System Adaptive Prediction Based On Hammerstein Modeling

Nonlinear system identification is an important branch of modern automatic control theory,which mainly uses the input and output data of the system to establish an equivalent mathematical model to realize the prediction and control of unknown systems.After long-term development,linear system identification has established a relatively complete identification system,while nonlinear system identification has developed slowly due to the complex nonlinear structure.In the nonlinear system identification,modular nonlinear models have attracted attention because of their simple structure and easy identification.Among which the Hammerstein model,as a typical modular nonlinear model,is widely used in nonlinear system identification and prediction scenarios due to its excellent identification performance.This thesis studies the adaptive prediction theory and algorithm problem of systems based on Hammerstein modeling.In order to solve the dual parameter optimization problem in the identification process,parameter mapping transformation is used to transform the bilinear optimization problem into optimization of intermediate variables.Two adaptive identification algorithms are proposed to address the shortcomings of nonlinear identification algorithms.Firstly,the original filtering problem is formulated as a nonconvex optimization problem,and the normalized minimum mean square method is used to calculate the solution of an initial convex optimization problem.Then,the solution is projected onto the nonconvex feasible domain,and a normalized minimum mean square algorithm based on Euclidean minimization is proposed to solve this nonconvex optimization problem.Due to the slow convergence speed and low identification accuracy of the normalized minimum mean square algorithm,a recursive least squares algorithm based on the alternating direction multiplier method is proposed.Firstly,the initial solution is obtained using ridge regression,and then the global optimal solution of the nonconvex optimization problem is solved using Euclidean minimization.The closed form expression of the optimal solution is derived.Finally,in order to further investigate the identification performance of the improved recursive least squares method,the common nonlinear echo cancellation problem in speech communication was introduced to verify the filtering effect of the proposed algorithm on nonlinear echo signals.In order to verify the performance of the proposed algorithm,the thesis conducted a series of simulation analysis experiments using the proposed algorithm and compared it with other similar algorithms.The experimental results show that the two proposed algorithms outperform similar algorithms in terms of identification accuracy and convergence speed,and have better convergence characteristics and robust performance;In the same environment,the improved recursive least squares algorithm has higher estimation accuracy and stability than the improved normalized least mean square algorithm;By simulating nonlinear acoustic echoes with real speech signals,it has been verified that the proposed improved recursive least squares method can effectively eliminate acoustic echoes,and has lower estimation error and higher return loss gain compared to similar algorithms.