信息物理融合系统建模的区间GMDH算法

Interval GMDH Algorithm for Cyber-physical System Modeling

针对信息物理融合系统(CPS)建模中存在的误差及误差累积问题,本文在数据处理分组方法(GMDH)的基础上,结合区间分析思想,提出了区间GMDH算法.算法首先对基于区间分析的集合反演算法(SIVIA)进行了改进,提出了c SIVIA算法.通过引入收缩算子,在保持解集不变的情况下,对参数估计的区间进行压缩,解决SIVIA算法进行二分搜索时出现的计算量大、耗时长以及死锁问题.其次,将GMDH的输入及计算转变成区间数和区间运算,用改进的c SIVIA算法对模型参数进行估计.最后,取区间参数的中点作为待估参数的点估计,再利用外准则对产生的中间模型进行筛选,以建立最终系统模型.实验表明本文提出的区间GMDH算法与原算法相比在精确度、抗噪性等方面得到明显改善,有效地解决了CPS建模中存在的误差和误差累积问题.

According to the error and error accumulation problem in Cyber-Physical System modeling,this paper proposes an i GMDH algorithm based on the GMDH and the idea of interval analysis. Firstly,the c SIVIA algorithm is proposed to improve SIVIA algorithm. By introducing contractor,the interval of the estimated parameters can be compressed under the condition that the solution set keeps unchanged,which solves the problem of large amount of computation,long time consuming and deadlock in the original SIVIA algorithm. Secondly,the input and calculation of the original GMDH algorithm are changed into the interval number and interval operation,and the model parameters are estimated by using the improved c SIVIA algorithm. Finally the midpoint is taken as the point estimation of the interval parameters,and then the intermediate model is filtered by using the external criterion,which are used to build the final system model. Experiments showthat the i GMDH algorithm can significantly improve the accuracy and noise immunity compared with the original algorithm,and effectively solve the problem of error and error accumulation in CPS modeling.