Research On Machinery Fault Diagnosis Technology Based On Partial Differential Equations

Mechanical equipment is a key part of modern manufacturing engeneering and an important material foundation of economic construction and social progress. But as time went by, mechanical equipment and its parts are susceptible to be damaged and then become failure, which may cause economic losses or even disaster, so research on mechanical fault diagnosis technology is of great weight. To extract the fault feactures from signals is the key work in mechanical fault diagnosis. Vibration signal contains abundant equipment running information, so vibration signal analysis becomes the common method of fault diagnosis. Vibration signal usually shows non-stationary characteristics when failure occurs in mechanical equipment. There are several non-stationary signal analysis methods, such as short time Fourier transform, Hilbert-Huang transform, wavelet transform, local mean decomposition and mophology transform, but each of these methods has some limitations, so new theory and method research and exploration are still vary necessary.Partial differential equation-PDE is an important branch of mathematics. It has a solid theoretical foundation, can filter noise and preserve edge very well, and has good performance of local adaptability and high flexibility. PDE is a data driven method, so it is widely used in image processing and computer vision and achieved fruitful results and great progress. Though PDE has excellent performance, there is few application in1d signal processing, so this paper aims at the application of the theory of PDE in fault diagnosis of mechanical equipment such as rotor system, gear and bearing. Main contents are as follows:(1)The basic theory and numerical solution method of PDE were introduced, emphatically about boundary conditions, finite difference method, variational principle and gradient descent flow, and then several common PDE models in image processing were introduced. These are all the theoretical foundation for the analysis in the following chapters.(2)Typical faults mechanism and characteristics of vibration signals in rotor system were intruduced. P-M model is a typical PDE method in image processing and has good performance. But it is effiency only for Gauss noise, but can not effectively filter random pulse noise. So an improved P-M model named adaptive gradient threshod P-M (AGTP-M) was proposed, which was tested by simulation signal and shows good performance. Then the improved method was used in rotor vibration signal denoising, and correlation dimension was used as the feature vector to classify rotor system fault types. (3)Typical gear faults mechanism and characteristics of vibration signals were intruduced. Local mean decomposition(LMD) is a non-stationary signal analysis method, and the achievement of local mean function and local envelope function is a key step in this method. In traditional LMD this is finishied by moving average, in which the average length is difficult to choose and will cost much computational time. For this problem, an improved LMD algorithm based on the PDE theoretical framework was proposed and used for gear vibration signal decomposition, and then the permutation entropy of each PF component was calculated and used to classify the typical gear fault types.(4)Typical bearing faults mechanism and characteristics of vibration signals were intruduced. Traditional diagnosis methods dose not use the time frequency diagram to extract useful information. In this paper, image decompositon method based on PDE was used to decomposse bearing vibaration time frequency diagram into structure subgraph and texture subgraph, and then by calculating the gray level co-occurrence matrix(GLCM) to get the feature vector. At last, bearing faults can be classified by LSSVM.(5)Traditional fault diagnosis methods are mainly on single fault. But compounded faults usually occurs. Morphological component analysis(MCA) is a signal decomposition method using morphological differences. When strong noise exists, MCA dose not work very well, so combined with PDE denoising technology, MCA method was applied to gearbox compounded faults diagnosis.