Signal Processing Method Based On Singular Value Decomposition And Its Application To Mechanical Fault Diagnosis

Singular value decomposition (SVD) is a modern numerical analysis method, and signal processing as an important branch of all its applications, realizing effective analysis of the nonlinear and non-stationary signal by using some matrix transform ways to process signal, is a unique signal processing tool. Therefore, this article starts from studies of the basic principle, important nature and significance of SVD, then launches in-depth discussions about SVD algorithm and signal processing methods based on SVD launched depth. The main works and research results are as follows:Firstly, aiming at problems of non-convergence, caused by utilizing the traditional QR iterative algorithm to carry out SVD calculation of the large-scale matrix, in-depth analysis and discussions combining with instances are launched, and a kind of multi-partition and double-direction shrink QR iteration algorithm is proposed, who can fulfill fast and accurate SVD calculation of the large-scale matrix.Secondly, signal separating theories of SVD under matrix mode are studied, a kind of signal de-noising method based on SVD under Hankel matrix is proposed, which utilizes genetic algorithm to optimize the matrix structure and the central difference quotient curve to select the effective singular values, and its nice de-noising effects is showed by examples.In addition, under the way when matrixes are constructed by continuously intercepting signal, influences on signal processing effects caused by different constructed matrix structure is discussed, a new method for signal singularity detection based on SVD is found, and the unique singularity detecting performance of this method is studied through comparisons with wavelet transform.Thirdly, several periodic detecting method, such as Singular Value Ratio (SVR) spectrum, improved SVR spectrum and Frobenious norm track etc. are introduced, and the failure reasons frequently caused by these methods when detecting the period of signals are analyzed, a delayed SVR spectrum method based on fixed matrix structure is put forward, and its stable periodic detection capabilities are verified in the analysis and processes of several test signals. Finally, different signal processing methods based on SVD are applied to diagnose different rotor system faults, which verify effectiveness and engineering practicability of these methods in the practical application.