Research On Multi-scale Chirplet Based Sparse Signal Decomposition And Its Application In The Fault Diagnosis Of Gearboxes

Gearbox is an indispensable part for connection and power transmission in machinery, and it is vulnerable to faults as well. The research on gearbox condition monitoring and fault diagnosis is of essential importance to the safe and stability of machinery.With features of on-line, real time, non-destructive detection, convenient, fast and accurate, gearbox's condition monitoring and fault diagnosis based on vibration signal processing is widely used in practice. When some faults occur in gearboxes, by which the impact caused will result in various degrees and forms of modulation. How to effectively extract the sidebands from the vibration signals, which are the features of faults, is a most important part in research of gearbox fault diagnosis. Due to the difficulty of dynamic sideband extraction and the problems of traditional time frequency analysis methods, which has insufficient time-frequency gathering property, weak at noise immunity and cannot effectively analyze non-stationary signals whose instantaneous frequency varies in a large scale, the present dissertation , funded by project"Sparse Signal Decomposition Based on Multi-scale Chirplet and Its Application to Mechanical Fault Diagnosis"(Project's Serial Number: 50875078) supported by National Natural Science Foundation of China and by project"Sparse Signal Decomposition with Amplitude Modulation Based on Multi-scale Chirplet and Its Application to Gearbox's Fault Diagnosis"(Project's Serial Number: 20090161110006) supported by Specialized Research Fund for the Doctoral Program of Higher Education, proposes a new signal processing method– Sparse signal Decomposition Method Based on Multi-scale Chirplet. The method is applied to the fault diagnosis of gearboxes with time-varying rotational speed. The problems such as dynamic sideband extraction of gearboxes with time-varying rotational speed, the rotational speed extraction which is needed for order tracking, the phase function extraction of multi-component non-stationary signals, and the design of self-adaptive time-varying filter are studied thoroughly. The main researches include:(1) Due to the limitations of traditional time frequency analysis methods, which cannot effectively analyze multi-component non-stationary signals whose instantaneous frequency change continuously in a large scale and has insufficient time-frequency gathering property, the dissertation proposes a complete and systematic method denominated by Sparse Signal Decomposition Based on Multi-scale Chirplet. The method, with good time frequency gathering property, decomposition adaptively, expression sparsely and strong noise immunity, is especially suitable for the analysis of multi-component non-stationary signals.(2) Due to the difficulty in extraction of dynamic modulation sidebands from the gearbox vibration signals under the circumstance of speed varying, the dissertation applied the Sparse Signal Decomposition Method Based on Multi-scale Chirplet to gearbox fault diagnosis, which can obtain carrier frequency and the time-varying modulation frequency accurately. Simulation and experiment prove that the method can precisely extract dynamic modulation sidebands which are the features of gearbox faults and it is especially suitable for gearbox fault diagnosis under the circumstance of drastic speed fluctuation.(3) Due to the inadequacies in noise immunity and precision of the traditional speed extraction methods based on instantaneous frequency estimation, the dissertation uses the Sparse Signal Decomposition Method Based on Multi-scale Chirplet to estimate rotational speeds in order tracking. Its application to gearbox fault diagnosis demonstrates that the method can accurately extract rotational speed signals, avoid the installation of speed measuring equipment in order tracking analysis and save costs.(4) In general decomposition method, it is difficult to extract phase function of multi-component non-stationary signals whose frequency curves are not parallel to each other. The present dissertation takes the advantage of Sparse Signal Decomposition Method Based on Multi-scale Chirplet to obtain phase function from multi-component non-stationary signals, which effectively solves the problem mentioned above. Simulation and application of bearing fault demonstrate that non-stationary signals can be transferred into stationary signals by using the phase function extracted by this method to carry out general decomposition, which makes it suitable to process non-stationary signals and diagnose gearbox faults under the circumstance of time-varying rotational speed.(5) In order to separate non-stationary signals, which are the compound of AM-FM signals linear added, into single AM-FM signal, the dissertation proposes a new self-adaptively time-varying filter design method. Firstly, the carrier frequency of single AM/FM signal is extracted by the Sparse Signal Decomposition Method Based on Multi-scale Chirplet, and then, by the extension of classical filter, a self-adaptively time-varying filter is designed who's central frequency is the carry frequency extracted. The single meshing frequency modulation signal can be filtered by the self-adaptive filter from gearbox vibration signals, which solves the problems that, under the circumstance of time-varying rotational speed, there are several meshing frequency modulation signals in multi-stage gearbox's vibration signals, and, when the frequency of irrelevant components overlap with the meshing frequency, it is difficult to separate them and process gearbox fault diagnosis.(6) In the fault diagnosis of multi-input and multi-output gearboxes and gearbox group (there are several gearboxes installed on one base, and the vibration signals influence each other), the orders of meshing frequency interfere with one another in the order tracking method, so it is difficult to use the order spectrum for fault diagnosis. In order to solve the problems mentioned above, a new method of fault diagnosis is proposed in the dissertation. Firstly, to extract meshing frequency modulation signals one by one with the adaptive time-varying filter using Sparse Signal Decomposition Method Based on Multi-scale Chirplet. Secondly, the order tracking is applied to the filtered signals. At last the fault diagnosis is conducted and complete. The method effectively suppresses the influences of other gear meshing vibration from unrelated transmission systems and other non-order noise signals onto order spectrum. It favorably solves the problem of order interference, and enhances order spectrum more clearly, which provides an effective method for the fault diagnosis of multi-input and multi-output gearbox and gearbox group.The Sparse Signal Decomposition Method Based on Multi-scale Chirplet proposed by the dissertation integrates the flexibility in atom selection, the sparseness of signal expression, and matching pursuit adaptively. It can effectively decompose multi-component non-stationary signals whose frequencies change linearly or curvedly. Simulation and application examples demonstrate that, the proposed methods of the dynamic modulation sidebands extraction, time-varying rotational speed extraction, phase function extraction and adaptive time-varying filter, can be effectively applied to the fault diagnosis complex gearboxes under time-varying rotational speed condition.