A Novel Method for Fault Diagnosis of the Two-Input Two-Output Nonlinear Mass-Spring-Damper System Based on NOFRF and MBPCA

Jialiang Zhang,Xiaoqian Zhang,Jie Wu,Zhiwei Gao

doi:10.1155/2021/8282762

Abstract

For fault diagnosis of the two-input two-output mass-spring-damper system, a novel method based on the nonlinear output frequency response function (NOFRF) and multiblock principal component analysis (MBPCA) is proposed. The NOFRF is the extension of the frequency response function of the linear system to the nonlinear system, which can reflect the inherent characteristics of the nonlinear system. Therefore, the NOFRF is used to obtain the original fault feature data. In order to reduce the amount of feature data, a multiblock principal component analysis method is used for fault feature extraction. The least squares support vector machine (LSSVM) is used to construct a multifault classifier. A simplified LSSVM model is adopted to improve the training speed, and the conjugate gradient algorithm is used to reduce the required storage of LSSVM training. A fault diagnosis simulation experiment of a two-input two-output mass-spring-damper system is carried out. The results show that the proposed method has good diagnosis performance, and the training speed of the simplified LSSVM model is significantly higher than the traditional LSSVM.

Highlights

In order to improve the training speed and reduce the storage requirement, the least squares support vector machine (LSSVM) multifault classifier is trained by the simplified LSSVM model and conjugate gradient algorithm in this study
Select 100 sets of feature data of nonlinear output frequency response function (NOFRF) as training samples and the remaining 100 sets as test samples. e fault diagnosis simulation of the massspring-damper system is carried out by the LSSVM simplified model and the traditional LSSVM model based on the conjugate gradient algorithm, respectively. e linear kernel function, polynomial kernel function, Gaussian radial basis (GRB) kernel function, exponential radial basis (ERB) kernel function [44], and multilayered perceptron (MLP) kernel [45] are chosen as kernel functions of the LSSVM multifault classifier, respectively
We studied the fault diagnosis of the nonlinear two-input two-output mass-spring-damper system combining NOFRF and multiblock principal component analysis (MBPCA)

Summary

Introduction

Fault diagnosis technologies have been widely used in manufacturing equipment, electric machine, wind power system, electronic equipment, and so on. A fault diagnosis method is proposed for a nonlinear two-input two-output mass-spring-damper system based on nonlinear output frequency response function and multiblock principal component analysis. E nonlinear output frequency response function is used to establish the system model and obtain the original fault feature data. Erefore, the NOFRFs of the two-input two-output nonlinear mass-spring-damper system can be estimated based on the least square criterion. The nonlinear stiffness coefficient of the mass-spring-damper system will be increased, and the nonlinear output frequency response functions will be changed significantly. Erefore, the original fault feature data obtained by NOFRF can effectively diagnose the nonlinear mass-spring-damper system. 3. Feature Extraction for NOFRF Based on MBPCA e data amount of NOFRF amplitudes of the two-input two-output nonlinear mass-spring-damper system is large. E least square support vector machine is used to construct a multifault classifier

Define the training sample dataset as

Define the Lagrangian function as

Identification result

Training time

Conclusions