工业过程稳态模型估计误差的渐近正态性分析:SISO情形

ASYMPTOTIC NORMALITY ANALYSIS OF THE ESTIMATION ERROR OF STEADY-STATE MODEL FOR INDUSTRIAL PROCESS: (SISO) CASE

本文研究了在相当弱的条件下工业过程稳态模型估计误差的渐近正态性。参数估计采用简单加权最小二乘法,并利用近似线性模型集。优化过程中正常的系统设定点阶跃变化作为辨识信号。据此证明了系统稳态模型估计误差渐近正态分布的结论。同时,还研究了估计量的收敛速度和对线性近似模型结构的渐近鲁棒性。仿真研究则探讨了在有限样本空间内,影响估计精度的若干因素。

This paper investigates the asymptotic normality of the estimation error of steady-state models of industrial processes in quite mild conditions. The estimate is formed from the estimated parameters of an approximate linear model which is strong consistent to the steady-staregain of the slow time-varying linear SISO system. In the parameter estimation, the weighted leastsquares method is employed. The input signal (the system set point) is the usual step change in the optimization procedure. The rate of convergence is given out in this paper. The stationarity and the distribution of the stochastic process are not demanded. Under some acceptable conditions, the robustness to the structure of the approximate linear model is achieved In simulaion study, it is shown that for limited length of the sampled data, the best choice of the structure of approximate models in the aspect of estimation precision is dependent upon the realization of the stochastic noise.