A Comparative Study of Formulations and Algorithms for Reliability-Based Co-Design Problems

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Tonghui Cui ◽  
James T. Allison ◽  
Pingfeng Wang
Keyword(s):  
Comparative Study ◽  
Design Optimization ◽  
System Design ◽  
Design Problem ◽  
Control Design ◽  
Engineering System ◽  
Design Strategies ◽  
Parameter Uncertainties ◽  
Horizontal Axis Wind Turbine ◽  
And Control

Abstract While integrated physical and control system co-design has been demonstrated successfully on several engineering system design applications, it has been primarily applied in a deterministic manner without considering uncertainties. An opportunity exists to study non-deterministic co-design strategies, taking into account various uncertainties in an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to ensure an optimized system design being obtained that satisfies all reliability constraints considering particular system uncertainties. While significant advancements have been made in co-design and RBDO separately, little is known about methods where reliability-based dynamic system design and control design optimization are considered jointly. In this article, a comparative study of the formulations and algorithms for reliability-based co-design is conducted, where the co-design problem is integrated with the RBDO framework to yield solutions consisting of an optimal system design and the corresponding control trajectory that satisfy all reliability constraints in the presence of parameter uncertainties. The presented study aims to lay the groundwork for the reliability-based co-design problem by providing a comparison of potential design formulations and problem–solving strategies. Specific problem formulations and probability analysis algorithms are compared using two numerical examples. In addition, the practical efficacy of the reliability-based co-design methodology is demonstrated via a horizontal-axis wind turbine structure and control design problem.

A Comparative Study of Formulations and Algorithms for Reliability-Based Co-Design Problems

2019 ◽  
Author(s):  
Tonghui Cui ◽  
James T. Allison ◽  
Pingfeng Wang
Keyword(s):  
Design Optimization ◽  
System Design ◽  
Engineering System ◽  
Design Strategies ◽  
Parameter Uncertainties ◽  
Horizontal Axis Wind Turbine ◽  
Reliability Based Design ◽  
System Design Optimization ◽  
Engineering System Design ◽  
And Control

Abstract Co-design, or integrated physical and control system design, has been demonstrated successfully for several engineering system design optimization applications, primarily in a deterministic manner. An opportunity exists to study non-deterministic co-design strategies, including incorporation of uncertainty-induced failures, into an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to increase the likelihood of having a feasible design that satisfies all reliability constraints. While significant recent advancements have been made in co-design and RBDO separately, limited work has been done where reliability-based dynamic system design and control design optimization are considered jointly. In this paper, the co-design problem is integrated with the RBDO framework to yield a system-optimal design and the corresponding control trajectory, which satisfy all reliability constraints in the presence of parameter variations. Different problem formulations and RBDO algorithms are compared through numerical examples. The design of a horizontal-axis wind turbine (HAWT) supported by a lattice tower (with parameter uncertainties) is presented to demonstrate the applicability of the proposed method.

Robust MDSDO for Co-Design of Stochastic Dynamic Systems

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Saeed Azad ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Dynamic System ◽  
Design Optimization ◽  
System Design ◽  
Design Problem ◽  
Integrated Design ◽  
Problem Formulation ◽  
Robust Design Optimization ◽  
Design Problems ◽  
Embodiment Design ◽  
And Control

Abstract Optimization of dynamic engineering systems generally requires problem formulations that account for the coupling between embodiment design and control system design simultaneously. Such formulations are commonly known as combined optimal design and control (co-design) problems, and their application to deterministic systems is well established in the literature through a variety of methods. However, an issue that has not been addressed in the co-design literature is the impact of the inherent uncertainties within a dynamic system on its integrated design solution. Accounting for these uncertainties transforms the standard, deterministic co-design problem into a stochastic one, thus requiring appropriate stochastic optimization approaches for its solution. This paper serves as the starting point for research on stochastic co-design problems by proposing and solving a novel problem formulation based on robust design optimization (RDO) principles. Specifically, a co-design method known as multidisciplinary dynamic system design optimization (MDSDO) is used as the basis for an RDO problem formulation and implementation. The robust objective and inequality constraints are computed per usual as functions of their first-order-approximated means and variances, whereas analysis-based equality constraints are evaluated deterministically at the means of the random decision variables. The proposed stochastic co-design problem formulation is then implemented for two case studies, with the results indicating the importance of the robust approach on the integrated design solutions and performance measures.

Robust MDSDO for Co-Design of Stochastic Dynamic Systems

2018 ◽  
Author(s):  
Saeed Azad ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Dynamic System ◽  
Design Optimization ◽  
System Design ◽  
Design Problem ◽  
Integrated Design ◽  
Problem Formulation ◽  
Robust Design Optimization ◽  
Design Problems ◽  
Embodiment Design ◽  
And Control

Optimization of dynamic engineering systems generally requires problem formulations that account for the coupling between embodiment design and control system design simultaneously. Such formulations are commonly known as combined optimal design and control (co-design) problems, and their application to deterministic systems is well-established in the literature through a variety of methods. However, an issue that has not been addressed in the co-design literature is the impact of the inherent uncertainties within a dynamic system on its integrated design solution. Accounting for these uncertainties transforms the standard, deterministic co-design problem into a stochastic one, thus requiring appropriate stochastic optimization approaches for its solution. This paper serves as the starting point for research on stochastic co-design problems by proposing and solving a novel problem formulation based on robust design optimization (RDO) principles. Specifically, a co-design method known as multidisciplinary dynamic system design optimization (MDSDO) is used as the basis for a RDO problem formulation and implementation. The robust objective and inequality constraints are computed per usual as functions of their first-order-approximated means and variances, whereas analysis-based equality constraints are evaluated deterministically at the means of the random decision variables. The proposed stochastic co-design problem formulation is then implemented for two case studies, with the results indicating a significant impact of the robust approach on the integrated design solutions and performance measures.

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.

MODELING AND CONTROL DESIGN OF AN ANGUILLIFORM ROBOTIC FISH

2012 ◽  
Vol 03 (04) ◽  
pp. 1250018 ◽  
Author(s):  
JIAN-XIN XU ◽  
XUE-LEI NIU ◽  
QIN-YUAN REN
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Control Design ◽  
Robotic Fish ◽  
Torque Control ◽  
Underactuated System ◽  
Parameter Uncertainties ◽  
Modeling And Control ◽  
Mode Control ◽  
And Control

In this paper, the modeling and control design of a biomimetic robotic fish is presented. The Anguilliform robotic fish consists of N links and N - 1 joints, and the driving forces are the torques applied to the joints. Considering kinematic constraints, Lagrangian formulation is used to obtain the dynamics of the fish model. The computed torque control method is applied first, which can provide satisfactory tracking responses for fish joints. Since this robotic fish is essentially an underactuated system, the reference trajectories for the orientation of the N links are planned in such a way that, at a neighborhood of the equilibrium point, the tracking task of N angles can be achieved by using N - 1 joint torques. To deal with parameter uncertainties that exist in the actual environment, sliding mode control is adopted. Considering feasibility and complexity issues, a simplified sliding mode control algorithm is given. A four-link robotic fish is modeled and simulated, and the results validate the effectiveness of reference planning and the proposed controllers.

A Problem Class With Combined Architecture, Plant, and Control Design Applied to Vehicle Suspensions

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Daniel R. Herber ◽  
James T. Allison
Keyword(s):  
Dynamic Optimization ◽  
Design Problem ◽  
Control Design ◽  
Vehicle Suspension ◽  
Engineering Systems ◽  
Linear Quadratic ◽  
Problem Class ◽  
Physical Elements ◽  
And Control

Here we describe a problem class with combined architecture, plant, and control design for dynamic engineering systems. The design problem class is characterized by architectures comprised of linear physical elements and nested co-design optimization problems employing linear-quadratic dynamic optimization. The select problem class leverages a number of existing theory and tools and is particularly effective due to the symbiosis between labeled graph representations of architectures, dynamic models constructed from linear physical elements, linear-quadratic dynamic optimization, and the nested co-design solution strategy. A vehicle suspension case study is investigated and a specifically constructed architecture, plant, and control design problem is described. The result was the automated generation and co-design problem evaluation of 4374 unique suspension architectures. The results demonstrate that changes to the vehicle suspension architecture can result in improved performance, but at the cost of increased mechanical complexity. Furthermore, the case study highlights a number of challenges associated with finding solutions to the considered class of design problems. One such challenge is the requirement to use simplified design problem elements/models; thus, the goal of these early-stage studies are to identify new architectures that are worth investigating more deeply. The results of higher-fidelity studies on a subset of high-performance architectures can then be used to select a final system architecture. In many aspects, the described problem class is the simplest case applicable to graph-representable, dynamic engineering systems.

Combined Plant and Controller Design Using Decomposition-Based Design Optimization and the Minimum Principle

2010 ◽  
Author(s):  
James T. Allison ◽  
Sam Nazari
Keyword(s):  
Optimal Control ◽  
Design Optimization ◽  
System Design ◽  
Physical System ◽  
Design Problem ◽  
Controller Design ◽  
Minimum Principle ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Augmented Lagrangian Coordination

An often cited motivation for using decomposition-based optimization methods to solve engineering system design problems is the ability to apply discipline-specific optimization techniques. For example, structural optimization methods have been employed within a more general system design optimization framework. We propose an extension of this principle to a new domain: control design. The simultaneous design of a physical system and its controller is addressed here using a decomposition-based approach. An optimization subproblem is defined for both the physical system (i.e., plant) design and the control system design. The plant subproblem is solved using a general optimization algorithm, while the controls subproblem is solved using a new approach based on optimal control theory. The optimal control solution, which is derived using the the Minimum Principle of Pontryagin (PMP), accounts for coupling between plant and controller design by managing additional variables and penalty terms required for system coordination. Augmented Lagrangian Coordination is used to solve the system design problem, and is demonstrated using a circuit design problem.

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