Choice of Explanatory Variables: a Multiobjective Optimization Approach

摘要

In process control applications it is often necessary to derive a suitable process model from input/output data using multivariable regression analysis. However, problems frequently arise in selecting an appropriate set of independent(explanatory) variables and/or in handling problems caused by correlation between the measurements. The multiobjective function based approach presented in this paper addresses both problems and is shown to produce excellent results in practicalapplications. The proposed method minimizes a user-specified combination of the following three criteria:1) the data matrix related residue,2) the observation or measurement related residue, and3) the condition number of the new data matrix of the selected explanatory variables.Four different algorithms for solving the resulting multiobjective optimization are compared. The model structure determined by applying the proposed method to a simulated process identification problem was identical to the actual model structure. Asecond successful application involved model structure determination for a 2 2 pilot plant process based on experimental input/output data.