Optimal Experiment Design in Nonlinear Parameter Estimation with Exact Confidence Regions
This work addresses the challenge of improving parameter estimation accuracy in nonlinear systems for researchers and practitioners in fields like control engineering, though it is incremental as it builds on existing optimal experiment design methods.
The paper tackles the problem of optimal experiment design for nonlinear parameter estimation by explicitly incorporating exact confidence regions instead of linearized approximations, resulting in a bilevel optimization formulation and demonstrating its effectiveness through small-scale case studies.
A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the available (experimental) degrees of freedom such that more informative measurements are obtained. Unlike the commonly used approaches, which base the OED procedure upon the linearized CRs, we explore a path where we explicitly consider the exact CRs in the OED framework. We use a methodology for a finite parametrization of the exact CRs within the OED problem and we introduce a novel approximation technique of the exact CRs using inner- and outer-approximating ellipsoids as a computationally less demanding alternative. The employed techniques give the OED problem as a finite-dimensional mathematical program of bilevel nature. We use two small-scale illustrative case studies to study various OED criteria and compare the resulting optimal designs with the commonly used linearization-based approach. We also assess the performance of two simple heuristic numerical schemes for bilevel optimization within the studied problems.