A Reliability-Based Formulation for Simulation-Based Control Co-Design Using Generalized Polynomial Chaos Expansion

Abstract

Combined plant and control design (control co-design, or CCD) methods are often used during product development to address the synergistic coupling between the plant and control parts of a dynamic system. Recently, a few studies have started applying CCD to stochastic dynamic systems. In their most rigorous approach, reliability-based design optimization (RBDO) principles have been used to ensure solution feasibility under uncertainty. However, since existing reliability-based CCD (RBCCD) algorithms use all-at-once (AAO) formulations, only most-probable-point (MPP) methods can be used as reliability analysis techniques. Though effective for linear/quadratic RBCCD problems, the use of such methods for highly nonlinear RBCCD problems introduces solution error that could lead to system failure. A multidisciplinary feasible (MDF) formulation for RBCCD problems would eliminate this issue by removing the dynamic equality constraints and instead enforcing them through forward simulation. Since the RBCCD problem structure would be similar to traditional RBDO problems, any of the well-established reliability analysis methods could be used. Therefore, in this work, a novel reliability-based MDF formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) has been proposed for RBCCD. To quantify the uncertainty propagated by the random decision variables, Monte Carlo simulation has been applied to the generalized polynomial chaos (gPC) expansion of the probabilistic constraints. The proposed formulation is applied to two engineering test problems, with the results indicating the effectiveness of both the overall formulation as well as the reliability analysis technique for RBCCD.

Investigations Into Uncertain Control Co-Design Implementations for Stochastic in Expectation and Worst-Case Robust

“…In this section, we start by discussing the optimal control structures under uncertainties in UCCD problems. These structures attempt to answer inherently different questions and have been used in separate studies in the literature [20,[25][26][27][28][29][30][31][32][33]. While these structures have a significant impact on the problem implementation and its associated solution, they have not been collectively discussed in the literature to the best of the authors' knowledge.…”

A Dendrite Net based decoupled framework for the reliability‐based control co‐design problem

“…Zhang et al 26 suggested a single-loop framework for RB-CCD by incorporating the approximate reliability information of random physical design into the deterministic optimization. Behtash and Alexander-Ramos 27 suggested a reliability-based formulation for simulation-based control co-design using a combination of generalized Polynomial Chaos expansion and Monte Carlo simulation. The above achievements are pioneering efforts in the field of RB-CCD and have been achieved in both theoretical analysis and engineering applications.…”

“…And Ref. 27 applied Monte Carlo simulation to the generalized polynomial chaos expansion of the probabilistic constraints according to the additional original system simulations. Hence, it is inevitable that the existing RB-CCD methods consume numerous computational resources to perform the time-consuming system simulations when encountering the RB-CCD problem in the sophisticated dynamic system.…”

“…used particle swarm optimization algorithm to solve a complex sub‐optimization problem based on the cross‐rate of the objective reliability index sample trajectory through original system simulations. And Ref 27 . applied Monte Carlo simulation to the generalized polynomial chaos expansion of the probabilistic constraints according to the additional original system simulations.…”