A novel intelligent predictive maintenance procedure for electrical machines

Transcription

1 A novel intelligent predictive maintenance procedure for electrical machines D.-M. Yang Department of Automation Engineering, Kao-Yuan University, No.1821 Chung-Shan Road, Loju Hsiang, Kaohsiung County, Taiwan 821 Abstract In this paper, a novel procedure has been developed for the condition monitoring of electrical machines. It is based on wavelet analysis and a singular value decomposition approach. The singular value decomposition method is used to extract salient features from the continuous wavelet coefficients. These features are used as inputs to an artificial neural networ (ANN) trained to identify the conditions of the monitored electrical machine under steady state operation. The ANNs are used to be an intelligent electrical machine condition detector. Results presented have shown that the approach developed can successfully applied and this proposed approach is effective for condition monitoring of electrical machines. KEY WORDS : Artificial neural networ, singular value decomposition, wavelet analysis 1 Introduction Diagnosis of malfunctions of process automation is important in modern manufacturing industries. Today s highly automated complex machinery systems require intelligently automated maintenance systems to effectively achieve the goals of Computer Aided Manufacturing (CAM) and Computer Integrated Manufacturing (CIM) and the maintenance function should involved in the move toward highly automated and integrated manufacturing systems. Three maintenance strategies have practically used in industry. The first is simply react to the machine breadown as and when it happens. This maintenance scheme is called breadown maintenance. This strategy can be used if the machine is inexpensive and the breadown does not cause any other damage. Otherwise, the cost of lost production, safety riss, and additional damage to other machines mae this scheme unacceptable. The second is to perform fixed time interval maintenance. Although this method reduced the chance of unexpected breadown, it has been found to be uneconomical. The stoppage for maintenance involves not only lost production time but also a high ris of introducing imperfections due to human error. The third is predictive (or condition-based) maintenance through condition monitoring, which depends on the condition of the machine. Condition-based maintenance (CBM) consists of continuously evaluating the condition of a monitored machine, without interrupting its operation, and successfully predicting the presence of faults before catastrophic breadown occurs. Such an approach can provide for properly planned maintenance and replacement of failing components at optimum periods. Thus, the application of a condition monitoring-based maintenance policy can help to minimise unnecessary costs and delays caused by the need to carry out unscheduled repairs. Induction machines are critical components in many industrial processes. In spite of their robustness and reliability, some faults are still unavoidable. Therefore, proper monitoring of electrical machines is highly cost-effective in reducing operation cost. The wavelet approach has advantages over traditional Fourier methods for signal analysis, particularly for signals containing discontinuities and shape spie. When Fourier transformation is performed, the

2 signal representation is moved from the time-domain to the frequency-domain. And this change of domain can lead to loss of information and to interpretation difficulties. This disadvantage is overcome in wavelet analysis which represents a signal by using shifted and scaled versions of a so-called mother wavelet and this enables examination of the frequency information of the signal as it evolves with time. This ability to represent simultaneously both time-domain and frequency-domain information is a significant advantage of the wavelet approach. The complex nature of information obtained from wavelet transforms mae subjective interpretation and diagnostic use difficult. In order to effectively interpret the wavelet map, the time-frequency domain is used instead of time-scale domain. Hence, time-frequency distributions of a couple of specifically simulated signals and the associated singular values performed by the singular value decomposition (SVD) technique are presented in this paper. In order to develop a reliable automatic diagnosis procedure to monitor the motor condition, artificial neural networs are employed as a motor automatic condition detector since they do not require an indepth nowledge of the behaviour of the motor system. Neural networs is a suitable analysis tool (Awadallah & Morcos, 2003) since their structure allows them to be trained to learn the characteristics of various motor conditions under different operating models. The training is performed using data obtained from the motor under various operating conditions. A training period is used to establish the weights and biases of the inter-connections of the networ. Once appropriately trained, the inter-connections within the networ itself form the desired input-output mapping which enhances recognition and diagnosis of the various motor conditions. In the following sections, a novel diagnostic procedure contains three procedures which will be introduced briefly in Section 2. Section 3 presents the simulation results of the proposed approach for a couple of specifically simulated signals and a real-time data acquisition system for experimental data collection. Section 4 introduces the implementation of artificial neural networs for automatic detection of the induction electrical machine condition and a conclusion will be presented in Section 6. 2 A novel diagnostic procedure 2.1 Wavelet analysis as the signal processing technique Wavelet analysis is an approach which decomposes a time-domain signal into components in different time windows and different frequency bands and presents the resulting information in the form of a surface in the time frequency plane, sometimes referred to as a scalogram (Rioul & Vetterli, 1991). The scalogram is similar in concept to the spectrogram but differs from in that the frequency resolution of the scalogram is logarithmic rather than linear, as is the case for the spectrogram. Because of the nature of the frequency resolution, the wavelet approach is more effective in analysing both the long-time, lowfrequency and the short-time, high-frequency content of a time signal. This characteristic is very useful for analysing pulse-lie and non-stationary signals.

3 Fig. 1 Morlet wavelet for f o = 1 The continuous wavelet transform of a square-integrable, continuous time signal x(t) is the inner product between x (t) and the analysing wavelet ψ ( ), which gives the wavelet coefficients a, b t 1 + * t b Wx ( a, b) = x( t), ψ a, b ( t) = x( t) ψ ( ) dt a a (1) where a is the dilation parameter governing the wavelet frequency b is the parameter localizing the wavelet function in the time domain and ψ * ( t) is the complex conjugate of the analysing wavelet ψ (t). There are a number of different complex or real valued functions used as analysing wavelets. The analysing wavelet used in this paper is the complex-valued Morlet wavelet (Farge, 1992), given by 2 M j2πf 0t t / 2 ψ ( t) = e e (2) where f is the central frequency of the Morlet wavelet and the value of f is taen 1 in this paper. o Figure 1 shows the real and imaginary parts of the Morlet wavelet together with its confining Gaussian envelope. An alternative formulation of the continuous wavelet transform can be obtained by transforming both the signal x (t) and the analysing wavelet ψ ( ) in the frequency domain: a, b t o ) * j(2πf ) b W ( a, b) = a X ( f ) Ψ ( af ) e df x + (3) * j(2πf ) b where X ( f ) and Ψ ) * t b ( af ) e are the Fourier transform of x (t) and ψ ( ) respectively. For an a easier implementation of wavelet transform, Equation (3) can be expressed in a discrete form as: ) W( a, b ) = a X ( f ) Ψ 2.2 Singular value decomposition for feature extraction m n m * ( a m f ) e j2πf b n The purpose of using a feature extraction procedure is to significantly reduce the quantity of data but, at the same time, retain the original salient information. It is well nown that the SVD has optimal decorrelation properties and provides a means of detecting dominant characteristics on a set of data. The (4)

4 SVD theorem states that any m by n matrix W can be decomposed and written as the product of matrices (Therrien, 1992). p T T W ( a, b ) = U V = λ u v (5) m n mm mn where the superscript, T, donates the transpose. U is an orthogonal m by m matrix made up of left singular vectors u, V is an orthogonal n by n matrix made up of right singular vectors v, and is an m by n matrix of non-negative real singular values and decrease monotonically from the upper left to the lower right of. The singular value of W are represented by λ 1 λ 2 λ 3... λp 0, where p = min( m, n) In most machine condition monitoring and diagnosis schemes, only the first one or two of the singular values will be considered since these account for the large majority of variations in the analysed data set. 2.3 Artificial neural networs as an automatic classifier Artificial neural networs (ANNs) can be used to identify and classify complex fault patterns without the need for a detailed nowledge of the behaviour of the system in which they occur or of the mechanics responsible for the generation of their characteristics. ANN design is premised on mimicing the human nervous system by using massively parallel nets composed of many computational elements connected by lins with adjustable weights. Of all the ANN types in current use, the multi-layer perceptron (MLP), trained using the bac-propagation algorithm (or a variant), is the most commonly applied. A full description of the MLP can be found in (Lippman, 1987). Pre-processing of the signals to be used as inputs to the networs can mae neural networ training more efficient due to a significant reduction of the dimensionality of the input data. Before training, it is also useful to scale the inputs and target outputs so that their values fall within a specified range. The normalization procedure used here, described in (Bishop, 1995), is V Vmin V n = ( ) (6) V V max min where V is the maximum magnitude across all of the input patterns and V is the minimum max magnitude across all of the input patterns. When the ANN training is complete, the performance of the ANN can be judged by the success rate (SR) of how many unseen test patterns are correctly classifier. The SR is defined as follows: UPC SR = 100% (7) TP where UPC is the number of unseen patterns correctly classified and TP is the total number of patterns. 3 Implementation In order to evaluate the performance of the proposed procedure, both simulated time series data and real time machine data collected in lab experiments are used to demonstrate the approach. 3.1 Simulated data generation nn = 1 min

5 Fig. 2 (a) A periodic impulse signal Fig.2 (b) Wavelet representation of Fig. 2(a) Fig. 2(c) The first right singular vector ( v1 ) Fig. 2(d) The second right singular vector ( v 2 ) To understand better wavelet representations, a number of simulated signals are analysed using the continuous wavelet transform approach and the singular value decomposition method for the preliminary study. The simulated signals are sampled at 1000 Hz. Figure 2(a) shows the periodic impulse signal x( t) = δ (cos(2πt)), where δ (t) is a Dirac delta function. A wide-band impulse frequency spectrum can be clearly seen from Figure 2(b). Figure 2(c) and (d) show the first and second right singular value decomposition from the wavelet coefficients. The impulse patterns in the periodic impulse signal can be easily caught by the SVD analysis. Figure 3(a) shows a stationary signal, which consists of two sinusoids, one at 25Hz and one at 60 Hz. The signal is given by: x( t) = cos(2π 25t) + cos(2π 60t) (6) In this signal, the frequencies and amplitudes of the two frequency components (25 Hz and 60Hz) do not change with time, which can be clearly identified in the wavelet representation, shown in Figure 3(b). The two sets of the first and second left singular vectors are plotted in Figures 3(c) and (d), which distinctively show the two separate frequency components in the stationary signal by the SVD analysis. From above simulation results obtained, they have demonstrated that SVD approach is capable of identifying salient patterns from stationary or non-stationary signals. From these singular values sets, they

6 can be used as characteristic features for on-line condition monitoring of electrical machines under various operations. Fig. 3(a) A stationary signal Fig. 3(b) Wavelet representation of Fig. 3(a) Fig. 3(c) The first left singular vector ( u1 ) Fig. 3(d) The second left singular vector ( u 2 ) 3.2 Experimental setup and real-time data acquisition Fig 4 : Experimental rig set-up layout

7 The experimental setup used in the study consists of a 2.2 W, 1740 rpm, 4-pole induction machine driving a 5 W DC generator via a flexible coupling, as shown in Figure 4. In order to test the proposed predictive maintenance procedure for condition monitoring of electrical machines, there are four conditions investigated in this experiment. The four conditions studied are: (1) Normal condition under no-load operation (NN) (2) Normal condition under full-load operation (NF) (3) Single phase open under no-load operation (SN) (4) Single phase open under full-load to dead operation (SF) A piezo-electric accelerometer was mounted on the housing of the induction electrical machine to measure vibration. The measured vibration signal was fed to the National Instruments SCC-ACC01 signal conditioning installed into the SC A real-time data acquisition device (Type NI 6062E) was used to record vibration signal. In this experiment, a total of 870 vibration signatures of 2048 points sampled at 4 Hz were recorded. 4 Experimental Results and discussion Figure 5 is depicted one of the vibration signatures for the induction electrical machine from normal operation to one of three phases open under no-load operation. Fig. 5 Vibration signal under no-load operation In order to automatic detection of the induction electrical machine condition, the multi-layer perceptron (MLP), trained using the bac-propagation algorithm is used in this study. Before training the ANN, it is useful to extract salient features. Otherwise garbage in and garbage out. The continuous wavelet transforms are used to perform signal analysis using equation (4) in order to get more diagnostic information. All the ANN input data are normalized between 0.1 and 0.9 using equation (6). The networ is trained using the bac-propagation algorithm. Since the MLP-type of neural networs is of the supervised learning class, target data is required to implement networ training. The target vectors are T defined as the four different patterns; T 1 = T [0.9,0.1,0.1,0.1 ], T 2 = [0.1,0.9,0.1,0.1 ], T T 1 = T [0.1,0.1,0.9,0.1 ] and T 1 = [0.1,0.1,0.1,0.9 ], for the no-load normal condition, full-load normal condition, no-load single phase open and full-load single phase open, respectively. 0.9 indicates the presence of a condition and 0.1 indicates absence of that condition.

8 The networs topology has 50 inputs nodes (corresponding to the first columns of the matrices U mm ), four output nodes (corresponding to four machine conditions examined) and 15 hidden nodes. The number of hidden nodes is determined using geometric pyramid rule which suggests the number of hidden layer nodes as being the square root of the product of number of input and output nodes (Hansen, 1998). The sigmoid function is chosen as the transfer function to ensure node outputs between 0 and 1. The collected files listed in the table 1 are divided into two groups. One is used to train the ANNs, the other is used to test the ANN performances. The learning coefficient and the momentum coefficient are chosen as 0.95 and 0.01, respectively. The trained networs gave 100% correct prediction for the training patterns, which indicates that the networs have been successfully trained. Table 1. File descriptions Case NN NF SN SF File index The performances of the trained networs were checed by using unseen patterns. The trained neural networs can classify the four different conditions with a high SR using equation (7), as listed in Table 2. Table 2. Performance of the networs Case NN NF SN SF SR 100% 100% 100% 80.71% 5 Conclusions The primary objective of this wor is focus on developing an integrated system using continuous wavelet transforms as a signal preprocessor and a SVD technique as salient feature extraction. The ANNs are used to be an intelligent motor condition detector. Results presented have shown that the approach developed can successfully applied and this proposed approach is effective for condition monitoring of electrical machines. Acnowledgements The author wish to than the National Science Council for their financial support under project numbers E and E References Awadallah, M.A. & Morcos M.M. (2003). Application of AI Tools in Fault Diagnosis of Electrical Machines and Drives An Overview. IEEE Transactions on Energy Conversion, 18(2), Bishop, C.M. (1995). Neural Networs for Pattern Recognition. Oxford: Oxford University Press. Farge, M. (1992). Wavelet Transforms and Their Applications to Turbulence. Annual Review of Fluid Mechanics, 24, Hansen, J.V. (1998). Comparative Performance of Bacpropagation Networs Designed by Genetic Algorithms and Heuristics. International Journal of Intelligent Systems In Accounting, Finance & Management. 7(2), Lippman, R.P. (1987). An Introduction to Computing with Neural Nets. IEEE ASSP Magazine. 4(2), Rioul, O and Vetterli M. (1991). Wavelets and Signal Processing. IEEE Signal Processing Magazine, 8,

9 Therrien, C.W. (1992). Discrete Random Signals and Statistical Signal Processing. Prentice Hall. New Jersy :Englewood Cliffs.