Signal Sparse Representation Method Based On Dictionary Design And Its Application In Gearbox Fault Diagnosis

Gearboxes have the function of transmitting torque,distributing power and changing transmission direction,and play a pivotal role in transportation vehicles.However,the gearbox in the vehicle is subjected to high-speed,heavy-duty operational environments for a long time,and its key components-gears and bearings will often fail,which leads to gearbox failure.If the gearbox failure is not detected and warned in time,then the vehicle will have huge safety risks,and even cause serious economic losses and casualties,so it is important to monitor and diagnose the status of the gearbox.The vibration signal of gearbox contains rich information of working condition,and it is one of the more extensive and effective methods to carry out gearbox fault diagnosis.As a vibration signal analysis method,the sparse representation method has good performance in gearbox fault feature extraction,but there are still some pressing issues that need to be addressed.On the one hand,the complexity of the gearbox vibration signal puts higher requirements on the accuracy and efficiency of the sparse representation method.On the other hand,the sparse representation method should try to avoid relying too much on a priori knowledge and improve the self-adaptability.Therefore,this paper investigates how to extract gearbox fault feature information accurately,efficiently and adaptively for gearbox fault diagnosis based on the sparse representation method.The main studies are as follows.(1)The vibration mechanism of key components in gearboxes is analyzed,and the important components of gearbox vibration signals are studied and parametrically modeled.A parametric wavelet dictionary that highly matches the vibration characteristics of the characteristic components of gearbox faults is established.A sparse representation singlecomponent optimization model based on l1-norm is constructed and a multi-component optimization model is derived.Based on the sparse representation single-component optimization model,the iterative process of Split Augmented Lagrangian Shrinkage Algorithm(SALSA)and Forward-Backward Splitting(FBS)is derived.(2)Study on the sparse representation method based on the tight-frame analytic dictionary and its application in gear fault diagnosis.The gear,a key component in gearboxes,is used as the research object,and the Tunable Q-factor Wavelet Transform(TQWT),which fits the vibration characteristics of gears,is introduced to construct a linear transform analytic dictionary,and the tight-frame property of TQWT is used to avoid the sparse representation.Optimizing the operations of high-dimensional matrices and inverse matrices in the solution process greatly improves the operational efficiency and enhances the practicality of the sparse representation method.By analyzing the nature of the penalty function,we propose to use the Minimax-Concave(MC)function instead of the l1-norm as the penalty function to construct the sparse representation optimization model.MC penalty function can not only promote the sparsity of the vibration signal well,but also solve the problem of amplitude underestimation with better amplitude fidelity of the characteristic components.Finally,the sparse representation coefficients are solved using the convex optimal solution algorithm to achieve the accurate reconstruction of the fault feature components and accurately extract the fault feature frequencies.(3)Research on the sparse representation method based on adaptive learning dictionary and its application in bearing fault diagnosis.Taking bearings,another key component in gearboxes,as the research object,we study the use of learning dictionaries to improve the adaptiveness of the sparse representation method to address the challenges of fixed structure and poor adaptiveness of the analytic dictionary.The analytic dictionary of specific basis functions is only for fixed fault types,and the sparse representation dictionary that does not match with the fault types has poor sparse representation.The adaptive learning dictionary not only inherits the high adaptivity of the learning dictionary,but can obtain the sparse representation dictionary that adaptively matches the internal features of the signal directly by learning training without a large amount of a priori knowledge acquired by the preliminary work.Moreover,the structure of the sample training matrix of the K-SVD algorithm is improved to enhance the operational efficiency.And the soft thresholding algorithm is used to enhance the noise immunity of the sparse representation method.Finally,with the excellent amplitude fidelity of the Generalized Minimax-Concave(GMC)function,the sparse representation coefficients are solved by the convex optimal solution algorithm to achieve the accurate reconstruction of the fault feature components.The proposed dictionary-based signal sparse representation method can accurately extract the fault characteristic components from the gearbox vibration signal and accurately diagnose the fault type of gearbox,which lays a solid theoretical foundation for the application of the sparse representation method in gearbox fault diagnosis field and has significant practical value and significance.