Understanding complex environmental systems: a dual approach

摘要

An approach to interpreting field data exploiting the duality of data- and theory-based models, and their associated methods of system identification, is presented. This approach seeks to overcome the respective limitations of the two branches of the duality: that theory-based models are not unambiguously identifiable from the observations, while a well-identified data-based model may not be capable of a satisfactory theoretical interpretation. The purpose of the approach is thereby to gain a deeper understanding of complex, poorly defined environmental systems. Recursive methods of time-series analysis are used to identify the data-based models (as transfer functions) and companion recursive methods, specifically the recursive prediction error (RPE) algorithm, are employed for structure identification and parameter estimation of the theory-based models (in ordinary differential equation forms). The results of these identification exercises for the two classes of models can be compared in terms of the macro-parameters of the studied system's time constant and steady-state gain. Two case studies are presented to illustrate the overall performance of the dual-thrust approach, on an activated sludge system and an aquaculture pond. It is found that: (1) as opposed to the exclusive use of either approach alone, more is to be gained through the joint application of the two classes of models, which historically have tended to reflect quite separate, unconnected approaches to interpreting environmental systems data; (2) to some extent, identifying the structure and estimating the parameters of one type of model can be readily improved by recourse to the corresponding results for the other; and (3) reconciliation of the results from identifying the two classes of model in the parameter space—of the time constant and steady-state gain—has significant advantages over the more familiar process of evaluating a model's performance in the terms of its (observed) state-space features.