time of the simple detection method003 mdash 003 7119879005 6119879 005 711987901 5119879 01 8119879015 5119879 015 811987902 5119879 02 811987905 4119879 05 10119879

Table 6 The monitoring values in Experiment 2

Time(s) Node 0 (gL) Node 1 (gL) Node 2 (gL) Node 3 (gL) Node 4 (gL) Node 5 (gL) Node 6 (gL) Node 7 (gL)5 000000 000000 000032 000000 000016 000000 000000 00000010 000000 000000 000242 000000 000548 000000 000000 00000015 000000 000000 000581 000000 001210 000000 000000 00000020 000000 000000 000790 000000 001726 000000 000000 00000025 000000 000000 001161 000000 003532 000000 000000 00000030 000210 000000 001661 000050 004532 000000 000033 00000035 001726 000000 005686 000415 006284 000242 001561 00000040 005686 000000 008422 001445 009608 003048 003206 00000045 006216 000000 010429 001877 012071 004081 005216 00000050 008441 000000 012990 005186 013163 007324 006912 00000055 009333 000000 014969 006784 015386 009186 008118 00000060 011235 000000 016957 008324 017286 010673 009559 00000065 012439 000000 018557 009804 017557 011449 011316 00000070 012959 000016 019014 011694 017957 012418 012663 00000075 013449 000129 019457 012245 018786 013122 013010 00008180 013673 000177 020385 012561 019957 013449 013449 00025885 014204 000242 020846 012888 020846 013990 013684 00029090 014643 000403 021135 013224 021019 014122 013847 00043595 014878 000516 021692 013786 021154 014714 014327 000613100 015114 000532 021808 014133 021346 015071 015200 000694105 015386 000726 022423 014776 021481 015343 015814 000823110 015686 000790 022885 015300 021558 015714 016043 000790115 016000 000839 023115 015829 021962 016214 016643 000839120 016329 001000 023462 016343 022154 016543 016814 001097125 016557 001194 023558 016986 022288 016814 017000 001161130 016757 001339 023885 017214 022365 017386 017114 001403135 016814 001484 023923 017329 022404 017414 017186 001597140 016857 001516 023942 017386 022500 017429 017229 001613145 016914 001613 023962 017414 022519 017457 017286 001694150 016929 001774 024000 017457 022519 017457 017300 001774155 016971 001887 024058 017486 022558 017471 017314 001887160 017014 001919 024077 017514 022577 017486 017357 002871165 017086 001935 024096 017543 022615 017514 017371 002968170 017114 002048 024115 017571 022635 017529 017414 003000175 017157 002065 024154 017614 022654 017557 017429 003016180 017171 002097 024173 017629 022712 017571 017457 003065

Journal of Sensors 7

Table 7 The detection time of different nodes in Experiment 2

Significance level Node 0 (s) Node 1 (s) Node 2 (s) Node 3 (s) Node 4 (s) Node 5 (s) Node 6 (s) Node 7 (s)005 50 95 40 50 40 50 50 100

200 cm

200 cm

7 5 3 1

6 4 2 0

(minus60 60) (minus20 60) (20 60) (60 60)

(minus60 20) (minus20 20) (20 20) (60 20)(0 0)

The source

Figure 2 The nodes deployment in Experiment 2

find the pollution is shown in Table 7 The detection methodis as (11)

The results show that the pollution can be detected bythe nodes only when there are some increasing concentrationsamples

From the results of the experiments above it can beenseen that in the simple detection method an appropriatedecision threshold is hard to be given so the pollution sourcedetection by using hypothesis testing is more preferableWhether the distribution of the sample noise is normal or notthe corresponding detection algorithms are available

6 Conclusions

Water pollution detection is important in the water environ-ment monitoring The pollution source detection problemsof the network and of the node are discussed based onhypothesis testing The sample size requirements in differentdetection problems are also analyzed In implementationexamples the proposed pollution detection algorithms aretestedThe effectiveness of the detection algorithms is provedThisworkmainly focuses on theoretical detection approachesbased on hypothesis testing In the future work moreproblems in the practical applications will be studied whenthe proposed detection algorithms are adopted such as theoptimized detection methods of the node related to largeor small concentration variations and the influences of theconcentration variations on the statistical distribution in thedistribution test step

Disclosure

The founding sponsors had no role in the design of the studythe collection analyses or interpretation of data the writingof the manuscript and the decision to publish the results

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this article

Acknowledgments

The research is sponsored by National Natural Science Foun-dation (NNSF) ofChina underGrant nos 61463053 61501337and 61471275 and Natural Science Foundation of GuizhouProvince in China under Grant LH[2015]7549 The authorswould like to thank Dr Li Chai in Wuhan University ofScience and Technology for the helpful suggestions

References

[1] J Wang X Wang X Ren and Y Shen A Water PollutionDetective System Based on Wireless Sensor Network Addison-Wesley Harlow UK 3rd edition 1999

[2] P Jiang H Xia Z He and ZWang ldquoDesign of a water environ-ment monitoring system based on wireless sensor networksrdquoSensors vol 9 no 8 pp 6411ndash6434 2009

[3] E V Hatzikos N Bassiliades L Asmanis and I VlahavasldquoMonitoring water quality through a telematic sensor networkand a fuzzy expert systemrdquo Expert Systems vol 24 no 3 pp143ndash161 2007

[4] B OrsquoFlynn R Martinez-Catala S Harte et al ldquoSmartCoasta wireless sensor network for water quality monitoringrdquo inProceedings of the 32nd IEEE Conference on Local ComputerNetworks (LCN rsquo07) pp 815ndash816 Dublin Ireland October 2007

[5] J HeidemannM Stojanovic andMZorzi ldquoUnderwater sensornetworks applications advances and challengesrdquo PhilosophicalTransactions of the Royal Society A Mathematical Physical andEngineering Sciences vol 370 no 1958 pp 158ndash175 2012

[6] J X He J Li and HW Yan ldquoAn architecture of geospatial sen-sor network for water quality monitoringrdquo Journal of Jilin Uni-versity (Earth Science Edition) vol 41 no 4 pp 1262ndash1266 2011

[7] N Harris A Cranny M Rivers K Smettem and E G Barrett-Lennard ldquoApplication of distributedwireless chloride sensors toenvironmentalmonitoring initial resultsrdquo IEEETransactions onInstrumentation and Measurement vol 65 no 4 pp 736ndash7432016

[8] Y Derbew andM Libsie ldquoAwireless sensor network frameworkfor large-scale industrial water pollution monitoringrdquo in Pro-ceedings of the IST-Africa Conference and Exhibition (IST-Africarsquo14) pp 1ndash8 Mauritius May 2014

8 Journal of Sensors

[9] J Yang L Chai and X Luo ldquoPollution source localization inlake environment based on wireless sensor networksrdquo in Pro-ceedings of the 31st Chinese Control Conference pp 6649ndash6654Hefei China July 2012

[10] X Luo L Chai and J Yang ldquoMobile diffusion source trackingin wireless sensor networksrdquo Control Theory and Applicationsvol 24 no 3 pp 143ndash161 2007

[11] X Luo L Chai and J Yang ldquoOffshore pollution source locali-zation in static water using wireless sensor networksrdquo ActaAutomatica Sinica vol 40 no 5 pp 849ndash861 2014

[12] J Yang X Luo and L Chai ldquoThe localization of pollution sou-rce in steady diffusion state in river based on wireless sensornetworksrdquo Chinese Journal of Sensors and Actuators vol 27 no10 pp 1423ndash1430 2014

[13] X Luo J Yang and L Chai ldquoWater pollution source detectionin wireless sensor networksrdquo in Proceedings of the IEEE Interna-tional Conference on Information andAutomation (ICIA rsquo15)mdashInconjunction with IEEE International Conference on Automationand Logistics pp 2311ndash2315 IEEE Lijiang China August 2015

[14] Z Peng T Yang and X LiangTheWater Environment Mathe-matical Model and Its Application Chemical Industry PressBeijing China 2007

[15] S S Shapiro and M B Wilk ldquoAn analysis of variance test fornormality (complete samples)rdquo Biometrika vol 52 no 3-4 pp591ndash611 1965

[16] B Thomas Serious Stats A Guide to Advanced Statistics for theBehavioral Sciences Palgrave Macmillan Press London UK2012

[17] R E Walpole R H Myers S L Myers and K Ye Probabilityand Statistics for Engineers and Scientists Pearson Prentice HallUpper Saddle River NJ USA 8th edition 2007

[18] Z Shen S Xie and C Pan Probability and Mathematical Sta-tistics High Education Press Beijing China 2005

[19] Sample size for nonparametric January 2016 httpswwwgra-phpadcomguidesprism6statisticsindexhtmstat samplesize for nonparametric htm

6 Journal of Sensors

Table 4 The monitoring values of node (105 705) in Experiment 1

Time(s) 119879 2119879 3119879 4119879 5119879 6119879 7119879 8119879 9119879 10119879Observations (gL) 0008 0009 0010 0015 0017 0019 0081 0217 0423 0748

Table 5 The detection results comparing with the simple detection method

Significance levels Detection time of 119905 test Threshold (gL) Detection time of the simple detection method003 mdash 003 7119879005 6119879 005 711987901 5119879 01 8119879015 5119879 015 811987902 5119879 02 811987905 4119879 05 10119879

Table 6 The monitoring values in Experiment 2

Time(s) Node 0 (gL) Node 1 (gL) Node 2 (gL) Node 3 (gL) Node 4 (gL) Node 5 (gL) Node 6 (gL) Node 7 (gL)5 000000 000000 000032 000000 000016 000000 000000 00000010 000000 000000 000242 000000 000548 000000 000000 00000015 000000 000000 000581 000000 001210 000000 000000 00000020 000000 000000 000790 000000 001726 000000 000000 00000025 000000 000000 001161 000000 003532 000000 000000 00000030 000210 000000 001661 000050 004532 000000 000033 00000035 001726 000000 005686 000415 006284 000242 001561 00000040 005686 000000 008422 001445 009608 003048 003206 00000045 006216 000000 010429 001877 012071 004081 005216 00000050 008441 000000 012990 005186 013163 007324 006912 00000055 009333 000000 014969 006784 015386 009186 008118 00000060 011235 000000 016957 008324 017286 010673 009559 00000065 012439 000000 018557 009804 017557 011449 011316 00000070 012959 000016 019014 011694 017957 012418 012663 00000075 013449 000129 019457 012245 018786 013122 013010 00008180 013673 000177 020385 012561 019957 013449 013449 00025885 014204 000242 020846 012888 020846 013990 013684 00029090 014643 000403 021135 013224 021019 014122 013847 00043595 014878 000516 021692 013786 021154 014714 014327 000613100 015114 000532 021808 014133 021346 015071 015200 000694105 015386 000726 022423 014776 021481 015343 015814 000823110 015686 000790 022885 015300 021558 015714 016043 000790115 016000 000839 023115 015829 021962 016214 016643 000839120 016329 001000 023462 016343 022154 016543 016814 001097125 016557 001194 023558 016986 022288 016814 017000 001161130 016757 001339 023885 017214 022365 017386 017114 001403135 016814 001484 023923 017329 022404 017414 017186 001597140 016857 001516 023942 017386 022500 017429 017229 001613145 016914 001613 023962 017414 022519 017457 017286 001694150 016929 001774 024000 017457 022519 017457 017300 001774155 016971 001887 024058 017486 022558 017471 017314 001887160 017014 001919 024077 017514 022577 017486 017357 002871165 017086 001935 024096 017543 022615 017514 017371 002968170 017114 002048 024115 017571 022635 017529 017414 003000175 017157 002065 024154 017614 022654 017557 017429 003016180 017171 002097 024173 017629 022712 017571 017457 003065

Journal of Sensors 7

Table 7 The detection time of different nodes in Experiment 2

Significance level Node 0 (s) Node 1 (s) Node 2 (s) Node 3 (s) Node 4 (s) Node 5 (s) Node 6 (s) Node 7 (s)005 50 95 40 50 40 50 50 100

200 cm

200 cm

7 5 3 1

6 4 2 0

(minus60 60) (minus20 60) (20 60) (60 60)

(minus60 20) (minus20 20) (20 20) (60 20)(0 0)

The source

Figure 2 The nodes deployment in Experiment 2

find the pollution is shown in Table 7 The detection methodis as (11)

The results show that the pollution can be detected bythe nodes only when there are some increasing concentrationsamples

From the results of the experiments above it can beenseen that in the simple detection method an appropriatedecision threshold is hard to be given so the pollution sourcedetection by using hypothesis testing is more preferableWhether the distribution of the sample noise is normal or notthe corresponding detection algorithms are available

6 Conclusions

Water pollution detection is important in the water environ-ment monitoring The pollution source detection problemsof the network and of the node are discussed based onhypothesis testing The sample size requirements in differentdetection problems are also analyzed In implementationexamples the proposed pollution detection algorithms aretestedThe effectiveness of the detection algorithms is provedThisworkmainly focuses on theoretical detection approachesbased on hypothesis testing In the future work moreproblems in the practical applications will be studied whenthe proposed detection algorithms are adopted such as theoptimized detection methods of the node related to largeor small concentration variations and the influences of theconcentration variations on the statistical distribution in thedistribution test step

Disclosure

The founding sponsors had no role in the design of the studythe collection analyses or interpretation of data the writingof the manuscript and the decision to publish the results

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this article

Acknowledgments

The research is sponsored by National Natural Science Foun-dation (NNSF) ofChina underGrant nos 61463053 61501337and 61471275 and Natural Science Foundation of GuizhouProvince in China under Grant LH[2015]7549 The authorswould like to thank Dr Li Chai in Wuhan University ofScience and Technology for the helpful suggestions

References

[1] J Wang X Wang X Ren and Y Shen A Water PollutionDetective System Based on Wireless Sensor Network Addison-Wesley Harlow UK 3rd edition 1999

[2] P Jiang H Xia Z He and ZWang ldquoDesign of a water environ-ment monitoring system based on wireless sensor networksrdquoSensors vol 9 no 8 pp 6411ndash6434 2009

[3] E V Hatzikos N Bassiliades L Asmanis and I VlahavasldquoMonitoring water quality through a telematic sensor networkand a fuzzy expert systemrdquo Expert Systems vol 24 no 3 pp143ndash161 2007

[4] B OrsquoFlynn R Martinez-Catala S Harte et al ldquoSmartCoasta wireless sensor network for water quality monitoringrdquo inProceedings of the 32nd IEEE Conference on Local ComputerNetworks (LCN rsquo07) pp 815ndash816 Dublin Ireland October 2007

[5] J HeidemannM Stojanovic andMZorzi ldquoUnderwater sensornetworks applications advances and challengesrdquo PhilosophicalTransactions of the Royal Society A Mathematical Physical andEngineering Sciences vol 370 no 1958 pp 158ndash175 2012

[6] J X He J Li and HW Yan ldquoAn architecture of geospatial sen-sor network for water quality monitoringrdquo Journal of Jilin Uni-versity (Earth Science Edition) vol 41 no 4 pp 1262ndash1266 2011

[7] N Harris A Cranny M Rivers K Smettem and E G Barrett-Lennard ldquoApplication of distributedwireless chloride sensors toenvironmentalmonitoring initial resultsrdquo IEEETransactions onInstrumentation and Measurement vol 65 no 4 pp 736ndash7432016

[8] Y Derbew andM Libsie ldquoAwireless sensor network frameworkfor large-scale industrial water pollution monitoringrdquo in Pro-ceedings of the IST-Africa Conference and Exhibition (IST-Africarsquo14) pp 1ndash8 Mauritius May 2014

8 Journal of Sensors

[9] J Yang L Chai and X Luo ldquoPollution source localization inlake environment based on wireless sensor networksrdquo in Pro-ceedings of the 31st Chinese Control Conference pp 6649ndash6654Hefei China July 2012

[10] X Luo L Chai and J Yang ldquoMobile diffusion source trackingin wireless sensor networksrdquo Control Theory and Applicationsvol 24 no 3 pp 143ndash161 2007

[11] X Luo L Chai and J Yang ldquoOffshore pollution source locali-zation in static water using wireless sensor networksrdquo ActaAutomatica Sinica vol 40 no 5 pp 849ndash861 2014

[12] J Yang X Luo and L Chai ldquoThe localization of pollution sou-rce in steady diffusion state in river based on wireless sensornetworksrdquo Chinese Journal of Sensors and Actuators vol 27 no10 pp 1423ndash1430 2014

[13] X Luo J Yang and L Chai ldquoWater pollution source detectionin wireless sensor networksrdquo in Proceedings of the IEEE Interna-tional Conference on Information andAutomation (ICIA rsquo15)mdashInconjunction with IEEE International Conference on Automationand Logistics pp 2311ndash2315 IEEE Lijiang China August 2015

[14] Z Peng T Yang and X LiangTheWater Environment Mathe-matical Model and Its Application Chemical Industry PressBeijing China 2007

[15] S S Shapiro and M B Wilk ldquoAn analysis of variance test fornormality (complete samples)rdquo Biometrika vol 52 no 3-4 pp591ndash611 1965

[16] B Thomas Serious Stats A Guide to Advanced Statistics for theBehavioral Sciences Palgrave Macmillan Press London UK2012

[17] R E Walpole R H Myers S L Myers and K Ye Probabilityand Statistics for Engineers and Scientists Pearson Prentice HallUpper Saddle River NJ USA 8th edition 2007

[18] Z Shen S Xie and C Pan Probability and Mathematical Sta-tistics High Education Press Beijing China 2005

[19] Sample size for nonparametric January 2016 httpswwwgra-phpadcomguidesprism6statisticsindexhtmstat samplesize for nonparametric htm

Journal of Sensors 7

Table 7 The detection time of different nodes in Experiment 2

Significance level Node 0 (s) Node 1 (s) Node 2 (s) Node 3 (s) Node 4 (s) Node 5 (s) Node 6 (s) Node 7 (s)005 50 95 40 50 40 50 50 100

200 cm

200 cm

7 5 3 1

6 4 2 0

(minus60 60) (minus20 60) (20 60) (60 60)

(minus60 20) (minus20 20) (20 20) (60 20)(0 0)

The source

Figure 2 The nodes deployment in Experiment 2

find the pollution is shown in Table 7 The detection methodis as (11)

The results show that the pollution can be detected bythe nodes only when there are some increasing concentrationsamples

From the results of the experiments above it can beenseen that in the simple detection method an appropriatedecision threshold is hard to be given so the pollution sourcedetection by using hypothesis testing is more preferableWhether the distribution of the sample noise is normal or notthe corresponding detection algorithms are available

6 Conclusions

Water pollution detection is important in the water environ-ment monitoring The pollution source detection problemsof the network and of the node are discussed based onhypothesis testing The sample size requirements in differentdetection problems are also analyzed In implementationexamples the proposed pollution detection algorithms aretestedThe effectiveness of the detection algorithms is provedThisworkmainly focuses on theoretical detection approachesbased on hypothesis testing In the future work moreproblems in the practical applications will be studied whenthe proposed detection algorithms are adopted such as theoptimized detection methods of the node related to largeor small concentration variations and the influences of theconcentration variations on the statistical distribution in thedistribution test step

Disclosure

The founding sponsors had no role in the design of the studythe collection analyses or interpretation of data the writingof the manuscript and the decision to publish the results

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this article

Acknowledgments

The research is sponsored by National Natural Science Foun-dation (NNSF) ofChina underGrant nos 61463053 61501337and 61471275 and Natural Science Foundation of GuizhouProvince in China under Grant LH[2015]7549 The authorswould like to thank Dr Li Chai in Wuhan University ofScience and Technology for the helpful suggestions

References

[1] J Wang X Wang X Ren and Y Shen A Water PollutionDetective System Based on Wireless Sensor Network Addison-Wesley Harlow UK 3rd edition 1999

[2] P Jiang H Xia Z He and ZWang ldquoDesign of a water environ-ment monitoring system based on wireless sensor networksrdquoSensors vol 9 no 8 pp 6411ndash6434 2009

[3] E V Hatzikos N Bassiliades L Asmanis and I VlahavasldquoMonitoring water quality through a telematic sensor networkand a fuzzy expert systemrdquo Expert Systems vol 24 no 3 pp143ndash161 2007

[4] B OrsquoFlynn R Martinez-Catala S Harte et al ldquoSmartCoasta wireless sensor network for water quality monitoringrdquo inProceedings of the 32nd IEEE Conference on Local ComputerNetworks (LCN rsquo07) pp 815ndash816 Dublin Ireland October 2007

[5] J HeidemannM Stojanovic andMZorzi ldquoUnderwater sensornetworks applications advances and challengesrdquo PhilosophicalTransactions of the Royal Society A Mathematical Physical andEngineering Sciences vol 370 no 1958 pp 158ndash175 2012

[6] J X He J Li and HW Yan ldquoAn architecture of geospatial sen-sor network for water quality monitoringrdquo Journal of Jilin Uni-versity (Earth Science Edition) vol 41 no 4 pp 1262ndash1266 2011

[7] N Harris A Cranny M Rivers K Smettem and E G Barrett-Lennard ldquoApplication of distributedwireless chloride sensors toenvironmentalmonitoring initial resultsrdquo IEEETransactions onInstrumentation and Measurement vol 65 no 4 pp 736ndash7432016

[8] Y Derbew andM Libsie ldquoAwireless sensor network frameworkfor large-scale industrial water pollution monitoringrdquo in Pro-ceedings of the IST-Africa Conference and Exhibition (IST-Africarsquo14) pp 1ndash8 Mauritius May 2014

8 Journal of Sensors

[9] J Yang L Chai and X Luo ldquoPollution source localization inlake environment based on wireless sensor networksrdquo in Pro-ceedings of the 31st Chinese Control Conference pp 6649ndash6654Hefei China July 2012

[10] X Luo L Chai and J Yang ldquoMobile diffusion source trackingin wireless sensor networksrdquo Control Theory and Applicationsvol 24 no 3 pp 143ndash161 2007

[11] X Luo L Chai and J Yang ldquoOffshore pollution source locali-zation in static water using wireless sensor networksrdquo ActaAutomatica Sinica vol 40 no 5 pp 849ndash861 2014

[12] J Yang X Luo and L Chai ldquoThe localization of pollution sou-rce in steady diffusion state in river based on wireless sensornetworksrdquo Chinese Journal of Sensors and Actuators vol 27 no10 pp 1423ndash1430 2014

[13] X Luo J Yang and L Chai ldquoWater pollution source detectionin wireless sensor networksrdquo in Proceedings of the IEEE Interna-tional Conference on Information andAutomation (ICIA rsquo15)mdashInconjunction with IEEE International Conference on Automationand Logistics pp 2311ndash2315 IEEE Lijiang China August 2015

[14] Z Peng T Yang and X LiangTheWater Environment Mathe-matical Model and Its Application Chemical Industry PressBeijing China 2007

[15] S S Shapiro and M B Wilk ldquoAn analysis of variance test fornormality (complete samples)rdquo Biometrika vol 52 no 3-4 pp591ndash611 1965

[16] B Thomas Serious Stats A Guide to Advanced Statistics for theBehavioral Sciences Palgrave Macmillan Press London UK2012

[17] R E Walpole R H Myers S L Myers and K Ye Probabilityand Statistics for Engineers and Scientists Pearson Prentice HallUpper Saddle River NJ USA 8th edition 2007

[18] Z Shen S Xie and C Pan Probability and Mathematical Sta-tistics High Education Press Beijing China 2005

[19] Sample size for nonparametric January 2016 httpswwwgra-phpadcomguidesprism6statisticsindexhtmstat samplesize for nonparametric htm

8 Journal of Sensors

[9] J Yang L Chai and X Luo ldquoPollution source localization inlake environment based on wireless sensor networksrdquo in Pro-ceedings of the 31st Chinese Control Conference pp 6649ndash6654Hefei China July 2012

[10] X Luo L Chai and J Yang ldquoMobile diffusion source trackingin wireless sensor networksrdquo Control Theory and Applicationsvol 24 no 3 pp 143ndash161 2007

[11] X Luo L Chai and J Yang ldquoOffshore pollution source locali-zation in static water using wireless sensor networksrdquo ActaAutomatica Sinica vol 40 no 5 pp 849ndash861 2014

[12] J Yang X Luo and L Chai ldquoThe localization of pollution sou-rce in steady diffusion state in river based on wireless sensornetworksrdquo Chinese Journal of Sensors and Actuators vol 27 no10 pp 1423ndash1430 2014

[13] X Luo J Yang and L Chai ldquoWater pollution source detectionin wireless sensor networksrdquo in Proceedings of the IEEE Interna-tional Conference on Information andAutomation (ICIA rsquo15)mdashInconjunction with IEEE International Conference on Automationand Logistics pp 2311ndash2315 IEEE Lijiang China August 2015

[14] Z Peng T Yang and X LiangTheWater Environment Mathe-matical Model and Its Application Chemical Industry PressBeijing China 2007

[15] S S Shapiro and M B Wilk ldquoAn analysis of variance test fornormality (complete samples)rdquo Biometrika vol 52 no 3-4 pp591ndash611 1965

[16] B Thomas Serious Stats A Guide to Advanced Statistics for theBehavioral Sciences Palgrave Macmillan Press London UK2012

[17] R E Walpole R H Myers S L Myers and K Ye Probabilityand Statistics for Engineers and Scientists Pearson Prentice HallUpper Saddle River NJ USA 8th edition 2007

[18] Z Shen S Xie and C Pan Probability and Mathematical Sta-tistics High Education Press Beijing China 2005

[19] Sample size for nonparametric January 2016 httpswwwgra-phpadcomguidesprism6statisticsindexhtmstat samplesize for nonparametric htm

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