Multidisciplinary Robust Design Optimization Research Articles

Multidisciplinary Robust Design Optimization Incorporating Extreme Scenario in Sparse Samples

Abstract Robust design optimization (RDO) is a potent methodology that ensures stable performance in designed products during their operational phase. However, there remains a scarcity of robust design optimization methods that account for the intricacies of multidisciplinary coupling. In this article, we propose a multidisciplinary robust design optimization (MRDO) framework for physical systems under sparse samples containing the extreme scenario. The collaboration model is used to select samples that comply with multidisciplinary feasibility, avoiding time-consuming multidisciplinary decoupling analyses. To assess the robustness of sparse samples containing the extreme scenario, linear moment estimation is employed as the evaluation metric. The comparative analysis of MRDO results is conducted across various sample sizes, with and without the presence of the extreme scenario. The effectiveness and reliability of the proposed method are demonstrated through a mathematical case, a conceptual aircraft sizing design, and an energy efficiency optimization of a hobbing machine tool.

A scalable problem to benchmark robust multidisciplinary design optimization techniques

A scalable problem to benchmark robust multidisciplinary design optimization techniques

Surrogate Model–Based Robust Multidisciplinary Design Optimization of an Unmanned Aerial Vehicle

Despite the many advantages of the design optimization technique, this method is costly for real engineering problems. This cost will increase sharply for issues with a multidisciplinary and uncertain nature and more than one objective function. In this paper, the metamodel concept has been used to overcome this problem. Because of the ability of neural networks to approximate the behavior of complex engineering systems, this tool has been used to create a surrogate model. Because multidisciplinary design optimization and robust design optimization methods have been used in this study and according to the high cost of the multidisciplinary analysis module, a surrogate model of this module has been made to reduce the imposed costs. To show the capability of the considered approach, robust multidisciplinary design optimization of an unmanned aerial vehicle (UAV) has been done. Take-off weight and cruise drag are the considered objective functions in this study, and the nondominated sorting genetic algorithm (NSGA-I) has been used for minimization of them. The optimization results show that the use of the metamodeling concept has reduced computational costs by 94.1%.

Developing a Multi-objective Multi-Disciplinary Robust Design Optimization Framework

The purpose of this study is to provide an efficient Multi-Objective Multidisciplinary Robust Design Optimization (MOMRDO) framework. To this end, Bi-Level Integrated System Synthesis (BLISS) framework is implemented as a fast Multi-disciplinary Design Optimization (MDO) framework. Progressive Latin Hypercube Sampling (PLHS) is developed as a Design of Experiment (DOE) of the Uncertainty Analysis (UA). This systematic approach leads to a fast, adaptive and efficient framework for Robust Design Optimization (RDO) of complex systems. The accuracy and performance of the proposed algorithm have been evaluated with various tests. Finally, the RDO of a hydrazine monopropellant thruster is defined as a case study. The results show that the proposed method is a fast and efficient method for the multi-objective optimization design of complex systems, and this approach can be used for other engineering applications as well.

Multidisciplinary robust design optimization considering parameter and metamodeling uncertainties

Multidisciplinary robust design optimization (MRDO) is a useful tool to improve the stability of the performance of complex engineering systems involving uncertainty. However, the majority of existing MRDO studies only consider the parameter uncertainty. Metamodeling uncertainty, defined as the discrepancy between the computer model and metamodel at un-sampled locations, is often overlooked in MRDO. To solve the multidisciplinary problems under parameter and metamodeling uncertainties, this paper proposes a new framework called MRDO under parameter and metamodeling uncertainties (MRDO-UPM). The collaboration model is used to select the samples which satisfy coupled state equations. The selected samples are employed to construct the Gaussian process metamodels of the objective, constraint, and multidisciplinary coupled functions. Monte Carlo simulation is adopted to quantify the compound impact of parameter and metamodeling uncertainties. The MRDO-UPM framework is employed to explore the optimum. The proposed framework is verified through a numerical example, and the design of a speed reducer and a liquid cooling battery thermal management system.

A Sequential Approach for Robust Multidisciplinary Design Optimization Under Mixed Interval and Probabilistic Uncertainties

Uncertainties cannot be ignored in the design process of complex multidisciplinary systems. Robust multidisciplinary design optimization methods (RMDOs) can treat uncertainties as specified probabilistic distributions when enough statistical information is available while they assign intervals for nondeterministic variables since designers may not have enough information to obtain statistical distributions, especially in the early stage of design optimization processes. Both types of uncertainties are very likely to appear simultaneously. In order to obtain solutions to RMDO problems under mixed interval and probabilistic uncertainties, this work proposed a new sequential RMDO approach, mixed SR-MDO. First, the robust optimization (RO) problem in a single discipline under mixed uncertainties is formulated and solved. Then, following the SR-MDO framework from the previous work, MDO problems under mixed uncertainties are solved by handling probabilistic and interval uncertainties sequentially in decomposed subsystem problems. Interval uncertainties are handled by using the worst-case sensitivity analysis, and the influence of probabilistic uncertainties in objectives, constraints, as well as in discipline analysis models is characterized by corresponding mean and variance. The applied SR-MDO framework allows subsystems in its full autonomy RO and sequential RO stages to run independently in parallel. This makes mixed SR-MDO be efficient for independent disciplines to work simultaneously and be more time-saving. Computational complexity of the proposed approach mainly relates to the double-loop optimization process in the worst-case interval uncertainties analysis. Examples are presented to demonstrate the applicability and efficiency of the mixed SR-MDO approach.

Maximum variation analysis based analytical target cascading for multidisciplinary robust design optimization under interval uncertainty

Analytical target cascading (ATC) is a generally used hierarchical method for deterministic multidisciplinary design optimization (MDO). However, uncertainty is almost inevitable in the lifecycle of a complex system. In engineering practical design, the interval information of uncertainty can be more easily obtained compared to probability information. In this paper, a maximum variation analysis based ATC (MVA-ATC) approach is developed. In this approach, all subsystems are autonomously optimized under the interval uncertainty. MVA is used to establish an outer-inner framework which is employed to find the optimal scheme of system and subsystems. All subsystems are coordinated at the system level to search the system robust optimal solution. The accuracy and validation of the presented approach are tested using a classical mathematical example, a heart dipole optimization problem, and a battery thermal management system (BTMS) design problem.

Multidisciplinary robust design optimization under parameter and model uncertainties

ABSTRACTModel uncertainty, defined as the difference between the actual physical system and the computer model, is usually overlooked in robust optimization (RO). In addition, engineering systems are often comprised of several subsystems or disciplines. The coupling characteristic between different disciplines incurs the difficulty of solving multidisciplinary design optimization (MDO) problems. In this article, a new method is proposed for multidisciplinary robust design optimization (MRDO) incorporating parameter and model uncertainties. In this method, the parameter uncertainty is described by an interval model. The model uncertainty is quantified by the Bayesian approach, which adds a bias function into the computer model to offset the output discrepancy between the actual physical system and the computer model. Meanwhile, Gaussian process models of the computer model and the bias function are constructed. Finally, an MRDO framework considering parameter and model uncertainties is established. The performance of the proposed method is tested through two MDO problems.

A set strategy approach for multidisciplinary robust design optimization under interval uncertainty

Uncertainties widely exist in complex engineering systems. Robust design is one of the most used method for designing under uncertainty and has been gaining more attention. For the wide range of uncertainties, this article proposes a multidisciplinary robust design optimization method based on the set strategy. In this method, a robust design model that utilizes the maximum variation analysis is developed for uncertainty analysis. Then, a set strategy–based approach is employed to build a system optimization model, which is used to coordinate the coupling variables between full autonomy subsystems and obtains a new design space. Finally, the system robust optimal solution and the optimal robust design space are obtained through the sequential optimization, which provide a direction for the subsequent analysis. Two mathematics examples and the speed reducer design problem are taken to verify the validity and accuracy of the proposed method. A practical engineering problem, namely, air cooling battery thermal management system design problem, is successfully solved by the proposed method.

Improved collaboration pursuing method for multidisciplinary robust design optimization

The collaboration pursuing method (CPM) is a computationally efficient approach for deterministic multidisciplinary design optimization (MDO). However, it has not been employed to handle problems with uncertainty. Moreover, obtaining actual uncertainty probability distributions is challenging. Compared to probability distributions, the interval information of uncertainties can be more easily obtained. Thus, multidisciplinary robust design optimization (MRDO) under interval uncertainty has been widely investigated. To overcome the inefficiency of existing methods for solving MRDO, this paper proposes an improved collaboration pursuing method (ICPM). In this method, the collaboration model (CM) is utilized to filter the samples that satisfy the coupled state equations in system analysis (SA) or multidisciplinary analysis (MDA). Then, a robustness discrepancy model (RDM) is developed to efficiently select candidate samples that meet the robustness requirements. Next, the mode pursuing sampling (MPS) method is utilized as a global optimizer to drive the optimization process and identify the robust optimum. Finally, a mathematical example and two engineering examples are utilized to evaluate the feasibility and effectiveness of the proposed method.

A new multidisciplinary robust design optimization framework for an autonomous underwater vehicle in system and tactic design

The design process of an autonomous underwater vehicle requires mathematical model of subsystems or disciplines such as guidance and control, payload, hydrodynamic, propulsion, structure, trajectory and performance and their interactions. In early phases of design, an autonomous underwater vehicle is often encountered with a high degree of uncertainty in the design variables and parameters of system. These uncertainties present challenges to the design process and have a direct effect on the autonomous underwater vehicle performance. Multidisciplinary design optimization is an approach to find both optimum and feasible design, and robust design is an approach to make the system performance insensitive to variations of design variables and parameters. It is significant to integrate the robust design and the multidisciplinary design optimization for designing complex engineering systems in optimal, feasible and robust senses. In this article, we present an improved multidisciplinary design optimization methodology for conceptual design of an autonomous underwater vehicle in both engineering and tactic aspects under uncertainty. In this methodology, uncertain multidisciplinary feasible is introduced as uncertain multidisciplinary design optimization framework. The results of this research illustrate that the new proposed robust multidisciplinary design optimization framework can carefully set a robust design for an autonomous underwater vehicle with coupled uncertain disciplines.

Aircraft robust multidisciplinary design optimization methodology based on fuzzy preference function

This paper presents a Fuzzy Preference Function-based Robust Multidisciplinary Design Optimization (FPF-RMDO) methodology. This method is an effective approach to multidisciplinary systems, which can be used to designer experiences during the design optimization process by fuzzy preference functions. In this study, two optimizations are done for Predator MQ-1 Unmanned Aerial Vehicle (UAV): (A) deterministic optimization and (B) robust optimization. In both problems, minimization of takeoff weight and drag is considered as objective functions, which have been optimized using Non-dominated Sorting Genetic Algorithm (NSGA). In the robust design optimization, cruise altitude and velocity are considered as uncertainties that are modeled by the Monte Carlo Simulation (MCS) method. Aerodynamics, stability and control, mass properties, performance, and center of gravity are used for multidisciplinary analysis. Robust design optimization results show 46% and 42% robustness improvement for takeoff weight and cruise drag relative to optimal design respectively.

Multidisciplinary robust design optimization based on time-varying sensitivity analysis

The performance of complex mechanical systems often degrades over time primarily due to time-varying uncertainties. Improving the design of such systems entails addressing time-varying uncertainties through Multidisciplinary design optimization (MDO). In this study, a multidisciplinary robust design optimization method that is based on time-varying sensitivity analysis is proposed. First, the indices for the time-varying reliability sensitivity of limit state functions are calculated by combining sensitivity analysis and an empirical correction formula. The propagation effects of these time-varying uncertainties are qualified by combining the simplified implicit uncertainty propagation and sequential quadratic programming methods. Finally, the robust design method is integrated with MDO to reduce the effects of time-varying uncertainties. The feasibility and effectiveness of the proposed method are illustrated with a mathematical problem and an engineering example.

A Sequential Robust Optimization Approach for Multidisciplinary Design Optimization With Uncertainty

One real challenge for multidisciplinary design optimization (MDO) problems to gain a robust solution is the propagation of uncertainty from one discipline to another. Most existing methods only consider an MDO problem in the deterministic manner or find a solution which is robust for a single-disciplinary optimization problem. These rare methods for solving MDO problems under uncertainty are usually computationally expensive. This paper proposes a robust sequential MDO (RS-MDO) approach based on a sequential MDO (S-MDO) framework. First, a robust solution is obtained by giving each discipline full autonomy to perform optimization without considering other disciplines. A tolerance range is specified for each coupling variable to take care of uncertainty propagation in the coupled system. Then the obtained robust extreme points of global variables and coupling variables are dispatched into subsystems to perform robust optimization (RO) sequentially. Additional constraints are added in each subsystem to keep the consistency and to guarantee a robust solution. To find a solution with such strict constraints, genetic algorithm (GA) is used as a solver in each optimization stage. The proposed RS-MDO can save significant amount of computational efforts by using the sequential optimization procedure. Since all iterations in the sequential optimization stage can be processed in parallel, this robust MDO approach can be more time-saving. Numerical and engineering examples are provided to demonstrate the availability and effectiveness of the proposed approach.

A variable-accuracy metamodel-based architecture for global MDO under uncertainty

A method for simulation-based multidisciplinary robust design optimization (MRDO) of problems affected by uncertainty is presented. The challenging aspects of simulation-based MRDO are both algorithmic and computational, since the solution of a MRDO problem typically requires simulation-based multidisciplinary analyses (MDA), uncertainty quantification (UQ) and optimization. Herein, the identification of the optimal design is achieved by a variable-accuracy, metamodel-based optimization, following a multidisciplinary feasible (MDF) architecture. The approach encompasses a variable (i) density of the design of experiments for the metamodel training, (ii) sample size for the UQ analysis by quasi Monte Carlo simulation and (iii) tolerance for the multidisciplinary consistency in MDA. The focus is on two-way steady fluid-structure interaction problem, assessed by partitioned solvers for the hydrodynamic and the structural analysis. Two analytical test problems are shown, along with the design of a racing-sailboat keel fin subject to the stochastic variation of the yaw angle. The method is validated versus a standard MDF approach to MRDO, taken as a benchmark and solved by fully coupled MDA, fully converged UQ, without metamodels. The method is evaluated in terms of optimal design performances and number of simulations required to achieve the optimal solution. For the current application, the optimal configuration shows performances very close to the benchmark solution. The convergence analysis to the optimum shows a promising reduction of the computational cost.

Robust design of Mars entry micro-probe with evidence theory and multi-fidelity strategies

Purpose – A multi-disciplinary robust design optimization method for micro Mars entry probe (no more than 0.8 m in diameter) is proposed. The purpose of this paper is to design a Mars entry probe, not only the geometric configuration, but the trajectory and thermal protection system (TPS). In the design optimization, the uncertainties of atmospheric and aerodynamic parameters are taken into account. The probability distribution information of the uncertainties are supposed to be unknown in the design. To ensure accuracy levels, time-consuming numerical models are coupled in the optimization. Multi-fidelity approach is designed for model management to balance the computational cost and accuracy. Design/methodology/approach – Uncertainties which cannot defined by usual Gaussian probability distribution are modeled with degree of belief, and optimized through with multiple-objective optimization method. The optimization objectives are set to be the thermal performance of the probe TPS and the corresponding b...

LOcal Uncertainty Processing (LOUP) method for multidisciplinary robust design optimization

In this paper, we develop an easy-to-implement approximate method to take uncertainties into account during a multidisciplinary optimization. Multidisciplinary robust design usually involves setting up a full uncertainty propagation within the system, requiring major modifications in every discipline and on the shared variables. Uncertainty propagation is an expensive process, but robust solutions can be obtained more easily when the disciplines affected by uncertainties have a significant effect on the objectives of the problem. A heuristic method based on local uncertainty processing (LOUP) is presented here, allowing approximate solving of specific robust optimization problems with minor changes in the initial multidisciplinary system. Uncertainty is processed within the disciplines that it impacts directly, without propagation to the other disciplines. A criterion to verify a posteriori the applicability of the method to a given multidisciplinary system is provided. The LOUP method is applied to an aircraft preliminary design industrial test case, in which it allowed to obtain robust designs whose performance is more stable than the one of deterministic solutions, relatively to uncertain parameter variations.

CO-KR-5 Multidisciplinary Robust Design Optimization for a Deep-sea Test Miner

Multidisciplinary design optimization(MDO) is developed from aerospace and automotive engineering encountered in the design that incorporates a number of interacting disciplines.Although MDO has been studied for deterministic parameters and variables,the likelihood of system failure can be often caused by variation of environmental or operating factors acting on the system.Thus,robust design which can find the best design solution minimizing the variance of response is necessary to obtain reliability of the system.This research is called multidisciplinary robust design optimization(MRDO).In this study,robust design of multidisciplinary systems,coupled with robust design using multiplicative decomposition method and bi-level integrated system synthesis method,is proposed.To validate proposed method,MRDO for a test deep-seamining vehicle system is conducted.

Efficient Hybrid-Game Strategies Coupled to Evolutionary Algorithms for Robust Multidisciplinary Design Optimization in Aerospace Engineering

A number of game strategies have been developed in past decades and used in the fields of economics, engineering, computer science, and biology due to their efficiency in solving design optimization problems. In addition, research in multiobjective and multidisciplinary design optimization has focused on developing a robust and efficient optimization method so it can produce a set of high quality solutions with less computational time. In this paper, two optimization techniques are considered; the first optimization method uses multifidelity hierarchical Pareto-optimality. The second optimization method uses the combination of game strategies Nash-equilibrium and Pareto-optimality. This paper shows how game strategies can be coupled to multiobjective evolutionary algorithms and robust design techniques to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid and non-Hybrid-Game strategies are demonstrated.

Multidisciplinary Robust Design Optimization of an Internal Combustion Engine

In this paper, we introduce a multidisciplinary robust design optimization formulation to evaluate uncertainty encountered in the design process. The formulation is a combination of the bi-level Collaborative Optimization framework and the multiobjective approach of the compromise Decision Support Problem. To demonstrate the proposed framework, the design of a combustion chamber of an internal combustion engine containing two subsystem analyses is presented. The results indicate that the proposed Collaborative Optimization framework for multidisciplinary robust design optimization effectively attains solutions that are robust to variations in design variables and environmental conditions.