Neuro-Fuzzy Sensor Fault Diagnosis of an Induction Motor

In this paper, a neuro-fuzzy fault diagnosis scheme is presented and its ability to detect and isolate sensor faults in an induction motor is assessed. This fault detection and isolation (FDI) approach relies on a combination of neural modelling and fuzzy logic techniques which can deal effectively with nonlinear dynamics and uncertainties. It is based on a two step neural network procedure: a first neural network is used for residual generation and a second fuzzy neural network performs residual evaluation. Simulation results are given to demonstrate the efficiency of this FDI approach.


Introduction
The problem of fault detection and isolation (FDI) is a crucial issue for the safety, reliability and performance of industrial processes.
The usual approach to fault diagnosis is based on hardware redundancy (multiple sensors, actuators and components) and uses a voting technique to decide if a fault has occurred and to locate it among the redundant system elements (Frank 1990).Instead, the analytical redundancy FDI approach, also referred to as the model-based FDI approach, makes use of a mathematical model of the monitored system [ (Frank 1990).The task of model based diagnosis methods consists of detecting faults that may occur in the system and which can be additive or multiplicative in nature.
Basically the FDI procedure consists of two main steps: generation of residuals which should be useful ___________________________________________ *Corresponding author's e-mail: m.l.benloucif@gmail.comfault indicators, and residual evaluation which involves decision making.The model-based FDI approach which has received intensive attention uses mainly state and parameter estimation techniques (Frank 1990).Model based FDI performance is directly related to the accuracy of the mathematical model of the monitored system.The effect of model uncertainties, disturbances and noise is therefore a key issue in model based fault diagnosis.
The main design requirements of model based fault diagnosis procedures are thus concerned with the problems of robustness with respect to model uncertainties and enhancement of sensitivity to faults.These requirements are contradictory so a trade off is needed to cope with sources of false alarms and missed detections.Two strategies may be used: an active strategy consisting in robust residual generation and a passive one through robust residual evaluation.Most of the existing model based FDI techniques rely on the use of linear system models (Benloucif andStaroswiecki 2002 andFrank 1990).Often, nonlinear systems are described by linear models with additive disturbances.Robust residual generation based on unknown input observers to achieve disturbance decoupling may provide an efficient solution to fault detection and isolation problems.As far as linear systems are concerned the problem of robust residual generation may be considered to be mature ( (Benloucif and Staroswiecki 2002, Frank 1990and Patton and Chen 1997) whereas the FDI problem for nonlinear dynamic systems has been investigated to a lesser extent (Benloucif and Balaska 2006;Garcia andFrank 1997 andJiang et al. 2001).
Alternatively, FDI can be performed using qualitative techniques such as expert systems, fuzzy logic, neural networks (Al;exandru et al. 2000;Benloucif and Mehennaoui 2002;Benloucif and Mehennaoui 2005;Chen and Lee 2002;Evsukoff et al. 1999;Frank 1990;Isermann 1998;Schneider and Frank 1996;Simani and Fantuzzi 2002;Takagi and Sugeno 1985, Theilliol et al. 1997and Uppal et al. 2002).To overcome the limitations of the analytical FDI approach, the actual trend integrates model based (analytical) and knowledge based (non analytical) methods in order to take advantage of their respective performances.Residual generation and residual evaluation for decision making may be achieved by using appropriate combinations of different techniques such as state estimation, parameter estimation, neural networks, fuzzy logic inference.
In (Benloucif and Mehennaoui 2002) a fault diagnosis procedure for linear systems used a combination of an analytical residual generator based on Kalman filtering and a fuzzy neural network for residual evaluation.In this work, an extension of the neuro-fuzzy FDI scheme given in (Benloucif and Balaska 2006) is proposed.It is based on a two step neural network procedure: The first network which has the ability to model a wide class of nonlinear dynamic systems acts as an on-line residual generator.The second network performs the decision making which consists in detecting and isolating a fault when it occurs.This neural network coupled to a fuzzy inference block acts as an on-line fault classifier.
The paper is organized as follows.In section 2 the model of the induction motor is presented, starting from the classical Park transformation.The architecture of the neuro-fuzzy scheme used for residual generation and evaluation is discussed in section 3. Simulation results are given in section 4 to illustrate the performance of the proposed neuro-fuzzy FDI scheme for sensor fault diagnosis of the induction motor.

Model of the Induction Motor
Assuming linear magnetic circuits and a balanced three-phase system in the (a, b, c) frame, the electrical equations of the induction motor expressed in the two-phase stationary (d, q) reference frame (Benloucif and Balaska 2006) are: (1) (2) where , I, V are the stator/rotor fluxes, currents and voltages expressed in the (d, q) reference frame.s is the angle between the stator reference frames (a, b, c) and (d, q), and r is the angle between the rotor reference frames (a, b, c) and (d, q).R s , R r , L s , L r are the stator/rotor resistances and inductances, respectively, and L m is the magnetizing inductance.For a squirrelcage IM the rotor voltages are zero.The mechanical equation is: (3) and dthe electromagnetic torque T e is given by: (4) A neuro-fuzzy network is based on the association of fuzzy logic inference and the learning ability of neural networks.
The neuro-fuzzy approach is a powerful tool for solving important problems encountered in the design of fuzzy systems such as: determining and learning membership functions, determining fuzzy rules, adapting to the system environment.
The main points of the residual evaluation procedure are described below.

Residual Fuzzification
It consists in converting the numerical values of residuals into linguistic variables.Each input (residual) may be described by three linguistic variables (Negative, Zero, Positive).Each linguistic variable is represented by a membership function which has generally a triangular or trapezoidal shape.The linguistic variable Zero defines the range where the residual may be considered to be unaffected by a fault.The linguistic variables Negative and Positive define the residual amplitude ranges indicating the presence of a fault.The corresponding membership functions give the extent to which a residual is or is not affected by a fault.

Neural Network Structure
For fault diagnosis it is desirable to use a neural network to model the nonlinear relationship between the fuzzified residuals and the fault decision functions.A multilayer perceptron network is therefore a good candidate.Moreover, to account for memory in the decision process it is necessary to use a recurrent neural network (RNN).The RNN may be implemented as a neural model described by: (11) where D k ( f i ), i = 1...n f , are the fault decision functions also referred to as fault indicators and f i are the faults acting on the process.The regression vector contains the fuzzy residuals R i (k), i = 1...n r , and the delayed decisions D k-1 (f i ), i = 1...n f .Because of the feedback introduced, the recurrent neural model may be realized by a three-layer MLP.This is illustrated by the example given in Fig. 5 which shows a residual evaluation scheme processing three residuals (r 1 , r 2 , r 3 ) to diagnose three faults (f 1 , f 2 , f 3 ).
The corresponding neural network has the following architecture: an input layer with 12 units representing all possible states of the fuzzy residuals together with the past decisions, a hidden layer having 4 units, and an output layer with 3 units each assigned to a decision function.The use of this RNN architecture ensures reliable dynamic decision making (Alexandru et al. 2000;Benloucif andMehennaoui, 2005 andChen andLee 2002).

Training
Prior to on-line use, network training is performed for all possible fault scenarios.During training a residual pattern corresponding, eg. to fault f 1 , is applied to the network input and a one is assigned to the corresponding output.The network weights are then adjusted by an appropriate algorithm thus enabling the neural network to learn the imposed input-output pattern.The use of the backpropagation algorithm is recommended (Benloucif and Mehennaoui 2005).The ultimate goal of the training is to achieve the extraction and selection of the necessary parameters defining the inference rules

Numerical Results
Results using MATLAB simulation are next presented to assess the ability of this diagnosis approach based on neural and fuzzy techniques to detect and isolate sensor faults in an induction motor.Its model expressed in the two-phase reference frame (d, q) is given by the nonlinear state space Eq. ( 5).
The squirrel-cage induction motor considered here has power rating of 1 kW and its electrical and mechanical parameters are as follows: Simulation is carried out with a sampling period of 1 msec, with 400 V and 50 Hz sinusoidal inputs.In normal operation, the outputs (I sd , I sq , ) and the electromagnetic torque T e are shown in Fig. 6.

Residual Generation
A NNARX model having the architecture shown in Fig. 3 has been used with the following parameters: Training of this MLP network was achieved by the Levenberg-Marquardt algorithm for different numbers of hidden neurons.For n h = 4, the output error cost reached at 36 iterations is E = 1.528e-002.After validation this NNARX model is used to generate the residuals: (12)

Residual Evaluation
After many tests on residuals for different fault sensor situations to achieve a good trade off between missed detections and false alarms, the following membership functions for each residual were selected: The RNN used in this simulation study is shown in Fig. 5. Its training is based on the rules summarized in Table 1 which have been obtained after many simulation tests.The learning operation realized by the backpropagation algorithm converged after 3600 epochs with a sum of squared error E=0.025.
Each row of the Inference table represents a rule.For example, rule 2 is expressed as: IF {residual 1 is positive and residual 2 is negative and residual 3 is zero} THEN sensor 1 is faulty.

Motor
Various simulation tests have been performed in scheme and the results are quite conclusive.Bias and drift type sensor faults are introduced during steady state conditions of the system.For illustrative purposes only a few fault scenarios summarized in Tables 2 to 4 are discussed.

Case 1
A bias type fault is injected on sensor 1 as described in Table 2.
The corresponding residuals are shown in Fig. 7.Although a single fault may induce changes in several residuals ( here a fault on sensor 1 affects positively the first residual and negatively the second residual at time t=2.5 sec) the decision functions ensure successful detection and isolation of the fault on sensor 1 as shown in Fig. 7.The neuro-fuzzy classifier has been trained to recognize the faulty situations from the fuzzified residual patterns according to the rule base given in Table 1.

Case 2
This fault scenario of bias faults on sensors 2 and 3 is described in Table 3.
The residuals and the corresponding decision functions are shown in Fig. 8.The faulty sensors are promptly detected and correctly isolated.

Case 3
This fault scenario uses drift faults on sensors 2 and  The diagnosis effectiveness in the presence of sensor drift faults is illustrated in Fig. 9.We notice a detection delay for fault sensor 2. delay, which is dependent on the slope of the drift, gives rise to a tem-

Conclusions
In this paper, a neuro-fuzzy scheme for on-line fault diagnosis was applied to the induction machine.This FDI approach relies on combinations of neural modelling and fuzzy logic which can deal effectively with nonlinear dynamics and uncertainties.
The proposed neuro-fuzzy FDI scheme is based on a two step procedure: a neural NNARX model is used for residual generation and a recurrent fuzzy neural network performs the residual evaluation task.Fault diagnosis is achieved by training the network to recognize the fault signatures from the patterns of the fuzzified residuals.The successful results obtained in simulation demonstrate the efficiency of this neuro-fuzzy diagnosis scheme to detect and isolate bias and drift sensor faults in an induction motor.

Figure
Figure 7. Faculty residuals and corresponding decisions (Case 1)

Table 1 . Inference table Table 2. Case 1 Table 3. Case 2Table 4 .
Case 3 3 as described in Table4.Drift faults are modelled as ramp functions with given slopes.