The Study Of Signal Processing And Diagnosis Based On Fractal Theory

As a newly developing subject, the Fractal Theory is suitable for analysis on complex systems. And it's a new trend of academic circles to take Fractal Theory into the field of fault analysis for mechanical system. We can use Fractal Theory to analyze on the state signal of the mechanical system, and take fractal dimension as characteristic information, we can analysis on motion state not only qualitatively but also quantitatively, so we will realize fault analysis of the complex mechanical system, and improve the capability of discrimination and analysis on fault, it is an effective method for the signal of the mechanical equipment. Study on the application of fractal signal simulation, parameter estimation, correlation dimension and multi-fractal spectrum in the signal processing and fault analysis.Firstly, fault signal feature extraction is taken as breakthrough point, the deficiencies of traditional methods are discussed, and fractal applied in the possibility and study method of fault signal analysis to mechanical system is analyzed.Secondly, the fractal signal simulation and its method is studied, the simulation of fractal signal is done on software platform of MATLAB, the estimation and comparison of fractal dimension is made, the estimated value got is nearly the same as the theoretical value, the cause of the error is analyzed, and the result proves that taking fractal dimension as complex nonlinear mechanical signal to analyze on performance is feasible theoretically.Then, take the diesel engine system as study object, use correlation dimension in the theoretical and experimental study. Study the calculation method of the correlation dimension, analyze the feasibility of taking correlation dimension as the extraction value of characteristic information, and have an analysis on the actual experimental data, the result shows that the correlation dimensions of mechanical vibration signal are different under different working states, having obvious fractal chareristic. The correlation dimension is sensitive to the fault of the equipment, and can reflect dynamic characteristics of the system. Therefore, taking correlation dimension as the sensitive factors of fault signal analysis is feasible, this method is simple,visuah feasible, it overcomes the difficulty in the extraction and analysis of fault characteristics.At last, for the three characteristic parameters of the multi-fractal spectrum: maximum f_max , width W and unsymmetrical degree B, they are applied in mechanical fault analysis to make theoretical and experimental study as the basis for signal analysis. The experimental results show that multi-fractal spectrum has better capability of the local analysis, combine correlation dimension with multi-fractal spectrum, consider the extraction of fault diagnosis characteristic quantity from the whole and partial views at the same time, improve the accuracy and reliability of fault analysis.