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

2021 ◽  
pp. 1-15
Author(s):  
Mohammad Behtash ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Dynamic System ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Polynomial Chaos ◽  
Probabilistic Constraints ◽  
Stochastic Dynamic ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
And Control ◽  
Stochastic Dynamic Systems

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.

Reliability-Based MDSDO for Co-Design of Stochastic Dynamic Systems

2019 ◽  
Author(s):  
Saeed Azad ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Design Optimization ◽  
System Design ◽  
Design Approach ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Stochastic Dynamic ◽  
Embodiment Design ◽  
And Control ◽  
The Impact ◽  
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 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 systems 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). 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 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 to indicate the impact of including reliability measures in co-design formulations.

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

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Saeed Azad ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Design Optimization ◽  
System Design ◽  
Design Approach ◽  
Probabilistic Constraints ◽  
Stochastic Dynamic ◽  
Design Decision ◽  
Combined Design ◽  
Embodiment Design ◽  
Control Optimization ◽  
And Control

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 optimization (co-design), 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.

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