In order to solve the problems of high identification limitation and low identification rate in nonlinear system identification with fixed structure and parameters, a Subsystem-based Structural Adaptive Filtering (SSAF) method for nonlinear system identification was proposed with introducing structural adaptation into the optimization of identification. Multiple subsystems with linear-nonlinear hybrid structure were cascaded to form the model for this method. The linear part is a 1-order or 2-order Infinite Impulse Response (IIR) digital filter with uncertain parameters, and the nonlinear part is a static nonlinear function. In the initial stage, the parameters of the subsystems were randomly generated, and the generated subsystems were connected randomly according to the set connection rules, and the effectiveness of the nonlinear system was guaranteed by the connection mechanism with no feedback branches. An Adaptive Multiple-Elites-guided Composite Differential Evolution with a shift mechanism(AMECoDEs) algorithm was used for loop optimization of the adaptive model until the optimal structure and parameters were found, that is, the global optimal. The simulation results show that AMECoDEs performs well on nonlinear test functions and real data sets with high identification rate and good convergence rate. Compared with the Focused Time Lagged Recurrent Neural Network (FTLRNN), the number of parameters used in SSAF is reduced to 1/10, and the accuracy of fitness is improved by 7%, which proves the effectiveness of the proposed method.

Focused on the issue that the traditional multiplierless Infinite Impulse Response (ⅡR) digital filters have fixed structure and poor performance, a random structure based design method for multiplierless ⅡR digital filters was proposed. Stable 2-order subsystems with shifters were directly used to design the multiplierless filter structure. Firstly, a set of encoding structures of the multiplierless digital filter were created randomly. Then, Differential Evolution with a Successful-Parent-Selecting Framework (SPS-DE) was used to optimize the multiplierless filter structure. The proposed method realized diversified structure design, and SPS-DE effectively balanced exploration and exploitation due to adopting a Successful-Parent-Selecting framework, which achieved good results in the optimization of the multiplierless filter structure. Compared with state-of-the-art design methods, the passband ripple of the multiplierless ⅡR filter designed in this paper is reduced by 43% and the stopband maximum attenuation is decreased by 40.4%. Simulation results show that the multiplierless ⅡR filter designed by the proposed method meets structural requirements and has good performance.

In order to further improve the performance of Infinite Impulse Response (IIR) digital filter, a design method of the IIR digital filter based on structure evolution and parameter evolution was proposed. Firstly, initial filter structure was got by using Genetic Algorithm (GA). Then, Differential Evolution (DE) was used to optimize the parameters of the filter. Finally, an improved optimization strategy was used to further optimize the parameters of the filter by using adjustment search-step and bidirectional heuristic search. Furthermore, the proposed method was applied to the design of low-pass filter and high-pass filter. Compared with the design method based on GA, the pass-band performance of low-pass filter based on the proposed method is not much different from that of the previous algorithm, however, the transition zone width of it is reduced by 65%, the minimum stop-band attenuation of it was reduced by 36.48 dB; the pass-band ripple of high-pass filter based on the proposed method is reduced by 75%, the transition zone width of it is reduced by 44%, and the minimum stop-band attenuation of it is reduced by 12.13 dB. Simulation results show that the proposed method can get effective filters with better performance, therefore it is suitable for the IIR digital filter design.

Focused on the issue that the transfer function of Infinite Impulse Response (IIR) digital filters is not optimal in the entire design process adopting traditional filter design methods, a structure evolution based design method for IIR digital filters using Genetic Algorithm (GA) was proposed. The method evolved the filter structure directly without the preparation of the transfer function. Firstly, the Structure Generation Instruction Sequences (SGIS) were generated randomly. Those SGIS not only controlled the process of structure generation but also represented those structures. Then, the SGIS were coded and seemed as chromosomes. Finally, GA was used to optimize those chromosomes to obtain a best filer. In the comparison experiments with the traditional coefficient evolution based design method for IIR digital filters using GA, the pass-band ripple of the proposed algorithm decreased by 40.58%, the transition zone width of it decreased by 87.62%, and the minimum stop-band attenuation of it declined by 9.22%.