NEURAL NETWORK APPROACH FOR SENSOR FAULT DETECTION AND ACCOMMODATION ZHENG JIE NATIONAL UNIVERSITY OF SINGAPORE 2004 NEURAL NETWORK APPROACH FOR SENSOR FAULT DETECTION AND ACCOMMODATION ZHENG JIE (M.Eng, B.Eng, XJTU) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2004 Acknowledgement During my years as a graduate student in National University of Singapore, I have benefited from interactions with many people whom I am deeply appreciate I would like to express my utmost gratitude to those who have guided and helped me throughout the course First of all, I am indebted to my supervisor, Dr Tan Woei Wan, for her unfailing guidance and encouragement Dr Tan’s successive and endless enthusiasm in research arouse my interests in various aspects of control engineering Special appreciation are also extend to all my colleagues in the Advanced Control Technology Laboratory I would like to thank Yang Yongsheng, Lo Chang How and Ge Pei for their invaluable comments encouragements and advice, as well as all the exchange of information in the lab I deeply appreciate the Research Scholarship granted by National University of Singapore which certainly helped to relieve my financial burden Without the grant, I would never have been able to further my studies Last but not least, I would like to thank my families for their endless love and encouragement i Contents Acknowledgement i Contents ii Summary v List of Figures vii Introduction 1.1 Background and motivation 1.2 Literature survey 1.3 Contributions 1.4 Organization of thesis MLP based approach for sensor fault detection and accommodation 11 2.1 Fault tolerant control using neural network 11 2.2 MLP based sensor fault detection and accommodation scheme 12 2.3 Simulation results for the MLP based sensor fault detector and accom- 2.4 modator 15 2.3.1 Modelling error of MLP 17 2.3.2 Fault detection and accommodation using MLP with TDL 18 Conclusion 20 Elman based approach for sensor fault detection and accommodation 21 ii 3.1 Elman network structure and dynamic training algorithm 21 3.1.1 Elman network structure 21 3.1.2 Training algorithm for dynamic mapping using Elman network 23 3.2 Simplified version of DBP algorithm 30 3.3 Simulation on Elman based sensor fault detection and accommodation 32 3.3.1 Modelling error of Elman network 33 3.3.2 Static Sensor Fault detection and accommodation using Elman network 3.3.3 33 Dynamic Sensor Fault detection and accommodation using Elman network 36 3.4 Discussions 37 3.5 Conclusion 41 Modelling of transportation delay 4.1 42 Modelling of second-order system with transportation delay using original Elman network 42 4.2 Modification of Elman network structure and the corresponding algorithm 46 4.3 Modelling system with transport delay using modified Elman network 4.4 Sensor fault detection and accommodation for process with transport de- 4.5 49 lay using modified Elman network 51 Conclusion 53 Neural network based sensor fault detection and accommodation on a liquid level system 54 5.1 Introduction of the Liquid Level system 55 5.2 Experimental verification of sensor fault tolerant approach based on Elman network 57 5.2.1 58 Elman network Model of the liquid level system iii 5.2.2 Experiment results on static sensor fault tolerant by Elman network approach 5.2.3 Experiment results on dynamic sensor fault tolerant by Elman network approach 5.3 5.4 67 Experimental verification of sensor fault tolerant approach based on MLP network 68 5.3.1 Modelling error of MLP network 69 5.3.2 Fault detection and accommodation using MLP network on coupled tank 71 Conclusion 72 Conclusions 6.1 63 73 Suggestions for future work 74 Bibliography 76 Appendix 79 iv Summary In most control systems, measuring systems are not only used to obtain basic plant information but also to provide feedback signals so that control actions can be computed The accuracy of the metrology system is a key element in such systems Any sensor fault will degrade the performance of the control system Hence, there is a need to detect and compensate for sensor fault conditions This report seeks to investigate if a neural network based fault detection and accommodation scheme is able to limit the influence of sensor faults on the performance of a nonlinear dynamic process The main component in the proposed approach is a neural network model of the process First, the possibility of using the well-known multi-layer-perceptron (MLP) with tapped delay line (TDL) memory was examined Although the TDL method equips the MLP with the capability to model a dynamic system, the simulation results show that the approach failed to compensate for sensor fault Furthermore, simulation results indicated that an Elman network with inputs generated by a TDL also failed to accommodate the sensor fault Since the Elman network has recurrent connections and is able to model dynamic systems, it is conjectured that the cause of failure is probably the TDL memory Motivated by the need to eliminate the TDL, one contribution of this report is developing an Elman network based fault detection and accommodation approach which can model the dynamic process without the utilization of a TDL memory Leveraging on the dynamic recurrent connections inside the Elman network, a dynamic system can be modelled directly by employing the simplified Dynamic Backpropagation (DBP) algorithm proposed in this report The simulation result obtained from a SISO v plant suggests that the proposed fault detection and accommodation approach is able to compensate for the sensor fault immediately after it is introduced To model the real dynamic process accurately, the Elman network based approach needs the ability to model the transport delay As the Elman network does not have this capability, the second contribution of this report is employing a modified Elman network with delay blocks and developing corresponding algorithm to learn the delay Simulation results on a second order system with transport delay show that the delay was learned accurately Since the purpose of learning transport delay is to gain the ability to detect and accommodate for sensor fault on systems with transport delay, simulation was also completed to examine the performance of the Elman network fault tolerant based control scheme Results show that both static and dynamic sensor fault were compensated successfully Finally, experiments on a nonlinear coupled-tank system were implemented to demonstrate the effectiveness of the Elman network based fault accommodation scheme An Elman network was successfully trained by the simplified DBP algorithm using data generated from the experimental setup Sensor fault tolerant experimental results on static or dynamic sensor fault demonstrate the feasibility and effectiveness of the proposed scheme It can be concluded that the Elman network based approach for maintaining the correct measurement regardless of the sensor fault is promising vi List of Figures 2.1 The basic idea of fault detection and accommodation by neural network 12 2.2 Structure of MLP 13 2.3 Block diagram of the sensor 15 2.4 Testing of dynamic modelling by TDL method 17 2.5 Modelling error of dynamic modelling by TDL method 18 2.6 Fault detection by TDL 19 2.7 Fault accommodation by TDL 20 3.1 Structure of Elman network 22 3.2 Structure of modified Elman network with self-feedback link 24 3.3 Recall result of Elman trained by DBP algorithm 28 3.4 Difference between Elman and system output 28 3.5 The values of ∂xl (k) x (k−1) ∂wi,j in epoch of 104 29 3.6 The values of ∂xl (k) x (k−1) ∂wi,j in epoch of 104 31 3.7 Block diagram of the sensor 32 3.8 Testing of dynamic modelling by Elman network trained 33 3.9 Residue signal generated by Elman network trained 34 3.10 Residue generated by the fault detection module 35 3.11 Control performance before and after 35 3.12 Difference between fault-free 36 3.13 Residue generated by the fault detection module 37 3.14 Control performance before and after 38 vii 3.15 Difference between fault-free 38 3.16 Testing of dynamic modelling by Elman with TDL method 39 3.17 Modelling error of dynamic modelling by Elman with TDL method 40 3.18 Residue signal generated by Elman network with TDL 40 3.19 Fault accommodation using Elman with TDL 41 4.1 Error decreasing curve during 1000 epoches of training 44 4.2 Testing of dynamic modelling by Elman network 44 4.3 Architecture of original Elman network 45 4.4 Architecture of Elman Network with time delay box 46 4.5 Testing of dynamic modelling by adaptive time delay Elman network 49 4.6 Modelling error of adaptive time delay DBP 50 4.7 Adaptation of transportation delay 50 4.8 Residue generated by the fault detection module 52 4.9 Control performance before and after 52 4.10 Difference between fault-free 53 5.1 Front view of coupled-tank control apparatus PP-100 56 5.2 Back view of coupled-tank control apparatus PP-100 56 5.3 Connecting the coupled tank control apparatus as two SISO plants 58 5.4 Input of training samples collected from experiment 59 5.5 Output of training samples collected from experiment 60 5.6 Overtraining phenomenon 60 5.7 The training and validation error for the first 1000 epoch 63 5.8 The training and validation error for the later part of the training process 64 5.9 Testing of dynamic modelling by Elman network trained 64 5.10 Modelling error of Elman network on coupled tank 65 5.11 Residue generated by the fault detection module in coupled tank experiment 66 5.12 Comparison of control performance viii 66 Validation results after training is stopped 0.7 MLP System 0.6 Validation results 0.5 0.4 0.3 0.2 0.1 0 100 200 300 400 500 600 Time (second) 700 800 900 1000 Figure 5.16: Testing of dynamic modelling by MLP network trained using standard back propagation Difference between MLP and system 0.025 0.02 Modelling error (cm) 0.015 0.01 0.005 −0.005 −0.01 −0.015 100 200 300 400 500 600 Time (second) 700 800 900 1000 Figure 5.17: Modelling error of MLP network on coupled tank using standard back propagation 70 square is 4.013e-5 which is comparable with the modelling error of the Elman network 5.3.2 Fault detection and accommodation using MLP network on coupled tank The MLP network trained by the standard back propagation algorithm is then used online to generate an estimated liquid level reading that is compared with the actual sensor reading in order to ascertain if the sensor is functioning properly Since the modelling error of the MLP network is comparable with that of the Elman network, the threshold used in the Elman network approach, which is 1.1, is also applicable to the MLP network based approach When the fault is introduced by multiplying the sensor reading by 1.6 at time 600s, the sensor reading changes suddenly It may be observed from Figure 5.18 that the residue signal exceeds the threshold after the faulty sensor is introduced Once the Residue generated by MLP network 0.5 Residue (cm) −0.5 −1 −1.5 −2 −2.5 −3 −3.5 200 400 600 Time (second) 800 1000 1200 Figure 5.18: Residue generated by the fault detection module in coupled tank experiment threshold is exceeded, the output of the Elman network is used as the feedback signal Figure 5.19 shows the performance of the closed-loop system before and after the oc71 currence of a fault It is evident that the proposed scheme failed to compensate for the fault Comparison of control performance before and after the fault accommodation is performed 40 no compensation with compensation 35 Liquid Level (cm) 30 25 20 15 10 200 400 600 Time (second) 800 1000 1200 Figure 5.19: Comparison of control performance before and after fault accommodation is performed 5.4 Conclusion This chapter presented experimental results obtained using the Elman network approach to detect and compensate for the sensor fault A nonlinear Elman network is adopted and changes to the training procedure was made in order to obtain a better model of the liquid level system The experimental fault accommodation results obtained when the sensor has static or dynamic fault show that the nonlinear Elman network based approach is able to detect the faulty liquid level sensor and successfully compensated for the fault Finally, the experimental result obtained using MLP based approach to detect and compensate for the sensor fault is presented The experimental results confirm the weakness of MLP based approach as explained in Chapter 72 Chapter Conclusions From the literature survey conducted in Chapter it is noted that a considerable amount of effort have gone into field of fault detection and accommodation Methods for achieving fault tolerant system either by hardware or by software have been proposed A considerable amount of the recent research on fault tolerant control are neural network based approaches A common feature of these approaches is the requirement to create an accurate dynamic model for the system Since the MLP is a well-studied neural networks and the TDL memory will enable it to model dynamic systems, a scheme that utilises a MLP with TDL memory for sensor fault detection and accommodation was examined in Chapter It is shown that the MLP with TDL based approach is able to detect the fault occurrence However, it failed to compensate for the fault Since an approach based on a static neural network failed, dynamic neural networks were considered A scheme that replaces the MLP with a recurrent network was proposed by Yong et al (1999) The dynamic characteristics of the Elman network are the reason why researchers use it to model the dynamic systems However, the TDL method was still used to generate the input signals of the network Simulation results presented in Chapter suggest that the scheme proposed by Yong et al (1999) is no different from the MLP with TDL method as it failed to accommodate the fault Since both schemes use the TDL method, it is reasonable to conclude that the utilization of TDL memory is the cause of the failure Further analysis and simulation study were conducted to investigate the influence of the TDL memory on dynamic system modelling and the re73 sults confirm that the utilization of TDL memory will degrade the network performance once the fault occurs This also help to explain the phenomena identified by Yu et al (1999) As a recurrent neural network performs self-feedback of its internal states, it can model a dynamic system without the need of TDL Therefore, an Elman network based fault detection and accommodation scheme that does not employ the TDL memory was implemented As the scheme relies on the accuracy of the Elman network model, the training of the Elman network then become an important area of the research Since the traditional back propagation algorithm failed to train the Elman network, a dynamic back propagation algorithm (DBP) was introduced to learn the weights Furthermore, since the DBP algorithm could cause the weights of the Elman network to blow up during the training process, a simplified DBP algorithm was developed that solved the problem The simulation results obtained from a SISO plant in Chapter suggest that the Elman network based approach can detect the sensor fault and then, successfully performed fault accommodation As the Elman network cannot learn the transport delay in system, the structure of the Elman network was modified such that the input layer contains delay blocks The corresponding algorithm to learn the delay is also provided After the simulation study and analysis, experimental research on static and dynamic sensor fault tolerant control was conducted on a liquid level system The experimental results presented in Chapter demonstrate that the Elman network based sensor fault detection and accommodation scheme is able to provide good performance on a practical non-linear system Meanwhile, the limitation of the fault tolerant scheme that utilises MLP with TDL memory is also verified by results obtained from experiments on the liquid level system 6.1 Suggestions for future work This project seeks to develop an Elman network based fault detection and accommodation scheme to maintain good control performance even when the sensor is faulty The experimental result obtained in this thesis is obtained using a SISO direction-independent 74 nonlinear system Since a lot of process have direction-dependent characteristics, e.g heating system, it is meaningful to extend the fault detection and accommodation scheme based on Elman network to direction-dependent systems Another area of work that may be conducted is to develop an Elman network based fault tolerant scheme for MIMO systems For MIMO systems which have only linear coupling, a MISO Elman network model may be implemented by dividing the MISO system into several SISO systems and then, using the existing SDBP algorithm to train the NN If the process exhibits nonlinear coupling, then a new method or scheme is probably needed Another drawback of the current fault detection and accommodation scheme is that it cannot distinguish between faults that occur in the sensor and the process Therefore, it would be useful to develop a method that is able to distinguish between faults in the various components of a closed-loop system The main advantage of using neural network is that it can model nonlinear systems Chapter presents experimental results that demonstrate that faults in a nonlinear liquid level system can be handled by the proposed Elman network approach In order to further explore the advantages offered by the neural network, research and experiments may be conducted to compare the performance of the proposed scheme against fault tolerant techniques developed based on linear system theory 75 Bibliography A.Berniert, M.Dapuzzo and L.Sansone (1994) A neural network approach for identification and fault diagnosis on dynamic systems IEEE Transactions on Instrumentation and 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Proceedings of the IEEE 78 78, 1550–1560 Williams, R.J and J.Peng (1990) An efficient gradient-based algorithm for on-line training of recurrent network trajectories Neural Computation 2, 490–501 Xuemei, Ren and Fei Shumin (2000) Recurrent neural networks for identification of nonlinear systems Proceedings of the 39th IEEE conference on decision and control, sydney, australia pp 2861–2866 Yong, Liu, Shen Yi and Hu Hengzhang (1999) A new method for sensor fault detection, isolation and accommodation IMTC/99 Proceedings of the 16th IEEE Instrumentation and Measurement Technology Conference 1, 488–492 77 Yu, D.L., J.B Gomm and D.Williams (1999) Sensor fault diagnosis in a chemical process via rbf neural networks Control Engineering Practice 7, 49–55 78 Appendix File used to initialize the training of Elman network k = 0; % index of training sample trainerror = 0; % def ine training error epoch = 1; % def ine epochs mt = 0.1; % def ine momentum f actor T H = zeros(10000, 1); % def ine training error history array num sample = 100; % number of training samples num hidden = 2; % number of neuron in hidden layer of Elman num output = 1; % number of neuron in output layer of Elman num input = 1; % number of neuron in context layer of Elman num context = num hidden; E = zeros(num sample, 1); % Def ine Cost f unction W y = zeros(num hidden, num sample); % weights f rom hidden layer to output layer W u = zeros(num hidden, num sample); % weights f rom input layer to context layer W x = zeros(num hidden, num context, num sample); % weights of hidden layer % variable related to training samples x = zeros(num hidden, num sample); % output value of hidden layer u = zeros(num sample, 1); % input value to the Elman (training input) yd = zeros(num sample, 1); % teaching signal value (training output) y = zeros(num sample, 1); % output value f rom the Elman v = zeros(num hidden, num sample); % inputs value to the hidden layer % variable related to validation samples 79 x v = zeros(num hidden, num sample); % output value of hidden layer u v = zeros(num sample, 1); % input value to the Elman (training input) yd v = zeros(num sample, 1); % teaching signal value (training output) y v = zeros(num sample, 1); % output value f rom the Elman v v = zeros(num hidden, num sample); % inputs value to the hidden layer f v = zeros(num hidden, 1); % dif f rential of hidden layer dE dW y = zeros(num hidden, 1); % def ine gradient of output layer dE dW u = zeros(num hidden, 1); % def ine gradient of input layer dE dW x = zeros(num hidden, num context); % def ine gradient of hidden layer dx dW x = zeros(num hidden, num hidden, num context, num sample); % variable will be used in DBP algorithm %IN IT IALIZE W EIGHT S W u(:, 1) = random( unif , −0.5, 0.5, num hidden, 1); W y(:, 1) = random( unif , −0.5, 0.5, num hidden, 1); W x(:, :, 1) = random( unif , −0.5, 0.5, num hidden, num hidden); validationerror = 0; % def ine validation error lr = 0.1; % def ine learning rate %Scale the training samples to [−1, 1] u = input(1 : num sample)/10; yd = temp1(2 : num sample + 1) ∗ 10; File used to training Elman network using SDBP algorithm while epoch W u(:, 1) = W u(:, num sample); W y(:, 1) = W y(:, num sample); f or i = : num hidden f or j = : num hidden 80 W x(i, j, 1) = W x(i, j, num sample); end end end %F eedf orward part of back propagation algorithm, calculate the %value in each layer of Elman network f or i = : num hidden v(i, 1) = W u(i, 1) ∗ u(1); x(i, 1) = tansig(v(i, 1)); end y(1) = 0; f or i = : num hidden y(1) = y(1) + W y(i, 1) ∗ x(i, 1); end f or k = : num sample f or i = : num hidden v(i, k) = W u(i, k − 1) ∗ u(k); f or j = : num hidden v(i, k) = v(i, k) + W x(i, j, k − 1) ∗ x(j, k − 1); end x(i, k) = tansig(v(i, k)); end y(k) = 0; f or i = : num hidden y(k) = y(k) + W y(i, k − 1) ∗ x(i, k); end 81 E(k) = 0.5 ∗ (yd(k) − y(k))2 ; % Cost f unction %Calculate gradient corresponding to input and output layer f or i = : num hidden dE dW y(i) = −(yd(k) − y(k)) ∗ x(i, k); f v(i) = dtansig(v(i, k), x(i, k)); dE dW u(i) = −(yd(k) − y(k)) ∗ W y(i, k − 1) ∗ f v(i) ∗ u(k); %update weights at input and output layer W u(i, k) = W u(i, k − 1) − lr ∗ dE dW u(i) + mu ∗ (W u(i, k − 1) − W u(i, k − 2)); W y(i, k) = W y(i, k − 1) − lr ∗ dE dW y(i) + mu ∗ (W y(i, k − 1) − W y(i, k − 2)); %Calculate gradient corresponding to hidden layer f or j = : num hidden dx dW x(i, i, j, k) = f v(i)∗x(j, k−1)+f v(i)∗W x(i, i, k−1)∗dx dW x(i, i, j, k− 1); dE dW x(i, j) = −(yd(k) − y(k)) ∗ W y(i, k − 1) ∗ dx dW x(i, i, j, k); W x(i, j, k) = W x(i, j, k − 1) − lr ∗ dE dW x(i, j) + mu ∗ (W x(i, j, k − 1) −W x(i, j, k − 2)); end end end %calculate training error e = yd − y; trainerror = sqrt(mse(e)) epoch = epoch + 1; %calculate validation error f or i = : num hidden v v(i, 1) = W u(i, 1) ∗ u v(1); x v(i, 1) = tansig(v v(i, 1)); 82 end y v(1) = 0; f or i = : num hidden y v(1) = y v(1) + W y(i, 1) ∗ x v(i, 1); end f or k = : num sample f or i = : num hidden v v(i, k) = W u(i, k − 1) ∗ u v(k); f or j = : num hidden v v(i, k) = v v(i, k) + W x(i, j, k − 1) ∗ x v(j, k − 1); end x v(i, k) = tansig(v v(i, k)); end y v(k) = 0; f or i = : num hidden y v(k) = y v(k) + W y(i, k − 1) ∗ x v(i, k); end end e v = yd v − y v; validationerror = sqrt(mse(e v)) %retrieve the smallest validation error point if validationerror < ref er W uf = W u; W yf = W y; W xf = W x; ref er = validationerror; end 83 %store the training error history T H(epoch, 1) = trainerror; V H(epoch, 1) = validationerror; if mod(epoch, 20) == save isbp.mat; end end 84 [...]... approach for sensor fault detection and accommodation 2.1 Fault tolerant control using neural network Neural networks have been widely used in fault detection applications Figure 2.1 shows the schematic diagram of a neural network based fault detection and accommodation scheme The neural network is trained by signals generated from the healthy system to create some kind of mapping between the input nodes and. .. thesis is as follows A fault tolerant control scheme using neural network was introduced in Chapter 2, followed by a MLP network based fault detection and accommodation scheme Simulation results showing the feasibility of using the MLP based fault tolerant scheme for sensor fault detection and accommodation of a SISO plant are presented Then, an Elman network based fault detection and accommodation scheme... second neural network classifier was also employed to isolate the sensor faults Experimental results on a chemical reactor process demonstrate the satisfactory 5 detection and isolation of the sensor faults Due to the weakness of static NN for fault detection and reconfiguration, Yong et al (1999) proposed a new method that uses dynamic neural networks for sensor fault detection, isolation and accommodation. .. fault detection and accommodation by neural network the type of neural network as well as the training algorithm should be chosen carefully The type of neural network in Figure 2.1 can be a MLP, a Radial Basis Networks (RBF)(Powell, 1985), an Elman network, a Jordan network (Jordan, 1986) and so on These neural networks are roughly classified into two categories: static neural networks and dynamic neural. .. the nonlinear Elman network based approach is able to detect the faulty liquid level sensor and successfully compensated for the fault The inability of the MLP plus TDL memory based scheme to provide fault tolerant control was also verified experimentally The research results shows that neural networks, especially the Elman network, is a good tool for sensor fault detection and accommodation 1.4 Organization... static neural network for fault accommodation 19 Figure 2.7: Fault accommodation by TDL 2.4 Conclusion The sensor fault detection and accommodation scheme, that comprises of a MLP with TDL memory is proposed in this chapter It is shown that dynamic mapping of plant and sensor can be achieved by incorporating TDL memory with a MLP Standard back propagation algorithm is used for training the MLP and a... where η is learning rate, ∆wiy (k),∆wiu (k) and ∆wi,j (k) can be determined 2.3 Simulation results for the MLP based sensor fault detector and accommodator In this section, the fault detection and accommodation results using a MLP with TDL memory are presented Figure 2.3 shows the sensor fault detection and accommodation scheme that consist of a MLP network and the TDL memory One category of processes... components The first step for achieving active fault- tolerance is fault detection The successful detection of a fault is followed by fault isolation, which is to locate a faulty component Finally, a reconfiguration mechanism is used to rearrange the system for achieving fault- tolerance Fault detection and fault tolerance systems can be implemented by intelligent hardware J.C.Yang and D.W.Clarke (1997) proposed... recurrent neural networks In this chapter, an Elman based approach for sensor fault detection and accommodation will be discussed Firstly, the architecture of Elman network is illustrated and an training algorithm to achieve dynamic mapping using Elman network is provided Then, a simplified training algorithm which requires less recursive substitutions is described Finally, an Elman based sensor fault detection. .. recurrent network instead of a static network The paper by Yong et al (1999) proposes a fault detection, isolation and accommodation scheme that employs an Elman network However, the inputs to the network are still derived from a TDL The use of past inputs and outputs to calculate the current outputs may cause the fault accommodation scheme to fail because faulty signals are fed to the neural network ... MLP based approach for sensor fault detection and accommodation 11 2.1 Fault tolerant control using neural network 11 2.2 MLP based sensor fault detection and accommodation. .. Chapter Elman based approach for sensor fault detection and accommodation In the previous chapter, a MLP based fault accommodation approach failed to compensate for a sensor fault It is conjectured... fault- free and uncompensated faulty and Difference between fault- free and compensated faulty faulty system output 3.3.3 Dynamic Sensor Fault detection and accommodation using Elman network Most