A Single-Loop Reliability-Based MDSDO Formulation for Combined Design and Control Optimization of Stochastic Dynamic Systems

Abstract

Optimization of dynamic engineering systems requires an integrated approach that accounts for the coupling between embodiment design and control system design, simultaneously. Generally known as combined design and control (co-design) optimization, these methods offer superior system's performance and reduced costs. Despite the widespread use of co-design approaches in the literature, not much work has been done to address the issue of uncertainty in co-design problem formulations. This is problematic as all engineering models contain some level of uncertainty that might negatively affect the system's performance, if overlooked. While in our previous study we developed a robust co-design approach, a more rigorous evaluation of probabilistic constraints is required to obtain the targeted reliability levels for probabilistic constraints. Therefore, we propose and implement a novel stochastic co-design approach based on the principles of reliability-based design optimization (RBDO) to explicitly account for uncertainties from design decision variables and problem parameters. In particular, a reliability-based, multidisciplinary dynamic system design optimization (RB-MDSDO) formulation is developed using the sequential optimization and reliability assessment (SORA) algorithm, such that the analysis-type dynamic equality constraints are satisfied at the mean values of random variables, as well as their most probable points (MPPs). The proposed approach is then implemented for two case studies and the results were benchmarked through Monte Carlo simulation (MCS) to indicate the impact of including reliability measures in co-design formulations.

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

“…The numerical RB-CCD problem in Example 2 is adapted from the classic Van Der Pol Oscillator control co-design problem, 25 which contains two physical variables 𝐱 𝑝 = [𝑥 1 , 𝑥 2 ], two state variables 𝝃 = [𝜉 1 , 𝜉 2 ], and one control input 𝑢. The mathematical (MM) model of this RB-CCD problem is given as: date in one batch 𝑚 = 10, the initial learning rate 𝛼 = 1, the training times 𝑇 = 1 × 10 6 , and the number of DD modules 𝑁 = 3.…”

“…The numerical RB‐CCD problem in Example 2 is adapted from the classic Van Der Pol Oscillator control co‐design problem, 25 which contains two physical variables $${{{\bf x}}}_p = [{x}_1,{x}_2]$$, two state variables $${{\bm \xi }} = [{\xi }_1,{\xi }_2]$$, and one control input u . The mathematical (MM) model of this RB‐CCD problem is given as: …”

“…Lu et al 24 presented a cross-rate-based RB-CCD approach consisting of the CCD stage and a reliability assessment stage, in which a sub-optimization problem based on the cross-rate of the objective reliability index sample trajectory is designed to obtain the shifting vector. Azad and Alexander-Ramos 25 proposed and implemented a novel stochastic RB-CCD approach using sequential optimization and reliability assessment to explicitly account for uncertainties from design decision variables and problem parameters in the dynamic system. 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.…”

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.…”

“…As an example, consider a system in which uncertainties stem from plant optimization variables. While it is possible to change the plant design in response to uncertainties in order to achieve reliability or robustness (using methods based on reliability-based CCD [25,39] or robust CCD [40], respectively), it might be more cost-effective to leverage the control effort, including its limits, to achieve such criteria. Therefore, OLMC may be more suitable for early-stage design, where plant and control spaces are explored for performance optimality, as well as reliability or robustness.…”