A systematic framework for improving the quality of continuous time models of dynamic systems based on experimental data is presented. The framework is based on an interplay between stochastic differential equation modelling, statistical tests and nonparametric modelling and provides features that allow model deficiencies to be pinpointed and their structural origin to be uncovered. More specifically, the proposed framework can be used to obtain estimates of unknown functional relations, in turn allowing unknown or inappropriately modelled phenomena to be uncovered. In this manner the framework permits systematic iterative model improvement. The performance of the proposed framework is illustrated through a case study involving a dynamic model of a fed-batch bioreactor, where it is shown how an inappropriately modelled biomass growth rate can be uncovered and a proper functional relation inferred. A key point illustrated through this case study is that functional relations involving unmeasured variables can also be uncovered.
Kristensen, N. R., Madsen, H., & Jørgensen, S. B. (2004). A Method for Systematic Improvement of Stochastic Grey-Box Models. Computers & Chemical Engineering, 28(8), 1431-1449. https://doi.org/10.1016/j.compchemeng.2003.10.003