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Fault detection of the boiler unit usingstate space neural
networks.
A. Czajkowski ∗ K. Patan ∗
∗ Institute of Control and Computation Engineering,University of
Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra;
(e-mail: {A.Czajkowski, K.Patan}@issi.uz.zgora.pl).
Abstract: This paper deals with the general information about
using state space neural networkmodels for purpose of the fault
detection on example of the boiler unit. The work presenteddeals
with problems such us selecting proper threshold for compromising
both fault sensitivityand early fault detection, designing proper
neural network structure or calculating performanceidices. All
simulation data used in experiments are collected from simulator of
the boiler unitimplemented in Matlab/Simulink.
Keywords: nnsysid, state space model, dynamic system, neural
network, fault detection.
1. INTRODUCTION
Recently it is observed an increasing development of theFault
Diagnosis (FD) methods for the Fault TolerantControl (FTC) system
desing purposes. It is straightlyconnected to the advantages of the
systems which canmaintain current performance as close to the
desirableone, and preserve stability conditions in the presence
offaults. Faults and equipment failures directly affect
theperformance of the control system and can result in
largeecomomic loses and violation of the safety regulations.During
the fault tolerant control system design the basicproblem is the
early detection and identification of pos-sible faults. The main
objective here is to use aproachesproviding the acceptable
behaviour of the control systemin the case of a critical fault and
to shutdown of the systemsafely. The paper focuses on the first
stage of FTC systemdesign which is the modelling of the system. In
this workto construct the model of the system the so called
StateSpace Neural Networks (SSNN) are applied. The SSNNmodel is
then used to carry out the fault detection byanalysing the
residual. The state space model estimatesthe state vector of the
system and in cases when states ofthe system are measurably
available residuals can be cal-culated as differences between
states and their estimates.The methodology presented in the paper
is tested on theaxample of a boiler unit.The paper is organized as
follows. Section 2 presents a gen-eral desciption of the boiler
unit and provides informationabout faulty scenarios considered. The
state space neuralnetworks are described in Section 3. Section 4
presents afault detection algorithm, while experimental results
areincluded in Section 5.
2. BOILER UNIT
The scheme of the boiler unit with process variablesmarked is
presented in Fig.1. The whole system consistsof the boiler, storage
tank, control valve with positioner,pump and transducers to measure
process variables. The
specification of process variables is shown in Table 1.
Theobjective of the control system is to keep a required levelof
the water in the boiler. The control system uses theclassical PID
controller.The reference signal is defined as follows:
r(t) =
0 for t
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Fig. 1. The boiler unit.
and output neurons. For the space state model the outputswhich
are fed back are unknown during training. Asa result, state space
models can be trainined only byminimizing the simulation error.In
spite of the fact that state space neural networks seem tobe more
promising that fully or partially neural networks,in practice a lot
of difficulties can be encountered :
• Model states do not approach true process states;• Wrong
initial conditions can deteriorate the perfor-
mance, especially when short data sets are used fortraining;•
Training can become unstable;• The model after training can be
unstable;
A very important property of the state space neural net-work is
that it can aproximate a wide class of non-lineardynamic
systems.Let consider such a nonlinear dynamic system governed bythe
following equatation:
x(k + 1) = g(x(k), u(k)) + f(x(k), u(k)) (4)
where g is a process working at the normal operatingconditions,
x (k) is the state vector u(k) is the controlinput vector and f
represents a fault affecting the process.A fault function f is a
function of both the state and theinput and in this way makes it
possible to model a widerange of possible faults not only additive
ones. Assumingthat the system considered is working at the normal
op-erating conditions without any fault occurrence then itsmodel is
governed by the following state equatation:
x̂(k + 1) = ĝ(x̂(k), u(k))
ŷ(k + 1) = Cx̂(k + 1)(5)
where ŷ is the output of the model and C is the
outputmatrix.Creating state space model according to that
equatationshould allow to easily detect the fault. In the case
ofskipping the fault function f in the model when the
faultysituation occured should be possible an observation
ofdiscrepancy between the output of the system and themodel. In
that case in this paper were used the residuumof the simulated
signal and modelled one.In cases when states of the system are not
measurablyavailable, to calculate the residual signal one should
com-pare the system and the model outputs according to (4).
e(k + 1) = y(k + 1)− ŷ(k + 1) (6)
In the ideal case the residual should be equal to zero. Inthe
case of a fault a significant change of the residual valueshould be
observed.It is necessary to mention that in cases when states of
thesystem are measurably available the residual vector can
bedefined as a difference between system and model states.
e(k + 1) = x(k + 1)− ŷ(k + 1) (7)
This representation is much more powerful than (4) andmay be
utilized in FTC systems to compensate the faulteffect. In the
nominal situation model should achieve thevalue of error close to
0. In case of fault it should be noticedthat the e(k+1 ) will
significantly change.
3.1 The NNSYID toolbox
The NNSYSID toolbox (Neural Network SyStem Identi-fication) was
implemented by (lit) as a toolbox for theMATLAB environment. It
provides the function NNSSIFwhich is an implementation of the state
space neural net-work innovation form as follows:
x(k + 1) = g(x(k), u(k), e(k))
y(k + 1) = Cx(k + 1)(8)
When assuming the network is trained properly, in nomi-nal
situation e(k) is equal 0 and makes possible to use thenext
function from the toolbox which is the NNSIMULfunction. This
function is described as it can simulate aneural network model of a
dynamic system from a sequenceof controls alone (not using observed
outputs). The sim-ulated output is compared to the observed output.
Forstate space models the residuals in the function are set to0.
Which makes (8) exactly same as (5) and makes possibleto use that
function to the fault detection based on (6).
4. FAULT DETECTION
To evaluate residuals and to obtain information aboutfaults,
simple thresholding can be applied. If residuals aresmaller than
the threshold value, a process is considered tobe healthy,
otherwise it is faulty. For fault detection, theresidual must meet
the ideal condition being zero in thefault-free case and different
from zero in the case of a fault.In practice, due to modelling
uncertainty and measurment
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noise, it is necessary to assign thresholds larger thanzero in
order to avoid false alarms. This operation causesa reduction in
fault detection sensitivity. Therefore, thechoice of the threshold
is only a compromise between faultdecision sensitivity and false
alarm rate.In order to select the threshold, in this paper method
ofς-standard deviation is used. Assuming that the residualis an N
(m, v) random variable thresholds are assigned tothe values :
T = m± ςv (9)
where m is mean and v standard deviation of residualsvalues and
ς, in the most cases, is equal to 1, 2 or 3. Theprobability taht a
sample exceeds the threeshold is equalto 0.15866 for ς = 1, 0.02275
for ς = 2 and 0.00135 for ς= 3.
4.1 Selecting the threshold
Based on residuals collected from simulation which areshown in
Fig.2, mean m and standard deviation v iscalculated as follows
:
m =1N
N∑i=1
ri = 0.0016 (10)
v =1
N − 1
N∑i=1
(ri −m)2 = 0.0093 (11)
Fig. 2. Simulation residuals used for selecting of
threshold.
Table 2. Thresholds for diffrent ς values.
ς threshold range
1 -0.0077 ÷ 0.01092 -0.0170 ÷ 0.02023 -0.0263 ÷ 0.0295
5. EXPERIMENTS
The experiments were divided into two parts. The firstgroup of
experiments was aimed on creating the optimalstructure of the
neural network model. For the trainingpurposes the training set
based on the data generated fromthe simulator of the boiler unit
implemented in Simulink
Fig. 3. Optimal structure of the state space neural
networkmodel
was created. In the experiments the best performancewas achieved
for the network with 5 neurons in thehidden layer with hyperbolic
tangent activation function.Designed model has 3 output states
(third order model).The neural network model structure is presented
on Fig.3.The modelling efficency for the training data is shown
inFig.4.
Fig. 4. Simulation of model with training data.
5.1 Fault detection
With well trained neural network model it was possible tostart
the experiments with the different faults situations.In simulation
the fault was introduced to boiler on the600th time sample and
stopped on the 1000th. The boilerunit is in the nominal state on
the 500th time sample.The desired water level in the boiler unit is
set on the value0.25, and the PID controller is adjusting the CV to
satisfythis. Simulated were 4 single-faults. As representativewere
chosen 2 which simulations of system and modeloutputs are presented
on the Fig.5 and Fig.6. There canbe easily noticed that on the
fault occurrence in bothsituations system’s behaviour differs from
trained model.For purpose of fault detection residuals are
calculated (6).Next step is calculating performance indices for
different
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Fig. 5. Simulation of first example fault.
Fig. 6. Simulation of fourth example fault.
values of ς used in selecting thresholds. In this paper areused
detection time tdt, false detection rate rfd and truedetection rate
rtd. Results are shown in Table 3.
Table 3. Performance indices for fault exam-ples.
fault ς tdt rfd rtdf1 1 13 0.0768 0.9700
2 21 0 0.95003 29 0 0.9300
f2 1 27 0.0768 0.93502 42 0 0.89753 57 0 0.8600
f3 1 6 0.0768 0.98752 6 0 0.98753 6 0 0.7900
f4 1 18 0.0768 0.95752 30 0 0.92753 42 0 0.8975
Examples of crossing different thresholds are shown on theFig.7
and Fig.8.
6. CONCLUSION
As was shown the neural network based state space inno-vations
form model of a dynamic system can be used to
Fig. 7. Error of the model (the first fault example).
Fig. 8. Error of the model (the fourth fault example).
the fault detection very well. In the both presented
faultysituation model behaved as expected and with use of
thethreshold made possible to discover the fault.Al tough there was
a lot of simplifying conditions ofresearch (as : only one input in
form of control value,static desired water level in storage tank,
only one faultin experiment) it shows the direction of the future
work.Next step in researches should be building the scenarioof
possibly realistic work of the boiler, and simulation ofmany faults
at once. If this kind of the model would alsoallow to detect the
fault within acceptable time limit, itcould be very useful to build
the fault tolerant controlbased on the approach of approximating
the fault functionas shown in (4).
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