Closed-Loop Drive Detection and Diagnosis of Multiple Combined Faults in Induction Motor Through Model-Based and Neuro-Fuzzy Network Techniques

: In this paper, a fault detection and diagnosis approach adopted for an input-output feedback linearization (IOFL) control of induction motor (IM) drive is proposed. This approach has been employed to detect and identify the simple and mixed broken rotor bars and static air-gap eccentricity faults right from the start its operation by utilizing advanced techniques. Therefore, two techniques are applied: the model-based strategy, which is an online method used to generate residual stator current signal in order to indicate the presence of possible failures by means of the sliding mode observer (SMO) in the closed-loop drive. However, this strategy is not able to recognise the fault types and it can be affected by the other disturbances. Therefore, the offline method using the multi-adaptive neuro-fuzzy inference system (MANAFIS) technique is proposed to identify the faults and distinguish them. However, the MANAFIS required a relevant database to achieve satisfactory results. Hence, the stator current analysis based on the HFFT combination of the Hilbert transform (HT) and Fast Fourier transform (FFT) is applied to extract the amplitude of harmonics due to defects occur and used them as an input data set for the MANFIS under different loads and fault severities. The simulation results show the efficiency of the proposed techniques and its ability to detect and diagnose any minor faults in a closed-loop drive of IM.


Introduction
Nowadays, modern industrial systems are becoming more and more complex and sophisticated. At the same time reliability, availability and operating safety have become very important and real challenges for today's businesses. However, the squirrel cage induction motor, by its construction and its robustness, ensures a wide range of application in industrial systems [1]. The evolutions of power electronics, microelectronics and microcomputing have made it possible to overcome the problem of the non-linearity of the machine and to realize control algorithms that can make the IM a formidable competitor of speed variable [2]. There are many methods dedicated to control induction motors, however, the controlled part is subjected to strong nonlinearities and temporal variables, it is necessary to design control algorithms ensuring the robustness of the process against the uncertainties on the parameters and their variations. The input-output feedback linearization control has focussed on the attention owing to the simple design and on the perfect decoupling between rotor speed and flux, as well as fast dynamic response, even too easy implementation, robustness to parameter variations, and load disturbances [3][4][5].
The use of this machine in several industrial applications can be affected by potential defects; mechanical origin (rolling bearing wear, eccentricity of the shaft ...), electrical or magnetic (stator inter-turn short circuit, broken rotor bars ...), and supply (network or converter) [6][7][8]. Furthermore, the static air-gap eccentricity and broken rotor bars faults are the most important causes of faults in IMs, which lead to produce oscillation in the rotor speed and mechanical vibrations causing damage in IM. These faults effects become more apparent by increasing their severities, particularly, in the open-loop drives [9].
The tasks of detection and diagnosis of failures are naturally found their place in the monitoring system at closed-loop of IM. These tasks related to the knowledge acquired on the encountered problems, which make the fault detection and diagnosis approaches divided into two wide categories: approach with model [10] and approach without model [11].
tool for conducting classification. The work by [31] the neuro-fuzzy technique has been used to detect the broken rotor bars using FTT to extract the features from the magnetic flux density, which were considered as an input for the proposed technique. In [32], a new methodology for stator inter-turn fault diagnosis of three-phase IM using ANFIS is presented, which is developed based on Sequence Component Phase Index and Sequence Component Amplitude Index for detection of fault location and fault severity. Furthermore, the fault diagnosis of squirrel-cage induction motor broken bars based on ANFIS identification method with subtractive clustering is presented by [33], this concept is implemented by primarily taking into account the information data extracted from the classical motor current signature analysis (MSCA), then ANFIS approach used this data set as an input for early rotor bar fault detection phase. In [34], the field of monitoring and diagnosing IM faults, particularly the stator short-circuit, the broken rotor bar faults and the mixed fault is carried out, based on the neuro-fuzzy network technique. Its knowledge base makes use of indicators derived from DWT analysis and spectral analysis of the stator current, which allows, in addition to the detection, the evaluation of the number of broken bars and the position of the turns in short-circuit. The hybrid model, known as FMM-CART (the Fuzzy Min-Max neural network and the Classification and Regression Tree), is used to detect and classify fault conditions of IM in both offline and online motor operations as reported in [35]. The broken rotor bars, stator winding, and unbalanced supply faults, are investigated to evaluate the effectiveness of FMM-CART. The signal harmonics are extracted from the power spectral density (PSD), and used them as the input data for faults classification with FMM-CART, the results indicate that method is able to detect and diagnosis the faults in the early stage. Authors in Ref. [36], investigated the current monitoring for effective broken rotor bar fault diagnosis in open loop of IM, by using a novel oblique RF (random forest) algorithms classifier. Therefore, the RF algorithm prove to be relevant for the motor diagnosis. Phuong et al. [37] presented a diagnosis methodology for incipient rolling element bearing failures; by extract useful features from incoming acoustic emission signals by using a wavelet packet transform based kurtogram. The linear discriminant analysis (LDA) technique is used to select the most discriminant bearing fault features from the original feature set. Then, a Naïve Bayes (NB) classifier used the selected fault features in order to classify the bearing fault conditions and it shows good accuracies for classification. Furthermore, the Authors in Ref. [38,39] used the vibrations analysis methods to diagnose the bearing faults by using, respectively; spectral kurtosis (SK) based feature extraction coupled with k-nearest neighbor (KNN) distance analysis, and an adaptive deep convolutional neural network (ADCNN), which is used the cyclic spectrum maps (CSM) of raw vibration signal as bearing health states. That is lead to automate feature extraction and classification process. Slaheddine et al. [40] improve the standard support vectors machines (SVM) by using support vector data description (SVDD) based on MCSA and stationary wavelet packet transform (SWPT) for feature extraction to diagnose broken rotor bar fault. Bensaoucha et al. [41] proposed a diagnostic technique based on NN for detecting and locating the inter turns short-circuit in one of three stator winding phases of IM, where the three-phase shift between the stator voltages and its currents are considered as inputs of the NN in order to develop an automatic fault detection and classification system. The authors in [42], used methods for bearing fault detection and diagnosis by means of the artificial neural network (ANN) and ANFIS. The multi-staged decision algorithm is developed based on ANN and ANFIS models. Both time and frequency domain parameters extracted from the vibration and current signals are used to train the ANN and ANFIS models, which are then used to detect and diagnose the severity of the bearing fault. The results revealed that ANFIS-based scheme is superior to the ANN-based one especially in diagnosing fault severity. As well, the ANFIS conception presents a limitation to identify the mixed faults due to a single output. Further, the most techniques of artificial intelligence are used in the literature for an open-loop machine process in several cases. Nevertheless, in closed-loop drives, the control-loop compensates the fault effect [43], which cause difficulty in diagnosis defects. Based on the aforementioned state of the art, the Multi-ANFIS (MANFIS) technique proposed in this work to overcome the problem of accuracy and single ANFIS output, which is used to identify and distinguish the mixed and the simple faults of the broken rotor bars and static air-gap eccentricity even at low slip in IM closed-loop drives. This technique used the features extracted from the HFFT technique under different loads and fault severities as an input data set for the training algorithm.
In this context, the important aim of this paper is to show another perspective with regard to the detection and diagnosis of the fault in a closed loop of induction motors. The reduced model of the IM dedicated to simulate two of faults: broken rotor bars and static air-gap eccentricity. The implementation of IOFL control by means of the SMO is proposed in order to estimate the stator current in healthy and faulty states of the induction machine. The model-based approach is operated for fast detection of incipient faults using SMO through the residual stator current. As well, the HFFT technique extracts the amplitudes of frequency components due to the defects occurs in IM from the stator current envelope (SCE) under different loads and fault severities. These features are considered as reliable indicators and used them as input data set for MANAFIS. The obtained results show the value of the proposed techniques for fault detection and diagnosis in a closed-loop drive of IM.

Spectrum of stator current envelope and model-based approach
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Hilbert transform is a signal analysis method used to extract the stator current envelope as illustrated in Fig. 1. However, the HT is a time domain convolution of a signal x(t) with the function 1/t, such as the phase current that is used to emphasize its local properties, as follows [25,44] : Where t is time, x(t) is a time-domain signal, * is the convolution indicates, and H[x(t)] is the Hilbert transform of x(t).
Spectrum analysis of stator current envelope via FFT technique allows the recognising the sidebands of fault frequency components, practically the broken rotor bars (2nsf) and static air-gap eccentricity (mfr).
A model-based approach is a concept of analytical redundancy by means of observers in terms of estimated and measured outputs ( −̑), The main equation of residual stator current rI(t) is written as [19].
where, Zp is a weighting matrix. The windowed norm can be performed to each residual as follows:

Reduced model of IM taking into account the faults
The study of any physical system often requires a modelling in order to simulate its behaviour against different constraints; to highlights the influence of defects on a measurable magnitude of the machine, and ensures to apprehend the mechanisms governing its operation [45,46]. The development of a mathematical reduced model is obtained from the multi-winding model of IM as shown in Fig. 3; taking into account the rotor faults such as broken rotor bars and static air-gap eccentricity. An extended Park's transformation will be applied to the rotor system to transform Nr bars system into (d, q) system. Afterwards, the system can be written as follows [43]: The total cyclic inductance of a stator phase is equal to the sum of the magnetizing and leakage inductances: where,  The electrical angle of two adjacent rotor meshes: The cyclic rotor inductance is given by the following: The principal inductance of a rotor mesh can be calculated by The mutual inductance between non-adjacent rotor meshes is defined by By considering the electromagnetic torque equation, the rotor speed is given as follows:

Broken rotor bar fault
The four terms resistances of broken rotor bar fault (Fig. 4) are given by: In this expression, the summation is applied to all bars with fault. Rbfk is the resistance of the bar index k from its initial value before the fault.

Static air-gap eccentricity fault
The static air-gap eccentricity fault is illustrated in Fig. 5, where the magnetomotive force of the stator windings is assumed sinusoidal. The winding function theory is applied for computational of mutual inductance between the stator coils and rotor loops in an induction motor taking into account the air-gap eccentricity fault can be expressed as [47,48]: The term nrk (θr, φ) is the winding distribution of Kth rotor loop, and Nsq(θr, φ) is called the modified winding function of phase ″q″. The inverse air-gap length at any position θr can be illustrated as: All the motor inductances can be calculated using Eq. (11) and [47,48].

Input-output feedback linearization control
The input-output feedback linearization strategy makes it possible to find a state feedback loop in order to transform a nonlinear system into a fully or partially linear one [5]. The technique requires measurements of the state vector x in order to transform a multi-input nonlinear control system into a linear and controllable one. The state space model of an induction motor in the (α, β) frame coordinate is given by [4]: Where the state and control vectors are expressed as: 1 - Figure 5. Static air-gap eccentricity Illustration.
where 3 The Lie derivative notation is used for state function h(x): Rn R along a vector field f(x) can be written as follows [4]: Iteratively, we get ℎ = � ( −1) ℎ�. The change of coordinates is defined as: Thus, the derivatives of the outputs are given in the new coordinate system by: This system can be written as: The decoupling matrix D(x) is defined as: The decoupling matrix D(x) has a singularity which occurs at the start-up of the IM ( 2 =0). To handle this situation, one can use an open loop controller at the start-up of the machine, thereafter switch to the nonlinear controller once the flux goes up to zero. The nonlinear state feedback control can be modelled as: This controller linearizes and decouples the system, resulting in: From Eq. (21), the input-output of a closed loop system is decoupled and linearized. To ensure perfect tracking of speed and flux references, U1 and U2 are chosen as follows: Where k1, k2, k3, and k4 are positive non-zero constants to be determined to make sure that closed loop system from Eq. (21), stable and to have a fast response to variable tracking.

Sliding mode observer
The reduced model of IM is used to design the SMO to establish a good compromise between the stability and the simplicity of the observer [15]. The state equation of the observer can be written in the following way: where s s s I2 is the identity matrix 2x2.
is the matrix of the observer correction gains.

Simulation results for Input-output feedback linearization control IM
The input-output feedback linearization control of IM used in the healthy and faulty state: 1.1 kW, 220V, 50Hz, 2-pole, a rotor with 16 bars were carried out using the Matlab/Simulink simulation package. The system parameters of the induction motor tested in this study are given in the Appendix. Fig. 6 presents the input-output feedback linearization control diagram block using the sliding mode observer for stator current and flux estimation.
The variable frequency drive (VFD) is considered as energy saving drives, but on the other hand it generates noise in the line currents. However, the input-output linearization control used pulse width modulation (PWM) by means of VFD for controlling of IM. This robust combination (IOFL control+ PWM) has the advantage to control a device with high precision and minimize the natural noise due to VFD, which allows a good diagnosis of IM. The VFD used in this simulation composed of a rectifier and IGBT inverter uploaded from Matlab/Simulink in order to take into account the noise. The PWM switching sequences are calculated with a commutation frequency equal to 4 kHz. A supply voltage of (400 V) is filtered through the rectifier in order to fix the UDC bus of the inverter. The noise generated by a VFD reduces its signal to noise ratio (SNR). A white Gaussian noise of 10 dB of SNR (low SNR) added to the output voltages (Ua, Ub, Uc), in order to model the other noise.

Healthy state of the machine
To illustrate the performances of the controller in a healthy state of IM, a simulation with reference speed equal to 2600 rpm is realized in Fig. 7, a nominal load torque equal to 3.5 Nm is applied at t=0.5s. The sampling rate considered in this simulation 10kS/s using the Matlab/Simulink simulation package. The system parameters of the induction motor tested in this study are given in the Appendix.
Electromagnetic torque follows the load torque, and the stator current has a very good dynamic and estimation accuracy, where the real and estimated current shows a perfect superposition. The quadratic rotor flux component qr Φ is maintained to almost zero. Direct rotor flux component dr Φ tracks the reference values adequately well. The speed reverse test is realized by reverse speed reference (25; -25 rpm) under nominal load torque, which applied at t=0.5s, where it is noted that the real rotor speed converges to the reference speed with very less errors and without any significant overshoot. The application of the load does not affect the rotor speed as shown in Figs. 7a and 8. The performance of the controller reveals a good robustness and convergence at rated and low speeds.

Fault detection and diagnosis of the machine
The fault detection and diagnosis approach of IM in closed loop drives is given in the following steps: Firstly, on-line fault detection using the model-based technique in order to highlight the appearance of incipient faults based on residual stator current. Finally, off-line diagnosis using a multi-neuro-fuzzy technique based on HFFT analysis of stator current.

IM fault detection
In order to detect faults and study their influences on the residual stator current of IM controlled by feedback linearization, the simulations are carried out with low SNR (10 dB), a reference speed equal to 2600 rpm and a load torque (TL=3.5 Nm) applied at t=0.5s. All faults are realised at t=1s and their severities changed at t=2s as illustrated in Figs. 9, 10, 11 and 12.  Table 1 show that the residual currents start with a very small value in a healthy state, socalled the threshold ||rIa || = 0.1 A, then increase abruptly when the broken rotor bar, static air-gap eccentricity or mixed fault occur at t=1s according to the fault types and their severities. This technique can be considered as a reliable indicator for rapid incipient faults detection, even at low slip.    However, the ||rIa|| are not only very sensitive to the faults occurrence but also to the modelling uncertainties, parameter variation, and unknown inputs such as external noise, which lead to false fault detection. To overcome this problem, neuro-fuzzy technique based on the proprieties of HFFT analysis is applied to confirm the true/false fault detection and identify the faults occurred in the IM.

Extraction of fault indicators
The spectrum analysis is performed on the stator current envelope using HFFT technique in order to extract the fault indicators under different load conditions (full load, half load and low load) and different severities of broken rotor bars and static air-gap eccentricity faults, as shown in Figs. 13 and 14. Mixed fault composite of one broken bar and 10% of static air-gap eccentricity (Nbb1εs10) is illustrated in Fig. 15. The HFFT signatures have been collected at a sampling rate of 10kS/s for the duration of 12s in each case.    Table 2 show the position of the fault harmonics appeared in frequencies 2sf and fr, respectively, for broken rotor bars and static air-gap eccentricity. However, the amplitude of the harmonic fault and its position due to broken rotor bars is very sensitive to the load varies, also to the defect severity (number of broken bars). Unlike, the position of the harmonic fault generated by static air-gap eccentricity kept the same position but its amplitude is affected by the defect severity. Therefore, by the surveillance of the amplitudes evaluation of the fault harmonics, the motor state can be predicted by using these relevant indicators.

IM Multi-ANFIS (MANFIS) diagnosis
A hybrid neuro-fuzzy technique brings the learning capabilities of neural networks to the fuzzy inference system of the Takagi-Sugeno type. The role of learning is the adjustment of the parameters of this fuzzy inference system. The strength of the adaptive neuro-fuzzy inference system is the ability to generate fuzzy rules using subtractive clustering or grid partitioning [49]. However, ANFIS is only suitable for the single output system. For a system with multiple outputs, ANFIS is placed side by side to produce a MANFIS. The number of ANFIS depends on the number of outputs required, and the input data is coupled to the separate outputs. Fig. 16 shows MANFIS architecture, the input data remains the same for each ANFIS; they also have the same initial parameters such as the initial step size, membership function type and number.
MANFIS network is used to identify automatically the broken rotor bars, static air-gap eccentricity faults, or both faults at the same time.
Two of the fault indicators have been chosen and grouped in a vector Ii= [I1; I2] presents the input vector data of the MANFIS network as illustrated in Fig. 17. Where I1 and I2 are respectively, the amplitude of harmonics 2sf and fr which are extracted from the simulation of the current envelope spectrum under different loads and fault severities. The network designed MANFIS consists of two ANFIS, each ANFIS has two inputs and one output. The input variables are I1 and I2, and the output variables are O1 for ANFIS1 and O2 for ANFIS2. For each input variable, three Gaussian membership functions are used.  The outputs data, as well as network learning errors, are shown in Fig. 18. We noticed that the learning errors are very less, which proves that the network has learned well sequences of broken rotor bars and air-gap eccentricity failures. The MANFIS diagnosis system has been tested under different loads and fault severities not taken in the learning phase of the machine (TL=0.7, 2.1, 2.8 Nm).
The results of the test illustrated in Figs. 20 and 22 show that the MANFIS outputs and their errors are able to report automatically in an efficient and reliable way the simple and mixed broken rotor bars and static air-gap eccentricity defects from the beginning of their appearances. This system also has a high accuracy to correctly distinguish between the healthy and faulty machine under different severities and load conditions. Table 3 presents a summary of other works and their respective results for comparison purposes.

Conclusion
This paper presents a fast detection and recognition approach of the mixed and simple fault, particularly, the broken rotor bars and the static air-gap eccentricity faults for IM in the closed-loop drive. The IOFL control is introduced in order to ensure the operation continuity of defected IM and to investigate the fault effect. A reduced model of IM with a rotor cage has been implemented in order to simulate the proposed faults, and also for the control and observer design.
This advanced approach required a good knowledge of the system, which leads to adopting two strategies for detection and diagnosis of the defects. Foremost, model-based strategy with the contribution of SMO has been used to generate the residual stator current for rapid incipient fault detection in the control scheme. Furthermore, the MANFIS technique is used to confirm if the residuals detected are induced by the faults or other disturbances, also distinguish and identify these faults. However, the amplitudes of fault harmonics 2sf and fr, respectively, due to the broken rotor bars and static air-gap eccentricity, are obtained via HFFT analysis under different load conditions and fault severities. These relevant amplitudes have been used as fault indicators and have been considered as two inputs data for the MANFIS. Moreover, the two MANFIS outputs data provide a high accuracy on the information of two defects studied, and prove that it is able to identify the fault types in the machines. The results obtained with this proposed approach are efficient and accurate to detect and identify the rotor faults of the IM operating in the closed-loop drive.