Neuromorphic Multiple-Fault Diagnosing System Based on Plant

Article pubs.acs.org/IECR

Neuromorphic Multiple-Fault Diagnosing System Based on Plant Dynamic Characteristics Shokoufe Tayyebi, Ramin Bozorgmehry Boozarjomehry,* and Mohammad Shahrokhi Department of Chemical and Petroleum Engineering, Sharif University of Technology, P.O. Box 14155-4838, Azadi Avenue, Tehran, Iran ABSTRACT: In many cases, multiple-fault diagnosis of plant-wide systems based on steady-state data is impossible. To solve this problem, a new diagnosis strategy based on neural networks has been proposed. In the suggested framework, the neural network is used as the diagnoser trained by a hybrid set of steady and dynamic characteristic data of the system. The dynamic characteristic data include overshoot and undershoot values of measured variables and their corresponding occurrence times. To evaluate its performance, the proposed scheme was used in the diagnosis of the concurrent faults of the Tennessee Eastman (TE) process. Various combinations of concurrent faults were considered in this assessment. The results indicate the generality, flexibility, and accuracy of the proposed algorithm such that it is capable of diagnosing various combinations (from single to sextuple) of simultaneous faults, whereas the other diagnosing methods used for the TE process are capable of distinguishing at most three simultaneous faults.

1. INTRODUCTION The design of accurate fault diagnosing systems aids process safety and also improves product quality. Therefore, in recent years, many researchers have conducted work on this topic and suggested various techniques for fault detection and diagnosis. Fault diagnosis methods can be divided into three major groups: model-based techniques, data-driven methods, and knowledge-based approaches.1,2 The first category isolates faults using the process model, and if the process model is accurate, it can be capable of detecting all faults including unexpected ones. Fault diagnosis based on signed directed graphs (SDGs),3 observer-based fault diagnosing methods,4,5 and fault-tree analysis techniques6 belong to this category. Despite their advantages, model-based techniques suffer from a major shortcoming: the fact that finding an appropriate and reliable model of a system is often impossible or very difficult and expensive. The second category consists of methods that are based on experimental and/or heuristic data for diagnosing process faults. Fault diagnosing techniques based on neural networks,7,8 Fisher discriminate analysis (FDA),9 and principle component analysis (PCA)10,11 are among the methods that belong to this category. Methods associated with knowledgebased approaches include fuzzy fault diagnosing systems12 and expert systems.13 As mentioned in the preceding paragraph, one of the intelligent fault diagnosing techniques is neural network systems. Because of their high potential for capturing nonlinear relationships, neural networks represent a powerful tool for fault diagnosis.14,15 Diagnosis of a plant-wide process is a complicated task because of the large number of variables and overlapping symptoms caused by different faults occurring in the plant. Vedam and Venkatasubramanian16 used the SDG technique to diagnose multiple faults in a fluidized catalytic cracking unit (FFCU), but the method has some limitations that can lead to the failure of multiple-fault diagnosis. Therefore, the PCA-SDG technique can be utilized to improve the performance of fault diagnosis. Chang et al.17 presented © 2013 American Chemical Society

fault trees and fuzzy inference mechanisms to isolate four unusual faults in the Tennessee Eastman (TE) process. The SDG method was used to diagnose single and double faults in the TE process by Maurya et al.3 Jakubek and Strasser7 proposed a PCA method based on neural networks for detecting four isolated faults in the TE process. Detroja et al.18 compared correspondence analysis (CA) and PCA-based fault detection and diagnosis methods for two cases of the TE process in which each case recognized two concurrent faults. The effect of the number of principle components on the detection of single faults of the TE process was studied by Tamura et al.19 Because the occurrence of multiple faults is inevitable in plants, the selected diagnoser system should be able to diagnose various concurrent faults rigorously. The conventional neuromorphic (neural-network based) diagnoser system is trained by steady-state data by applying these data as the input vector of the neural network. This network cannot diagnose different faults when the symptoms are similar. The proposed neuromorphic diagnosing framework resolves this shortcoming by using the dynamic characteristic data. The proposed framework can correctly distinguish concurrent faults whose symptoms based on the steady-state values of the outputs are similar. In addition, a technique is proposed to detect the steady-state condition of a process. To test the performance of the proposed scheme, the TE process was used. Despite the fact that this process has been used widely as a benchmark for fault diagnosis purposes, there are several cases in this system that are not considered in the literature. The performance of the proposed scheme in plant-wide fault diagnosis is demonstrated by applying this scheme for fault diagnosis of the TE process Received: Revised: Accepted: Published: 12927

September 5, 2012 June 20, 2013 August 16, 2013 August 16, 2013 dx.doi.org/10.1021/ie400136w | Ind. Eng. Chem. Res. 2013, 52, 12927−12936

Industrial & Engineering Chemistry Research

Article

impossible) to detect multiple faults even under steady-state conditions. It should also be noted that a fault diagnosing system even in steady-state mode can help avoid the progression of abnormal events and reduce productivity losses. Because the detection of multiple faults under steady-state conditions is considered in this work, in what follows, a new method for the detection of steady-state conditions is proposed. It should be noted that such a detection technique should be applied in an algorithmic manner. The detection of a steady state can be achieved by monitoring various statistical moments of the signal (e.g., mean, standard deviation). If these values do not change in a specific time span and remain constant, one can assume that the system is at its steady state. In this study, the system is assumed to be at its steady state if the following conditions are satisfied

when two to six simultaneous faults with overlapping data occur. The main advantage of the proposed framework over alternative diagnosing methods is the fact that it is capable of diagnosing up to six concurrent faults, whereas the existing methods can diagnose up to three concurrent faults.20 This article is organized as follows: In section 2, the neuralnetwork-based fault diagnosis technique in general is described. The new algorithm for the recognition of the steady-state condition is proposed in section 3. The proposed method for fault detection including dynamic characteristic data is presented in sections 4 and 5. Section 6 consists of a brief review of the TE plant characteristics and its control structure. In section 7, the performance of the proposed method in diagnosing multiple faults for TE process is demonstrated, and finally, concluding remarks are made.

max[|max(V ) − mean(V )|, |mean(V ) − min(V )|] < εi j |max(V ) − min(V )|

2. NEUROMORPHIC FAULT DIAGNOSIS Various researchers have shown that artificial neural networks (ANNs) provide an efficient identification method for processes whose mechanistic models are either impossible or too costly to obtain. In such a case, the nonlinear behavior of the system can be approximated by a neural network whose neurons have simple nonlinear transfer functions such as relay, saturated linear, or sigmoid functions. The learning algorithms of the ANN by which the synaptic weights and other adjustable parameters of the network are obtained, use training data requiring little or no a priori knowledge of the process.21 Various neural network architectures are available for fault detection and diagnosis; they can be either supervised or unsupervised networks. Examples of the first category are radial basis function networks and multilayer perceptrons, whereas Kohonen networks represent an example of unsupervised networks.22 The feed-forward back-propagation network has been broadly used in fault diagnosis systems based on neural networks.23 This network consists of an input layer, a number of hidden layers, and an output layer. Typically, the outputs of each neuron in a layer are connected to all of the neurons in the next layer. The input and output training data contain variables relevant to faults and the corresponding symptoms of the process, respectively. The numbers of neurons in the input and output layers are equal to the number of measured variables and the number of potential faults in the process, respectively. The deviations from the normal values of the measured variables are used as the network inputs, whereas the ith output of the network corresponds to the ith fault of the process. The outputs of the neural diagnoser are binary variables representing the occurrence of a fault (if the corresponding value is 1) or the lack of fault occurrence (if the corresponding value is 0).23 The number of hidden neurons depends on the number of training data and the number of neurons that exist in the input and output layers. The optimum number of neurons for the hidden layer(s) must be selected iteratively so that the network error criterion is fulfilled.

(1)

|vij, k − vij, k − 1| /(tk − tk − 1) < 0.0001|vij, k|

(2)

where V = (vij, k , vij, k − 1 , ..., vij, k − K s)

(3)

In eqs 1−3, mean, max, and min denote the mean, maximum, and minimum values, respectively. νji is the value of the ith measured variable under the jth set of operating conditions. ε and k represent the threshold vector and the sampling time, respectively. The correct detection of the steady state depends strongly on the chosen threshold vector. It should be emphasized that the left-hand side of inequality 1 represents the maximum deviation of the mean value as normalized for each measured variable after several sampling times (Ks). Ks depends on the behavior of the system and its measured variables. The left-hand side of inequality 2 approximates the derivative of the measured variable and should be less than 0.01% of the measured variable if the system is at its steady state. In this method, one needs to identify solely the various operating modes in the system. In fact, the only knowledge that one needs to determine an appropriate threshold vector is the time scales and spans of various measured signals. Because any signal has its corresponding threshold, any change in conditions, such as slow drifts, could influence the threshold vector, which is represented in the form of a new operating mode. Consequently, the maximum value of the thresholds corresponding to each signal in the various modes can be selected accordingly (using simulation or experimental data). In systems with slow and fast dynamics, it should be noted that the selection of Ks based on a low sampling rate will increase the computational demands, as well as the duration after which the fault diagnosis algorithm can be triggered, which is not desired. Furthermore, the selection of Ks based on a high sampling rate can lead to false detection of steady-state conditions, giving poor diagnosis results. This is because the fast dynamic signal can reach its steady state when the slow dynamic signal is still far from its steady-state value. This means that Ks estimated on the basis of a single sampling rate cannot guarantee an accurate detection of steady-state conditions in systems containing signals with different sampling rates. Hence, any signal is evaluated according to its corresponding Ks value for the identification of steady-state conditions. It should be

3. NEW METHOD FOR STEADY-STATE DETECTION Although it is desirable to diagnose multiple faults during the system transition state, most fault diagnosis publications and the majority of the research in this area are focused on steadystate fault detection techniques, and few schemes have been proposed for fault diagnosis during plant startup, shutdown, or grade transition.24 This is because it is extremely difficult (if not 12928

dx.doi.org/10.1021/ie400136w | Ind. Eng. Chem. Res. 2013, 52, 12927−12936


Article

considering the fact that Pi,min and Pi,max might be similar for two different faults, to diagnose the faults uniquely, Pi,min and Pi,max along with their corresponding times of occurrence (namely, ti,min and ti,max, respectively) are also used in the input vector of the diagnosing function. Because Pi,min and Pi,max are the outputs of measuring devices that can usually be logged in the data acquisition system, the only requirement is to assign a watchdog for that signal such that, as soon as the value of the signal becomes lower/greater than the previously obtained Pi,min/Pi,max value, the newly measured value along with the time of measurement should be logged. This is a ready-made function in all data acquisition systems for each signal that has a trend and/or history. Therefore, the diagnosing function is presented as

noted that the system reaches steady-state conditions when all of these signals have reached to their steady values.

4. FAULT DIAGNOSING SYSTEM BASED ON DYNAMIC CHARACTERISTIC DATA As mentioned previously, most fault diagnosing algorithms have been developed for fault detection under steady-state conditions, whereas there are cases when two different faults can lead to the same steady-state conditions. For such cases, additional data should be used for fault detection. Transient characteristic data can be used for this purpose. In this section, a procedure is proposed for fault detection under such a situation. In general, a state-space model for a continuous-time nonlinear system can be represented as

F = ⌀(uss , yss , Pmax , Pmin , tmin , tmax )

x(̇ t ) = φ[x(t ), u(t ), d(t ), f (t )] y(t ) = g[x(t )]

According to this approach, the dynamic characteristics and steady-state values of the measured signals are used as the input vector of the diagnosing system. Considering the fact that, in general the structure of diagnosing function is not known, and the inherent capability of the neural networks in function approximation, one can use a neural network to approximate such a function based on its input−output data sets. On the other hand, the use of auxiliary input variables corresponding to dynamic characteristic points of each measured signal increases the dimensions of the diagnosing function. This, in turn, makes the training of the network approximating the diagnosing function more difficult and time-demanding. To mitigate this shortcoming, the four dynamic characteristic data values along with the steady-state data values have been merged to obtain a hybrid parameter that takes into account the effects of all of the parameters on the diagnosing system. Consequently, this hybrid parameter (denoted as ID) is proposed to uniquely distinguish concurrent faults whose symptoms based on the steady-state values of the outputs are similar. To do this, it is natural to use some characteristic information of system dynamics. The maximum and minimum values of the signal and their corresponding times of occurrence are good candidates for this purpose. The hybrid parameter ID is thus defined as

(4)

where x ∈ n is the state vector, u ∈ m is the vector of known input signals, d ∈ l is the unknown input (or disturbance) vector, f ∈ r is the fault vector, y ∈ q denotes the vector of measured output values, and t is the time. φ: n × m × l × r → n and g: n → q denote vectors of nonlinear functions. In a fault diagnosis system, it is desired to obtain a unique mapping that presents the relation between symptoms and their corresponding faults. Such a mapping that reflects the diagnosing function can be mathematically defined as F = ⌀[u(t ), y(t ), θ ]

(5)

where ⌀:  ×  →  represents the vector of discriminant process fault functions and F and θ are vectors of faults that have occurred and parameters required to uniquely distinguish the faults, respectively. In addition,  represents a hypercube with one corner at the origin and a length of 1. The elements of the output vector whose values are beyond a specific threshold (e.g., 0.75) indicate the occurrence of faults in the system. Because fault diagnosis of a system is usually performed under its steady-state conditions, the diagnosing function can usually be written as m

F = ⌀(uss , yss )

q

(7)

r

⎛ v ⎞ vi ,max − vi ,min i ⎟⎟ IDi = ⎜⎜ ⎝ vi̅ ,normal vi ,normal,max − vi ,normal,min ⎠ ⎡ ⎤ Pi ,maxPi ,minti ,maxti ,min ⎢ ⎥ ⎢⎣ vi̅ ,normal 2 max 2(ti ,max , ti ,min) ⎥⎦

(6)

where uss and yss are the vectors of measured input and output variables, respectively, at steady state. It is important to note that at least one of the symptoms or measured variables (u and y) should be distinctive in different faulty situations to accurately diagnose different faults. In many processes, multiple different faults might result in similar symptoms. In these cases, the faults resulting in similar symptoms are indistinguishable. To overcome this problem, input vector should be selected in such a way that different faults cause distinctive symptoms. In the present study, both information related to the history of the process and steadystate information have been utilized to achieve distinctive symptoms. Accordingly, one can use characteristic points of the dynamic trend of each measured variable to uniquely distinguish and detect various faults. In this study, the minimum (Pi,min) and maximum (Pi,max) values of measured variables throughout the time frame during which the system reaches its new steady state are recorded. To effectively diagnose multiple faults, it is important to observe distinctive faults symptoms for various situations. Hence,

(8)

where max indicates the maximum value, i is the index of the input variable to the neural network system, and IDi is ith input of the neural network. vi is the value of the ith measured variable in the faulty situation; vi̅ ,normal is the average value of the ith measured variable under normal conditions; vi,max and vi,min are the maximum and minimum values, respectively, of the ith measured variable in the faulty situation; and vi,normal,max and vi,normal,min are the maximum and minimum values, respectively, of the ith measured variable under normal conditions. As mentioned earlier, the effects of both dynamic and steady-state characteristic data are taken into account in the structure of the defined hybrid parameter. In fact, the first term on the righthand side of eq 8 corresponds to the steady-state data, whereas the second term corresponds to the dynamic characteristic data of the ith measured variable. This parameter is the product of 12929



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two terms, each of them showing some characteristic information of the signal: The first term reflects the normalized steady-state value of the signal, which shows the signal value in the new situation. The second term in the hybrid parameter shows the characteristic points of the track through which the signal reaches its new steady-state value and is used to uniquely identify the evolution of the system from its previous state to its newly established steady state (either faulty or normal). The four dynamic characteristic data (Pmax, tmax, Pmin, tmin) are used in the second term in such a way that the whole term is normalized and dimensionless. To have similar values of the hybrid parameter for a signal, both its new steady-state value and the four dynamic characteristic data should be the same, which is very rare. To illustrate the proposed approach based on the hybrid parameter, an example is presented in the remainder of this section. Consider a nonlinear system described by a state-space model as

Figure 2. Variations of the measured outputs versus time for the second scenario.

x1̇ = −2x1 + u1 + e−0.01tu2 x 2̇ = −0.02x12x 2 − x 2 0.5t e−0.1tu2 + 3

(9)

and 0.20, respectively, in the second faulty scenario. Hence, despite the similarity of the outputs for both cases, the hybrid parameters have completely distinct values which can uniquely reflect the system status in both scenarios.

where the initial states are x1(0) = 0.3 and x2(0) = 60, with u1 = 4 and u2 = 3 under normal conditions. Furthermore, the measured outputs are y1 = x1 y2 = x 2

(10)

5. FAULT DIAGNOSING SYSTEM BASED ON THE TRANSFORMATION OF DYNAMIC CHARACTERISTIC DATA

where they have been corrupted by zero-mean white noises. Faults 1 and 2 are defined as a decrease of 25% in u1 and an increase of 33% in u2, respectively. The performance of the proposed approach is illustrated for two faulty conditions. In the first scenario, fault 1 has occurred, whereas in the second scenario, faults 1 and 2 have occurred. The measured outputs for the two scenarios are shown in Figures 1 and 2, respectively.

Training a fault diagnosing neural network based on the hybrid parameter given by eq 8 can be extremely difficult (if not impossible) for a system whose measured variables differ by several orders of magnitude. The hybrid parameters might differ by several orders of magnitude relative to each other depending on the system state. In such a situation, the effects of the much smaller parameters as the inputs of the neural network trained are undermined or overlooked compared to those corresponding to inputs with higher values. On the other hand, increasing the synaptic weights corresponding to these inputs does not solve the problem, because the parameters with small values can have large values when the state of the system changes. To overcome this problem, logarithmic transformation is applied to force the neurons out of their saturation regions so the effects of small inputs are magnified appropriately. In fact, using logarithmic transformation of the hybrid parameters keeps the neurons of the hidden layer out of their saturation regions for all data points used in the training of the network. It should be noted that the dynamic characteristic data are used as the solution for the wrong diagnosis of faults having overlapping symptoms. Therefore, to increase the effect of the dynamic characteristic data, rather than using the logarithm of the hybrid parameters, we apply the logarithm of the dynamic characteristic data multiplied by the logarithm of the steady-state characteristic data as the input of the diagnosing system. This reasoning leads to the following definition for the inputs of the network

Figure 1. Variations of the measured outputs versus time for the first scenario.

These figures show the steady-state values of the two measured outputs in both scenarios are 1.5 and 66. Therefore, the conventional neural diagnoser that is trained by the steady-state data cannot distinguish these two faulty situations. However, the values of the hybrid parameters (IDs) used as the inputs of the proposed diagnosing network are 1.8 × 10−3 and 0.27, respectively, in the first faulty scenario and 6.7 × 10−3 12930



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⎛ v vi ,max − vi ,min i IDi = sign⎜⎜ ⎝ vi̅ ,normal vi ,normal,max − vi ,normal,min ⎞ ⎟⎟ vi̅ ,normal 2 max 2(ti ,max , ti ,min) ⎠ Pi ,maxPi ,minti ,maxti ,min

log

log

vi

vi ,max − vi ,min

vi̅ ,normal vi ,normal,max − vi ,normal,min Pi ,maxPi ,minti ,maxti ,min vi̅ ,normal 2 max 2(ti ,max , ti ,min)

(11)

The hybrid variables in eq 11 are analogous to the corresponding variables in eq 8. Because each part of the hybrid parameters might become either negative or positive, to make the transformation possible and yet distinguish negative and positive deviations from the normal values of the signal, the absolute value of each part is transformed, and the sign of the hybrid parameter is kept through the use of the sign function, whose value is +1 or −1 depending on the sign of its argument. Furthermore, the logarithmic transformation is multiplied by the sign of its argument to cover almost all points of the input space. By using such a hybrid parameter, one can reduce the dimension of the search space to its original value prior to the use of dynamic characteristic data (i.e., m). Such an approach can be easily generalized to design multiple-fault diagnosis systems for plants having undetectable faults based on steadystate characteristic data. To highlight the advantage of the transformation given by eq 11 over that given by eq 8, IDs were calculated for the example system discussed in section 4 using both transformations and are listed in Table 1. As can be seen from this table, the IDs based on eq 11 have the same order of magnitude, whereas the magnitudes of those calculated using eq 8 differ noticeably.

Figure 3. Schematic diagram of the TE process.

Table 2. Measured Variables of the TE Process no. of variable

ID1 first faulty scenario second faulty scenario

−3

1.8 × 10 6.7 × 10−3

log ID1

log ID2

0.27 0.20

0.62 0.48

−0.24 −0.53

22

2 3 4 5 6

D feed (stream 2) E feed (stream 3) A and C feed (stream 4) recycle flow (stream 8) reactor feed rate (stream 6) reactor pressure (stream 7) reactor level reactor temperature purge rate (stream 9) product separator temperature product separator level product separator pressure product separator underflow (stream 10) stripper level stripper pressure stripper underflow (stream 11) stripper temperature stripper steam flow compressor work reactor cooling water outlet temperature

23 24 25 26 27

separator cooling water outlet temperature component A in stream 6 component B in stream 6 component C in stream 6 component D in stream 6 component E in stream 6

28

component F in stream 6

29 30 31 32

component component component component

33 34

component E in stream 9 component F in stream 9

35

component G in stream 9

36 37 38

component H in stream 9 component D in stream 11 component E in stream 11

39 40 41

component F in stream 11 component G in stream 11 component H in stream 11

8 9 10 11 12 13

15 16 17 18 19 20 21

6. CASE STUDY To evaluate the performances of the proposed framework based on steady-state and dynamic data, a benchmark that contains most of the intricacies and challenges of a plant-wide system should be selected. Because the Tennessee Eastman process contains large numbers of measurements and manipulated variables and overlapping faults, it was used as the plant-wide benchmark for evaluating the performances of the proposed scheme. Downs and Vogel25,26 proposed the TE process simulator whose process flow diagram is shown in Figure 3. It includes five major unit operations: a two-phase reactor, a stripper, a separator, a compressor, and a condenser. Reactants A, C, D, and E, along with inert component B, produce products G and H and byproduct F. The control structure enforces constraints corresponding to safe process operation to avoid process shutdown.27 The measured variables of the TE process are presented in Table2. The measurements have been corrupted by zero-mean white noises. The plant has seven operating modes. The various

variable name

A feed (stream 1)

14

ID2

no. of variable

1

7

Table 1. IDs Calculated Based on Eqs 8 and 11

variable name

A in stream 9 B in stream 9 C in stream 9 D in stream 9

disturbances that can occur during the process are listed in Table 3.

7. RESULTS AND DISCUSSION To demonstrate its effectiveness, the proposed scheme has been applied to the TE process for fault detection. In subsection 7.1, the selected faults and their interactions are presented. The results of implementation of the proposed steady-state identification method and diagnosis of the system based on static and dynamic characteristic data and the transformation of dynamic characteristic data are presented in subsections 7.2−7.4, respectively. 7.1. Selected Faults and Their Interactions. He et al.28 suggested 11 faults covering all types of disturbances. These faults were divided into four groups based on the good representation of overlapping data, as indicated in Table 4. 12931



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Table 3. Available Disturbances in the TE Process case

disturbance

type

1 2 3 4 5 6 7 8

A/C feed ratio, B composition constant B composition, A/C ratio constant D feed temperature Reactor cooling water inlet temperature Condenser cooling water inlet temperature A feed loss C heater pressure loss-reduced availability A, B, C feed composition

9

D feed temperature

10

C feed temperature

11

reactor cooling water inlet temperature

12

condenser cooling water inlet temperature

13 14 15 16−20 21

reactor kinetics reactor cooling water valve condenser cooling water valve unknown valve for stream 4 fixed at the steady-state position

step step step step step step step random variation random variation random variation random variation random variation slow drift sticking sticking unknown constant

Table 4. Selected Faults in Four Groups group 1

group 2

group 3

group 4

fault 3 fault 4 fault 11




Various combinations of faults belonging to group 3 are such that there is less interaction among the occurring faults.28 Because fault 9 exists in both the third and fourth groups, omission of the third group does not affect the results of the performance evaluation. Therefore, in this study, group 3 was not considered in the performance evaluation of the proposed framework, and the remaining three groups (groups 1, 2, and 4), in which the percentages of overlapping data were higher than in group 3, were selected. The selected groups contain nine faults. In addition, group 2 has more overlaps among its faults and also between its faults and the faults belonging to other groups. This fact is illustrated in Figure 4. A multidimensional figure must be employed to investigate the effects of faulty conditions on all measured variables of the process owing to the large number of measured variables. Therefore, the average normalized values of the measured variables were defined to compare the effects of these variables through a two-dimensional figure. The difference between the mean and maximum values of a measured variable divided by the difference between the maximum and minimum values is defined as the average normalized value of the measured variable. Figure 4a shows a plot of the average normalized values of the measured variables when faults 3, 4, and 8 and faults 3, 11, and 8 occur. Figure 4b shows the average normalized values of the measured variables when faults 8 and 12; faults 8 and 15; and faults 8, 12, and 15 occur. Although 123 (41 × 3) distinct points must be shown in Figure 4b under different prevailing faulty situations, most of the points representing various measurements are nearly or strictly coincident, which shows overlapping symptoms caused by

Figure 4. Interactions between fault 8 and the faults in groups (a) 1, (b) 2, and (c) 4.

different faults occurring in the TE process. Figure 4c shows the average normalized values of the measured variables when faults 9, 14, and 8 and faults 9 and 8 occur. Figure 4 exhibits the interactions between fault 8 and the faults belonging to fault groups 1 and 4. All combinations of six faults (single to sextuple) that exist in groups 1 and 2 and groups 1 and 4 were studied to evaluate the performance of the proposed strategy 12932



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for fault diagnosis. There are 136 various concurrent faults in these groups. To cover the combinations of faults in groups 1, 2, and 4, a pair of faults having more interactions with each other was selected from each of these groups. Similarly to the previous illustrations, the interactions between faults in the three groups (1, 2, and 4) were investigated. The results of this investigation shows that faults 3 and 4 in group 1, faults 8 and 15 in group 2, and faults 9 and 14 in group 4 have more overlaps and were selected as pairs of faults. Therefore, combinations of these six faults (double to sextuple) were also added to the 136 various concurrent faults in the TE process. 7.2. Implementation of the Proposed Steady-State Identification Method. To recognize the steady state under both normal and abnormal modes, selection of the threshold criteria should be generalized. For instance, the behaviors of the second measured variables in normal mode and upon the occurrence of fault 8 are shown in Figure 5.

Figure 6. Variations of the second measured variable with time when faults 8 and 15 occur in the TE process.

vector was fixed as the vector containing the elements that were the maxima of the corresponding elements of the obtained threshold vectors. In the TE process, because the sampling times of various signals do not differ by even an order of magnitude (e.g., 0.1 and 0.25 h), the values of Ks for various signals were assumed to be the same. The sampling time for collecting data was set to 0.25 h. The value of Ks was chosen through an ad hoc iterative manner. Because the plant usually reaches its steady state in approximately 8 h (which contains 32 samples of the measurements), one could use this value to obtain the initial estimate for Ks. As mentioned previously, large values of Ks increase both the computational demands and the duration after which the fault diagnosis algorithm can be triggered, which is not desired. On the other hand, small values of Ks can lead to false detection of steady-state conditions, giving poor diagnosis results. Hence, it seems that there is an optimum value for Ks, which can be obtained by halving the value of Ks for which steady-state detection under various conditions is successful. The halving procedure of Ks is continued until steady-state detection fails. The minimum of Ks at which such detection for various conditions is successful is chosen as the optimum value of Ks. This procedure led to a value of 8 as the optimum value of Ks for the TE process. The obtained values of Ks and the threshold vector resulted in consistent and reliable detection of the steady states under various operating conditions. 7.3. Implementation of the Proposed Scheme Based on Static and Dynamic Characteristic Data. As stated earlier, the TE process, as a standard benchmark, was selected for evaluating the effectiveness of the proposed scheme. As can be seen from Table 2, the number of measured variables is 41, and the number of selected faults is 6. Hence, the network that can be used for fault diagnosis should have 41 and 6 neurons in its input and output layers, respectively. As mentioned previously, the number of hidden layers and their corresponding neurons can be found by trial and error. First, a network based on steady-state data was designed. For this network, one hidden layer was considered, and the appropriate number of hidden neurons was found to be 22, which means that increasing the number of hidden-layer neurons above 22 did not improve the network efficiency noticeably. A schematic diagram of the proposed network is shown in Figure 7. A total

Figure 5. Behaviors of the second measured variable in various situations (normal mode and occurrence of fault 8).

As can be seen in Figure 5, the steady conditions are not fixed and change from one situation to another. Therefore, the steady-state conditions of each case should be evaluated according to its corresponding situation. If the threshold vector is evaluated based only on normal operating conditions, then the proposed approach cannot recognize the steady state in a faulty situation. However, the threshold vector should be chosen such that it can be used for various operating conditions, including both normal and faulty operations. Analysis of the operating data of the plant shows that the threshold vector can be obtained based on the normal operating conditions along with the cases in which fault 3, fault 8, or fault 9 has occurred. Each of these faults represents its corresponding group. These representatives were obtained based on a sensitivity analysis of various alternatives in each group, and they were selected because the threshold vectors are more sensitive to these faults than to the other alternatives in each group. For instance, as Figure 6 shows, assuming that the threshold vector is determined based on the cases in which fault 15 of group 2 has occurred results in incorrect steady-state detection, whereas the determined thresholds based on fault 8 can correctly recognize the steady-state conditions. After all threshold vectors had been determined, the final threshold 12933



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to the effects caused when fault 8 is the only fault occurring in the system. To overcome this restriction, a neural network with input and output layers similar to those of the previous network was used for fault diagnosis in the presence of multiple concurrent faults. The network had one hidden layer with 18 neurons, which was obtained by trial and error as explained earlier. This network was trained by dynamic characteristic data of the TE process. It should be noted that the transfer functions of the neurons in this network were exactly the same as those used in the network trained by steady-state data. One should also note that the structure of the network with dynamic characteristic data as the inputs was simpler than that of the network trained by steady-state data. This shows that using dynamic characteristic data facilitates fault diagnosis when the system is subjected to multiple concurrent faults. The error trends of various network diagnosers (i.e., networks based on steady-state data and dynamic characteristic data) are presented in Figure 9.

Figure 7. Structure of the feed-forward neural network used in fault diagnosis.

of 10000 data points were generated, of which 25% were used for testing and the remainder were used for training. All weights and biases were initialized to small random values at the beginning of training. Back-propagation with conjugate gradient was used as the training algorithm. The input vector to the ANN was normalized, with elements (i.e., normalized measured variables) varying between −1 and 1, whereas the outputs of the ANN were the binary variables representing the occurrence of a fault (for a corresponding value of 1) or the lack of fault occurrence (for a corresponding value of 0). The transfer functions of neurons in the hidden and output layers were chosen to be “tan-sigmoid” and “log-sigmoid”, respectively. Figure 8 shows the minimum output of the proposed neuromorphic diagnoser based on steady-state data for various cases of multiple faults.

Figure 9. Errors of the proposed neuromorphic diagnoser based on the steady-state and dynamic characteristic data versus epochs.

Figure 9 shows that the minimum errors of the networks trained by steady-state data and by dynamic characteristic data did not ultimately fulfill the minimum acceptable error threshold. However, the network trained by the dynamic characteristic data gave less error than the network trained by the steady-state data. 7.4. Implementation of the Diagnosing System Based on the Transformation of Dynamic Characteristic Data. Because the network trained by dynamic characteristic data could not satisfy the minimum desired error threshold, a network trained by transformed dynamic characteristic data was designed. Similarly to the previous network, it had one hidden layer with 16 neurons. In addition, the transfer functions of the neurons in this network were exactly the same as those of the previous networks. Figure 10 shows the error trend of this network. As can be seen, the network error trained by the logarithmically transformed dynamic data reached the desired threshold (i.e., 1 × 10−3). For the purpose of fault diagnosis, the output threshold was set to 0.75. In Figure 11, the minimum values of the outputs of neurons corresponding to the faults occurring in the system are shown. As this figure shows, there were some cases in which the output

Figure 8. Minimum output of the neuron corresponding to correctly diagnosed faults for the proposed neuromorphic diagnoser based on steady data.

As shown in Figure 8, the network trained by the steady-state characteristic data was able to detect the single faults, but it could not correctly diagnose various multiple faults. This is because the effects of the combination of faults 8 and 15 are very similar to the effects of the combination of faults 8, 12, and 15, as shown in Figure 4a. This similarity can also be seen in Figure 4b,c. Unfortunately, there is a significant problem in dealing with faults coupled with fault 8. This is due to the nature of fault 8, whose coupling with some specific faults (i.e., faults 12 and 15) leads to effects on measured variables similar 12934



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Figure 12. Performances of various neuromorphic diagnosers. Figure 10. Error performance of the proposed neuromorphic diagnoser versus epochs.

consisted of 16 neurons) than the structure of its counterparts in the previous case. Table 5 compares the training results of the three methods based on the steady-state data, the dynamic characteristic data, Table 5. Comparison of Training Results of the Proposed Methods type of proposed method steady data dynamic characteristic data transformation of dynamic characteristic data

number of neurons: input/hidden/output

time of traininga (%)

0.126 0.017

41/22/6 41/18/6

232 108

1 × 10−3

41/16/6

0

error goal (MSE)

a

Basis of the comparison is the transformed dynamic characteristic data (last row of the table).

and the transformation of the dynamic characteristic data. These results indicate that the neural network based on the transformed dynamic characteristic data gave less error with fewer of hidden neurons than the other alternatives. He et al.28 presented a new fault diagnosis approach with variable-weighted kernel Fisher discriminant analysis that can diagnose up to three multiple faults for the TE process, whereas the approach proposed in this study can diagnose various combinations of six concurrent faults.

Figure 11. Minimum neuron output corresponding to correctly diagnosed faults for various networks.

of the network for a fault that actually occurred in the system was about 0.3, which represents the false diagnosis of these faults. Such cases did not occur for the diagnoser using logarithmically transformed dynamic characteristic data, whereas the diagnosers based on steady-state or dynamic characteristic data severely suffered from this shortcoming. This result is demonstrated in Figure 12, which compares the performances of various neuromorphic diagnosers based on the percentage of correctly diagnosed faults. In other words, the network whose inputs were logarithmic transformations of dynamic data was able to diagnose all faults, from single to sextuple, correctly and outperformed the other alternatives. The results presented in Figures 11 and 12 reveal the capability of the proposed framework for multiple-fault diagnosis. The interesting point confirming the rationale behind the transformation of the dynamic characteristic data is the fact that the structure of the network that could successfully accomplish fault diagnosis was simpler (its hidden layer

8. CONCLUSIONS In plant-wide systems, because of system complexity and overlapping symptoms, conventional neural networks operating based on steady-state characteristic data are not usually capable of diagnosing multiple concurrent faults. A neuromorphic framework based on augmented input containing steady-state characteristic data along with newly defined dynamic characteristic data was proposed and used as a plant-wide fault diagnoser. Because fault diagnosis should be performed when the system is at its steady state, a new algorithm for the detection of system steady states was also proposed. The performances of neuromorphic diagnosers based on the augmented inputs were compared with that of the conventional neuromorphic diagnostic system whose inputs are steady-state characteristic data. The comparison shows that the proposed method 12935



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(15) Behbahani, R.M..; Jazayeri-Rad, H.; Hajmirzaee, S. Fault Detection and Diagnosis in a Sour Gas Absorption Column Using Neural Networks. Chem. Eng. Technol. 2009, 32 (5), 840. (16) Vedam, H.; Venkatasubramanian, V. PCA-SDG based process monitoring and fault diagnosis. Control Eng. Pract. 1999, 7, 903. (17) Chang, S. Y.; Lin, C. R.; Chang, C. T. A fuzzy diagnosis approach using dynamic fault trees. Chem. Eng. Sci. 2002, 57, 2971. (18) Detroja, K. P.; Gudi, R. D.; Patwardhan, S. C. Plant-wide detection and diagnosis using correspondenceanalysis. Control Eng. Pract. 2007, 15, 1468. (19) Tamura, M.; Tsujita, S. A study on the number of principal components and sensitivity of fault detection using PCA. Comput. Chem. Eng. 2007, 31, 1035. (20) Verron, S.; Tiiplica, T.; Kobi, A. Fault detection and identification with a new feature selection based on mutual information. J. Process Control 2008, 18, 479. (21) Vachtsevanos, G.; Lewis, F.; Roemer, M.; Hess, A. B. Intelligent Fault Diagnosis and Prognosis for Engineering Systems; Wiley: New York, 2006. (22) Gomm, J. B.; Weerasinghe, M.; Williams, D. Diagnosis of process faults with neural networks and principal component analysis. Proc. Inst. Mech.Eng. E 2000, 214, 131. (23) Liu, W. An extended Kalman filter and neural network cascade fault diagnosis strategy for the glutamic acid fermentation process. Artif. Intell. Eng. 1999, 13, 131. (24) Kim, M.; Yoon, S. H.; Domanski, P. A.; Payne, W. V. Design of a steady-state detector for fault detection and diagnosis of a residential air conditioner. Int. J. Refrig. 2008, 31, 790. (25) Downs, J. J.; Vogel, E. F. A plant-wide industrial process control problem. Comput. Chem. Eng. 1993, 17, 245. (26) McAvoy, T. J.; Ye, N. Base control for the Tennessee Eastman problem. Comput. Chem. Eng. 1994, 18, 383. (27) Golshan, M.; Boozarjomehry, R. B.; Pishvaei, M. R. A new approach to real time optimization of the Tennessee Eastman challenge problem. Chem. Eng. J. 2005, 112, 33. (28) He, X. B.; Yang, Y. P.; Yan, Y. H. Fault diagnosis based on variable-weighted kernel Fisher discriminant analysis. Chemom. Intell. Lab. Syst. 2008, 93, 27.

outperforms the conventional neuromorphic diagnoser for the detection of multiple concurrent faults. It was also shown that the proposed scheme can correctly diagnose various combinations of six concurrent faults of the TE process (from two to six simultaneous faults). This achievement reflects the major advantage of the proposed approach, which is its ability to perform fault diagnosis in situations where multiple concurrent faults with overlapping symptoms have occurred. However, the main restriction of the proposed approach is its dependence on plant data when various faults have occurred. It should be noted that this restriction is not serious, because most plants are monitored and controlled based on powerful supervisory control and data acquisition (SCADA) systems in which the logs and trends of signals for various situations are gathered and archived quite easily.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +98-21-66164599. Fax: +98-21-66022853. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Neuromorphic Multiple-Fault Diagnosing System Based on Plant

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