1 Introduction

Electric induction motors are components of great importance in the majority of industrial plants equipment. They are largely used in the actuation of pumps, compressors, fens, processing equipment, and load handling and in several other applications. These frequent usages are mostly due to the motors characteristics such as: robustness, simple mechanic, and easy adaptation for several operation conditions. However, during its functioning, the electric motors are subjected to large loads, exposed to aggressive environment, which, together with its natural aging, can cause the failure of the equipment.

The several faults that occur in the induction machines may induce severe consequences in the industrial process. The main problems are related to the raise of the production costs, the worsen of the process condition and security, and the worsen in the final product quality. Much of these faults are progressives. The vibration analysis has been one of the techniques more used for detection and diagnosis of faults due to its features like ease of usage, relatively low cost, non-intrusive techniques, and so on. Besides, through the analysis of the signals, spectrum one can detect defects both mechanical and electrical origin.

The increasing necessity of the monitoring and diagnosis of machines and industrial equipment has increased the research of new techniques of signal-processing analysis, with the objective of obtaining relevant information about the condition of a machine or equipment from the measured data [1]. Classical techniques of signal processing of time series, such as the fast Fourier transform, power spectral density, correlation methods, and other techniques based on integral transform and statistical analysis, have been used for decades in the fault detection of machines and mechanical components [2,3,4]. These techniques are very efficient and are fully consolidated in engineering solutions when used for analysis in the stationary regime. In Martin-Diaz et al. [5], it is presented a method for the detection of cracks in a rotor of a three-phase electric motor fed by a frequency inverter under different load scenarios using classical signal-processing techniques. Still, in the stationary regime, consolidated results of fault detection and identification of more frequencies associated with faults using spectral analysis can be found in Delgado-Arredondo et al. [6] and Talhaoui et al. [7]. However, the results show that these kinds of analysis are not effective in the detection of non-repetitive anomalies or when the faults occur in a short time duration and in the analysis of non-stationary and transient signals [2].

In the last two decades, the wavelet transform has been used with success in several areas of scientific knowledge, especially in the monitoring and fault detection in mechanical systems, beside of other engineering branches. There are lots of studies that make a use of this transform with relatively accomplishment, as one can see in Yan et al. [8]. In addition, in Kar and Mohanty [9], a wavelet transform analysis is presented and compared with a Fourier-based one. The importance of the usage of techniques based on the wavelet transform can be noted given the number of works published in the area. For example, in Yan and Gao [10], applications of the wavelet transform and other emerging techniques such as the Hilbert–Huang transform are presented for detection and monitoring of faults in mechanical systems.

A great number of works are aimed in the characterization of transient phenomena through the use of wavelet-based techniques. The analysis done in Widodo and Yang [11] demonstrates the efficiency of the wavelet transform in the analysis of such phenomena. Other works make comparisons between the wavelet with classical techniques such as Fourier transform for non-stationary signals analysis, where the advantages in the usage of wavelet-based techniques can be seen [12,13,14,15]. In general, techniques based on the wavelet transform are widely used for parameter extraction in several engineering applications. The use of statistical classifiers and specialized systems has been widely used for the detection and classification of failures in mechanical systems [16,17,18]. In addition, wavelet transform-based techniques have been largely used with machine learning, neural, and statistical classification for applications of fault detection in electric motors [19,20,21,22,23]. Other applications have been using successfully for the same purpose wavelet together with neural networks and fuzzy logic-based techniques [24,25,26]. The literature presents several applications of techniques based on the wavelet transform for fault detection in other kinds of rotating machines in the non-stationary regime [27,28,29,30,31].

The main contribution of this paper is to present the use and comparison of techniques of dimensionality reduction, together with the wavelet packet transform, for the detection of faults in electric motors by means of the analysis of vibrations signals in non-stationary operations (during the start of the motor). In the methodology proposed, three techniques for dimensionality reduction are used: the principal components analysis (PCA), the linear discriminant analysis (LDA), and the independent components analysis (ICA).

2 Mathematical background

2.1 Wavelet packet transform (WPT) energy entropy

Wavelet packet transform (WPT) is the generalization of the classic wavelet transform. In the WPT, the coefficients of detail are decomposed at the first decomposition level, generating what is known in the literature as wavelet packet tree [32]. In this way, results are obtained with better time- and frequency-domain resolution [33, 34]. The wavelet packet transform of a signal x(t) is defined in:

$$\begin{aligned} x^{n,j}_{p} = 2^{-j/2}\int \limits _{R} x(t) \overline{\mu _{n}(2^{-j} t-p)}\mathrm{{d}}t \end{aligned}$$
(1)

where \(\mu _n(t)\) is the function wavelet packet; j represents the number of decomposition levels, also known as scale parameters; the symbol p represents the position parameter; and n is the number of packets (frequency sub-band) due to the decomposition process. To the signal x(t), decomposed by WPT, the following expression is used:

$$\begin{aligned} & w_{2n}(t)= sqrt{2}\sum _{l}h(k)W_n(2t-1)\nonumber \\ & w_{2n+1}(t)= \sqrt{2}\sum _{l}g(k)W_n(2t-1). \end{aligned}$$
(2)

In Eq. (2), h(k) and g(k) are orthogonal, so that multiresolution analysis of orthogonal wavelet decomposition can be applied to wavelet packet decomposition to get the signal wavelet packet, which in turn is expressed by Learned and Willsky [34]:

$$\begin{aligned} g^n_j = \sum _k d_k^{j,n}\mu _n(2^j t -k), \end{aligned}$$
(3)

where \(d_n^{j,n}\) is decomposition coefficient.

The energy method calculation of each packet from decomposition WPT is a more robust signal representation than using directly the decomposition coefficients. The energy associated with the wavelet packet decomposition is given by:

$$\begin{aligned} E_i = \int \limits _{-\infty }^{+ \infty }x_j^i(t) {\rm {d}} t. \end{aligned}$$
(4)

The total signal energy is expressed by:

$$\begin{aligned} E_{\rm {tot}} = \sum _{i=1}^{2^j}E_i. \end{aligned}$$
(5)

The wavelet packet energy represents energy stored in a particular frequency band and is mainly used in this study to extract the dominant frequency components of the signal. The energy of each sub-band is defined as \(E_i\). In practical signal analysis engineering, the energy has usually a great value [35, 36]. The normalized energy value, which corresponds to the energy of each wavelet packed, is given by:

$$\begin{aligned} P_\mathrm{{l}} = \frac{E_i}{E_{\mathrm{{tot}}}} \end{aligned}$$
(6)

where \(P_{\rm {l}}\) can be assumed as the probability distribution of each sub-band.

The concept of entropy has been widely used as a measure of the system disorder. In this paper, the entropy is obtained by the WPT. The energy probability distribution for each sub-band is given by Eq. (6). Using the definition proposed by Shannon, the entropy is expressed by:

$$\begin{aligned} S = - \sum P_\mathrm{{l}} \ln (P_\mathrm{{l}}). \end{aligned}$$
(7)

For better classification, some important features may derive from these coefficients. Entropy is useful, because it is a tool to measure the uncertainty of the information content for a given system, and it is often used in signal processing, information theory, pattern recognition, and so on. Some typical types of entropy are Shannon entropy, log energy entropy, Renyi entropy, and Tsallis entropy. Entropy can be computed based on energy [37]. The information across time and frequency domains of the vibration signal can be accurately detailed using the wavelet packet decomposition techniques. Since in the wavelet packet analysis, the details are divided into smaller sub-bands, it is more flexible than discrete wavelet analysis. Based on wavelet packet analysis, a lot of basis (in the vector space) are produced that lead to more detailed representation of signal in the time–frequency domains.

2.2 Feature dimension reduction methods

2.2.1 Principal component analysis (PCA)

Principal component analysis (PCA) is a statistical technique applied in several fields and it is widely used to find patterns in high dimension data, reducing the redundancy of information presented in a data block through the projection of the original data group onto a subspace which has reduced dimensions and defined some orthogonal variables that contain the most part of the original data variance.

Let us consider \(X = {x_1, x_2, ..., x_m}\) a set of data which has the dimension m. X can be decoupled in the following way showed by Eq. (8):

$$\begin{aligned} X = TP^T = \sum _{i=1}^{m}t_i p_i^T, \end{aligned}$$
(8)

which is defined as the principal component vector and \(p_i\) is the score vector. The least important components, which generally describe the noise presented in the data, can be discarded without losing significant information. In this way, the matrix X can be rebuilt as the summation that involves an estimation value \(\hat{X}\) and the residual effect E, so

$$\begin{aligned} \hat{X} = \sum _{i=1}^{k} t_i p_i^T, \end{aligned}$$
(9)
$$\begin{aligned} X = \hat{X} + E, \end{aligned}$$
(10)

where k represents the number \(t_1 ... t_k\) of principal components. The score vectors form a reduced dimension subspace to be used for subsequent analysis.

In the study, principal component analysis (PCA) is used as feature extraction and data dimensionality reduction. A long study concerning this technique can be seen in Varanis and Pederiva [38] and Jolliffe [39].

2.2.2 Linear discriminant analysis—LDA

Linear discriminant analysis (LDA), also known as Fisher analysis, is a statistic multivariate method used for obtaining the characteristics that distinguish the members of a group from the other in a way that, knowing the characteristics of a new individual, the group, where it belongs can be predicted [40]. For the purpose of reducing the dimensionality of the data using LDA, the covariance matrix belonging to the class is defined as:

$$\begin{aligned} S_{W} = \sum _{k=1}^K S_k, \end{aligned}$$
(11)

in which

$$\begin{aligned} S_k = \sum _{n\in C_{k}} (x_{n}-m_{k})(x_{n}-m_{k})^T. \end{aligned}$$
(12)

Being

$$\begin{aligned} m_k = \frac{1}{N_\mathrm{{K}}} \sum _{n\in C_{k}} x_{n}. \end{aligned}$$
(13)

In Eq. (13), \(N_\mathrm{{K}}\) is the patterns in the class \(C_\mathrm{{K}}\), \(x_n\) is the nth element of the vector of characteristics, and k is the total number of classes present in the data. The covariance matrix between the classes is defined as:

$$\begin{aligned} S_{B} = \sum _{k=1}^k N_k(m_{k}-m)(m_k-m)^T, \end{aligned}$$
(14)

where m represents the data global mean, and can be defined as:

$$\begin{aligned} m = \frac{1}{N} \sum _{n=1}^{N}x_n = \frac{1}{N} \sum _{n=1}^{N} N_k M_k. \end{aligned}$$
(15)

The total covariance matrix is defined as:

$$\begin{aligned} S_t = S_W + S_B, \end{aligned}$$
(16)

so that the projection matrix can be calculated as:

$$\begin{aligned} W = \arg _W \max {(WS_W W^T)^{-1}(WS_B W_T)}, \end{aligned}$$
(17)

\(\arg _W \max\), returns the position x in which W is maximized.

From the projection matrix, the LDA coefficients are obtained, as shown in

$$\begin{aligned} y = W^t x. \end{aligned}$$
(18)

In Eq. (18), x denotes the characteristic vector.

In the study, Linear Discriminant Analysis (LDA) is used as feature extraction and data dimensionality reduction. A deeper study concerning LDA can be seen in Xanthopoulos et al. [41].

2.2.3 Independent component analysis (ICA)

The independent component analysis (ICA), when applied in a data, produces independent components which in fact constitute the basis of the subspace in which the signals will be represented [40].

The technique can be presented in the form of \(S = [S_1,{\ldots },S_M]^T\), which is a random vector with M component statistically independent. Applying the linear transformation like \(A \rightarrow S\) (considering A a \(n \times m\) matrix), the vector X can be obtained by the following:

$$\begin{aligned} X = AS. \end{aligned}$$
(19)

For the sake of simplicity, it is considered that \(m=n\), so that each component h(k) will be given as:

$$\begin{aligned} X_i = \sum _{j=1}^M a_{ij}S_j. \end{aligned}$$
(20)

In Eq. (20), \(i=1,{\ldots },M\) and \(a_i = [a_{i1},{\ldots },a_{iM}]\) is the vector containing the i-esim line of the matrix A, so that the vector \(X_i\) is given by:

$$\begin{aligned} X_i = a_i^T S. \end{aligned}$$
(21)

The independent components analysis consists in the estimative of the matrix A and the vector S [41]. Analytically, it consists in a transformation W that when applied to X produces statistically independent components, so that

$$\begin{aligned} \hat{S} = WX = WAS, \end{aligned}$$
(22)

where and are inverse of each other.

In the study, independent component analysis (ICA) is used as feature extraction and data dimensionality reduction. A deeper study concerning ICA can be seen in Stone [42].

3 Experimental setup

3.1 Test bench

The experiments were performed in the Faculty of Mechanical Engineering of the University of Campinas in the Vibration and Control Laboratory. The test bench used in this work (Fig. 1) consists of a three-phase induction motor {1}, a direct current machine {4}, a bench of variable electrical resistances, a three-phase varivolt, a measuring system, and a microcomputer. The direct current machine works as an electric generator, powering the electrical resistances bench, actuating as load to the induction motor. Varying the current of excitation of the electromagnetic field of the DC generator or altering the resistance bench, one can vary the load of the motor. In Fig. 1, a general view of the test bench can be seen.

Fig. 1
figure 1

Test bench

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The faults were introduced in the electric motor, WEG (FH 88747), cage rotor, 5 CV, 1730 rpm, 220 V, 60 Hz, 4 poles, N category, 44 bars, 36 slots, SKF 6205–2Z bearing, ID-1, 100L frame, B class of isolation, FS 1.15, Ip/In 7.5, IP 55, and 13.8 A. To perform the electric faults test, such as short circuit between the stator winding turns, the induction motor was modified. To simulate a low isolation, between the electrical coils in the same phase, four derivations were extracted in a coil. These derivations were organized externally and linked in series (two at a time) with a resistance bench, from 1 to 100 W (each one), connected in parallel, which are then added to the circuit by means of a group of interrupters for the current intensity control, keeping always the nominal load of the motor.

The electric generator is coupled with the motor through flexible coupling {2} and a torque meter {3} of S. Himmelstein and Company, model MCRT 9-02T(1-3), 0–7500 rpm, bidirectional and maximum torque of 1000 lb-in, which, however, was not used in this work.

Each coil consists in 26 spirals with a 16 diameter. As each phase is formed with 6 coils, there are a total of 156 spirals per phase. Thus, the setup allows the analysis of the low isolation between at least two spirals and at maximum ten for a given phase, corresponding to the percentages 1.2% (2/156) and 6.4% (10/156) of low isolation, respectively. The short-circuit current was limited to 10 A inserting resistors between the terminals of the spirals in short circuit, so that the motor could work in an indefinite time and without the isolation commitment of it as well as characterizing the beginning of a real situation of low isolation (short circuit) between spirals.

The excitation by phase unbalance was obtained inserting a variable electrical resistance in series with one of the source phases of the electric motor. For the mechanical faults, the unbalancing was added through the insertion masses in the axle end not coupled with the motor. The mechanical clearance was inserted loosening the electric motor fixation bolt. The start up was performed with the load related to the DC motor inertia. After that, in the stationary regime, the load was added through the motor control system until it reached 80.0% of the nominal load. All the tests were performed in the same conditions.

For all the detection of all the faults, the accelerometers were positioned in four different locations, as one can see in Fig. 2, where they are called: accelerometer 1 (ACC1), accelerometer 2 (ACC2), accelerometer 3 (ACC3), and accelerometer 4 (ACC4).

Fig. 2
figure 2

Position of the accelerometers in the induction motor

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3.2 Vibration signal acquisition

In the data acquisition, the NI-6251 board of National Instruments was used. The vibration signals were subjected to an anti-aliasing filter with a 2 kHz of cut frequency. Before the tests were done, the test benches were balanced and aligned with the purpose of eliminate vibrations from undesirable sources. In this manner, it was possible to determine the normal work condition of the motor–generator coupling (bench signature), which was found to be 0.5 mm/s of vibration amplitude in the stationary regime, according to the standard VDI 2056, (VDI 1964). The signals were obtained in the radial plane (vertical and horizontal positions) of the electric motor, both in the coupling and venting side.

The signals were taken with a 5 kHz sample frequency and 20480 points (Fig. 3), with the purpose of analyzing the entire frequency band in which the faults are identified.

Fig. 3
figure 3

Vibration signals measured (20480 points)

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It was measured randomly 480 vibration signals, being them divided into the faults imposed: 240 signals were measured for each of the mechanical faults in the fault and faultless condition, and 240 signals were measured for each of the electrical faults in the fault and faultless condition; all of these measured in the non-stationary regime (motor start up). In Fig. 3, one can see a vibration signal sample of the motor in the start up, using 20480 points. As one can see by the figure, with this number of points, the signal present the stationary and non-stationary regime of the motor. For the faultless condition, 960 signals were obtained in the non-stationary regime in 240 measurements which were performed using the four accelerometers positioned in the induction motor (Fig. 2). As for the fault condition, 240 signals in the non-stationary regime were obtained for each fault condition (Table 1) from 60 measurements (for each fault condition) which were performed randomly and with the four accelerometers. The accelerometers used were DeltaTron Accelerometer-Type 4508 Brüel & Kjær, which has a frequency range from 0.3 Hz to 8 kHz. The acquisition system used was the USB-6251 from National Instruments and a Brüel & Kjær Model signal conditioning.

Table 1 Summary of the conditions introduced in the motor through the test bench
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Table 1 presents a summary of the conditions introduced in the motor through the test bench.

4 Proposed methodology—parameters extraction and classification

4.1 Vibration signal processing

The literature shows that the application of the wavelet transform to non-stationary signals demonstrates the ability of this technique to capture the frequency variations of the signals and to detect short-term transients with an excellent time scale and time–frequency location [6], overcoming the limitations presented by techniques based on the Fourier transform. Figure 4 shows a random sample of an induction motor vibration signal for analysis (Fig. 4a) and the frequency response based on the wavelet transform for the non-stationary (Fig. 4b) and steady-state regime (Fig. 4c).

Fig. 4
figure 4

CWT applied to a sample vibration signal

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The method proposed for the classification consists in the application of the WPT to the signals until the fourth level of decomposition using different wavelet filters (Daubechies, Symlet, Coiflet, and Discrete Meyer) resulting in 16 frequency sub-bands or packets. The decomposition until the fourth level showed to be sufficient for the detection of irregularities in the startup signal frequency spectrum.

The energy, the relative energy, and the entropy of each frequency sub-band of the fourth level are then calculated. Another point that justifies the use of the WPT decomposition only until the fourth level is that the energy distribution pattern of the signals analyzed has more concentration until the sixteenth frequency sub-band. Figure 5 presents the wavelet packet relative energy signature for a decomposition using the DMey filter for each fault.

Fig. 5
figure 5

Wavelet packet energy signature for each class

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4.2 Dimensionality reduction

The energy–entropy vector is first obtained for each signal using the values obtained from the wavelet packet sub-band relative energy and entropy calculations. The vector obtained has 64 characteristics were half of them are relative energy parameters and the other half are entropy parameters. The characteristic vector’s dimensionality of each signal is reduced using separately the PCA, ICA, and LDA methods. For all of these methods used, five reduction components are used. Finally, the classification is done using the parameters of the new reduced vector with the use of the k-nearest neighbors algorithm (k-NN). Figure 6 presents the diagram of the proposed methodology for the signal acquisition and the parameter extraction and classification.

The energy and entropy parameters associated with the WPT without the characteristic vector dimensionality reduction are not sufficient for the classification to be done efficiently, as shown in Varanis and Pederiva [43]. In addition, all algorithms and vibration signals processing steps were done using the software MATLAB.

Fig. 6
figure 6

Block diagram of the proposed methodology

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5 Results and discussion

The extraction of the relative energy and entropy parameters from the start up signals of the motor is done using different wavelet filters (see Sect. 4.1) to the data set (see Sect. 3.2), thus obtaining the energy–entropy vector for each signal. After the construction of the energy–entropy vector, a dimensionality reduction is done by means of the PCA, LDA, or ICA techniques (see Sect. 4.2). The reduced vector is then used for the classification by means of a k-NN classifier.

For the classification of the mechanical and electric faults, five classes will be considered for the following motor conditions: faultless, short circuit, phase imbalance, unbalance, and mechanical clearance (Table 1). In addition, the classification is done using the following neighbors’ number: k = 3, 5, 7, and 9. The results showed no significant variations in the hit rates for the values of k used. In addition, 30% of the signals measured were used for training and 70% for classification.

In Table 2, the hit rates for the faults classification are showed using wavelet-PCA, LDA, and ICA together with the Daubechies filters with the motor working in the non-stationary regime. Through the wavelet-LDA analysis, one can see a high hit rate for the proposed filters, and despite being small, a slight raise in the rate with the filter support rising. This occurs due to the fact that the perfect reconstruction of the signal, done through the application of the inverse wavelet transform (IWT), in the discrete of packet form, requires a high support and a wavelet form compatible with the signal form. Filters with low support generally alter the form of the signal [44].

Table 2 Global hit rates in the fault classification in the non-stationary operation (Daubechies filters)
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In Table 3, the hit rates for fault characterization are presented using the Wavelet-PCA, LDA, and ICA using Coiflet filters, which were also done with the motor in the non-stationary operation.

Table 3 Global hit rates in the fault classification in the non-stationary operation (Symlet filters)
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Table 4 shows the results of the hit rates using the symlet and discretized Meyer filters, with the motor in the same operational condition as in the other cases. In addition, it is possible to note the relation between the filter support and the global hit rates.

Table 4 Global hit rates in the fault classification in the non-stationary operation (Coiflets and DMeyer filters)
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In this work, a development of a modern and efficient model for automatic classification of anomalies in electric motors by means of the wavelet packet decomposition techniques was presented. The classification was made through the characteristic extraction and waveform analysis using the energy and entropy parameters. The understanding of the synthesis (composition) and analysis (decomposition) processes in the wavelet packet transform, as the application of a low-pass and high-pass filter bench followed by a subsampling (of in the analysis) or preceded by a super sampling (if in the synthesis), is fundamental to the method efficiency, since the filter selection is done by this understanding.

The method proposed reduces the size of the data dimensionality and the recognition of the main features of the signal without losing the original ones. It is worth noting the efficiency in the anomaly classification of the signals and the high hit rates in the non-stationary regime. The experimental results showed a potential in the implementation of this technique in a monitoring and fault detection system, which is a relevant result in these applications.

The LDA and the PCA are studied as methods of characteristics dimension reduction to optimize the recognition algorithm and improve the classification rate. It was demonstrated that the most efficient fault classification can be achieved by the LDA. Besides, the results show that the LDA improves significantly the recognition measures in association with all filters used for decomposition. It is worth noting the anomaly classification of the signals and the high hit rates in the non-stationary regime, which is the main advantage of the proposed method. In addition, the ICA-based method did not show adequate to this application.

Therefore, the conception of this characteristics extraction system (wavelet-PCA and wavelet-LDA) allows one to perform the fault classification in a robust way and with great speed in the result acquisition, allowing its application in a real-time system, since even using an extremely simple classifier (k-NN), high hit rates in the motor fault classification were obtained. The use of techniques based on wavelet transform in non-stationary signals demonstrated the capacity of this technique in following the frequency variations of the signals and also to detect short-duration transients, with an excellent time-scale position, surpassing lots limitations presented by the techniques based on the Fourier transform.

It should be noted that the usage of only the relative energy and entropy is not sufficient for the correct fault classification. As for the use of only these parameters, the global hit rates were low. For this reason, it was proposed the use of the reduction methods.

As seen, one can conclude that the techniques used, as well as the model proposed for the classification, allow a great number of application possibilities in the monitoring and fault detection area, gaining a more precise characterization of the machine conditions, which improves the decision making process, overpassing the limitations presented by the basic techniques based on the Fourier transform.

Given the use of the wavelet filters for data extraction, it was noted that:

  • The decomposition and reconstruction filters have to present frequency responses with the same characteristics as the high- and low-band filters.

  • The decomposition and reconstruction filters have to present similar behavior as the QMF filters.

  • The Haar filter presented the worst results in the classifications due to the fact that is an finite impulse response (FIR)-type filter with linear phase; its response in frequency is very far from the ideal and low support.

  • The Daubechies, Symlet, and Coiflets also presented high hit rates because of being FIR type filters with nonlinear phase and frequency response tending towards the ideal as the support is raised. For that reason, the best hit rates are observed when filters with higher supports are used (DMey, Daub-40, Sym10, coif4, and coif5).

  • The Discrete Meyer filter presented the best results in the great majority of the tests because of being an infinite impulse response (IIR)-type filter with phase close to linear. The frequency response with this filter is good, near to ideal and high support.

6 Conclusion and remarks

The proposed method reduces the size of the data dimensionality and it recognizes the main characteristics of the signal without losing the signal’s original ones. It is worth noting the efficiency in the classification of the anomalies of the signals analyzed and the high hit rates in the motor’s start up, which is undoubtedly the main vantage of the proposed method. The experimental results pointed out to a potential implementation of these techniques in a monitoring or fault detection system. The work proved to be of great importance in the monitoring, fault detection, and signal classification contexts. Therefore, the conception of this characteristic extraction method (wavelet-PCA, wavelet-ICA, and wavelet-LDA) allows one to perform the fault classification in a reliable manner and with great rapidity, which makes it possible the application in a real-time system, because a simple and intuitive classifier (k-NN) was used and satisfactory hit rates in the fault classification of the motor studied were obtained. This is so because the LDA, besides reducing the dimension of the data, makes their discrimination, which is not done in the PCA, which shows more adequate for a stationary regime analysis [43]. The method based on the ICA is adequate in other types of analysis such as combined faults. In addition, the combination of the Discrete Meyer (DMey) wavelet filter and the LDA technique is seen as the best alternative for the characteristic extraction in the non-stationary regime, considering the application presented.