Term Elimination and Optimal Experiments for Model Reduction

Models of complex systems, particularly thermofluid models of chemical processes, tend to be computationally and mathematically complex, consisting of many differential algebraic equations. Use of such models for applications beyond simple simulation, including optimization and controls development, can be infeasible due to their complexity. Model reduction methods are applied to develop reduced order models that adequately reflect the input-output behavior of higher-fidelity models, with significantly less computational cost. Currently practiced model reduction techniques are frequently based on projections [1], regressions, or surrogate modeling [2] [3]. The abstracted reduced models produced with these methods are effective for approximating outputs, but do not generally retain the physically meaningful parameters of the original model or system.

This work presents a novel method for the creation and evaluation of reduced order models, using a high-fidelity model as a basis. The proposed method consists of two key algorithmic processes. The first is a method for generating reduced models from an original model by heuristically directed term elimination. This process selectively removes or replaces parameters, variables, functions, and equations form the original model, creating a new candidate reduced model with each manipulation. The second key process is the selection of the most suitable reduced models from the candidate set by the evaluation of optimal experiments using a T-optimal design criterion. The candidate set of reduced models for the optimal experiments are those that are found to be suitable representations of the original for a nominal experiment. Similar formulations using different design criteria have been previously explored for use in the selection of kinetic models [4] [5] and fault detection and isolation [6].

Eqs. (1) and (2) enumerate the optimal experiment design problem, wherein  are the outputs, state variables, equations, initial conditions, and parameters of the original model while correspond to the reduced model. The input trajectory  is selected to maximize the weighted error in the outputs of the reduced model as compared to the original, integrated over the duration of the experiment. The parameter values of the reduced model, , are adjusted to minimize error and better approximate the original model. The resulting optimal design vector   characterizes the experiment which will demonstrate the worst-case performance of the parameterized candidate reduced model at representing the original model within the state space of interest.  If the observed maximum error from the optimal experiment is within a specified threshold, the reduced model can be considered as suitable.

	(1)
	(2)

The proposed method is demonstrated by application to some classic chemical process models, including homogenous and spatially discretized reactor models. It is observed that the method can autonomously recreate and select reduced models which match those identified in existing literature. It is also shown that the optimal experiment design approach can more reliably identify unsuitable reduced models as compared to experiments with nominal inputs or those with inputs at minimum or maximum values. Application to larger models of varying structure is performed in order to quantify the computational cost advantages achievable by the selected reduced models.

  Acknowledgment

This work was sponsored by the UTC Institute for Advanced Systems Engineering (UTC-IASE) of the University of Connecticut and the United Technologies Corporation. Any opinions expressed herein are those of the authors and do not represent those of the sponsor.

  References

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