A Health Degree Evaluation Algorithm for Equipment Based on Fuzzy Sets and the Improved SVM

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1 Journal of Computational Information Systems 10: 17 (2014) Available at A Health Degree Evaluation Algorithm for Equipment Based on Fuzzy Sets and the Improved SVM Tian XIA 1, Xiaohui CAI 2, Yongbo YANG 1, Dabo ZHANG 1, 1 School of Information, Liaoning University, Shenyang , China 2 State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang , China Abstract Classification accuracy is a pivotal problem for SVM. We propose an algorithm of SVM soft-output to improve the Classification accuracy. This algorithm is achieved by removing the limit of sign function of every node in the output layer, which makes samples belong to a category by probability. Furthermore, the fault status evaluation is achieved with a kind of health degree evaluation algorithm based on fuzzy sets and SVM. The contrast experiment results show that the proposed method has higher superiority than other methods, and it can be used for the monitoring and fault diagnose of industrial equipments. Keywords: Health Degree; Fuzzy Sets; SVM; Fault Diagnosis 1 Introduction Rolling bearings consist one of the most widely used industrial machine elements, and it is the interface between the stationary and the rotating part of the machine. Statistically, about 30% of the rotating machinery faults are caused by the damage of the bearings. Hence, as one of the important parts of running machines, both condition monitoring and fault diagnosis are very necessary for rolling bearings. SVM can be used in many fields. It has many advantages over the neural network in convergence speed. X li [2], a scholar of Northeastern University, imported a improved SVM into the fault detection of rolling bearing; Z Shen [2], a scholar of Xi an Jiao tong University, proposed a new model based on EMD and TSVM to solve the problem which is caused by lacking fault samples of the gear reducer during fault diagnosis; M Li [3], a scholar of LanZhou University of Science and Technology, customized a kernel function of SVM for speaker identification task. Meanwhile, a great progress in the research of fault diagnosis and sub-health control has been achieved because of the science and technology development. Brazilian scholar, Laurentys [4], projected an artificial immune system for fault detection based on artificial immune reconstruction Project supported by the National Nature Science Foundation of China (No ). Corresponding author. address: dbzhangneu@gmail.com (Dabo ZHANG) / Copyright 2014 Binary Information Press DOI: /jcis11619 September 1, 2014

2 7630 T. Xia et al. /Journal of Computational Information Systems 10: 17 (2014) model; American scholar, Paoli [5], imported the concept of Safe-control and Active Fault Tolerant Control into fault diagnosis to reconfigure regulatory policies. In this paper, we propose a algorithm of soft-output to enchance the classification accuracy of SVM. Furthermore, the concept of Health Degree (HD) based on fuzzy sets is proposed to calculate the HD of bearings. Ultimately, we combine the HD with the improved SVM for a clear description of bearing fault state, which leads to a better evaluating effect. 2 The Improved SVM Vapnik and the Bell Labs have been devoted to the research on machine learning since 1960s, which lays a foundation of SVM [5]. SVM is a machine learning algorithm based on the structured risk minimization principle. Its good generalization comes from the right scale of the limit sample information between the learning ability and complexity of a model. SVM can be used to solve the nonlinear and high-dimensional practical problems in small-sample pattern recognition, which leads to be a hot spot in the machine learning field. Fig. 1: Topological structure of the improved SVM 2.1 The idea of soft output of SVM In practical applications, SVM has a different performance on classification for different samples because of the ambient noise. For instance, the samples cannot be classified into a certain classification in some certain problems but can only be classified by a probability. Therefore, it is not suitable to adopt y i { 1, 1} as the output value for class information. Nondeterministic classifying ability is necessary for SVM so that the samples can be classified even with uncertainty, which is called the soft-output for SVM in this paper. We try to remove the limit of sign function here, and a continuous function is employed to map the certain output y i to section (, + ) to achieve the soft-output for SVM. SVM with soft-output ability can be applied to transform the low-dimensional input into the high-dimensional by kernel function to match the nonlinear function. The topological structure of the improved SVM is as same as the original. Every intermediate node corresponds to a support

3 T. Xia et al. /Journal of Computational Information Systems 10: 17 (2014) vector, but the output is a linear combination of the intermediate nodes (there is no limitation of sign function, namely y i ranging of the whole real number). As it is shown in Fig The idea of soft output of SVM The soft-output for SVM is both a promotion of diagnosis and an application of function fitting. Firstly, the linear function f(x) = ω x+b is used to fit data (x i, y i ), i = 1, 2, n, x i R n, y i R. Suppose that all samples can fit the accuracy of ε due to the linear function, namely { yi ω x i b ε, i = 1, 2, n (1) ω x i + b y i ε The method of controlling the complexity of function set is as same as maximizing withinclass scatter which is to minimize 1 2 ω 2, namely, making the regression function smoothest. Considering the error of fitting, relaxation factors ξ i 0 and ξi 0 are imported. And the formula (1) turns to be { yi ω x i b ε + ξ i ω x i + b y i ε + ξi, i = 1, 2, n (2) The optimized target changes into minimizing 1 2 ω 2 +C n (ξ i+ξ i ) = 0. The penalty degree of the samples whose error beyond ε is controlled by a constant C > 0. The optimized target transforms into a simple dual quadratic programming problem by the same method: max( ε (αi + α i ) + y i (αi α i ) 1 2 (αi α i )(αj α j )(x i x j )) (3) j=1 (α i αi ) = 0 s.t., i = 1, 2, n (4) 0 α i C The optimal classification function based on above becomes: f(x) = (ω x) + b = (αi α i )(x i x) + b (5) For most samples, its corresponding α i and αi equal 0, which is as same as the binary-class SVM. A small piece of α i and αi that does not equal 0 is associated with the samples with a sharp change. The kernel function K(x i, x) can be imported to replace the formula (5) to achieve nonlinear function approximation. When selecting the kernel function, SVM usually selects RBF kernel function. Penalty parameter C and kernel function parameter σ may have a great influence on SVM. Therefore, in order to get an SVM with good generalization, a suitable kernel function parameter σ must be selected to map the data to a suitable feature space. And a suitable penalty parameter C is needed to make sure of the best scale between the confident range and empirical risk of SVM.

4 7632 T. Xia et al. /Journal of Computational Information Systems 10: 17 (2014) The Combination of the Fuzzy Set and the Fault State 3.1 The HD evaluation of the fault state Given the fact that the working pattern of the mechanical system turns from health to fault, the proposition of HD is benefit for design and decision [6]. Three levels, fault, sub-health and health, are defined to evaluate the fault state of rolling bearing in this paper. As is shown in Table 1. Table 1: Fault status level No. The Range of HD Health Level Description of Fault State 1 0 HD 0.2 fault fault state HD 0.8 sub-heath running with damage HD 1 health health state 3.2 The combination of the fuzzy sets and the improved SVM 1. Define the fuzzy sets based on the improved SVM The idea of probability and statistic is used in fuzzy statistical algorithm for reference. The subjection degree can be determined by it in some cases. Considering that the characteristic of SVM matching the membership function and calculating the subjection degree, a fuzzy set is established in this paper: Ã = health (6) The domain of discourse X is the HD set, and suppose that X = [0, 1]. According to the fact that an SVM only has an output point, the paper makes a bold promotion for the subjection degree, and the membership function Ã(x) ranges from (, + ). 2. Calculating the HD by the subjection degree In order to calculate the HD, it must achieve the mapping from the subjection degree (, + ) to the HD [0, 1]. The sigmoid function is selected as promoting function here. For SVM, the subjection degree can be transformed into the HD as follows: HD = f(α) = e να (7) α is the generalized subjection degree calculated by the improved SVM for the health set; ν is a positive coefficient to be determined.

5 T. Xia et al. /Journal of Computational Information Systems 10: 17 (2014) Experiment and Performance Evaluation 4.1 Data preprocessing The experimental data of rolling bearings used for the experimental analysis in the following is from Case Western Reserve University Electrical Engineering Laboratory [7]. When the motor load is 0HP or 3HP, the Accelerometer Data (AD) of the driven in the normal status and fault status is selected. In this paper, when the motor load is 0HP, HD of the normal status is defined as 1; Similarly, when the motor load is 3HP (High load status can be considered as a sub-health status), HD of the normal status equals 0.75; Meanwhile, when the motor load is 0HP, HD of the fault status can be designated as 0. And the time-domain signals has been acquired [8]. 4.2 The HD calculation of the improved SVM When calculating the member ship degree of the health set by the improved SVM, the data of 90 states is selected. The member ship degree of the health set is obtained by 48 groups of the test data. And HD can be calculated by the member ship degree through formula (11) (Here). The member ship degree, HD and the faulty state of 18 groups softest data are listed below. As is shown in Table 2. Table 2: Fault State Evaluation of Rolling Bearing Data Sources Membership Degree for Health Set HD Fault state AD in normal status when load is 0 HP AD in normal status when load is 3 HP AD of the outer race in fault status when load is 0 HP AD of the inner race in fault status when load is 0 HP AD of the ball in fault status when load is 0 HP health health health health health health sub-health sub-health sub-health sub-health sub-health sub-health fault fault fault fault fault fault

6 7634 T. Xia et al. /Journal of Computational Information Systems 10: 17 (2014) As is apparently shown in Table 1 above, when load is 0HP, HD of rolling bearing in normal status floats between 0.93 and 0.94 and HD of the outer race in fault status, the inner race in fault status and the ball in fault status is below 0.04, which means the evaluation matches the expected result; Meanwhile, when load is 3HP, HD of rolling bearing in normal status floats between 0.76 and 0.79, and the evaluation matches sub-health. 4.3 Experimental result A contrast experiment is made to validate the method in this paper. The method was compared with the fault detection algorithm of an improved BP neural net work proposed in the literature [9], and the result is shown in Fig. 2. Fig. 2: HD of 18 groups of test sample It can be seen in Fig. 2 that HD calculated by the improved SVM is closer to the expected value. When combined with fuzzy sets, SVM can only promote the membership degree in a relatively reasonable condition. Compared with BP neural network, SVM is not so perfect. However, when dealing with the test data (the number of test sample is 90 and the test sample is 48), the accuracy of SVM is much higher than BP neural network. From this point, SVM has a large advantage over the process of the small sample. As is shown in Table 2 and Fig. 2, the assumption of our study is corresponding to the practical situation and the evaluation of running states of rolling bearings is reasonable. HD provides a strong basis for the maintenance and service of rolling bearings. The evaluation and decisionmaking of the state of rolling bearings can be decided according to the algorithm which includes control, adjustment, maintenance and monitoring.

7 T. Xia et al. /Journal of Computational Information Systems 10: 17 (2014) Conclusion Based on the data driven, we propose an algorithm of an improved SVM over machine learning. After consulting the relevant information, the concept of sub-health is imported to describe the process that the mechanical equipment turns from health to fault. And the improved SVM fault evaluation algorithm is combined with the fuzzy sets and it is applied to the rolling bearing experimental data of Case Western Reserve University. The result of lots of contrast experiments shows that the improved SVM has good performance on a rolling bearing health evaluation. And it can be used to describe the level of rolling bearings fault status definitely. References [1] X. Li and A. N. Zheng, Rolling element bearing fault detection using support vector machine with improved ant colony optimization [J], Measurement, 2013, 46 (5): [2] Z. Shen, X. Chen and X. Zhang, A novel intelligent gear fault diagnosis model based on EMD and multi-class TSVM [J], Measurement, 2012, 45 (1): [3] M. Li, Y. F Zhang, J. Q Li, Y. Zhang, An Improved SVM Approach for Speaker Identification [J], Journal of Computational Information Systems, 2008Vol. 4 (1): [4] Laurentys, Palhares and Caminhas, Design of an artificial immune system based on Danger Model for fault detection [J], Expert Systems with Applications, 2010, 37 (7): [5] Paoli, Sartini and Lafortune, Active fault tolerant control of discrete event systems using on line diagnostics [J], Automatica, 2011, 47 (4): [6] Anand, Panigrahi and Mathur, Stream flow fore casting by SVM with quantum behaved particle Swarm optimization [J], Neurocomputing, 2013, 101: [7] P. Zhang, B. Zhang and D. S. He, Wearability reliability vector analysis of mechanical element swith intermediate state [J], Mechanical Research & Application, 2010, 6: [8] Case Western Reserve University, Bearing Data Center Seeded Fault Test Data, ase.edu/bearingdatacenter/pages/download-data-file. [9] Y. B. Yang, L. Y. Zhang, L. Zhang, X. H. Cai and S. L. Zhang, The Health Degree Evaluation of Rolling Element Bearing Using an Improved BP Neural Network [J], Journal of Information & Computational Science, 2010, 6: [10] L. Zhang and L. Y. Zhang, Prediction of Rolling Load in Hot Strip Mill by Innovations Feedback Neural Networks [J], Journal of iron and steel research, international, 2007, 14 (2):