Optimal Bayesian experiment design for nonlinear dynamic systems with chance constraints. (May 2019) - Paulson, Joel A.; Martin-Casas, Marc; Mesbah, Ali
Highlights: Optimal Bayesian experiment design for parameter inference in constrained nonlinear systems. Using surrogate models based on arbitrary polynomial chaos for efficient sample-based computation of the expected utility function. Chance constrained handling in Bayesian experiment design. Abstract: The optimal design of experiments is crucial for maximizing the information content of data across a wide-range of experimental goals. This paper presents a Bayesian approach to optimal experiment design (OED) for parameter inference in constrained, dynamic, and nonlinear systems under noisy, incomplete, and indirect measurements. Bayesian OED maximizes an expected utility objective, which accounts for prior and posterior uncertainty in the model parameters from an information-theoretic standpoint. Due to the complicated form of the expected utility, it must be estimated using sample-based methods and, in particular, a nested Monte Carlo estimator that is expensive to evaluate using the full dynamic model. We propose a novel surrogate model based on arbitrary polynomial chaos (aPC), which readily applies to any type of prior distribution. The aPC expansions are constructed locally at each design visited during the iterative optimization procedure. The main cost in aPC, which is the determination of the expansion coefficients, is minimized by estimating these coefficients from only a minimal set of dynamic model evaluations. Although sample-based estimators can also be applied to the chance constraints, this leads to a potentially large number of binary variables, such that a smooth moment-based approximation is preferred in this work. Numerical simulations indicate that the proposed surrogate can significantly lower the computational cost of the Bayesian OED, while guaranteeing the original chance constraints are satisfied without noticeably increasing the average time to find a solution. As such, this methodology appears to have the potential to pave the way for real-time or sequential dynamic experiment design in a fully Bayesian setting.