Trivial Principal Component Method With Extended Capability For Modeling

Paper #:
  • 2017-01-0220

Published:
  • 2017-03-28
Abstract:
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 and it determines linear coefficients of the model by using the trivial Eigen vector corresponding to the least Eigen value. Generally linear modeling accuracy depends on strength of nonlinear and interaction terms as well as measurement error. In this paper, TPC method is extended to analyze residual (error) vector to identify significant higher order and interaction terms that contribute to the error. Subsequently, the system behavior can be further refined by including those terms in building the model. Additionally, an iterative TPC analysis is proposed for the first time to correct the model gradually till the least Eigen value becomes minimum. For illustration, example problems are presented to bring out the potential and novelty of the TPC method for improved modeling and compared with the results of linear regression method.
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