Incorporation of engineering knowledge into the modeling process: a local approach

Abstract

Process modelling is the foundation of developing process controllers for monitoring and improving process/system health. Modelling process behaviours using a pure empirical approach might not be feasible due to limitation in collecting large amount of data. Engineering models provide valuable information about processes' general behaviours but they might not capture distinct characteristics in the particular process studied. Many recent publications presented various ideas of using limited experimental data to adjust engineering models for making them suitable for certain applications. However, the focuses there are global adjustments, where modification of engineering models impacts the entire model-application region. In practice, some engineering models are only valid in a part of experimental data domain. Moreover, many discrepancies between engineering models and experimental data are in local regions. For example, in a chemical vapour deposition process, at high temperatures a process may be described by a diffusion limited model, while at low temperatures the process may be described by a reaction limited model. To address these problems, this article proposes two approaches for integrating engineering and data models: local model calibration and local model averaging. Through the local model calibration, the discrepancies between engineering's first-principle models and experimental data are resolved locally based on experts' feedbacks. To combine models adjusted locally in some regions and also models required little adjustments in other regions, a model averaging procedure based on local kernel weights is proposed. The effectiveness of the proposed method is demonstrated on simulated examples, and compared against a well-known existing global-adjustment method.