Identification Of Time-varying System Parameters Using The Wavelet Analysis Theory

The wavelet analysis theory is the large number of academic groups and fields of common concern to a hotspot. It is the math scientists, applied mathematicians and data-processing engineers in their respective fields, respectively, an independent study found that after decades of exploration, has established a formal system of mathematics, and its increasingly solid theoretical foundation. The wavelet analysis theory and Fourier transform, the window Fourier transform time are compared to the space-time and frequency local transformation, and thus more effective in extracting data from the signal information. Through operation functions and so on expansion and translation carries on the multi-criterion refinement analysis to the function or the signal, has solved many difficult problems which in the Fourier transformation cannot solve, thus the wavelet analysis theory is honored as in the harmonic analysis history"mathematics microscope".This article has introduced the wavelet analysis theory the systems control domain, mainly has studied the wavelet analysis theory in the system identification application situation, first introduced briefly the system identification basic theory knowledge and the wavelet analysis basic theory, in the following concrete application, in based on the Haar wavelet orthogonal standard base's foundation, the use differentiate matrix and the nature, has conducted the research to a kind of misalignment distribution parameter system parameters identification question; In the time-varying system parameter's identification, has introduced in the wavelet analysis theory Mallat algorithm, and used this algorithm would be carried out time-varying parameters so that the problem into a problem for time-invariant coefficients,and has discussed the filter and the resolution depth choice, deletes chooses the coefficient the method and so on. This article has also made the elaboration to the wavelet network's theory, outlines the multi-resolution wavelet network in the nonlinear system identification application. Specifically as follows:The second chapter has drawn out the system identification definition from system model's definition, described the identification step specifically through the system identification's flow chart, and introduced the linear system and nonlinear system's commonly used mathematical model and the identification method separately.The third chapter introduced the wavelet basic theory briefly. Especially in the wavelet theory's some core, this article can apply theory. Mainly introduces the theory of multi-resolution analysis of wavelet decomposition and reconstruction algorithm. The fourth chapter proposed approaches the transformation based on the orthogonal wavelet the method, in the Haar wavelet orthogonal standard base's foundation, the use differentiate matrix and the nature, has conducted the research to a kind of misalignment distribution parameter system parameters identification question. The more complex partial differential equation description's misalignment distribution parameter system transformation will be originally a group of algebra matrix equation, the union least squares method, determined treats the identification the system parameters, avoided carrying on the multiple integral operations to the partial differential equation tedious, simplified the question solution process.The fifth chapter discussed time-varying system's parameter identification method. First introduced the least squares method as well as the forgetting factor least squares method; Then has drawn out the wavelet analysis identification method, with Mallat algorithm when the time-varying parameters would be carried out so that the problem into a problem for time-invariant cofficients; Finally studied has implemented this method some actual contents: The filter and the resolution depth's choice, the equation coefficient delete elect, and has given the concrete example simulation result.The sixth chapter introduced the wavelet network theory as well as in nonlinear system's application situation emphatically. It has analyzed three kind of wavelet networks (wavelet base network, wavelet neural network and multi-class wavelet network) structure. The seventh chaper ,namely at the end of this article's concluding remarks, the article made room for improvement or areas for further research.