基于信源熵的残差相关性度量方法

A Measurement for Residual Correlation Based on Information Entropy

在动态模型残差序列的相关分析中融入信源熵的概念,构造了一种具有普适意义的统计量———“残差熵”,它的直观物理意义是残差序列中所残留的信息量,可以定量地反映残差序列逼近白噪声的程度.文章在正态假设的基础上推导出“残差熵”的估算公式.理论分析和实例计算都表明:“残差熵”可以作为一种有效的度量方法用于动态模型的适应性检验和定阶.与传统的检验方法相比,该物理量充分利用了残差序列的随机分布信息,因而显示出更好的模型辨识性能.

Information entropy being fused in residual correlation analysis of dynamic model, this paper constructs a general diagnostic quantity named “residual entropy”, which means the amount of information left in residual series, and indicates the approximation degree of residual to white noise. The paper also gives the estimation expressions of residual entropy on normal distribution hypothesis. The numerical experiment of a fire control accuracy test demonstrates that residual entropy can be used as a measure for dynamic model checking and order determination. By comparison with conventional methods included Loss function, FPE, AIC and BIC, residual entropy makes full use of stochastic distributions of residual series, so it provides more effective identification and checking performance.