(19h) A Critical Comparison of Stochastic and Worst-Case Robust Approaches to Optimal Experiment Design

Dynamic models are indispensable tools for analysis, optimization, and control of complex technical systems. Construction of accurate models relies on experiments, which should provide as much system information as possible while being safe and least intrusive to the nominal system operation. However, generating informative system data can be cost, time, and labor intensive. To this end, model-based methods have been developed for optimal design of experiments, generally aiming at systematically maximizing the information content of experiments while fulfilling the operational limitations of the system and possibly reducing the cost of experiment [1].

This work considers optimal experiment design (OED) for parameter estimation, where experiments are designed to generate informative data for the adequate estimation of model parameters. However, as OED is based on the current best estimateof the model parameters and initial conditions, two problems are likely to arise due to parametric uncertainty: (i) the predicted information content of the experiment can differ from that of the real experiment and (ii) the system constraints may be violated during the experiment, leading to potentially unsafe and ineffective experimental conditions. Thus, ensuring the robustness of the designed experiments to system uncertainties is critical to both effectively enhancing the information content of the experiment as well as enforcing the system constraints [2].

In this work we will discuss two formulations for OED that can explicitly account for the system uncertainty – a stochastic OED formulation based on probabilistic descriptions of uncertainties and a worst-case robust OED formulation. The stochastic OED formulation relies on generalized polynomial chaos [3], for which an efficient sample-based implementation is presented. The worst-case robust OED formulation, on the other hand, requires second-order sensitivities in the OED objective function [4], necessitating the use of efficient automatic differentiation tools for the third and fourth order derivatives. The OED approaches are implemented in CasADi, a dedicated framework for efficient algorithmic differentiation and numerical optimization [5], and are illustrated on a benchmark biological system. The performance of the OED approaches is critically evaluated in terms of their theoretical formulation, computational complexity, and extensibility to larger scale systems.

References

[1] Franceschini, G. and Macchietto, S. (2008). Model-based design of experiments for parameter precision: State of the art. Chemical Engineering Science, 63, 4846-4872.

[2] Asprey, S. and Macchietto, S. (2002). Designing robust optimal dynamic experiments. Journal of Process Control, 12(4), 545-556.

[3] Mesbah, A. and Streif, S. (2015). A probabilistic approach to robust optimal experiment design with chance constraints. In: International Symposium on Advanced Control of Chemical Processes(ADCHEM), 100 -105.

[4] Telen, D., Logist, F., Van Derlinden, E. and J. Van Impe J. (2012). Robust Optimal Experiment Design: A Multi-Objective Approach. In Proceedings of the 7th Vienna International Conference on Mathematical Modelling – MATHMOD.

[5] Andersson, J. (2013). A General-Purpose Software Frame-work for Dynamic Optimization. PhD thesis, KU Leuven, Department of Electrical Engineering