Hammerstein Model Identification Based On Least Angle Regression Algorithm

Hammerstein model is a common block structure nonlinear model,which is composed of a static nonlinear link and a dynamic linear link in series.It can be used to describe a large class of nonlinear processes such as p H neutralization process,blast furnace ironmaking process and heat exchanger.Because it can better reflect the process characteristics and facilitate the design of control system,the identification of this model has become a major research focus in the field.Considering that many industrial systems contain time delays,and the existence of time delay makes the control system unable to respond in time and affects the control quality.In order to ensure the control effect,it is necessary to consider the time delay identification problem when studying the model identification problem.In addition,how to determine the order of the model is also an inevitable and important problem in the process of Hammerstein model identification.Therefore,the joint identification of parameters,time delay and order of Hammerstein model is of great significance.Inspired by sparse identification method and regression analysis theory,this paper studies a sparse system identification algorithm for joint identification of time delay,order and parameters of Hammerstein model based on the least angle regression(LAR)algorithm from the perspective of model selection.The specific research contents are as follows.(1)For the multiple input single output(MISO)Hammerstein system described by a linear combination of known basis functions in nonlinear part and the linear part being a controlled autoregressive(CAR)model,the sparse identification algorithm based on LAR is studied based on the LAR algorithm and the Akaike information criterion model selection criteria.The algorithm replaces the unknown structure information in the system by setting the maximum nonlinear order and the input regression length,thus the high-dimensional sparse identification model and sparse parameter vector are obtained,and then the non-zero parameters in the sparse parameter vector are selected step by step to obtain a concise estimation model.Finally,the time delay and order estimates are obtained according to the sparse structure of the parameter vector,and the mixed parameters are separated to obtain the final identification results.The simulation results show the effectiveness of the proposed algorithm.(2)On the basis of research content(1),based on the geometric properties of LAR algorithm,the law of angle change is obtained,and the absolute angle stopping criterion(AASC)is derived.The effectiveness of AASC criterion is proved theoretically,and the sparse identification algorithm of LAR(AS-LAR)based on AASC is obtained.Compared with the sparse identification algorithm using traditional model selection criteria,the proposed algorithm greatly reduces the amount of computation.The simulation results show that the algorithm is effective,and requires less computation and has strong antiinterference ability compared with similar algorithms.(3)On the basis of research content(2),for the MISO Hammerstein system described by the controlled autoregressive moving average(CARMA)model with the linear part disturbed by colored noise,based on the AS-LAR sparse identification algorithm,combined with the iterative identification technology,the unmeasurable noise part of the model is iteratively estimated to obtain a complete information matrix,an iterative AS-LAR(AS-LARI)sparse identification algorithm based on iterative identification is studied.Simulation results show the effectiveness of the proposed algorithm.(4)To achieve online identification,a modified AS-LAR(AS-MLAR)online sparse identification algorithm based on recursive matrix and an iterative AS-MLAR(AS-MLARI)online sparse identification algorithm are further studied.Firstly,the recursive process of LAR algorithm is reconstructed by introducing a recursive matrix,which simplifies the calculation steps of high-dimensional inverse matrix,improves the stability and computational efficiency of the algorithm,thus ensures the online identification effect;Furthermore,an online identification mechanism is established for MISO Hammerstein-CAR and Hammerstein-CARMA model.Simulation results show the effectiveness of the proposed algorithm.To sum up,this paper studies and derives a series of identification algorithms based on sparse identification method and regression analysis theory,with LAR algorithm as the core,for the joint identification of parameters,time delay and order of MISO Hammerstein model.The effectiveness of each algorithm is verified by simulation.