- Email: [email protected]
Optimal Training Algorithm Application to Design an Associative Memory for Fault Diagnosis at a Fossil Electric Power Plant
8th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (SAFEPROCESS) August 29-31, 2012. Mexico City, Mexico
Optimal Training Algorithm Application to Design an Associative Memory for Fault Diagnosis at a Fossil Electric Power Plant Jose A. Ruz-Hernandez ∗ Dionisio A. Suarez ∗∗ Ramon Garcia-Hernandez ∗ Edgar N. Sanchez ∗∗∗ Maria U. Suarez-Duran ∗ ∗
Universidad Autonoma del Carmen, Av. 56 # 4 Esq. Av. Concordia, Col. Benito Juarez, C.P. 24180, Cd. del Carmen, Campeche, MEXICO, e-mail: {jruz,rghernandez}@pampano.unacar.mx ∗∗ Instituto de Investigaciones Electricas, Calle Reforma No. 113, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, MEXICO, e-mail: [email protected] ∗∗∗ CINVESTAV, Unidad Guadalajara, Apartado Postal 31-430, Plaza La Luna, Guadalajara, Jalisco C.P. 45091, MEXICO, e-mail: [email protected] Abstract: This paper presents the development and application of a neural networks-based scheme for fault diagnosis, including detection and classification, for the steam generator of a fossil electric power plant. The scheme is constituted by two components: residual generation and fault classification. The first component generates residuals via the difference between measurements coming from the plant and a neural network predictor. The neural network predictor is trained with healthy data collected from a full-scale simulator reproducing reliably the process behavior. For the second component detection thresholds are used to encode the residuals as bipolar vectors which represent fault patterns. The fault patterns are stored in an associative memory based on a recurrent neural network which is trained via optimal training algorithm. The scheme is evaluated on-line via a full-scale simulator to diagnose the main faults appearing in this kind of power plants when load power is constant and when the operator is carrying out load power changes. Furthermore, the fault diagnosis strategy is be able to distinguish when the operator is carrying out load power changes free of fault as normal operating conditions. Keywords: Computational intelligence methodology, neural associative memory, neural network predictor, fault diagnosis, fossil electric power plant. 1. INTRODUCTION Due to increasing demands on reliability and safety of technical processes, various fault detection and diagnosis methodologies have been proposed in the literature, which can be broadly divided into model based techniques, knowledge-based methodologies and empirical or signal processing techniques, Patton et al. (2000). Fault diagnosis is usually performed by a three steps algorithm, Frank (1994). First, one or several signals are generated which reflect faults in the process behavior. These signals are called residuals. On the second step, the residuals are evaluated. A decision, regarding time and location of possible faults, is obtained from the residuals. Finally, the nature and the cause of the fault is analyzed by the relations between the symptoms and their possible causes. In order to describe the fault free nominal behavior of the process under supervision, a mathematical model is employed; due to this fact, the term model-based fault diagnosis is used. Model-based approaches have dominated the fault diagnosis research for many years, Frank (1990). The main disadvantage of this method is that, being based on a mathematical model, it can be very sensitive to modelling errors, parameter variations, noise and disturbances. The success of the model-based method 978-3-902823-09-0/12/$20.00 © 2012 IFAC
756
is heavily dependent on the quality of the models; accurate modelling for a complex nonlinear system is very difficult to achieve in practice. Different applications of fault detection and diagnosis to industrial processes, which include conventional and computational intelligence techniques are reported in Korbicz et al. (2004). A power plant application which combines analytical redundancy and Petri nets is described in Prock (2000); however, as a consequence of the high number of modular fault detection units a lot of alarms are occurred. Most of the power plant applications use a combination of analytical/computational intelligence tools (Korbicz et al. (2004) and Koppen-Seliger et al. (1995)). Using adequate data base and methods for on-line and/or offline training, neural networks are able to reproduce the dynamics of complex nonlinear systems; after training, they can estimate quite precisely the output of nonlinear systems, Patton et al. (1994), Koppen-Seliger and Frank (1995). Employing measurements of the process under normal operation, if possible, or with the help of a realistic simulator, a suitable neural network can be trained to learn the process input-output behavior. The residuals generated using a neural network predictor can be evaluated via thresholds to obtain fault patterns. The
10.3182/20120829-3-MX-2028.00293
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
fault pattern recognition can be done by means other neural network, which allows to isolate different faults. This paper presents a neural network scheme for fault diagnosis. It uses for residual generation a predictor, which consists of a bank of recurrent multilayer perceptron neural network models. Fault classification is carried out by an associative memory, which is based on a recurrent neural network trained via optimal training algorithm. The scheme is evaluated on-line using a fullscale simulator to diagnose the main faults appearing in this kind of power plants. 2. PROBLEM DESCRIPTION Fault diagnosis for fossil electric power plants is a task carried out by human operators, who recognize typical faults via supervision of key variables evolution. Adequate fault detection and diagnosis aids will help the human operator in order to take the right decisions to maintain the required electric energy production, avoiding failures and even accident risky to humans and the environment, CNCAOI (1997). For this kind of plants, the main faults can be clustered as: faults related to temperature control of the superheat and reheat, faults related to combustion control and faults related to the steam generator drum water level. In order to understand the first group of faults, it is helpful to briefly describe the steam generator and superheated and reheated steam systems. A simplified scheme is presented in Fig. 1, which illustrates the main components of a typical steam generator and superheating/reheating systems. Feedwater from the economizer enters the steam drum, and by forced circulation, the drum water flows down the downcomers and rises through the furnace wall tubes to generate steam by means of the hot combustion gases in the furnace. The water and steam in the drum are separated by steam separators and the steam becomes superheated as it passes through the various superheaters. The turbine exhaust steam is again superheated in the reheater before generating power in the intermediate and low pressure turbines. For this system, the main automatic control loops are the superheat temperature control and the reheat temperature control. The first one is controlled by the superheat spray, and the second one is controlled by the burners inclination angle, as well as by the reheat spray.
unsuitable start-up operations. In presence of this fault, the combustion gases do not circulate properly and the waterwall tubes are not suitable cold. Additionally, the water level on the steam generator drum goes down and the level control tries to keep it by means of varying the feedwater flow. However if the maximum value of this flow is reached, and the water level continues to decrease, the low level monitoring orders the steam generator out of operation. If this order takes a long time to be executed or if it is not performed, the waterwall tubes operating normally will suffer strong damages. This fault also diminishes the drum pressure which causes reductions of superheat and reheat pressures. The combustion control tries to correct this situation by increasing the air flow and the fuel flow; these actions could increase the furnace pressure beyond the allowed limit, and as a consequence the steam generator would be taken out of operation. If the human operator, in presence of this fault, does not carry out the adequate corrective actions, the healthy waterwall tubes could be damaged due to thermal stress. The turbine will also suffer from thermal and mechanical stress. Due to space limitations, the description of the other faults is not included. 3. SCHEME FOR FAULT DIAGNOSIS The scheme proposed in this paper has two components: residual generation and fault classification. The scheme is displayed in Fig. 2. The first component is based on comparison between the measurements coming from the plant and the predicted values generated by a neural network predictor. The predictor is based on neural network models which are trained using healthy data from the plant. Controller
Inputs Set Points
Process
States
x(k )
u (k - 1) Faults
Neural Network Predictor
xˆ(k ) Residual s Fault Diagnosis and Isolation via Associative Memory
r (k )
Upper Drum
Fault i
USS
Economizer
Fig. 2. Neural network-based scheme for fault diagnosis
SH1
Low Temperature SH To Purger Tank
To SH2 Temperation
High Temperature SH
Reheated Flash Tank
Intermediate Temperature SH Boiler Waterwalls
From feedwater system
In this paper, the plant is represented by a full-scale simulator. The differences between these two values, named as residuals, constitute a good indicator for fault detection. The residuals are calculated as ri (k) = xi (k) − x ˆi (k), i = 1, ..., n (1) where xi (k) are the plant measures and x ˆi (k) are the predictions. The residuals should be independent of the system operating state under nominal plant operation conditions. In absence of faults, the residuals are only due to noise and disturbance. When a fault occurs in the system, the residuals deviate from zero in characteristic ways, Chen and Patton (1999).
SH4
B C F
RH2 RH1
VRF
SH3
From feedwater system Recirculation
Lower Drum
Fig. 1. Steam generator with superheater and reheater As an example, we discuss about waterwall tubes breaking. It could be due to inadequate design, selection of materials, and/or 757
For the second component, residuals are encoded in bipolar or binary vectors using thresholds to obtain fault patterns. These
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
fault patterns are used to train an associative memory-based on a recurrent neural network, which is employed to carry out the fault diagnosis.
u7 (.) = Steam water flow (L/min). u8 (.) = Burner inclination angle (o ). and the output variables are
3.1 Residual Generation
x1 (.) = Power output (MW).
For residual generation purposes the neural network model replaces the analytical one describing the process under normal operation. The predictor is obtained using system identification theory via neural network modelling with nonlinear structures Nφrgaard et al. (2000). To achieve the identification is necessary to collect experimental data, which are obtained from a fullscale simulator. The neural networks training is done using the series-parallel scheme. After finishing the training, the neural networks can be applied for residual generation (Fig. 3); its weights are fixed and it is used as a parallel scheme to carry out predictions.
x2 (.) = Furnace pressure (Pa). x3 (.) = Drum level (m). x4 (.) = Reheat temperature (K). x5 (.) = Superheat temperature (K). x6 (.) = Reheat pressure (Pa). x7 (.) = Drum pressure (Pa). x8 (.) = Differential pressure (%). x9 (.) = Fuel temperature into burners (K).
x(k)
x10 (.) = Feedwater temperature (K).
+
These variables are taken into account as key variables to detect each fault as described in CNCAOI (1997). Wj represents the weights for each neural network model. The lag structure of each neural network model (na and nb ) is determined using the same criterion as in Nφrgaard (2000), which is based on Lipschitz quotients.
x(k )
Process
+
r (k )
q-1 Neural Network Predictor
xˆ(k )
-
Residual Generation
Fig. 3. Scheme for training and application of neural networks for residual generation.
fault inception time fault evolution time
2
0
−100
0
100
400
0
100
2
300
0
100
r4 (K)
300
400
100
200
300
400
time (s)
0
100
200
300
400
time (s)
−0.5
0
100
200
300
−1
400
0
100
200
300
0
100
200 300 time (s)
400
0
100
200
400
20
time (s)
0 −50
0
0
0
300
0 −1
400
200
time (s)
1
time (s)
50 r5 (K)
200
0x 107 100
0 −2
400
0
−50
u1 (.) = Fuel flow (T/H).
200
x 10
0 −2
400
time (s)
50
where j = 1, · · · , 10 and the input variables are:
300
time (s)
0.2
−0.2
(2)
200
200 0
x ˆj (k) = Fj [Wj , xj (k − 1), ..., xj (k − na ), u1 (k − 1), ..., u1 (k − 6), ..., u8 (k − 1), ..., u8 (k − nb )]
5
100
r3 (m)
The neural network predictor is designed using ten neural network models, which are trained via the Levenberg-Marquardt Learning Algorithm. Each neural network is a recurrent multilayer perceptron. The networks have one hidden layer with hyperbolic tangent or linear activation functions and a single neuron with a linear activation function as the output layer. The neural network models are obtained employing the toolbox NNSYSID for MATLAB1 , Nφrgaard (2000). The models have eigth input variables and a one output variable with a NNARX (Neural Network AutoRegressive, eXternal input) estructure as:
The residual generation scheme is implemented for six faults: waterwall tubes breaking, superheater tubes breaking, superheated steam temperature control fault, dirty regenerative preheater, velocity variator of feedwater pumps operating at maximum value and blocked fuel valve named as fault 1 to fault 6, respectively. Even if all the mentioned faults are taken into account, in this paper, due to space limitations, for explaining the process to generate residuals and fault patterns, only fault 1 is considered. For this fault, data base is acquired with a fullscale simulator for 75% of initial power output (225 MW), 15 % of severity fault, 2 minutes for inception and 8 minutes of simulation time. The residuals are close to zero before fault inception. After that, residuals deviate from zero in different ways. These residuals are displayed in Fig. 4. r6 (Pa)
u(k -1)
r7 (Pa)
Neural Network Training
r8 (%)
-
xˆ(k )
r10 (K)
Neural Network
r9 (K)
q-1
r1 (MW)
Process
r2 (Pa)
u(k -1)
400
time (s)
0
−20
300
time (s)
u2 (.) = Air flow (T/H). Fig. 4. Residuals for fault 1.
u3 (.) = Condensate flow (L/min). u4 (.) = Superheat spray (Kg/s).
3.2 Fault Classification
u5 (.) = Feedwater flow (T/H). Fig. 5 presents a scheme which illustrates the fault classification procedure. The previous stage generates a residual vector with ten elements, the absolute value of each residual is evaluated by
u6 (.) = Replacement of condensate (L/s). 1
MATLAB is a trademark of The Math Works, Inc.
758
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
detection thresholds (τi ). Detection thresholds are presented in Table 1. This evaluation provides a set of residuals encoded as T bipolar vectors [s1 (k), s2 (k), ..., s10 (k)] , where:
si (k) =
(
−1 if | ri (k)| < τi i = 1, 2, .., 10
possible. The patterns obtained are used, based on the synthesis optimal training algorithm proposed in Ruz-Hernandez et al. (2008), to train the recurrent neural network and to design the respective associative memory as a way to isolate faults. Fault patterns for all the six faults previously mentioned, are displayed in Table 2, where α0 indicates normal operation.
1 if |ri (k)| ≥ τi
Table 2. Fault patterns α0
α1
α2
α3
α4
α5
α6
-1
1
-1
-1
-1
-1
1
-1
1
-1
-1
-1
-1
-1
-1
1
1
1
1
1
1
-1
1
-1
1
-1
-1
-1
-1
1
1
1
-1
-1
1
-1
1
-1
1
-1
1
1
-1
1
1
1
1
-1
1
-1
-1
-1
-1
-1
-1
1
-1
1
-1
-1
-1
1
1
-1
1
-1
-1
-1
-1
1
Residuals
Detection Thresholds
Bipolar Vector
Associative Memory for Diagnosis
An associative memory based on a recurrent neural network is designed for fault classification. The recurrent neural network considered in the present paper is given by:
Fault i
x˙ = −Ax + T sat(x) + I
Fig. 5. Fault classification scheme.
τi 25 MW 30 Pa 0.022 m 10 K 4K
i 6 7 8 9 10
τi 20000 Pa 420000 Pa 0.85 % 0.24 K 10 K
For fault diagnosis, these encoded residuals are fed as input bipolar vectors to an associative memory. Encoded residuals for fault 1 are displayed in Fig. 6. fault inception time fault evolution time
1 s6
s1
1 0
−1
0
100
200
300
0
−1
0
100
200
300
400
s3
s8 0
100
200
300
400
s9
s4
400
0
100
200
300
400
The following synthesis problem concerns the design of (3) for associative memories. Given m + 1 vectors α0 , α1 , α2 , ..., αm in the set of n-dimensional bipolar vectors, B n , choose {A, T, I} in such a manner that: (1) α0 , α1 , α2 , ..., αm are stable memory vectors of system (3). (2) the system has no oscillatory and chaotic solutions. (3) the total number of spurious memory vectors (i.e., memory vectors which are not desired) is as small as possible, and the domain (or basin) of attraction of each desired memory vectors is as large as possible.
0
100
200
300
400
0
100
200
300
400
0
100
200 300 time (s)
400
1
0
0
100
200
300
0
−1
400
1 s10
1 s5
300
0
−1
1
0
−1
200
1
0
−1
100
0 −1
1
−1
0
1 s7
s2
1
0
100
200
300
400
It is assumed that the initial states of (3) satisfy |xi (0)| ≤ 1 for i = 1, ..., n. System (3) is a variant of the analog Hopfield model with activation function sat(·).
0
−1
400
y = sat(x) where x ∈ R is the state vector, x˙ denotes the derivative of x with respect to time t, y ∈ D n = {x ∈ Rn : −1 ≤ xi ≤ 1} with i = 1, ..., n is the output vector, A = diag [a1 , ..., an ] with ai > 0 for i = 1, ..., n, T = [Tij ] ∈ Rn is a connection matrix, I = [Ii ] ∈ Rn is a bias vector and T sat(x) = [sat(x1 ), ..., sat(xn )] represents the activation function, where ( 1 if xi > 1 sat(xi ) = xi if −1 ≤ xi ≤ 1 −1 if xi < −1 n
Table 1. Detection thresholds i 1 2 3 4 5
(3)
0 −1
time (s)
Fig. 6. Encoded residuals for fault 1. Once residuals are encoded, it is necessary to analyze them to select the fault patterns to be stored in the associative memory. This selection is done in order to discriminate adequately every fault, to reduce false alarms and to isolate faults as soon as 759
The previous synthesis problem can be solved by applying the optimal training algorithm proposed in Ruz-Hernandez et al. (2008) which combines the optimal hyperplane algorithm using to train support vector machines and the synthesis algorithm to design associative memories proposed by Liu and Lu (1997). Synthesis Optimal Training Algorithm: Given m training patterns αk , k = 1, 2, . . . , m which are known to belong to class
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
C1 (corresponding to Z = 1) or C2 (corresponding to Z = -1), the weight vector W i can be determined by means of the following algorithm. 1. Start out by solving the quadratic programming problem given by 1 F (Λi ) = (Λi )T P − (Λi )T QΛi (4) 2 under the constraints (Λi )T Y i = 0, Y i = [αi1 , αi2 , ..., αim ] Λi ≥ 0 to obtain the Lagrange multipliers (Λi )T =[λ1i , λ2i , . . . , λm i ]. 2. Compute the weight vector m X i λki αik α−k = [w1i , w2i , . . . , wni , wn+1 ] Wi =
1 y6
y1
(4)
0
−1
0
100
200
300
400
0
100
200
300
400
100
200
300
y8
0
400
y9
y4
0
0
100
200
300
400
100
200
300
400
0
100
200
300
400
0
100
200
300
400
0
100
200
300
400
1 y10
y5
For this algorithm, it is always required to choose µi > 1, without loss of generality, one can usually select A as the identity matrix. Furthermore, one can see that there are no restrictions on how many bipolar vectors can be stored as a stable memories in system (3). This implies that storage capacity can be very large. The corresponding convergence analysis can be reviewed in Ruz-Hernandez et al. (2008). The synthesis algorithm is programmed in MATLAB to train the recurrent neural network such that fault patterns are stored as stable memory vectors. The number of neurons is n = 10 and the patterns are m + 1 = 7 and µ = 1.15. The matrices {A, I, T } are: A = the identity 10 × 10 matrix, I = [-0.07, -0.54, 0.40, -0.40, 0.0, 0.37, 0.06, -0.72, 0.01, -0.07]T and 0.46 0.16 0.00 -0.01 0.11 0.01 0.11 0.14 0.20 0.31
0
0
−1
0
−1
400
1
1
3. Choose A = diag[a1 , a2 , . . . , an ] with ai > 0. For i, j = 1, 2, . . . , n choose Tij = wji if i 6= j, with µi > 1, Tij = wji + i + bi . ai µi − 1 if i = j and Ii = wn+1
300
0 −1
1
−1
200
1
0
−1
100
0
−1
1 y3
W i α−k + bi ≤ −1, if αik = −1 and for k = 1, 2, . . . , m where αk α−k = ... 1
y7
y2
(5)
0
1
0
−1
0
−1
1
W i α−k + bi ≥ 1, if αik = 1
0
100
200 300 time (s)
0
−1
400
time(s)
Fig. 7. Fault pattern retrieved by associative memory, fault 1.
4.2 Fault Diagnosis when operator is carrying out load power changes This case considers a fault appearing when the operator carries out load power changes to satisfy the electric power demand required by the users. As in the first case, faults have an inception time of 120 seconds. Fig. 8, Fig. 9 and Fig. 10 illustrate load power changes made by the operator, encoded residuals used as input bipolar vector to associative memory and retrieved fault pattern when fault 1 occurs, respectively. As expected, fault pattern α1 is retrieved. 255
250
245
240 MW
T
Fig. 7 displays retrieved fault pattern by associative memory when load power is constant and fault 1 appears. It is clear that fault pattern α1 is retrieved when encoded residuals as illustrated in Fig. 6, contain enough information about this fault pattern. Fault pattern α1 is retrieved before fault evolution time is finished. fault inception evolution time
k=1
0.18 0.60 0.00 0.27 0.00 0.00 0.00 -0.27 0.18 0.18 0.00 0.00 0.75 0.00 0.00 0.20 0.40 0.00 0.20 0.00 -0.01 0.16 0.00 0.79 0.11 0.35 0.11 -0.18 -0.12 -0.01 0.00 0.00 0.00 0.00 1.15 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.11 0.37 0.00 0.77 -0.11 0.03 0.25 0.03 0.08 0.01 0.35 0.04 0.11 -0.16 0.79 0.06 -0.19 0.08 0.18 -0.27 0.00 -0.27 0.09 0.09 0.09 0.60 0.09 0.18 0.15 0.14 0.19 -0.13 -0.12 0.26 -0.19 0.00 0.69 0.15 0.31 0.16 0.00 -0.01 0.11 0.01 0.11 0.14 0.20 0.46
4.1 Fault Diagnosis when load power is constant
1
for i = 1, 2, . . . , n, such that
=
diagnosis via this associative memory using full scale simulator as plant. These cases are described as follows.
235
4. FAULT DIAGNOSIS APPLICATION 230
The associative memory is evaluated, with the matrices fixed using encoded residuals as input bipolar vectors. According to encoded residual analysis and selected fault patterns, if an encoded residual as an bipolar vector contains enough information about storage pattern in associative memory then corresponding fault pattern is retrieved. Three cases are considered for fault 760
225
220
0
50
100
150
200
250 time (s)
300
350
400
450
Fig. 8. Load power changes made by the operator when fault 1 occurs.
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
1
fault inception time fault evolution time
1
300
−1
400
s7 0
100
200
300
400
100
200
300
400
s9
s4
s2
−1
0
100
200
300
400
100
200
300
400
0
100
200
300
0
−1
400
100
200
300
s10 0
100
200 300 time (s)
400
s6 300
400
1
0
100
200
300
400
0
0
100
200
300
400
200 300 time (s)
−1
1
1
0
0
−1
100
−1 1
0
100
200
300
400
0
100
400
Fig. 9. Input bipolar vector to associative memory when load power changes are made by the operator and fault 1 occurs.
100
200
300
400
0
100
200
300
400
0
100
200
300
400
−1
0
100
200
300
400
0
100
200 300 time (s)
400
1
0
0
0
0
1
400
0
−1
200
0
−1
0
1
0
100
1
−1
0
1
0
0
0
s3
s3
s8 0
1 s5
1
400
0
−1
1
−1
300
1
0
−1
200
0
−1
1
−1
100
s4
s2
0
−1
0
1
s7
200
s8
100
0
−1
s9
0
1
−1
s5
−1
0
s1
0
1
0
s10
s6
s1
1
200 300 time (s)
400
0
−1
Fig. 12.
Encoded residuals when load power changes are made by the operator.
fault inception time fault evolution time
1 y6 y7 0
100
200
300
y8
y3
0
0
100
200
300
y9
y4
0
100
200
300
−1
400
0
100
200
300
100
200
300
−1
400
y10 0
100
200 300 time (s)
200
300
400
100
200
300
−1
400
1
100
200 300 time (s)
−1
400
100
200
300
400
4.3 Normal operating conditions diagnosis when operator is carrying out load power changes free of faults. In this case, the proposed scheme for fault diagnosis is evaluated in presence of load power changes free of faults. This changes are generally made by the operator (see Fig. 11). Encoded residuals as input bipolar vector to associative memory are displayed in Fig. 12 which shows that s6 (k) take values between -1 and +1 during a short transient time. However, in Fig. 13 the associative memory retrieves α0 indicating normal operating conditions. 255
250
245
y5
200
300
400
−1
0
100
200
300
400
0
100
200
300
400
0
100
200
300
400
0
100
200
300
400
1 0
0
100
200
300
400
0
100
200
300
400
−1 1 0 −1 1
0 −1
100
0
0
1
Fault pattern retrieved by associative memory when load power changes are made by the operator and fault 1 occurs.
0
1
0 0
Fig. 10.
MW
−1
0 0
0 −1
400
100
1
1
0
0
0
0 0
0 −1
400
1
1
1
1 y5
0
−1
400
0
−1
400
0
1
−1
300
1
1
−1
200
1
−1
400
100
0
y2
y2
−1
0
1
y6
400
y7
300
y8
200
0
y9
100
1
y10
0
0 −1
y3
−1
y1
0
y4
y1
1
0
100
200
300
time (s)
400
0
−1
time (s)
Fig. 13.
Fault pattern retrieved by associative memory when load power changes are made by the operator free of faults.
5. FAULT DIAGNOSIS RESULTS Neural network-based scheme for fault diagnosis described in this work, constitutes a stage of the development of a help intelligent system for the fossil electric power plant operator. Taking into account the fault appearing when load power is constant, Fig. 14 illustrates diagnosis results for fault 1. Diagnosis results for fault 1 appearing when the operator carries out load power changes is illustrated in Fig. 15. Fig. 16 presents diagnosis result which is obtained when the operator carries out load power changes free of faults. Diagnosis result indicates that normal operating condition is occurring.
240
Diagnosis results displays that two logic values are possible for each fault indicator. For each indicator, the logic state placed as 1 indicates that corresponding fault pattern has been retrieved by associative memory and the logic state placed as 0 indicate that this fault is not occurring. If the logic state for each fault indicator is zero, then fossil electric power plant is operating on normal conditions. This information is very easy to be interpreted by the operator.
235
230
225
0
50
100
150
200
250
300
350
400
450
time (s)
Fig. 11. Load power changes free of faults. 761
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
ACKNOWLEDGEMENTS
Fault 1 Fault 2
1 0.5
0.5
0 0 1
Fault 3
0 0 1
Fault 4
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
The authors wish to thank the following mexican institutions: the GSP of the Instituto de Investigaciones Electricas (IIE) and the Universidad Autonoma del Carmen (UNACAR) for supporting this research. REFERENCES
0.5 0 0 1
Fault 5
100
0.5 0 0 1
0.5 0 0 1
Fault 6
50
50
100
150
200
250
300
350
400
450
50
100
150
200
250 time (s)
300
350
400
450
0.5 0
0
Fig. 14. Diagnosis result for fault 1 appearing when load power is constant.
Fault 1
1 0.5
Fault 2
0 0 1
Fault 3
0.5
Fault 4
0.5
Fault 5
0 0 1
0.5
0 0 1
0 0 1
0 0 1 Fault 6
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250 time (s)
300
350
400
450
0.5
0.5 0
0
Fig. 15. Diagnosis result for fault 1 a appearing when operator is carrying out load power changes.
Fault 1 Fault 2
1 0.5
0.5
0 0 1
Fault 3
0 0 1
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250 time (s)
300
350
400
450
0.5
Fault 4
0.5
Fault 5
0 0 1
0.5
0 0 1
0 0 1 Fault 6
50
0.5 0
0
Fig. 16.
Diagnosis result when the operator carries out load power changes free of faults.
6. CONCLUSIONS The results demonstrate that the neural predictor proposed in this paper is a feasible alternative for the residual generation. The detection thresholds allow to obtain fault patterns to train an associative memory based on a recurrent neural network. The associative memory is designed and applied via optimal training algorithm for fault diagnosis in fossil electric power plants. 762
Chen, J. and Patton, R.J. (1999). Robust Model Based Fault Diagnosis for Dynamic Systems. Kluwer Academic, Massachusetts, USA. CNCAOI (1997). Manual del Centro de Adiestramiento de Operadores Ixtapantongo: M´odulo III, Unidad 1. Comisi´on Federal de Electricidad, Mexico. Frank, P. (1990). Fault diagnosis in dynamic system using analytical and knowledge based redundancy - a survey and some results. Automatica, 26(3), 459–474. Frank, P. (1994). Diagnostic procedure in the automatic control engineering. Automatic Control Engineering, 2, 47–63. Koppen-Seliger, B. and Frank, P.M. (1995). Fault detection and isolation in technical processes with neural networks. In Proceedings of the 34th Conference on Decision & Control, 2414–2419. New Orleans, USA. Koppen-Seliger, B., Kiupel, N., Kellinghaus, H.S., and Frank, P. (1995). Fault diagnosis concept for a high-pressurepreheater line. In Proceeedings of the 34th Conference on Decision & Control, 2383–2390. New Orleans, USA. Korbicz, J., Koscielny, J., Kowalczuk, Z., and Cholewa, W. (2004). Fault Diagnosis: Models, Artificial Intelligence, Applications. Springer-Verlag, Berlin, Germany. Liu, D. and Lu, Z. (1997). A new synthesis approach for feedback neural netwoks based on the perceptro´ n training algorithm. IEEE Transactions on Neural Networks, 8(6), 1468–1482. Nφrgaard, M. (2000). Neural network based system identification toolbox for user with matlab, version 2. Technical Report 00-E-891, Technical University of Denmark. Nφrgaard, M., Ravn, O., Poulsen, N., and Hansen, L. (2000). Neural Networks for Modelling and Control of Dynamic Systems. Advanced Textbooks in control and Signal Processing. Springer-Verlag London Limited. Patton, R.J., Frank, P.M., and Clark, R.N. (2000). Issues of Fault Diagnosis for Dynamic Systems. Springer-Verlag, Berlin, Germany. Patton, R., Chen, J., and Siew, T. (1994). Diagnosis in nonlinear dynamics systems via neural networks. In Proceedings of CONTROL’94, 1346–1351. University of York, UK. Prock, J. (2000). On-line detection and diagnosis of sensor and process faults in nuclear power plants. In R.J. Patton, P.M. Frank, and R.N. Clark (eds.), Issues of Fault Diagnosis for Dynamic Systems, 339–377. Springer-Verlag, Berlin, Germany. Ruz-Hernandez, J.A., Sanchez, E.N., and Suarez, D.A. (2008). Algoritmo de entrenamiento optimo para disear una memoria asociativa de diagnostico de fallas. Revista Iberoamericana de Automatica e Informatica Industrial, 5, 115–123.
Optimal Training Algorithm Application to Design an Associative Memory for Fault Diagnosis at a Fossil Electric Power Plant Jose A. Ruz-Hernandez ∗ Dionisio A. Suarez ∗∗ Ramon Garcia-Hernandez ∗ Edgar N. Sanchez ∗∗∗ Maria U. Suarez-Duran ∗ ∗
Universidad Autonoma del Carmen, Av. 56 # 4 Esq. Av. Concordia, Col. Benito Juarez, C.P. 24180, Cd. del Carmen, Campeche, MEXICO, e-mail: {jruz,rghernandez}@pampano.unacar.mx ∗∗ Instituto de Investigaciones Electricas, Calle Reforma No. 113, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, MEXICO, e-mail: [email protected] ∗∗∗ CINVESTAV, Unidad Guadalajara, Apartado Postal 31-430, Plaza La Luna, Guadalajara, Jalisco C.P. 45091, MEXICO, e-mail: [email protected] Abstract: This paper presents the development and application of a neural networks-based scheme for fault diagnosis, including detection and classification, for the steam generator of a fossil electric power plant. The scheme is constituted by two components: residual generation and fault classification. The first component generates residuals via the difference between measurements coming from the plant and a neural network predictor. The neural network predictor is trained with healthy data collected from a full-scale simulator reproducing reliably the process behavior. For the second component detection thresholds are used to encode the residuals as bipolar vectors which represent fault patterns. The fault patterns are stored in an associative memory based on a recurrent neural network which is trained via optimal training algorithm. The scheme is evaluated on-line via a full-scale simulator to diagnose the main faults appearing in this kind of power plants when load power is constant and when the operator is carrying out load power changes. Furthermore, the fault diagnosis strategy is be able to distinguish when the operator is carrying out load power changes free of fault as normal operating conditions. Keywords: Computational intelligence methodology, neural associative memory, neural network predictor, fault diagnosis, fossil electric power plant. 1. INTRODUCTION Due to increasing demands on reliability and safety of technical processes, various fault detection and diagnosis methodologies have been proposed in the literature, which can be broadly divided into model based techniques, knowledge-based methodologies and empirical or signal processing techniques, Patton et al. (2000). Fault diagnosis is usually performed by a three steps algorithm, Frank (1994). First, one or several signals are generated which reflect faults in the process behavior. These signals are called residuals. On the second step, the residuals are evaluated. A decision, regarding time and location of possible faults, is obtained from the residuals. Finally, the nature and the cause of the fault is analyzed by the relations between the symptoms and their possible causes. In order to describe the fault free nominal behavior of the process under supervision, a mathematical model is employed; due to this fact, the term model-based fault diagnosis is used. Model-based approaches have dominated the fault diagnosis research for many years, Frank (1990). The main disadvantage of this method is that, being based on a mathematical model, it can be very sensitive to modelling errors, parameter variations, noise and disturbances. The success of the model-based method 978-3-902823-09-0/12/$20.00 © 2012 IFAC
756
is heavily dependent on the quality of the models; accurate modelling for a complex nonlinear system is very difficult to achieve in practice. Different applications of fault detection and diagnosis to industrial processes, which include conventional and computational intelligence techniques are reported in Korbicz et al. (2004). A power plant application which combines analytical redundancy and Petri nets is described in Prock (2000); however, as a consequence of the high number of modular fault detection units a lot of alarms are occurred. Most of the power plant applications use a combination of analytical/computational intelligence tools (Korbicz et al. (2004) and Koppen-Seliger et al. (1995)). Using adequate data base and methods for on-line and/or offline training, neural networks are able to reproduce the dynamics of complex nonlinear systems; after training, they can estimate quite precisely the output of nonlinear systems, Patton et al. (1994), Koppen-Seliger and Frank (1995). Employing measurements of the process under normal operation, if possible, or with the help of a realistic simulator, a suitable neural network can be trained to learn the process input-output behavior. The residuals generated using a neural network predictor can be evaluated via thresholds to obtain fault patterns. The
10.3182/20120829-3-MX-2028.00293
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
fault pattern recognition can be done by means other neural network, which allows to isolate different faults. This paper presents a neural network scheme for fault diagnosis. It uses for residual generation a predictor, which consists of a bank of recurrent multilayer perceptron neural network models. Fault classification is carried out by an associative memory, which is based on a recurrent neural network trained via optimal training algorithm. The scheme is evaluated on-line using a fullscale simulator to diagnose the main faults appearing in this kind of power plants. 2. PROBLEM DESCRIPTION Fault diagnosis for fossil electric power plants is a task carried out by human operators, who recognize typical faults via supervision of key variables evolution. Adequate fault detection and diagnosis aids will help the human operator in order to take the right decisions to maintain the required electric energy production, avoiding failures and even accident risky to humans and the environment, CNCAOI (1997). For this kind of plants, the main faults can be clustered as: faults related to temperature control of the superheat and reheat, faults related to combustion control and faults related to the steam generator drum water level. In order to understand the first group of faults, it is helpful to briefly describe the steam generator and superheated and reheated steam systems. A simplified scheme is presented in Fig. 1, which illustrates the main components of a typical steam generator and superheating/reheating systems. Feedwater from the economizer enters the steam drum, and by forced circulation, the drum water flows down the downcomers and rises through the furnace wall tubes to generate steam by means of the hot combustion gases in the furnace. The water and steam in the drum are separated by steam separators and the steam becomes superheated as it passes through the various superheaters. The turbine exhaust steam is again superheated in the reheater before generating power in the intermediate and low pressure turbines. For this system, the main automatic control loops are the superheat temperature control and the reheat temperature control. The first one is controlled by the superheat spray, and the second one is controlled by the burners inclination angle, as well as by the reheat spray.
unsuitable start-up operations. In presence of this fault, the combustion gases do not circulate properly and the waterwall tubes are not suitable cold. Additionally, the water level on the steam generator drum goes down and the level control tries to keep it by means of varying the feedwater flow. However if the maximum value of this flow is reached, and the water level continues to decrease, the low level monitoring orders the steam generator out of operation. If this order takes a long time to be executed or if it is not performed, the waterwall tubes operating normally will suffer strong damages. This fault also diminishes the drum pressure which causes reductions of superheat and reheat pressures. The combustion control tries to correct this situation by increasing the air flow and the fuel flow; these actions could increase the furnace pressure beyond the allowed limit, and as a consequence the steam generator would be taken out of operation. If the human operator, in presence of this fault, does not carry out the adequate corrective actions, the healthy waterwall tubes could be damaged due to thermal stress. The turbine will also suffer from thermal and mechanical stress. Due to space limitations, the description of the other faults is not included. 3. SCHEME FOR FAULT DIAGNOSIS The scheme proposed in this paper has two components: residual generation and fault classification. The scheme is displayed in Fig. 2. The first component is based on comparison between the measurements coming from the plant and the predicted values generated by a neural network predictor. The predictor is based on neural network models which are trained using healthy data from the plant. Controller
Inputs Set Points
Process
States
x(k )
u (k - 1) Faults
Neural Network Predictor
xˆ(k ) Residual s Fault Diagnosis and Isolation via Associative Memory
r (k )
Upper Drum
Fault i
USS
Economizer
Fig. 2. Neural network-based scheme for fault diagnosis
SH1
Low Temperature SH To Purger Tank
To SH2 Temperation
High Temperature SH
Reheated Flash Tank
Intermediate Temperature SH Boiler Waterwalls
From feedwater system
In this paper, the plant is represented by a full-scale simulator. The differences between these two values, named as residuals, constitute a good indicator for fault detection. The residuals are calculated as ri (k) = xi (k) − x ˆi (k), i = 1, ..., n (1) where xi (k) are the plant measures and x ˆi (k) are the predictions. The residuals should be independent of the system operating state under nominal plant operation conditions. In absence of faults, the residuals are only due to noise and disturbance. When a fault occurs in the system, the residuals deviate from zero in characteristic ways, Chen and Patton (1999).
SH4
B C F
RH2 RH1
VRF
SH3
From feedwater system Recirculation
Lower Drum
Fig. 1. Steam generator with superheater and reheater As an example, we discuss about waterwall tubes breaking. It could be due to inadequate design, selection of materials, and/or 757
For the second component, residuals are encoded in bipolar or binary vectors using thresholds to obtain fault patterns. These
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
fault patterns are used to train an associative memory-based on a recurrent neural network, which is employed to carry out the fault diagnosis.
u7 (.) = Steam water flow (L/min). u8 (.) = Burner inclination angle (o ). and the output variables are
3.1 Residual Generation
x1 (.) = Power output (MW).
For residual generation purposes the neural network model replaces the analytical one describing the process under normal operation. The predictor is obtained using system identification theory via neural network modelling with nonlinear structures Nφrgaard et al. (2000). To achieve the identification is necessary to collect experimental data, which are obtained from a fullscale simulator. The neural networks training is done using the series-parallel scheme. After finishing the training, the neural networks can be applied for residual generation (Fig. 3); its weights are fixed and it is used as a parallel scheme to carry out predictions.
x2 (.) = Furnace pressure (Pa). x3 (.) = Drum level (m). x4 (.) = Reheat temperature (K). x5 (.) = Superheat temperature (K). x6 (.) = Reheat pressure (Pa). x7 (.) = Drum pressure (Pa). x8 (.) = Differential pressure (%). x9 (.) = Fuel temperature into burners (K).
x(k)
x10 (.) = Feedwater temperature (K).
+
These variables are taken into account as key variables to detect each fault as described in CNCAOI (1997). Wj represents the weights for each neural network model. The lag structure of each neural network model (na and nb ) is determined using the same criterion as in Nφrgaard (2000), which is based on Lipschitz quotients.
x(k )
Process
+
r (k )
q-1 Neural Network Predictor
xˆ(k )
-
Residual Generation
Fig. 3. Scheme for training and application of neural networks for residual generation.
fault inception time fault evolution time
2
0
−100
0
100
400
0
100
2
300
0
100
r4 (K)
300
400
100
200
300
400
time (s)
0
100
200
300
400
time (s)
−0.5
0
100
200
300
−1
400
0
100
200
300
0
100
200 300 time (s)
400
0
100
200
400
20
time (s)
0 −50
0
0
0
300
0 −1
400
200
time (s)
1
time (s)
50 r5 (K)
200
0x 107 100
0 −2
400
0
−50
u1 (.) = Fuel flow (T/H).
200
x 10
0 −2
400
time (s)
50
where j = 1, · · · , 10 and the input variables are:
300
time (s)
0.2
−0.2
(2)
200
200 0
x ˆj (k) = Fj [Wj , xj (k − 1), ..., xj (k − na ), u1 (k − 1), ..., u1 (k − 6), ..., u8 (k − 1), ..., u8 (k − nb )]
5
100
r3 (m)
The neural network predictor is designed using ten neural network models, which are trained via the Levenberg-Marquardt Learning Algorithm. Each neural network is a recurrent multilayer perceptron. The networks have one hidden layer with hyperbolic tangent or linear activation functions and a single neuron with a linear activation function as the output layer. The neural network models are obtained employing the toolbox NNSYSID for MATLAB1 , Nφrgaard (2000). The models have eigth input variables and a one output variable with a NNARX (Neural Network AutoRegressive, eXternal input) estructure as:
The residual generation scheme is implemented for six faults: waterwall tubes breaking, superheater tubes breaking, superheated steam temperature control fault, dirty regenerative preheater, velocity variator of feedwater pumps operating at maximum value and blocked fuel valve named as fault 1 to fault 6, respectively. Even if all the mentioned faults are taken into account, in this paper, due to space limitations, for explaining the process to generate residuals and fault patterns, only fault 1 is considered. For this fault, data base is acquired with a fullscale simulator for 75% of initial power output (225 MW), 15 % of severity fault, 2 minutes for inception and 8 minutes of simulation time. The residuals are close to zero before fault inception. After that, residuals deviate from zero in different ways. These residuals are displayed in Fig. 4. r6 (Pa)
u(k -1)
r7 (Pa)
Neural Network Training
r8 (%)
-
xˆ(k )
r10 (K)
Neural Network
r9 (K)
q-1
r1 (MW)
Process
r2 (Pa)
u(k -1)
400
time (s)
0
−20
300
time (s)
u2 (.) = Air flow (T/H). Fig. 4. Residuals for fault 1.
u3 (.) = Condensate flow (L/min). u4 (.) = Superheat spray (Kg/s).
3.2 Fault Classification
u5 (.) = Feedwater flow (T/H). Fig. 5 presents a scheme which illustrates the fault classification procedure. The previous stage generates a residual vector with ten elements, the absolute value of each residual is evaluated by
u6 (.) = Replacement of condensate (L/s). 1
MATLAB is a trademark of The Math Works, Inc.
758
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
detection thresholds (τi ). Detection thresholds are presented in Table 1. This evaluation provides a set of residuals encoded as T bipolar vectors [s1 (k), s2 (k), ..., s10 (k)] , where:
si (k) =
(
−1 if | ri (k)| < τi i = 1, 2, .., 10
possible. The patterns obtained are used, based on the synthesis optimal training algorithm proposed in Ruz-Hernandez et al. (2008), to train the recurrent neural network and to design the respective associative memory as a way to isolate faults. Fault patterns for all the six faults previously mentioned, are displayed in Table 2, where α0 indicates normal operation.
1 if |ri (k)| ≥ τi
Table 2. Fault patterns α0
α1
α2
α3
α4
α5
α6
-1
1
-1
-1
-1
-1
1
-1
1
-1
-1
-1
-1
-1
-1
1
1
1
1
1
1
-1
1
-1
1
-1
-1
-1
-1
1
1
1
-1
-1
1
-1
1
-1
1
-1
1
1
-1
1
1
1
1
-1
1
-1
-1
-1
-1
-1
-1
1
-1
1
-1
-1
-1
1
1
-1
1
-1
-1
-1
-1
1
Residuals
Detection Thresholds
Bipolar Vector
Associative Memory for Diagnosis
An associative memory based on a recurrent neural network is designed for fault classification. The recurrent neural network considered in the present paper is given by:
Fault i
x˙ = −Ax + T sat(x) + I
Fig. 5. Fault classification scheme.
τi 25 MW 30 Pa 0.022 m 10 K 4K
i 6 7 8 9 10
τi 20000 Pa 420000 Pa 0.85 % 0.24 K 10 K
For fault diagnosis, these encoded residuals are fed as input bipolar vectors to an associative memory. Encoded residuals for fault 1 are displayed in Fig. 6. fault inception time fault evolution time
1 s6
s1
1 0
−1
0
100
200
300
0
−1
0
100
200
300
400
s3
s8 0
100
200
300
400
s9
s4
400
0
100
200
300
400
The following synthesis problem concerns the design of (3) for associative memories. Given m + 1 vectors α0 , α1 , α2 , ..., αm in the set of n-dimensional bipolar vectors, B n , choose {A, T, I} in such a manner that: (1) α0 , α1 , α2 , ..., αm are stable memory vectors of system (3). (2) the system has no oscillatory and chaotic solutions. (3) the total number of spurious memory vectors (i.e., memory vectors which are not desired) is as small as possible, and the domain (or basin) of attraction of each desired memory vectors is as large as possible.
0
100
200
300
400
0
100
200
300
400
0
100
200 300 time (s)
400
1
0
0
100
200
300
0
−1
400
1 s10
1 s5
300
0
−1
1
0
−1
200
1
0
−1
100
0 −1
1
−1
0
1 s7
s2
1
0
100
200
300
400
It is assumed that the initial states of (3) satisfy |xi (0)| ≤ 1 for i = 1, ..., n. System (3) is a variant of the analog Hopfield model with activation function sat(·).
0
−1
400
y = sat(x) where x ∈ R is the state vector, x˙ denotes the derivative of x with respect to time t, y ∈ D n = {x ∈ Rn : −1 ≤ xi ≤ 1} with i = 1, ..., n is the output vector, A = diag [a1 , ..., an ] with ai > 0 for i = 1, ..., n, T = [Tij ] ∈ Rn is a connection matrix, I = [Ii ] ∈ Rn is a bias vector and T sat(x) = [sat(x1 ), ..., sat(xn )] represents the activation function, where ( 1 if xi > 1 sat(xi ) = xi if −1 ≤ xi ≤ 1 −1 if xi < −1 n
Table 1. Detection thresholds i 1 2 3 4 5
(3)
0 −1
time (s)
Fig. 6. Encoded residuals for fault 1. Once residuals are encoded, it is necessary to analyze them to select the fault patterns to be stored in the associative memory. This selection is done in order to discriminate adequately every fault, to reduce false alarms and to isolate faults as soon as 759
The previous synthesis problem can be solved by applying the optimal training algorithm proposed in Ruz-Hernandez et al. (2008) which combines the optimal hyperplane algorithm using to train support vector machines and the synthesis algorithm to design associative memories proposed by Liu and Lu (1997). Synthesis Optimal Training Algorithm: Given m training patterns αk , k = 1, 2, . . . , m which are known to belong to class
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
C1 (corresponding to Z = 1) or C2 (corresponding to Z = -1), the weight vector W i can be determined by means of the following algorithm. 1. Start out by solving the quadratic programming problem given by 1 F (Λi ) = (Λi )T P − (Λi )T QΛi (4) 2 under the constraints (Λi )T Y i = 0, Y i = [αi1 , αi2 , ..., αim ] Λi ≥ 0 to obtain the Lagrange multipliers (Λi )T =[λ1i , λ2i , . . . , λm i ]. 2. Compute the weight vector m X i λki αik α−k = [w1i , w2i , . . . , wni , wn+1 ] Wi =
1 y6
y1
(4)
0
−1
0
100
200
300
400
0
100
200
300
400
100
200
300
y8
0
400
y9
y4
0
0
100
200
300
400
100
200
300
400
0
100
200
300
400
0
100
200
300
400
0
100
200
300
400
1 y10
y5
For this algorithm, it is always required to choose µi > 1, without loss of generality, one can usually select A as the identity matrix. Furthermore, one can see that there are no restrictions on how many bipolar vectors can be stored as a stable memories in system (3). This implies that storage capacity can be very large. The corresponding convergence analysis can be reviewed in Ruz-Hernandez et al. (2008). The synthesis algorithm is programmed in MATLAB to train the recurrent neural network such that fault patterns are stored as stable memory vectors. The number of neurons is n = 10 and the patterns are m + 1 = 7 and µ = 1.15. The matrices {A, I, T } are: A = the identity 10 × 10 matrix, I = [-0.07, -0.54, 0.40, -0.40, 0.0, 0.37, 0.06, -0.72, 0.01, -0.07]T and 0.46 0.16 0.00 -0.01 0.11 0.01 0.11 0.14 0.20 0.31
0
0
−1
0
−1
400
1
1
3. Choose A = diag[a1 , a2 , . . . , an ] with ai > 0. For i, j = 1, 2, . . . , n choose Tij = wji if i 6= j, with µi > 1, Tij = wji + i + bi . ai µi − 1 if i = j and Ii = wn+1
300
0 −1
1
−1
200
1
0
−1
100
0
−1
1 y3
W i α−k + bi ≤ −1, if αik = −1 and for k = 1, 2, . . . , m where αk α−k = ... 1
y7
y2
(5)
0
1
0
−1
0
−1
1
W i α−k + bi ≥ 1, if αik = 1
0
100
200 300 time (s)
0
−1
400
time(s)
Fig. 7. Fault pattern retrieved by associative memory, fault 1.
4.2 Fault Diagnosis when operator is carrying out load power changes This case considers a fault appearing when the operator carries out load power changes to satisfy the electric power demand required by the users. As in the first case, faults have an inception time of 120 seconds. Fig. 8, Fig. 9 and Fig. 10 illustrate load power changes made by the operator, encoded residuals used as input bipolar vector to associative memory and retrieved fault pattern when fault 1 occurs, respectively. As expected, fault pattern α1 is retrieved. 255
250
245
240 MW
T
Fig. 7 displays retrieved fault pattern by associative memory when load power is constant and fault 1 appears. It is clear that fault pattern α1 is retrieved when encoded residuals as illustrated in Fig. 6, contain enough information about this fault pattern. Fault pattern α1 is retrieved before fault evolution time is finished. fault inception evolution time
k=1
0.18 0.60 0.00 0.27 0.00 0.00 0.00 -0.27 0.18 0.18 0.00 0.00 0.75 0.00 0.00 0.20 0.40 0.00 0.20 0.00 -0.01 0.16 0.00 0.79 0.11 0.35 0.11 -0.18 -0.12 -0.01 0.00 0.00 0.00 0.00 1.15 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.11 0.37 0.00 0.77 -0.11 0.03 0.25 0.03 0.08 0.01 0.35 0.04 0.11 -0.16 0.79 0.06 -0.19 0.08 0.18 -0.27 0.00 -0.27 0.09 0.09 0.09 0.60 0.09 0.18 0.15 0.14 0.19 -0.13 -0.12 0.26 -0.19 0.00 0.69 0.15 0.31 0.16 0.00 -0.01 0.11 0.01 0.11 0.14 0.20 0.46
4.1 Fault Diagnosis when load power is constant
1
for i = 1, 2, . . . , n, such that
=
diagnosis via this associative memory using full scale simulator as plant. These cases are described as follows.
235
4. FAULT DIAGNOSIS APPLICATION 230
The associative memory is evaluated, with the matrices fixed using encoded residuals as input bipolar vectors. According to encoded residual analysis and selected fault patterns, if an encoded residual as an bipolar vector contains enough information about storage pattern in associative memory then corresponding fault pattern is retrieved. Three cases are considered for fault 760
225
220
0
50
100
150
200
250 time (s)
300
350
400
450
Fig. 8. Load power changes made by the operator when fault 1 occurs.
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
1
fault inception time fault evolution time
1
300
−1
400
s7 0
100
200
300
400
100
200
300
400
s9
s4
s2
−1
0
100
200
300
400
100
200
300
400
0
100
200
300
0
−1
400
100
200
300
s10 0
100
200 300 time (s)
400
s6 300
400
1
0
100
200
300
400
0
0
100
200
300
400
200 300 time (s)
−1
1
1
0
0
−1
100
−1 1
0
100
200
300
400
0
100
400
Fig. 9. Input bipolar vector to associative memory when load power changes are made by the operator and fault 1 occurs.
100
200
300
400
0
100
200
300
400
0
100
200
300
400
−1
0
100
200
300
400
0
100
200 300 time (s)
400
1
0
0
0
0
1
400
0
−1
200
0
−1
0
1
0
100
1
−1
0
1
0
0
0
s3
s3
s8 0
1 s5
1
400
0
−1
1
−1
300
1
0
−1
200
0
−1
1
−1
100
s4
s2
0
−1
0
1
s7
200
s8
100
0
−1
s9
0
1
−1
s5
−1
0
s1
0
1
0
s10
s6
s1
1
200 300 time (s)
400
0
−1
Fig. 12.
Encoded residuals when load power changes are made by the operator.
fault inception time fault evolution time
1 y6 y7 0
100
200
300
y8
y3
0
0
100
200
300
y9
y4
0
100
200
300
−1
400
0
100
200
300
100
200
300
−1
400
y10 0
100
200 300 time (s)
200
300
400
100
200
300
−1
400
1
100
200 300 time (s)
−1
400
100
200
300
400
4.3 Normal operating conditions diagnosis when operator is carrying out load power changes free of faults. In this case, the proposed scheme for fault diagnosis is evaluated in presence of load power changes free of faults. This changes are generally made by the operator (see Fig. 11). Encoded residuals as input bipolar vector to associative memory are displayed in Fig. 12 which shows that s6 (k) take values between -1 and +1 during a short transient time. However, in Fig. 13 the associative memory retrieves α0 indicating normal operating conditions. 255
250
245
y5
200
300
400
−1
0
100
200
300
400
0
100
200
300
400
0
100
200
300
400
0
100
200
300
400
1 0
0
100
200
300
400
0
100
200
300
400
−1 1 0 −1 1
0 −1
100
0
0
1
Fault pattern retrieved by associative memory when load power changes are made by the operator and fault 1 occurs.
0
1
0 0
Fig. 10.
MW
−1
0 0
0 −1
400
100
1
1
0
0
0
0 0
0 −1
400
1
1
1
1 y5
0
−1
400
0
−1
400
0
1
−1
300
1
1
−1
200
1
−1
400
100
0
y2
y2
−1
0
1
y6
400
y7
300
y8
200
0
y9
100
1
y10
0
0 −1
y3
−1
y1
0
y4
y1
1
0
100
200
300
time (s)
400
0
−1
time (s)
Fig. 13.
Fault pattern retrieved by associative memory when load power changes are made by the operator free of faults.
5. FAULT DIAGNOSIS RESULTS Neural network-based scheme for fault diagnosis described in this work, constitutes a stage of the development of a help intelligent system for the fossil electric power plant operator. Taking into account the fault appearing when load power is constant, Fig. 14 illustrates diagnosis results for fault 1. Diagnosis results for fault 1 appearing when the operator carries out load power changes is illustrated in Fig. 15. Fig. 16 presents diagnosis result which is obtained when the operator carries out load power changes free of faults. Diagnosis result indicates that normal operating condition is occurring.
240
Diagnosis results displays that two logic values are possible for each fault indicator. For each indicator, the logic state placed as 1 indicates that corresponding fault pattern has been retrieved by associative memory and the logic state placed as 0 indicate that this fault is not occurring. If the logic state for each fault indicator is zero, then fossil electric power plant is operating on normal conditions. This information is very easy to be interpreted by the operator.
235
230
225
0
50
100
150
200
250
300
350
400
450
time (s)
Fig. 11. Load power changes free of faults. 761
SAFEPROCESS 2012 August 29-31, 2012. Mexico City, Mexico
ACKNOWLEDGEMENTS
Fault 1 Fault 2
1 0.5
0.5
0 0 1
Fault 3
0 0 1
Fault 4
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
The authors wish to thank the following mexican institutions: the GSP of the Instituto de Investigaciones Electricas (IIE) and the Universidad Autonoma del Carmen (UNACAR) for supporting this research. REFERENCES
0.5 0 0 1
Fault 5
100
0.5 0 0 1
0.5 0 0 1
Fault 6
50
50
100
150
200
250
300
350
400
450
50
100
150
200
250 time (s)
300
350
400
450
0.5 0
0
Fig. 14. Diagnosis result for fault 1 appearing when load power is constant.
Fault 1
1 0.5
Fault 2
0 0 1
Fault 3
0.5
Fault 4
0.5
Fault 5
0 0 1
0.5
0 0 1
0 0 1
0 0 1 Fault 6
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250 time (s)
300
350
400
450
0.5
0.5 0
0
Fig. 15. Diagnosis result for fault 1 a appearing when operator is carrying out load power changes.
Fault 1 Fault 2
1 0.5
0.5
0 0 1
Fault 3
0 0 1
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250 time (s)
300
350
400
450
0.5
Fault 4
0.5
Fault 5
0 0 1
0.5
0 0 1
0 0 1 Fault 6
50
0.5 0
0
Fig. 16.
Diagnosis result when the operator carries out load power changes free of faults.
6. CONCLUSIONS The results demonstrate that the neural predictor proposed in this paper is a feasible alternative for the residual generation. The detection thresholds allow to obtain fault patterns to train an associative memory based on a recurrent neural network. The associative memory is designed and applied via optimal training algorithm for fault diagnosis in fossil electric power plants. 762
Chen, J. and Patton, R.J. (1999). Robust Model Based Fault Diagnosis for Dynamic Systems. Kluwer Academic, Massachusetts, USA. CNCAOI (1997). Manual del Centro de Adiestramiento de Operadores Ixtapantongo: M´odulo III, Unidad 1. Comisi´on Federal de Electricidad, Mexico. Frank, P. (1990). Fault diagnosis in dynamic system using analytical and knowledge based redundancy - a survey and some results. Automatica, 26(3), 459–474. Frank, P. (1994). Diagnostic procedure in the automatic control engineering. Automatic Control Engineering, 2, 47–63. Koppen-Seliger, B. and Frank, P.M. (1995). Fault detection and isolation in technical processes with neural networks. In Proceedings of the 34th Conference on Decision & Control, 2414–2419. New Orleans, USA. Koppen-Seliger, B., Kiupel, N., Kellinghaus, H.S., and Frank, P. (1995). Fault diagnosis concept for a high-pressurepreheater line. In Proceeedings of the 34th Conference on Decision & Control, 2383–2390. New Orleans, USA. Korbicz, J., Koscielny, J., Kowalczuk, Z., and Cholewa, W. (2004). Fault Diagnosis: Models, Artificial Intelligence, Applications. Springer-Verlag, Berlin, Germany. Liu, D. and Lu, Z. (1997). A new synthesis approach for feedback neural netwoks based on the perceptro´ n training algorithm. IEEE Transactions on Neural Networks, 8(6), 1468–1482. Nφrgaard, M. (2000). Neural network based system identification toolbox for user with matlab, version 2. Technical Report 00-E-891, Technical University of Denmark. Nφrgaard, M., Ravn, O., Poulsen, N., and Hansen, L. (2000). Neural Networks for Modelling and Control of Dynamic Systems. Advanced Textbooks in control and Signal Processing. Springer-Verlag London Limited. Patton, R.J., Frank, P.M., and Clark, R.N. (2000). Issues of Fault Diagnosis for Dynamic Systems. Springer-Verlag, Berlin, Germany. Patton, R., Chen, J., and Siew, T. (1994). Diagnosis in nonlinear dynamics systems via neural networks. In Proceedings of CONTROL’94, 1346–1351. University of York, UK. Prock, J. (2000). On-line detection and diagnosis of sensor and process faults in nuclear power plants. In R.J. Patton, P.M. Frank, and R.N. Clark (eds.), Issues of Fault Diagnosis for Dynamic Systems, 339–377. Springer-Verlag, Berlin, Germany. Ruz-Hernandez, J.A., Sanchez, E.N., and Suarez, D.A. (2008). Algoritmo de entrenamiento optimo para disear una memoria asociativa de diagnostico de fallas. Revista Iberoamericana de Automatica e Informatica Industrial, 5, 115–123.