Trivial Principal Component Analysis (TPCA): An Improved Modeling Approach

Trivial Principal Component method (TPC) was developed recently to model a system based on measured data. It is a statistical method that utilizes Eigen-pairs of covariance matrix obtained from the measured data. It determines linear coefficients of a model by using the trivial eigenvector corresponding to the least eigenvalue. In general, linear modeling accuracy depends on the strength of nonlinearity and interaction terms as well as measurement error. In this paper, the TPC method is extended to analyze residual (error) vector to identify significant higher order and interaction terms that contribute to the modeling error. Subsequently, these additional terms are included for constructing a robust system model. Also, an iterative TPC analysis is proposed for the first time to correct the model gradually till the least eigenvalue becomes minimum. For illustration, example problems are presented to bring out the potential and novelty of the TPC method for improved modeling and the results are compared with linear regression model.