Research On The Sparse Representation Of Gearbox Compound Fault Features With Wavelet Dictionaries

As a critical mechanical component for transmitting power, gearbox has been widely used in modern industry, whose operation status is absolutely of great importance to the normal operation of the whole mechanical instrument. Due to its complicated structure and harsh working condition, gearbox is proven to be easily damaged and broken down. Therefore, it is extremely significant to develop proper condition monitoring and fault diagnosis methods for gearbox so as to prevent the unexpected machine fault during operation and even casualties. In engineer practice, there is always more than one fault in the gearbox, which is manifested as compound fault. Different kinds of faulty components existing in the same captured vibration signal may generate interaction and coupling among them, making it more challenging to extract the compound fault features. Hence, it is of great scientific value to research the methods of extracting the gearbox compound fault features.This thesis is financially supported by the Natural Science Foundation of China “Signal Transients Extraction under the Frame of Sparsity and Its Application in Rotating Machine Fault Diagnosis”(No. 51375322). With the aim of gearbox compound fault features extraction, novel fault diagnosis methods which represent the compound fault features in sparse coefficients with different wavelet dictionaries are proposed in this thesis. The theory basis and application research are both studied deeply.When a fault occurs to a gear or a bearing, both of which are important elements for gearbox, periodic transient impulses are induced in its vibration signal. Such transients always contain vital information of fault feature of the defective element. It is, therefore, of great significance to extract the transients. Gearbox compound fault, which is considered as the combination of gear fault and bearing fault in this study, often creates two different kinds of transient impulse responses in the vibration signal. Hence, the main goal of the gearbox compound fault diagnosis is to separate and extract the two kinds of transients. Signal sparse representation which represents the transients by a series of sparse coefficients is an effective method in feature extraction and diagnosis from the noisy background. Based on the transient and sparse nature of the vibration signal of bearing and gear, the thesis proposes to represent the two different kinds of transients in sparse coefficients with overcomplete wavelet dictionaries, respectively. A method of the overcomplete dictionary construction is adapted in this thesis according to the characteristics of the fault vibration signal, in which the correlation filtering is used to calculate the optimal wavelet atom and the time parameter of the atom is translated to construct the wavelet dictionary.The objective function for sparse representation model contains the data fidelity and the penalty term, either of which can be optimized to solve the objective function to get the sparse vector. In this thesis the former date fidelity is firstly optimized by introducing the split augmented Lagrangian shrink algorithm to solve the convex optimization problem. Then, in order to optimize the latter penalty term, the majorization minimization algorithm which designs a quadratic function of the general form is proposed to resolve the objective function. These two proposed methods covert the transients into a series of sparse coefficients, from which the type of fault can be identified. Both the simulated and experimental studies verify the effectiveness of these two proposed methods in extracting the gearbox compound fault features.In summary, this thesis proposes two methods based on the sparse representation theory to diagnose the gearbox compound fault which is comprised of bearing and gear localized faults using different wavelet dictionaries. The effectiveness of the proposed methods has been examined. This research in the thesis enriches the methods for extracting the compound fault features, which is of considerable value in the field of mechanical fault diagnosis.