The autoregressive moving average exogenous （ARMAX） model is commonly adopted for describing linear stochastic systems driven by colored noise. The model is a finite mixture with the ARMA component and external inpu...The autoregressive moving average exogenous （ARMAX） model is commonly adopted for describing linear stochastic systems driven by colored noise. The model is a finite mixture with the ARMA component and external inputs. In this paper we focus on a parameter estimate of the ARMAX model. Classical modeling methods are usually based on the assumption that the driven noise in the moving average （MA） part has bounded variances, while in the model considered here the variances of noise may increase by a power of log n. The plant parameters are identified by the recursive stochastic gradient algorithm. The diminishing excitation technique and some results of martingale difference theory are adopted in order to prove the convergence of the identification. Finally, some simulations are given to show the reliability of the theoretical results.展开更多
On the basis of genetic algorithm, an intelligent search approach to determination of parameters of ARMAX(Autor Regressive Moving Average model with external input) processes was proposed. By representing the system w...On the basis of genetic algorithm, an intelligent search approach to determination of parameters of ARMAX(Autor Regressive Moving Average model with external input) processes was proposed. By representing the system with pole and zero pairs and repairing illegal chromosomes, the search space is limited to stable schemes. In calculation of objective function the "shifted data window" was designed, so that every input output pair is used to guide the evolution and the "Data Saturation" is avoided. To prevent premature convergence, the adaptive fitness function was introduced, the conventional crossover and mutation operator was modified and the "catastrophic mutation" which is based on Metropolis mechanism was adopted. So the performance of convergence to the global optimum is improved. The validity and efficiency of proposed algorithm were illustrated by simulated results.展开更多
基金the National Natural Science Foundation of China (No. 60474026)
文摘The autoregressive moving average exogenous （ARMAX） model is commonly adopted for describing linear stochastic systems driven by colored noise. The model is a finite mixture with the ARMA component and external inputs. In this paper we focus on a parameter estimate of the ARMAX model. Classical modeling methods are usually based on the assumption that the driven noise in the moving average （MA） part has bounded variances, while in the model considered here the variances of noise may increase by a power of log n. The plant parameters are identified by the recursive stochastic gradient algorithm. The diminishing excitation technique and some results of martingale difference theory are adopted in order to prove the convergence of the identification. Finally, some simulations are given to show the reliability of the theoretical results.
文摘On the basis of genetic algorithm, an intelligent search approach to determination of parameters of ARMAX(Autor Regressive Moving Average model with external input) processes was proposed. By representing the system with pole and zero pairs and repairing illegal chromosomes, the search space is limited to stable schemes. In calculation of objective function the "shifted data window" was designed, so that every input output pair is used to guide the evolution and the "Data Saturation" is avoided. To prevent premature convergence, the adaptive fitness function was introduced, the conventional crossover and mutation operator was modified and the "catastrophic mutation" which is based on Metropolis mechanism was adopted. So the performance of convergence to the global optimum is improved. The validity and efficiency of proposed algorithm were illustrated by simulated results.
