Mechanical Compound Fault Analysis Method Based on Shift Invariant Dictionary Learning and Improved FastICA Algorithm

Nailong Wu,Xinyuan Chen,Haodong Yuan

doi:10.3390/machines9080144

Abstract

For mechanical compound fault, it is of great significance to employ the vibration signal of a single-channel compound fault to analyze and realize the separation of multiple fault sources, which is essentially the problem of single-channel blind source separation. Shift invariant K-means singular value decomposition (shift invariant K-SVD) dictionary learning is suitable to extract the periodic and repeated fault features of a rotating machinery fault, hence in this article a single-channel compound fault analysis method is put forward which combines shift invariant K-SVD with improved fast independent component analysis (improved FastICA) algorithm. Firstly, based on single-channel compound fault signal, the shift invariant K-SVD algorithm can be used for learning multiple latent components that can be constructed as a virtual multi-channel signal. Then the improved FastICA algorithm is utilized to realize the separation of multiple fault source signals. With regard to the FastICA algorithm, the third-order convergence Newton iteration method is adopted to improve convergence speed. Moreover, in order to address the problem that FastICA is very sensitive to initialization, a steepest descent method can be applied. The experimental analysis of the compound fault of rolling bearing verifies that the presented method is effective to separate multiple fault source signals and the improved FastICA algorithm can increase convergence rate and overcome the problem of sensitivity to initialization.

Highlights

In the field of mechanical fault diagnosis, sparse representation has been extensively employed [1,2,3,4,5]
We propose a new mechanical compound fault analysis method combining shift invariant K-means singular value decomposition (K-SVD) and improved fast independent component analysis (FastICA) based on the steepest descent method and third-order convergence Newton iteration method to achieve single-channel blind source separation
Shift invariant K-SVD is conducted for a single-channel mechanical compound fault signal to learn multiple basis functions and corresponding latent components that can be constructed as a virtual multi-channel signal

Summary

Introduction

In the field of mechanical fault diagnosis, sparse representation has been extensively employed [1,2,3,4,5]. We utilized shift invariant K-SVD to acquire basis functions, their corresponding latent components can be obtained and constructed as virtual multi-channel signal. We propose a new mechanical compound fault analysis method combining shift invariant K-SVD and improved FastICA based on the steepest descent method and third-order convergence Newton iteration method to achieve single-channel blind source separation. Shift invariant K-SVD is conducted for a single-channel mechanical compound fault signal to learn multiple basis functions and corresponding latent components that can be constructed as a virtual multi-channel signal. K-SVD dictionary learning algorithm is employed to obtain basis functions and their corresponding latent components and the multiple latent components can constitute virtual multi-channel signals. ICA is conducted to separate multiple source signals using the constructed virtual multi-channel signal

Shift Invariant K-SVD Algorithm

Single-Channel BSS with Shift Invariant K-SVD

FastICA

Improved FastICA

Steepest Descent Method

Third-Order Convergence Newton Iteration

Description of the Experiment

Asbecan be observed

Estimated sourceimproved signal using improved

Compound of Rolling

11. Rolling bearing with outer inner racecompound and rolling element fault

Conclusion