An interval fault diagnosis method for rotor cracks

https://doi.org/10.1016/j.compeleceng.2020.106752Get rights and content

Highlights

  • A interval rotor crack fault diagnosis method, called IN_LSOSVM, is proposed.

  • Interval rotor crack fault samples are classified by IN_LSOSVM.

  • The optimal Gauss kernel function parameters can be selected by GSO.

  • The experiment results validate the effectiveness of the proposed method.

Abstract

Aiming at the problem that the traditional fault diagnosis methods cannot deal with the uncertain samples, this paper proposes an interval fault diagnosis method and its parameter optimization. First, the interval Gauss function is used to construct the kernel of the proposed interval fault diagnosis method. The weights and offsets of this interval method are calculated by solving the equality equation. Second, with the goal of maximizing the classification accuracy, the Glowworm swarm optimization algorithm is used to select the parameters of this method. Finally, the experimental results of the rotor crack interval fault samples and the University of California Irvine samples show that this method has higher classification accuracy than the traditional interval classification methods.

Introduction

Due to the fatigue, a rotor will become cracked and the stiffness of the shaft will decrease. A rotor crack fault will have a greater impact on the normal operation of the rotor, and serious accidents may even occur. Therefore, crack fault detection is of great significance to ensure production [1]. In recent years, scholars have carried out a series of studies on rotor crack faults. Song summarized the main reasons for crack faults and put forward a diagnostic mechanism [2]. Guo et al. analyzed the dynamic characteristics of a rotor with respiratory cracks and verified the reliability of the crack detection method using empirical mode decomposition (EMD) [3]. Yu et al. proposed a finite element model of a cracked rotor by considering the influence of shear force. They analyzed and obtained the system responses of a double cracked rotor in different speed zones and different crack locations [4]. However, unlike the ideal conditions of smoothness and noninterference, a rotor often works under complex conditions such as variable loads and speeds. Furthermore, some other vibration sources in the same frequency band also occur in the fault vibration signal of a rotor crack. For these reasons, fault samples are obtained as interval values. The traditional fault diagnosis method is only applicable to deterministic fault samples, and so it cannot play any role in the fault diagnosis of interval crack fault samples.

Compared with the defects of the traditional rotor crack fault diagnosis model, the interval analysis model describes the uncertain attributes in a rotor crack in interval form and uses the width of the interval to deal with the uncertainties. The interval theory defines various operating rules in detail. These features extend the fault diagnosis model in the interval domain and make the diagnosis process more reliable and effective. Therefore, the interval model is an important method to realize rotor crack fault diagnosis under complex working conditions. Some scholars have conducted in depth research and achieved rich research results. For example, Sun et al. [5] proposed a single clustering anomaly detection algorithm for interval samples. Moreover, an interval subdivision detection strategy is proposed to dispose of the unbalanced interval widths. Finally, the effect of the proposed algorithm is verified by combining an artificial data set and the University of California Irvine (UCI) data set. Utkina combined the one class support vector machine and interval theory and used interval data to train and test the one class support vector classification model. The principle of this method is to convert the interval data into deterministic data with different weights [6]. Nour proposed the interval Principal Component Analysis (IPCA) method. In this paper, three IPCA methods are constructed: central IPCA, midpoint radius IPCA and symbolic covariance IPCA. The results show that the IPCA method has a higher fault detection rate than the classical PCA method [7].

The least squares one class support vector machine (LSOSVM) overcomes the dependence on large samples using structural risk minimization theory and seeks a balance between the complexity of the model and its learning ability [8]. Moreover, the LSOSVM seeks to minimize the sum of the distances from all training objects to the hyperplane and thus most of the training objects may lie close to the hyperplane. Therefore, the proximity to such a hyperplane can better reflect the proximity to the training set. To make the best of the advantages mentioned above, this paper proposes the interval least squares one class support vector machine (IN_LSOSVM) to realize the classification of interval rotor crack faults. The proposed IN_LSOSVM uses the interval upper bound and lower bound to construct the interval Gauss kernel function to realize the classification of interval fault samples. In the IN_LSOSVM, the interval Gauss kernel function width parameter and penalty parameter have great influences on the performance of machine learning. The kernel function width parameter reflects the correlation degree of the support vector. If the value of the width parameter is too small, the connection of the support vector will be relaxed, and it cannot guarantee a better generalization ability. If the value of the width parameter is too large, the mutual influence of the support vectors will be enhanced, but it will be difficult for the accuracy to meet the requirements. In addition, if the value of the penalty parameter is too small, the penalty for the error will be smaller, which will lead to the increase of the model training error, but the generalization ability will be enhanced. If the value of the penalty parameter is too large, the training error of machine learning will be reduced, but the generalization ability will be weakened. To ensure the high accuracy of the IN_LSOSVM model, glowworm swarm optimization (GSO) is utilized to select the optimum values of the interval Gauss kernel function width parameter and penalty parameters in this paper [9].GSO is a member of the intelligent optimization algorithm family. GSO is inspired by the bioluminescent behavior of glowworms in nature. In the initial stage, different amounts of luminescent elements are randomly distributed in a certain space. They emit different brightness light to each other. Over time, glowworms in space gradually approach brighter glowworms than them. After a period of time, all glowworms will eventually gather in or near the brightest position in the space to complete a task similar to optimization. The algorithm mainly includes the brightness intensity, attractiveness, update formula and evolutionary principle. Because of its few parameters and easy implementation, GSO has been widely used in optimization, classification and engineering [10], [11], [12], [13], [14], [15], [16].GSO has the advantages of a simple structure, strong operability, fast convergence speed and high accuracy. It can automatically search for the optimum values of the interval kernel function width parameter and penalty parameters by guiding the glowworm population to search for the optimum solution in a given solution space.

This paper is organized as follows. Section 2 introduces the theory of the least squares one class support vector machine. Section 3 proposes the IN_LSOSVM method and interval Gaussian kernel function. Section 4 uses GSO to select the parameters for the IN_LSOSVM method. Section 5 analyzes the classification results of the UCI data. Section 6 applies the IN_LSOSVM to rotor crack faults diagnosis, and presents the comparison results with other methods. Finally, the conclusion is presented in Section 7.

Section snippets

Least squares one class support vector machine

Young-Sik Choi [17] proposed the least squares one class support vector machine in 2009. The least squares one class support vector machine uses the quadratic loss function and equality constraints to minimize the distance from the training sample to the hyperplane. Therefore, most training samples will be located near the hyperplane, and so the proximity can be expressed using the distance from the sample to the hyperplane. The objective function of the least squares one class support vector

IN_LSOSVM method based on Gauss interval kernel

The traditional least squares one class support vector machine aims at deterministic fault samples. Compared with the traditional method, the proposed IN_LSOSVM aims at uncertain interval fault samples. Moreover, instead of converting interval numbers into exact values like mean values, the endpoints of interval numbers are used directly in the IN_LSOSVM method. This section first gives some operating rules for interval numbers.

If R represents the set of real numbers, the interval numbers can

IN_LSOSVM based on glowworm swarm optimization

The selection of the parameters of the IN_LSOSVM has a great influence on the classification accuracy. The rational selection of the parameters can improve the accuracy of the proposed algorithm, reduce the errors, and effectively improve the local convergence problem. In this section, GSO is used to select the penalty parameter C andthe interval Gauss kernel width parameter σ of the IN_LSOSVM method. Generally, the bigger the penalty parameter is, the stronger the nonlinear fitting ability.

The classification experiment using the UCI data

In this experiment, the UCI data are used to test the classification performance of the IN_LSOSVM based on GSO. All programs are implemented using MATLAB R2014a. The experimental environment is a Lenovo desktop computer with an Intel core i3-550 3.20 GHz CPU and 8.00GB of memory. Regarding the processed data, seven quantitative datasets of 3 commonly used UCI datasets are selected for the experiments. The description is shown in Table 1. Each attribute of all three datasets is quantitative. The

The rotor crack fault experiment

Due to the influence of gravity, a rotor system is subjected to large lateral bending when rotating at a high speed. The bending fatigue stress is prone to produce transverse cracks perpendicular to the axis of the crack surface. When the rotor is subjected to large torque, it is also possible to have oblique cracks with a certain angle between the crack surface and the axis. Most of the rotor fracture accidents are caused by transverse cracks. Ensuring the equipment security is an important

Conclusion

Interval fault samples are a special kind of fault diagnosis object. At present, there are relatively few studies on the fault diagnosis of interval data. In order to solve the interval rotor crack fault classification problem, this paper proposes an interval least squares one class support vector machine by introducing the interval Gauss kernel function. The validity of this new method is verified by the interval vibration signal of a rotor crack. The main conclusions are presented as follows.

  • 1)

Declaration of Competing Interest

No conflict of interest exits in the submission of this manuscript.

Author statement

Yongqi CHEN, write the paper, Chengjun GUO, method

Yongqi Chen was born in Linchuan, Jiangxi, P.R. China, in 1977. He received a PhD degree from Tongji University, P.R. China. Now, he works in the College of Science and Technology, Ningbo University. His research interests include fault diagnosis, intelligent algorithms, and statistical learning.

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      Citation Excerpt :

      Recently, a novel collaborative sparse classification framework was used for aero-engine’s gear-hub by Zhang [37], which collaborates the prior knowledge based sparse filtering and data-driven classification strategy. An interval fault diagnosis method is proposed in Ref. [38], where the interval Gauss function is used to construct the kernel function. Sayyad investigates the relation between the first two natural frequencies and cracks location, where the crack is simulated by an equivalent spring connecting the two finite elements [39] or wavelet spectral finite element method [40].

    Yongqi Chen was born in Linchuan, Jiangxi, P.R. China, in 1977. He received a PhD degree from Tongji University, P.R. China. Now, he works in the College of Science and Technology, Ningbo University. His research interests include fault diagnosis, intelligent algorithms, and statistical learning.

    Chengjun Guo was born in Jiangsu, Xuzhou, P.R. China, in 1984. He received a master's degree from Changchun University, P.R. China. Now, he works in the College of Science and Technology, Ningbo University. His research interests include control technology and big data analysis.

    This paper is for CAEE special section SI-cps. Reviews processed and recommended for publication to the Editor-in-Chief by Guest Editor Dr. Zhihan Lv.

    1

    This research is supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No. LY16E0 50001, the Ningbo Natural Science Foundation (2019A610118) and the K.C. Wong Magna Fund of Ningbo University.

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