摘要
针对软测量建模中的变量选择问题,提出了一种结合信息论中最大熵和互信息的方法。该方法采用最大熵原理,对软测量中各辅助变量和主导变量的概率分布进行估计,得到主导变量和各辅助变量间的互信息,这些互信息间接地反映了主导变量和各辅助变量间的相关性,包括线性相关和非线性相关。然后产生随机样本并计算和主导变量间的互信息,重复多次该过程就可以得到一个无关变量和主导变量间的互信息样本。用T检验寻找一个阈值作为判断相关性的标准。对于互信息小于阈值的变量作不相关变量处理,并结合测试效果筛选出最佳的软测量辅助变量。仿真结果证明,基于互信息的软测量变量选择方法具有直观、简单实用和可靠性高的优点,并且有效地改善了模型的估计精度。
In order to solve the problem of variables selection for soft sensor, a method of combining maximum entropy and mutual information is proposed. The mutual information between the predicted variables and the secondary variables is obtained by maximum entropy principle estimating the probability distribution of every secondary variable and the predicted variables, which indirectly reflects the correlation including linear correlation and nonlinear era＇relation between the predicted variable and the secondary variables. Then produce a random sample and calculate the mutual information between the predicted variable sample and the random sample, and repeat this process many times can get a mutual information sample. A threshold value is obtained by T-test approach as a criterion to judge the correlation of variables. When the mutual information between the predicted variable and a secondary variable is less than the threshold value, the secondary variable is as an independent variable. The secondary variables are selected by combination of the pres- ented method and cross test. The simulation result shows that the method of a variable selection for soft sensor based on mutual information is intuitive, simple, practical and high reliability, and it effectively improve the estimation precision of the model.
出处
《控制工程》
CSCD
北大核心
2012年第4期562-565,593,共5页
Control Engineering of China
基金
国家自然科学基金(60674092)
江苏省高技术研究项目(工业部分)(BG2006010)
江苏高校优势学科建设工程资助项目
高等学校学科创新引智计划资助(B12018)
江南大学博士研究生科学研究基金(JUDCF12030)
关键词
软测量
变量选择
最大熵
互信息
soft sensor
variable selection
maximum entropy
mutual information
