Elsevier

Neurocomputing

Volume 152, 25 March 2015, Pages 36-44
Neurocomputing

Identification of resonance states of rotor-bearing system using RQA and optimal binary tree SVM

https://doi.org/10.1016/j.neucom.2014.11.021Get rights and content

Abstract

Aiming to the dynamic nonlinearity of rotor-bearing system in the mechanical and fluid resonance states, a new method combining Recurrence Quantification Analysis (RQA) with optimal binary tree Support Vector Machine (SVM) is proposed for characterizing and identifying the resonance states. RQA is used to obtain the nonlinear characteristic parameters which are able to effectively represent the resonance states without large amount of measurement data. The binary tree SVM is ordered according to the rank of state Mahalanobis distances in the feature vector space. In order to more precisely classify the feature zones, the RQA features are optimally selected as the inputs for each classifier of binary tree SVM by means of the Fish score evaluation. The practical experiments are performed on the cylindrical shaft-journal bearing test rig and the results demonstrate the effectiveness and superiority of the proposed method.

Introduction

Rotor-bearing system as an important asset exists in a wide range of industry applications, and the identification of unstable operation states is crucial to its design and usage. The instability of rotor-bearing system generally is induced by the rotationally asymmetric inertia or transverse crack, which would alter the system vibration behaviors and cause the severe vibrations. The instability with transverse crack is mainly due to the influence of “breathing effects” on the dynamic behavior of a rotating shaft. The effects of cracks on rotor system instability were investigated in Refs. [1] and [2], and the transverse crack breathing mechanism was analyzed in Refs. [3] and [4]. Extensive efforts also have been devoted to study the instability behaviors of rotor-bearing systems with asymmetric inertia, which are usually caused by the coupled effects of the nonlinear oil film force, unbalanced centrifugal force, journal whirl inertia force, rotor gravity and other external load. Among these instability behaviors, the resonance is one of the most typical one that needs to be specially considered in the system operation.

When the rotor-bearing system operates in the resonance states, the response vibration gets very strong with large amplitude, which is very harmful and might lead to the catastrophic failure of the whole rotating machine [5]. Generally, the rotor-bearing system mounted on the radial fluid film bearings has two types of resonance: mechanical and fluid, which usually appear in form of rotor critical frequency resonance, oil whirl, and oil whip and mixed resonance, etc. In the viewpoint of state linearity, the existence of resonance in any form means that the rotor-bearing system has lost its linear stability (called as the practical stability defined by Muszynska [6]) and entered the nonlinear stable or unstable state. The rotor critical speed resonance is a short time transient vibration at the shaft natural frequency caused by the inertia force of rotor perturbation. The oil whirl resonance is a self-excited fluid film resonance at the frequency close to half of the rotating speed, caused by the journal tangential force originating from the interaction of circumferential flow and the dynamics of the rotor [7]. When the rotation speed reaches twice the first natural frequency, the self-excited vibration frequency remains constant and close to the first natural frequency. This behavior is the oil whip resonance. In the significance of engineering application, when the system enters the resonance state, it would not immediately lose its operating effectiveness. As long as the vibration amplitude is below the maximum safe limit, the system in this kind of nonlinear stability can still operate safely, temporarily, but less effectively, not for long time. If without control, the continuous resonance will do a fatal damage on the system, especially when its vibration amplitude is beyond the maximum safe limit. Therefore, the automatic detection and timely identification of resonance state in rotor-bearing system are of paramount importance to improve the reliability, safety and efficiency of the production process.

In the resonance state, the system presents strong dynamic non-linearity, which has been thoroughly studied in literature [8], [9]. Meanwhile, the resonance also is the main source of frequency coupling which causes the interaction of the natural frequency of components or system with the other frequencies. The frequency coupling makes it difficult to get the useful signal characteristics with the conventional spectrum analysis methods such as amplitude–frequency response, spectrum cascade, vibration waveform, orbit, Poincare section [10], wavelet analysis and resigned scalograms [11], time-frequency distribution [12], etc. These conventional methods which are mostly based on the pre-assumption of stationary or linear signals, usually lack the robustness to the nonlinear dynamic signals, even lead to a certain degree of inaccuracy in the resonance state identification. To name a few, the conventional Fourier spectrum has low frequency resolution if without enough sampling points. The full spectrum has the limitation in distinguishing the first critical frequency resonance from oil whip. The axis orbit is greatly affected by the interference of noises, even completely fails in identifying the states. To construct an intelligent and automatic fault identification system, other technologies combined with the spectral characteristics, orbit characteristics or statistics parameters are introduced, such as artificial neural networks, [13] Support Vector Machine (SVM) [14], decision tree [15], and Bayesian networks [16]. It is worth noticing that the effectiveness of these technologies depends on the selection of appropriate parameters and the optimization of training model. These characteristic parameters obtained from the long enough time sampling series generally are complex and disordered. If with a small number of fault samples, these methods could present poor generalization, even lead to incorrect identification results.

As the analyzed above, the vibration signal of rotor-bearing system under the resonance states evolves the fluctuation and presents nonlinear characteristic. So it is better to use the reliable nonlinear characteristics to describe and differentiate these resonance states. A useful tool to deeply understand the nonlinear dynamic properties is Recurrence Quantification Analysis (RQA), which is a nowadays recognized good method to deal with non-stationary, non-linear and relatively short data series [17]. RQA has an increasing number of applications in processing nonlinear chaotic behaviors of engineering system, such as investigating non-stationary work in the diesel engine acceleration [18], evaluating bearing performance degradation [19], studying car vibration transient behavior [20], etc.

In this paper, RQA is used to characterize the short-time resonance vibration signals. Afterwards, in order to identify the different resonance states, the ordered binary tree SVM is taken as a classifier and the RQA features are optimally selected and put into the classifier according their sensitivity to different resonance states. Finally, the experiments are conducted on the rotor-bearing test bench to verify the effectiveness of the proposed method.

Section snippets

Dynamics and nonlinearity of the resonance

The rotor-bearing system resonance is described as dynamic because it closely related to the speed. It is mainly affected by the interaction of three elements: rotor, oil film and bearing. These elements are partially mechanical (solid materials) and partially fluid (lubrication oil). The mechanical characteristics related to the rotor, e.g. the shaft mass, are generally speed independent, while the fluid characteristics related to the fluid film bearing, e.g. the oil film thickness, are

Recurrence Quantification Analysis

RQA is a method of nonlinear data analysis for the investigation of dynamical system, aiming to quantify differently appearing Recurrence Plots (RPs) based on small-scale structures. RPs are graphical tolls which visualize the recurrence behavior of the phase space trajectory of dynamical system. For a series {x1,x2,,xN} with length N, it is embedded into the space Rm with embedding dimension m and time delay τ according to nonlinear dynamic theory. The RP can be briefly described asRi,j=Θ(εx

SVM

SVM is originally designed for binary classification that is the most advanced one, generally, designed to solve pattern recognition problems. Its main ideal is transforming the data into a high dimensional feature space to find an optimal hyper-plane that separates the data belonging to different classes with large margins in a high dimensional space. Assuming there are samples from two classes(x1,y1)(x2,y2)(xi,yi),xiRN,yi{1,+1}where xi is input sample and yi is output class, y has two

Experiment setup

In this work, the experiment test rig is an asymmetric journal bearing supported rotor system illustrated in Fig. 2. The experiment setup consists of a rigid cylindrical shaft supported by two cylindrical journal bearings, with a supporting journal bearing on the right end near the driving motor and an oil film journal bearing at the left end. Two discs are mounted on the shaft, with one at the mid-plane between the two bearings and the other near the left oil film bearing. The shaft is not of

Conclusions

The contributions of this paper contain: (1) in order to investigate the dynamic nonlinear characteristics of a rotor supported by asymmetric journal bearings under various resonance states, the unified vibration model of the system with complex dynamic stiffness is analyzed based on the equivalent cross-coupling spring and damping stiffness theory. (2) Recurrence quantification analysis was utilized to characterize the dynamic nonlinearity of rotor-bearing system under different operation

Acknowledgment

The supports for this research under Chinese National Science Foundation Grant (No. 51475052) and fundamental Research Funds for the Central Universities (CDJZR12115501 and CDJZR14110004) are deeply appreciated.

Xiaofeng Liu was born at 1980 in China. She is associate professor of Chongqing University in China. Dr. Liu is interested in Engineering Signal analysis, Measurement technology, pattern identification,etc. She has published more than 20 journal papers. Dr. Liu received her Ph.D. from Chongqing University, in Mechanical Engineering.

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    Xiaofeng Liu was born at 1980 in China. She is associate professor of Chongqing University in China. Dr. Liu is interested in Engineering Signal analysis, Measurement technology, pattern identification,etc. She has published more than 20 journal papers. Dr. Liu received her Ph.D. from Chongqing University, in Mechanical Engineering.

    Lin Bo was borne at 1972 in China. He is Professor of Chongqing University in China. Dr. Bo is interested in Noise and Vibration, Measurement technology, Fault diagnosis etc. He has published more than 40 journal papers and has more than 20 year professional experiences in intelligent instrument measurement and other industries. Dr. Bo received his B.Sc. from Zhongbei University , his M.Sc. and Ph.D. from Chongqing University, all in Mechanical Engineering.

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