基于k-近邻互信息的前向式变量选择方法及在水质参数软测量中的应用

Forward variable selection method based on k-nearest neighbor mutual information and its application in soft sensor modeling of water quality parameters

软测量技术通过构造易测量的辅助变量与难测量的主导变量间的数学模型,实现对难测变量的实时预测.为有效分析辅助变量间的相关性和冗余性并实现变量精选,本文提出了一种基于k-近邻互信息的前向式变量选择方法.该方法以变量前向累加互信息值最大化为准则选择相关变量,同时计算每次累加变量与已选择变量子集间的互信息值来判断所累加变量是否为冗余变量,通过设定冗余互信息阈值,实现冗余变量的剔除,得到最优辅助输入变量子集.基于数值案例仿真结果验证了本文所提变量选择方法的可行性与有效性,在准确选取辅助变量的同时降低了算法复杂度.最后,该方法成功应用于污水处理过程中出水生化需氧量(biochemical oxygen demand,BOD)预测模型的输入变量选择上,利用精选出的辅助变量有效提高了模型预测精度.

Soft sensor technology realizes real-time prediction of difficult-to-measure variables by constructing a mathematical model between easy-to-measure auxiliary variables and difficult-to-measure primary variables.In order to effectively analyze the correlation and redundancy between variables and realize the selection of auxiliary variables,this paper proposes a forward variable selection method based on k-nearest neighbor mutual information.Based on the criterion of maximizing the forward cumulative mutual information value of input variables to select correlated variable,and the redundant mutual information value between each new added variable and the subset of selected variables is calculated to judge whether the added variable is redundant variables.By setting the threshold of redundant mutual information value,the redundant variables are eliminated,and the optimal subset of auxiliary input variables can be obtained.The simulation results based on a numerical case verify the feasibility and effectiveness of the variable selection method proposed in this paper,which not only accurately selects auxiliary variables but also reduces the complexity of the algorithm.Finally,the method was successfully applied to the selection of input variables for the effluent biochemical oxygen demand(BOD) prediction model in the wastewater treatment process,and the selected auxiliary variables were used to effectively improve the prediction accuracy of the model.