S-transform and ANFIS for detecting and classifying the vibration signals of induction motor

Abstract

In this paper, a hybrid approach is proposed for detecting and classifying the vibration signal of induction motor. The proposed hybrid technique is the combination of S-transformation algorithm and adaptive neuro fuzzy inference system (ANFIS) method. Here, the proposed hybrid method contains two processes, such as, fault detection and classification process. Initially, the pre-processing is applied in the electric motor vibration signal. In the fault detection process, significant features from vibration signals are extracted through the S-transformation algorithm. Consequently, the ANFIS classification technique is employed to classify the signal into the faulty or the normal. The proposed hybrid technique is implemented in MATLAB working platform. The performance of the proposed hybrid technique is evaluated with five types of faulty vibration signals. The performance of the proposed hybrid method is compared with the existing method such as S-transform-RBFNN and S-transform-FFBNN. Analyze these methods with the help of statistical measures such as, accuracy, sensitivity and specificity value.

Keywords

Pre-processing fault classification S-transformation RBFNN and ANFIS

1 Introduction

In the industry, Induction motors are normally employed because of its robustness, effortlessness of its construction and require minimum maintenance [1]. We cannot hold off from the chance of failure although induction motors are reliable [2]. The induction motor faults can be classified into bearing failures, stator faults, rotor faults, air gap eccentricity, mechanical vibrations, etc. [3]. The bearing fault occurs in motor is due to the unnecessary load, rise of temperature inside the bearing, use of bad lubricant and so on [4]. Once any mechanical part of the motor wears or breaks up, it results in alter in oscillations and accordingly the vibration spectrum will differ. In addition, any imperfection in air gap flux distribution changes the torque and therefore results in change in vibration pattern [5]. These letdowns may be very dangerous to the motor and thus early detection of failure is necessary before they affect the complete operational performance [6]. Measurements and watching of parameters such as vibration, temperature, noise level and power consumption can be helped [7] to identify the trends of enhancing faults and discover the sources of problems. Therefore, the

appropriate condition monitoring method of motor is

necessary.

Condition monitoring of induction motor have an exigent task for engineers in industries. There are many

conditions monitoring methods accompanied by vibration monitoring, thermal monitoring, and chemical monitoring. All these monitoring methods required high-priced sensors or specialized devices [8]. There are several tools available and which used for measuring the speed, output torque, vibrations, temperature, flux densities etc. [9] for watching the sensors. In some situations, to recognize the survival of an incipient bearing failure, vibration monitoring techniques are employed [10]. Vibration monitoring is a reliable tool for bearing failures. The vibration data typically have error signatures and salient error features because of the direct measurement of the crucial signal and post of the vibration sensor. Vibration-based monitoring methods, both in the time and frequency domains, have been largely used for detection and diagnosis of bearing imperfections [11]. Placing a sensing device on the motor might not be possible or practical alternatively [12] in several applications.

Under a light load, several faults have related symptoms, and the fault may not be obvious while the motor is operating as not all the faults can be recognized with a single measurement technique. In addition, there is a lack of detailed understanding of the effect of the faults on the outputs of different sensor types [13]. These sensors are jointly combined which allows for competent monitoring of the machines condition with algorithms and architectures. The most well-known methods of induction motor condition watching use the steady state spectral components [14]. The steady state techniques are motor current signature analysis (MCSA), extended park’s vector approach (EPVA) and discrete wavelet transform (DWT) to recognize the error in the motor [15]. Well-known signal processing tools of Fourier, Wavelet, and Hilbert–Huang transformations are applied to accomplish motor current data to take away required features for motor fault detection [16].

The conventional method systems have number of limitations such as inflexible, high cost, hardware limitations which are very much dependent upon specialized devices. In most recent years, the error detection of electrical machines moved from traditional methods to AI technique [17]. The induction motors are subject to the occurrence of incipient faults [18]. There are quite a lot of types of ANNs that are suitable in diagnosing Induction motor bearing. These are for example, FFNN, EN, RBFNN and ANFIS networks. For instance RBFNN can coach quicker than FFNN and its covered layer is easier to know than that of FFNN [19, 20]. Moreover, the ANFIS system is more precise than the other models [21]. For categorizing and detecting the errors of the electric motor, the S-transformation and ANFIS is proposed in the text. The proposed control strategies are made cleared in Section 3. The most recent research works are disputed in Section 2. The results and discussion of the proposed strategy is described in Section 4. The Section 5 finishes the document.

2 Recent research work: A brief review

Numbers of research work are previously existed in literature which is based on errors watching of electrical motor. A few of them are reassessed here.

Konar et al. [22] have offered a Support Vector Machine (SVM) with nonstop wavelet transform (CWT) for examining a bearing fault detection plan of three-phase induction motor. CWT has not been extensively used in the field of condition monitoring even though much better effects can been attained compared to the generally employed DWT based methods. The encouraging effects attained from their analysis was hoped to set up a base for condition monitoring method of induction motor which would be easy, fast and overcome the restrictions of traditional data-based models/methods.

A conditional random field (CRF) model based classifier for enhancing the diagnosis accuracy has been proposed by Guofeng Wang et al. [23]. The feature vectors sequences and the fault categories were linked by an undirected graphical model in their projected model, in which their connection was represented by a global conditional probability distribution. The main advantage of the CRF in comparison with the HMM model was that it can depict the temporal dynamic information among the observation sequences and state sequences without assuming the independence of the input feature vectors. Consequently, the interrelationship among the adjacent observation vectors can furthermore be illustrated and integrated into the model, which makes the classifier more robust and accurate than the HMM. To Four kinds of bearing vibration signals which correspond to normal, inner race pit, outer race pit and roller pit respectively were collected from the test rig in order to assess the efficiency of their proposed method. The CRF and HMM models were put up to perform fault classification by taking the sub band energy features of wavelet packet decomposition (WPD) as the observation sequences. Furthermore, to improve the evaluation accuracy of the classifier, K-fold cross validation method was adopted. It has been shown that the accuracy rate of classification using the CRF model was higher than the HMM by the analysis and comparison under different fold times.

Duygu Bayram et al. [24] have presented a wavelet based neuro detector approach applied to recognize the aging indications of an electric motor. Study of the aging indications which could be observed in the low frequency region, was performed by vibration signals. Further mainly, two vibration signals were observed for healthy and faulty cases which were calculated from the related electric motor. Multi Resolution Wavelet Analysis (MRWA) was used in order to accomplish low and high frequency bands of the vibration signals. As a result for recognizing the aging properties in the spectra, the Power Spectral Density (PSD) of the sub band for the healthy case was employed to coach an Auto Associative Neural Network (AANN). The PSD amplitudes, which were computed for the faulty case, were applied to input nodes of the coached network for the re-calling process of AANN.

A hybrid soft computing replica has been proposed by Manjeevan Seera et al. [25] having the Fuzzy Min-Max (FMM) neural network and the Classification and Regression Tree (CART) for motor fault recognition and analysis. Mainly, the hybrid model, recognized as FMM-CART, was used to differentiate and classify error conditions of induction motors in both offline and online surroundings. A chain of tests was performed, whereby the Motor Current Signature Analysis (MCSA) method was used to form a database having stator current signatures under different motor conditions. The signal harmonics from the PSD were eliminated, and used as the discriminative input features for fault classification with FMM-CART. Three main induction motor conditions, viz. broken rotor bars, stator winding faults, and unbalanced supply, were used to evaluate the competence of FMM-CART.

A health index Mahalanobis distance (MD) has been suggested by Xiaohang Jin et al. [26] to point out the health condition of cooling fan and induction motor based on vibration signal. Anomaly detection and fault classification were completed by comparing MDs, which were computed based on the feature data set removed from the vibration signals under normal and abnormal conditions. As MD was a non-negative and non-Gaussian distributed variable, Box–Cox transformation was applied to exchange the MDs into normal distributed variables, such that the properties of normal distribution could be used to find out the ranges of MDs related to dissimilar health conditions. Experimental data of cooling fan and induction motor were applied to authenticate the suggested approach. Their effects demonstrate that the early stage failure of cooling fan caused by bearing generalized-roughness faults could be identified effectively, and the dissimilar unbalanced electrical faults of induction motor could be categorized with a higher precision by Mahalanobis–Taguchi system.

Jafar Zarei et al. [27] have suggested an artificial neural network (ANNs) for finding out the bearing defects of induction motors. In their technique, the vibration signal passes through removing non-bearing fault component (RNFC) filter, planned by neural networks, in order to eliminate its non-bearing fault components, and after that enters the second neural network that uses pattern recognition methods for fault classification. Four dissimilar categories comprise; healthy, inner race defect, outer race defect, and double holes in outer race were examined. Their suggested method performances were examined and compared to the usual fault detection techniques that employ frequency-domain characteristics. Here, the proposed technique is employed for identifying the vibration signal of induction motor. The proposed hybrid technique is the combination of S-Transformation algorithm and ANFIS. Here, the S-Transform is used to extract the features from the vibration signals attained from ball bearing in five conditions that is- Normal, IR, BB, centered OR, opposite OR and orthogonal OR fault. After that, the faults are classified by using ANFIS.

3 Analysis of bearing fault vibration signals in the induction motor

The vibration signals are evaluated in both the normal and the faulty conditions in the induction motor. Faults of the induction motor are occurred due to mechanical and electrical stresses where the causes of the mechanical stress are overloads and abrupt load changes which in turn create bearing faults and rotor bar breakage. Outer race (OR) fault, Inner race (IR) fault and ball bearing (BB) fault are the faults created by the impulse vibrations which are formed at a specific frequency if a fault occurs in a bearing. In faulty stipulations, difficult time series waveforms are generated by these vibration signals. After that, different characteristic frequencies are evaluated using the some equations for various kinds of faults. Then the IR fault can be described in reference with the frequency level and the rate, at which the bearing balls go by during the point of fault on the inner race, is the rate that depends by the IR fault frequency. And also, the rate for which, the difference of inner race and angular speed of cage is proportional, each ball is shifted across the flaw point. The fault frequency of the inner race defect is also proportional to the number of balls in the bearing. The OR fault frequency depends on the rate at which bearing balls cross the point of fault on the OR. The OR fault rate is directly proportional to the variation of angular speed. The OR fault frequency is also proportional to the number of balls in the bearing. There are three positions namely centred, opposite and orthogonal in which the OR faults should be stated. The BB upholds the balls at consistently balanced positions and helps the rolling of balls along the raceways. In the rotating period of the motor shaft, the bearing cage rotates at a steady angular velocity. The angular velocities means that the inner and outer race angular velocities. In order to evaluate the induction motor’s vibration a signal, the proposed hybrid technique is utilized which is detailed in Section 3.1.

3.1 Using S-transform and ANFIS for detecting and classifying the vibration signals

With the help of the proposed method, evaluation of the vibration signals of induction motor is carried out. Two cases are considered for the vibration signals namely, normal condition and faulty condition. Primarily, the vibration signals are subjected to the pre processing operations to attain the noiseless signal. After that, by applying the S-transformation on both vibrating and normal signals, features are extracted. Subsequently, the extracted features are fed as the input to ANFIS in order to classify the bearing faults effectively whereas the bearing faults are arisen in the motor based on particular condition. The proposed controller block diagram is illustrated in Fig. 1. Here, the vibration signals of the induction motor are analyzed in the normal, IR, BB, centered OR, opposite OR and orthogonal OR fault conditions. These OR, IR and BB fault signal frequencies are calculated by using the following equations, $f_{OR} = \frac{N}{2} [F_{r} * (1 - ψ cos β)]$ (1)

$f_{IR} = \frac{N}{2} [F_{r} * (1 + ψ cos β)]$ (2) $f_{BB} = \frac{1}{2 ψ} [F_{r} * (1 - {(ψ)}^{2} {cos}^{2} β)]$ (3) where, ψ is the denoted as the $(\frac{d}{D})$ . Then d, D are the inner and outer raceway diameters and f _r is the rotational frequency, β is the slip angle.

These various frequencies are calculated depending on their faults. The rotational frequency is denoted as F _r. The vibration signals are pre-processed. At this point, the input of the vibration signals is précised as the X _N (t). The input sampling signal frequently comprises noise, so the noise moreover encloses random disturb signal. The sampling signal curve is unsmooth, and there are also some spurs because of the extensive frequency band of the random disturb signal, and majority of high frequency. The sampling signal should be pre-processed in order to obtain a smooth curve. The signal processing method applied to remove the repetitive signals from the additive noise. The raw information is partitioned into sections of equal length associated to the synchronous signal and after that standard together. In this way the adequate averages the arbitrary noise is terminated and the desired signal is left.

$\begin{matrix} X_{N} (t) & = (x_{1} (t), x_{2} (t), x_{3} (t), \\ x_{4} (t) \dots \dots x_{i} (t) \dots \dots x_{n} (t)) \end{matrix}$ (4)

The signals can function the five points smooth to smooth the curve. The subsequent equations are applied to dealing out the data. $x_{1} (t) = {x_{1}^{1} (t), (x_{1}^{2} (t), x_{1}^{3} (t)), x_{1}^{4} (t), x_{1}^{5} (t)}$ (5) $x_{2} (t) = {(x_{2}^{1} (t), x_{2}^{2} (t)), x_{2}^{3} (t), x_{2}^{4} (t), x_{2}^{5} (t)}$ (6) $x_{n} (t) = {x_{n - 4}^{1} (t), x_{n - 3}^{2} (t), x_{n - 1}^{3} (t), x_{n - 2}^{4} (t), x_{n}^{5} (t)}$ (7)

After that, the pre processing is carried out the original signals can be obtained. The detailed description of the proposed technique is explained in below section.

3.1.1 Feature extraction of vibration signals using S-transformation

In this section, the S-transformation [28] is employed for extracting the features of the vibration signals of the electric motor. Here, the vibration signals are furnished as the input signals of the S-transform. The input signals are expressed by the following equation, $S_{T_{d}, f} = \int_{- \infty}^{\infty} x_{N} (t) w_{d} (T_{d} - t, f) e^{- i ω t} dt$ (8) where, x _N (t) and w _d is denoted as the vibration signal and the Gaussian windowing function respectively. The Gaussian windowing function (w _d) selected as a positive value which is denoted as the following, $w (T_{d} - t, f) = \frac{| f |}{k \sqrt{2 π}} e^{\frac{- f^{2}}{2 P^{2}} ({(Γ - t)}^{2})}$ (9)

In the above equation, f, t, T _d and P signify the frequency of the signal, the time, time delay and scaling factor correspondingly. The scaling features of the signals supervise the time-frequency resolution. Subsequently, by performing the invertible S-transform, the windowing function of the signal is got normalized. From the Fourier transform of the signal x _N (t) and ${\hat{x}}_{N} (f)$ signals, the S-transform can furthermore be computed directly. As a result, the convolution of the signal is assessed by applying Equation. (10) and the convolution property is employed to the Fourier transform. Next, acquired signal is named as follows, $S_{T_{d}, f} = x_{N} (t) w_{d} (t, f) e^{- i ω t} dt$ (10) $S_{T_{d}, f} = F^{- 1} ({\hat{x}}_{N} (α + f) {\hat{w}}_{d} (α, f))$ (11)

Here, F ^-1 is the inverse Fourier transform and α is the Fourier transform pair of t. Then the Gaussian window function is determined by using Equation (12) and the S-transform is described that that summing S _{T_d,f} over T _d yields the spectrum of x. By using the Equation (13), the ${\hat{x}}_{N} (f)$ is determined. $S_{T_{d}, f} = \int_{- \infty}^{\infty} ({\hat{x}}_{N} (α + f)) e^{- 2 {(\frac{k α π}{f})}^{2}} e^{i 2 π α T} d α$ (12) ${\hat{x}}_{N} (f) = \int_{- \infty}^{\infty} S_{T, f} dt$ (13)

From the above equation defines the inverse S-transform through the inverse Fourier transform of the spectrum of x _N (t). The given vibration signals of the electric motor can be extracted based on the selection of windowing function, after that the vibration signals of the electric motors are extracted properly.

3.2 Faults classification using ANFIS

ANFIS architecture comprises five layers of nodes. Out of five layers, the first and the fourth layers possess adaptive nodes whereas the second, third and fifth layers possess fixed nodes [29]. The structure of ANFIS having five layered feed-forward neural network is shown in Fig. 2. In both neural network (NN) and fuzzy logic (FL), the inputs are given to the input layer (as input membership function) and the output is obtained from the output layer (as output membership functions). The input characteristics could be mapped with the input membership functions regarding Fuzzy inference system, then mapping the input membership function to rules, and then rules to a couple of output features, output features to output membership functions and then lastly output membership rights operate to single valued output. This resultant single valued output is usually obtained since the conclusion in which relates to the desired output. The particular fuzzy membership functions are usually picked randomly in a predetermined number. Fuzzy inference could be well-designed merely within the Systems, which is the user is usually pre-defined and the rule structure dependant on their interpretation from the features from the variables. Moreover, ANFIS employs the least squares and back propagation being a merged calculation for evaluating the membership functionparameters.

Here, the input and output of ANFIS is represented as X _i ={ x ₁, x ₂, …… x _n } and Y = { y ₁, y ₂, y ₃, y ₄, y ₅, y ₆} respectively. Each rule contains the unity weight and the learning process of ANFIS is carried out on the classified signals. In the ANFIS architecture, two fuzzy if-then rules based on a first order Sugeno model are considered. The Rule basis of the ANFIS is of the form: $\begin{matrix} Rule 1 : If (X_{1} {isA}_{1}) and (X_{2} {isB}_{1}) then (f_{1} = s_{1} X_{1} + t_{1} X_{2}) + r_{1} \\ Rule 2 : If (X_{1} {isA}_{2}) and (X_{2} {isB}_{2}) then (f_{2} = s_{2} X_{1} + t_{2} X_{2}) + r_{2} \\ Rule 3 : If (X_{1} {isA}_{3}) and (X_{2} {isB}_{3}) then (f_{3} = s_{3} X_{1} + t_{3} X_{2}) + r_{3} \\ Rule 4 : If (X_{1} {isA}_{4}) and (X_{2} {isB}_{4}) then (f_{4} = s_{4} X_{1} + t_{4} X_{2}) + r_{4} \\ Rule 5 : If (X_{1} {isA}_{5}) and (X_{2} {isB}_{5}) then (f_{5} = s_{5} X_{1} + t_{5} X_{2}) + r_{5} \\ Rule 6 : If (X_{1} {isA}_{6}) and (X_{2} {isB}_{6}) then (f_{6} = s_{6} X_{1} + t_{2} X_{6}) + r_{6} \end{matrix}$

Here, the fuzzy sets are denoted as A _i and B _i and the output of the rectified signal is (f _i) got from the fuzzy region. The design parameters are specified as s _i, t _i and r _i respectively which are calculated from the training process.

3.2.1 ANFIS process in different Layers

Here, the step by step process of ANFIS is explained in the vaious layers as detailed below:

Process 1: First Layer of ANFIS

Here, the inputs are assigned and processed to the initial stage of ANFIS viz. node-i. The outputs are the fuzzy membership grades of the inputs. Then the ANFIS nodes are represented as follows $S_{i}^{1} = δ A_{i} (X_{i})$ (14) where, A _i is denoted as the linguistic label which linked with this node function. Then $S_{i}^{1}$ is represented as the membership function of A _i. The bell shaped function is selected by using δA _i (X _i) which is a maximum value of 1 and a minimum value as 0, like the generalized bell function: $δ_{k} (X_{i}) = \frac{1}{1 + (\frac{X_{i}^{2 ni} - A_{i}^{2 ni}}{m_{i}^{2 n_{i}}})}$ (15)

Process 2: Second Layer of ANFIS

In this layer, each node is a circle node tagged ‘Π’ which multiplies the incoming signals and sends the product out. For example, $S_{i}^{2} = δ A_{i} (X_{1}) X_{1} δ L (X_{2}) = w_{i}, for i = 1, 2$ (16)

From the above equation, every node output signifies the firing strength of a rule.

Process 3: Third Layer of ANFIS

In this layer, every node is a circle node marked ‘N’ symbolizing normalization. The i-th node estimates the ratio of the i-th rule firing strength to the summation of all rules firing strengths: $S_{i}^{3} = \frac{w_{i}}{w_{1} + w_{2}} = \bar{w}, for i = 1, 2 \dots 6$ (17) For simplicity, the outputs of this layer are termed as normalized firing strengths.

Process 4: Fourth Layer of ANFIS

The captioned stage comprises square nodes I which embodies some transfer functions in it. $S_{i}^{4} = \bar{w_{i}} (s_{i} X_{1} + t_{i} X_{1} + c_{i} X_{1}) = \bar{w} f_{i}$ (18)

Where i = 1, 2, … 6 and $\bar{w_{i}}$ is the output of layer. Then the parameter sets are denoted as (s _i, t _i, c _i). The parameters in this stage are characterized as consequent parameters

Process 5: Fifth layer of ANFIS

In the final layer, a solitary circle node is present which is branded as ‘Σ’ that estimates the overall output as the summary of all incoming signals, i.e., $S_{i}^{5} = \sum \bar{w_{i}} f_{i}$ (19)

The final stage output of ANFIS is minimized the error signal, which is correctly classified as preferred output. The performance of ANFIS is tested by giving more number of signals.

4 Results and discussion

The proposed hybrid technique is implemented in MATLAB/Simulink working platform. Here, the vibration signals are assessed in the healthy and faulty case motors. By employing S-transform, the feature extraction signals are gathered from the normal and faulty case motors. Prior to this, the pre-processing function is carried out in the input signal for banishing the noises. Subsequently, the extracted faulty & healthy signals are executed on the input of the ANFIS. Later on, the inputs signals are categorized into various kinds of signals. The classified outputs are No fault, IR fault, centred OR fault, opposite OR fault, orthogonal fault and BB fault. Here, the performance of the proposed hybrid method is analyzed with the 12k and 4k drive end bearing fault conditions. The accomplishment of the technique is assessed and its performances are illustrated.

4.1 Performance analysis and evaluation metrics in 12k drive end bearing faults

Now, we proceed with the evaluation of the performance of the proposed hybrid method. The disturbance signal is measured with the various amplitudes at the diverse time instants. The performance analysis of the different faults of the induction motor signals is pictured in the Fig. 3(a, b, and c). The approximate motor speed and the fault diameter are denoted as 1772 rpm and 0.007 inches respectively. Thereafter, these vibration signals are pre-processed and their performances are assessed in normal and faulty conditions of the motor. Likewise, the amplitude of the disturbance signal in IR fault, BB fault, centered OR fault, opposite OR fault and orthogonal OR faulty condition are estimated and pre-processed. Subsequently, S-Transformation is done for attaining the extracted feature signal and performances are demonstrated. Then, the signals are classified accurately by means of ANFIS. The proposed method feat is assessed with the S-transformation-FFNN and DWT-RBFNN. By means of S-transformation together with RBFNN, the classified signals are appropriately identified and their performances are demonstrated in Fig. 6. In the DWT-RBFNN technique, DWT is used for getting the decayed signals and their performances are shown in the Fig. 5. Thereafter, the signals are detected and classified by means of RBFNN. The normal and IR, BB, centered, opposite & orthogonal fault signals are represented in Fig. 3.

The six kinds of vibration signals are divided into small segments if equal length related to the synchronous signal and then averaged together. Hence, the faulty signals are effortlessly recognized. The kind of pre-processing depends on the nature of the signal. In this procedure, the Fig. 3(a) signals are divided into 0–10, 10–20, 20–30, 30–40, 40–50 and 50–60 (seconds) time instants. Thus the random noise is cancelled and the preferred signal is ushered in. Then, the faulty signals are easily recognized. In the same way, IR, OR and BB faulty signals are divided into these periods and these are pre-processed. The pre-processing IR, OR and BB signals are shown.

In the Fig. 5, the pre-processed 12k bearing faulty signals are normalized by using S-transformation and their performances are illustrated in the Fig. 5(a, b, and c). Similarly, the performance of another faults are determined.

The decomposed signals are applied to the ANFIS. The ANFIS is used to classify the signal whether it is faulty or not. Thereafter the extracted signals of normal, IR, centered, opposite and orthogonal OR faulty signals are applied to the input of the ANFIS and feat of the proposed technique is estimated analyzed. Now, the faulty (IR fault, OR fault & BB fault) and healthy induction motor vibration signals are assessed. The feat of the proposed hybrid method is contrasted with the S-transform-RBFNN, wavelet transform-RBFNN and S-transform-FFNN methods. The innovative method, S-transform-R BFNN, S-transform-FFNN and DWT-RBFNN methods are assessed in terms of accuracy, sensitivity and specificity. These parameters are estimated in the six conditions like IR faulty signal, centered, opposite, orthogonal OR faulty signal, BB faulty signal and No fault condition.

Similarly, the 48k drive end bearing faulty signals are evaluated and their performances are analyzed. Moreover, they are determined from the TP, FP, TN and FN values. Then the accuracy value is calculated in the four types of fault signal condition of induction motor. Accuracy is defined as a ratio of the number of correctly classified patterns to the total number of patterns. In the fault condition of the induction motor, the sensitivity values are calculated. Ratio of the number of correctly detected and classified positive patterns to the total number of actual positive patterns is called as sensitivity. Also, the specificity value is calculated in the fault condition of induction motor. Specificity is defined as a ratio of the number of correctly detected and classified negative patterns to the total number of actual negative patterns. These values are calculated by using the formulae, which are presented in [30]. Then the TP, TN, FP and FN values are tabulated in the various methods. Based on these values, the Accuracy, Sensitivity and Specificity values are calculated and tabulated in Tables 2 and 3.

In the proposed hybrid technique (S-transform -ANFIS), the feature of faulty signals is employed as the input of the ANFIS network. The no fault, IR, OR and BB fault of the induction motor is recognized from this neural network, also, the performance are evaluated. The TP, FP, TN, and FN values are determined from the neural network output. They are employed to assess the accuracy, sensitivity and specificity of the normal, IR, OR and BB faults of an induction motor. The proposed hybrid technique output is estimated and recorded. Moreover, accuracy, sensitivity and specificity vales of the current methods are estimated from the normal, IR, OR and BB faults of an induction motor and included in Table 1. Thus the accuracy, sensitivity and specificity of the new-fangled technique are determined and contrasted with the traditional approaches.

In the Table 2, represents the performance metrics of 12k drive end bearing faults in various methods. In the IR fault condition, the overall accuracy, sensitivity and specificity of the proposed integrated techniques are 96.25% , 93% and 96.5% . But, the accuracy, sensitivity and specificity of S-transform-RBFNN are 90.5% , 90% and 91% . Then the accuracy, sensitivity and specificity values of S-transform-FFNN are 89.75% , 88 and 91. Also, the accuracy, sensitivity and specificity of DWT-RBFNN are 89% , 87% and 91% . In centered OR fault condition, the accuracy, sensitivity and specificity of the proposed integrated techniques are 95.75% , 93% and 98.75% . But, the accuracy, sensitivity and specificity of S-transform-RBFNN are 88.5% , 87% and 90% . Also, the accuracy, sensitivity and specificity of S-transform-FFNN are 90.25% , 88.5% and 92% . It is clear that the proposed hybrid technique is efficient for locating the faulty condition of induction motor. Likewise, the BB faulty and No fault conditions accuracy, sensitivity and specificity values are estimated. Similarly, the performance metrics of 48k drive end bearing faults in various methods are analyzed and evaluated their accuracy, sensitivity and specificity values. And their comparison results are drawn in the Fig. 7.

4.2 Performance analysis and evaluation metrics in 48k drive end bearing faults

In this section, the proposed hybrid technique (S-transform -ANFIS) is analyzed in the 48k drive end bearing fault condition. Here, the approximate motor speed is 1772 rpm and the motor load is specified as 1. Then the fault diameter of the motor is 0.007 inches. The no fault, IR, OR and BB fault of the induction motor is recognized by using ANFIS, also, the performance are evaluated. The TP, FP, TN, and FN values are evaluated and also calculated the accuracy, sensitivity and specificity values of the induction motor. Here, the BB fault signals is analyzed and evaluated their pre-processing and features extraction signal which is illustrated in the Fig. 6. Similarly, all types of signals are analyzed and evaluated their performances.

Here, the performances of proposed hybrid method and existing methods are determined. The performance of proposed method is analyzed with the 12k and 48k drive end bearing fault conditions and it’s illustrated in the following figures.

From the above illustration, the accuracy, sensitivity and specificity values are analyzed with the six types of different conditions and their performances are evaluated. Similarly, the overall accuracy, sensitivity and specificity of 48k drive end bearing fault conditions are analyzed by using the proposed hybrid method. In orthogonal OR fault condition, the overall accuracy, sensitivity and specificity of the proposed integrated techniques are 95.75% , 93% and 9.75% . But, the accuracy, sensitivity and specificity of S-transform-RBFNN are 90.25% , 88.5% and 92% . Also, the accuracy, sensitivity and specificity of DWT-RBFNN are 87.5% , 86% and 89% . The classification rate of the proposed method is about 95% and the existing s-transform-RBFNN, S-transform-FFNN and DWT- RBFNN is about 90.5% , 87.5% , 85% respectively. However, the computation time of the proposed technique is about 2.149462 sec and for existing techniques, the computation time is 4.009416 sec, 3.459965 and 5.83428 sec respectively. From this, it is depicted that the proposed technique has better classification rate and computation time than that of the existing method. The testing results show that the proposed approach provides significantly high fault classification rate, accuracy, sensitivity & specificity and a better performance than previousapproaches.

5 Conclusion

The proposed technique has tested with 12k and 48k drive end bearing fault conditions of induction motor. The proposed method was implemented in MATLAB platform. The motor vibration signal was executed on the input of pre-processing stage. The pre-processed signals are applied to the S-transform. The extracted features are gathered from the output of S-transform. The extracted features are in the form of vector and applied to the ANFIS. The output of the ANFIS network has located the state of the induction motor as faulty or normal, and categorized the kind of faults. Now, the performance of the proposed method is assessed and the output of the proposed technique is contrasted with S-transform-RBFNN, S-transform-FFNN and DWT-RBFNN. Thus, the accuracy, sensitivity and specificity values of the new and old methods are estimated and contrast. The comparative outcomes are shown that the proposed controller classifies the faults efficiently compared with the other methods.

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