Nonlinear Model Identification and Data Reconciliation Using Kernel Principal Component Regression

Abstract

Reconciliation of process data is an important preprocessing technique, the main purpose of which is to obtain accurate estimates of variables and model parameters. Reconciliation requires a process model which is generally developed using first principles. For many complex processes, the development of such models is difficult and time-consuming. In this work we propose a novel alternative method for steady state data reconciliation of nonlinear processes which does not require a functional model between variables to be specified a priori. A nonlinear model relating the variables is developed from a given data set, while simultaneously obtaining accurate estimates of the measured variables. The method we propose combines concepts drawn from Kernel Principal Components Regression with an error-in-variables model parameter estimation technique. Simulation studies demonstrate that the proposed approach is able to improve the accuracy of measured variables. The identified nonlinear model is also useful for reconciling future measurements of the process.

Hamiltonian Monte Carlo-Based D-Vine Copula Regression Model for Soft Sensor Modeling of Complex Chemical Processes

“…The third method is PCR which selects 95% of the principal elements. The fourth method is KPCR with the component selected by 95%; the kernel width is 9. The fifth method is PLS regression with three principal elements.…”

“…8 Among them, data-based soft sensor methods are gaining popularity because they do not require prior knowledge. The most commonly used data-based modeling techniques are multivariate statistical methods, such as principal component regression (PCR), 9 partial least squares regression (PLS) 10 for linear processes, and their variants, such as kernel PCR (KPCR) 11,12 and kernel PLS (KPLS) 13 for nonlinear processes. In addition, machine learning methods, such as artificial neural networks 14 and support vector regression 15 have been widely used to establish soft sensor models for nonlinear processes.…”