System model development with ill-conditioned data: case studies of trihalomethane formation in drinking water

Abstract

Trihalomethane (THM) and other by-products are formed by the reaction of free chlorine and organic precursors. The collective effects of different raw water quality and chlorine treatment measures are used as candidate variables in the formulation and parameter estimation of models to predict THM concentration in treated water. Some of these predictor variables involving raw water quality (state variables) are highly correlated. In addition, retrospective studies often involve treatment measures (control variables) which, either because of practical exigencies or poor design, are correlated. As a result of correlations among variables, regression models that are fit with ordinary least squares are of questionable merit because model parameter estimates are generally poor. Yet, the potential value of such studies and modelling efforts should not be ignored. An approach consisting of the use of condition indexes and variance-decomposition proportions, ridge regression, and path analysis is used for model development. These techniques are used to identify the extent and possible causes of ill-conditioning, and to offer a means of rationally eliminating predictor variables that are considered to cause ill-conditioning or to have an insignificant effect on prediction. Four case studies are used to demonstrate the approach and to show that our final models contain only predictor variables that are both statistically and physically significant. Critical evaluation of the models reinforces theoretical concepts for explaining THM formation in finished water.

Keywords:

• water quality
• mathematical model
• linear regression
• trihalomethane