Design Optimization Of Dynamic Systems Research Articles

A Crossrate-Based Approach for Reliability-Based Multidisciplinary Dynamic System Design Optimization

In practical applications, the multidisciplinary dynamic system design optimization (MDSDO)-based solution is limited by uncertainty, which causes random variation in the physical design variable in the static discipline and the equation of state in the dynamic discipline. To address the lack of reliability of the MDSDO solution, a crossrate-based MDSDO approach (C-MDSDO), consisting of the MDSDO stage and a reliability assessment stage, is proposed in this paper. In the reliability assessment stage, a sub-optimization problem based on the crossrate of the objective reliability index sample trajectory is designed to obtain the shifting vector, which is employed to obtain a sufficiently reliable solution. In addition, the proposed approach adopts a sequential problem-solving framework that avoids nested optimization and a reliability assessment. One numerical case and two engineering cases were employed to validate the effectiveness of the proposed method. The results show that the reliability of the proposed solutions significantly improved.

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

Abstract Combined plant and control design (control co-design (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 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 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 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.

Robust Combined Design and Control Optimization of Hybrid-Electric Vehicles Using MDSDO

Identifying a true, system-level optimal solution for hybrid-electric vehicle (HEV) powertrains requires methods such as combined design and control optimization (co-design) to account for the coupling between powertrain design and optimal energy management strategies. Despite the widespread application of co-design techniques to HEV powertrains in recent years, limited research has been done to account for the inherent uncertainties present in these systems. This is problematic as such uncertainties may not only impact HEV powertrain component sizing and control strategies, but also overall vehicle performance and cost-both of which are critically-important in the fiercely-competitive automotive industry. One way to address this issue is to apply a stochastic dynamic system optimization technique known as robust multidisciplinary dynamic system design optimization (R-MDSDO) to the HEV powertrain co-design problem. This method ensures that the HEV powertrain co-design solution, including its system performance and cost, explicitly accounts for random variations within the system and its problem formulation using concepts from robust design optimization. Therefore, in this study, we formulate and solve a robust co-design problem for a power-split HEV powertrain using R-MDSDO to identify the optimal component designs, state trajectories, and control trajectories such that the vehicle powertrain cost is minimized. The robust solution is then compared to the solution from the associated deterministic problem, with the results indicating that accounting for system uncertainty has a significant impact on HEV powertrain co-design.

Simultaneous Combined Optimal Design and Control Formulation for Aircraft Hybrid-Electric Propulsion Systems

A key challenge in the design of hybrid-electric propulsion systems (HEPSs) for aircraft is the complexity involved in handling efficient sizing of the components as well as control synergy between multiple power sources. To handle this challenge effectively, combined optimal design and control (codesign) methods that enable the integration of energy management optimization along with vehicle sizing are required. Even though some studies have explored such methods, they have done so in a computationally intensive nested formulation with limited depth on the design and control modeling aspect. This paper addresses these issues by posing the system codesign problem using a simultaneous formulation of multidisciplinary dynamic system design optimization (MDSDO). The simultaneous formulation generally facilitates superior computational performance while the MDSDO method solves codesign problems from a more balanced perspective between design- and control-related variables. This method is applied in this paper to aircraft HEPS design with an objective of determining the optimal propulsion component designs and supervisory control strategy that minimizes total energy consumption. The hybrid configuration is compared with its conventional counterpart on the basis of system efficiency. In addition to that, a parametric study on the battery energy density is presented to explore the near-term viability of HEPS for aircraft.

A Decomposition-Based Optimization Algorithm for Combined Plant and Control Design of Interconnected Dynamic Systems

AbstractStrong coupling of the physical and control parts within complex dynamic systems should be addressed by integrated design approaches that can manage such interactions. Otherwise, the final solution will be suboptimal or even infeasible. Combined design and control (co-design) methods can tackle this issue by managing the mentioned interactions and can result in superior optimal solutions. Current co-design methods are applicable to simplified non-interconnected systems; however, these methods might be impractical or even impossible to apply to real-world interconnected dynamic systems, hindering designers from obtaining the system-level optimal solutions. This work addresses this issue by developing an optimization algorithm which combines a decomposition-based optimization strategy known as analytical target cascading (ATC) with a co-design-centric formulation of multidisciplinary dynamic system design optimization (MDSDO). Considering the time-dependent linking variables among the dynamic systems’ components, a new consistency measure has also been proposed to manage such quantities in the optimization process. Finally, a plug-in hybrid electric vehicle powertrain, representative of an interconnected dynamic system, has been studied to validate the new algorithm’s results against the conventional all-at-once (AAO) MDSDO. Although the numerical results from the ATC-MDSDO slightly deviate from those in the AAO-MDSDO, this method can play a crucial role as a benchmark when the AAO solution is unattainable or a distributed design paradigm is required.

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 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.

Robust MDSDO for Co-Design of Stochastic Dynamic Systems

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.

PHEV powertrain co-design with vehicle performance considerations using MDSDO

The complexity of plug-in hybrid-electric vehicles (PHEVs) motivates the simultaneous integration of component design and supervisory control strategy decisions. Methods from combined optimal design and control (co-design) are generally used to manage such integrated system design decisions. Although several studies have investigated the PHEV powertrain co-design problem, the impact of key vehicle performance criteria such as 0–60 mph acceleration time and all-electric-range (AER) has rarely been explicitly included in such system co-design problems. This is problematic as these vehicle performance criteria strongly affect component sizing and control strategy in a way that a non-performance-based co-design solution could become sub-optimal. Therefore, this study addresses this issue by formulating and solving a PHEV powertrain co-design problem that explicitly includes vehicle-level performance constraints. In particular, a three-phase, PHEV powertrain co-design problem is solved to simultaneously identify the optimal supervisory control strategies during the acceleration performance and standard duty cycle phases, along with the optimal component designs spanning all phases (acceleration performance, standard duty cycle, and AER performance) such that the vehicle powertrain cost is minimized. A relatively new, balanced co-design approach known as multidisciplinary dynamic system design optimization (MDSDO) is used to solve the problem. The optimal design and standard duty cycle supervisory control trajectories are compared to the solution of a non-performance-based co-design problem. The results indicate that the formal inclusion of vehicle performance criteria in a co-design problem significantly affects component design and supervisory control strategies.

Performability-Based Design Optimization of Dynamic systems

Performability-Based Design Optimization of Dynamic systems

Computer aided analysis and optimal design of mechanical systems using vector-network techniques

Stringent tolerances on mechanical components has created increasingly severe demands on the quality of new mechanical designs. The mathematical models used to simulate the various types of mechanical systems these days need to incorporate an optimization algorithm capable of predicting and improving the efficiency of an initial design. Hence, this article presents an extension of the vector-network model for the computer aided simulation and design optimization of dynamic systems. The method is based on a simplistic topological approach which is incorporated into an efficient numerical optimization process used to solve non-linear problems. The procedure casts, simultaneously, the three-dimensional equations of motion and the objective function into a symmetrical format, always yielding an optimum solution. The algorithm serves as a basis for a “self-formulating” computer program which simulates the best system response, given only the system description as input. The effectiveness of this approach is demonstrated in the analysis of a 3-D eight DOF vehicle model. In this example, allowable values for design parameters and suspension types are incorporated in order to minimize the performance variables which are beneficial for comfort without unduly compromising road holding capabilities.

Interactive design optimization of dynamic systems

This paper describes an interactive environment for dynamic response optimization problems. It is shown that with proper interactive facilities and designer intervention, the optimal design process can be more flexible, efficient and effective in solving practical design problems. The process can be initiated with a rough design model for the problem. As the iterations progress and insight is gained into the problem, the model can be interactively refined, without stopping the process, to obtain the final solution. Two example problems — a system dynamics problem and a control problem — are used to study and show advantages of the designer interaction. It is concluded that interactive optimum design capabilities offer more opportunities to the designer to obtain better designs.