Multidisciplinary Design Optimization Method Research Articles

A robust global optimization approach to solving CO problems – enhanced design space decrease collaborative optimization

Collaborative optimization (CO) is a decomposition-based multidisciplinary design optimization method that sometimes suffers from two predominant drawbacks: computational inefficiency and nonexistence of Lagrange multipliers when the system-level optimization solution is system-level feasible. To overcome aforementioned drawbacks, we propose enhanced design space decrease collaborative optimization (EDSDCO). It can notably simplify the system-level optimization problem through modifying the system-level consistency equality constraints that exist in the standard CO to create some linear inequality constraints with no tolerance. Thus, the aforementioned drawbacks, mainly resulted by the use of equality forms of consistency constraints, can be successfully overcome. During the process of optimization, the updated system-level solution space is constantly decreased; meanwhile, the original feasible region is entirely preserved throughout regardless of whether the constraints are convex. Consequently, the global optimum can be obtained when the system-level optimization solution moves into the original feasible region. In EDSDCO, the starting point is not introduced to the formulas of subsystem or system-level optimization. Therefore, the optimum obtained using EDSDCO cannot be affected by the parameters of the starting points, which certainly enhances EDSDCO's robustness. EDSDCO converges faster than design space decrease collaborative optimization for two reasons: deleting more original infeasible region fragments per iteration and more efficient decision to choose the next solution subspace. In order to illustrate the proposed method's capabilities, we describe the principles and process of EDSDCO and discuss its application to three optimization problems: a numerical test problem, gear reducer design problem, and combustion of propane problem.

Reliability-Based Multidisciplinary Design Optimization under Correlated Uncertainties

Complex mechanical system is usually composed of several subsystems, which are often coupled with each other. Reliability-based multidisciplinary design optimization (RBMDO) is an efficient method to design such complex system under uncertainties. However, the present RBMDO methods ignored the correlations between uncertainties. In this paper, through combining the ellipsoidal set theory and first-order reliability method (FORM) for multidisciplinary design optimization (MDO), characteristics of correlated uncertainties are investigated. Furthermore, to improve computational efficiency, the sequential optimization and reliability assessment (SORA) strategy is utilized to obtain the optimization result. Both a mathematical example and a case study of an engineering system are provided to illustrate the feasibility and validity of the proposed method.

Multidisciplinary Design Optimization of a Swash-Plate Axial Piston Pump

This work proposes an MDO (multidisciplinary design optimization) procedure for a swash-plate axial piston pump based on co-simulation and integrated optimization. The integrated hydraulic-mechanical model of the pump is built to reflect its actual performance, and a hydraulic-mechanical co-simulation is conducted through data exchange between different domains. The flow ripple of the pump is optimized by using a MDO procedure. A CFD (Computational Fluid Dynamics) simulation of the pump’s flow field is done, which shows that the hydrodynamic shock of the pump is improved after optimization. To verify the MDO effect, an experimental system is established to test the optimized piston pump. Experimental results show that the simulated and experimental curves are similar. The flow ripple is improved by the MDO procedure. The peak of the pressure curve is lower than before optimization, and the pressure pulsation is reduced by 0.21 MPa, which shows that the pressure pulsation is improved with the decreasing of the flow ripple. Comparing the experimental and simulation results shows that MDO method is effective and feasible in the optimization design of the pump.

Evaluation of Multidisciplinary Design Optimization Methods and Applying Single Level Frameworks in Unmanned Aerial Vehicle (UAV) Design

Evaluation of Multidisciplinary Design Optimization Methods and Applying Single Level Frameworks in Unmanned Aerial Vehicle (UAV) Design

A Simulation-based Research on Passive District

Abstract This paper is aiming to propose a new design concept named passive district which assists designer to improve district energy efficiency and reduce energy demand by smart urban design without mechanical dynamics method. Furthermore, specific simulation-based experiment is implemented to demonstrate the research methodology on correlation between urban form and energy performance, in which the workflow is summarized as follows: definition of constants and variables, modeling, simulation, data sorting and decision making. This urban modeling integrates the morphological factors together including grid size, floor area ratio, cover ratio, passive zone ratio, surface to volume ratio and so on and compares the energy impact respectively. Particularly a method of multi-disciplinary design optimization (MDO) is applied to analyze how multiple factors affect energy use comprehensively and support scientific decision making. Finally, as conclusion the application potential of passive district is discussed.

Multi-objective optimization of coronary stent using Kriging surrogate model

BackgroundIn stent design optimization, the functional relationship between design parameters and design goals is nonlinear, complex, and implicit and the multi-objective design of stents involves a number of potentially conflicting performance criteria. Therefore it is hard and time-consuming to find the optimal design of stent either by experiment or clinic test. Fortunately, computational methods have been developed to the point whereby optimization and simulation tools can be used to systematically design devices in a realistic time-scale. The aim of the present study is to propose an adaptive optimization method of stent design to improve its expansion performance.MethodsMulti-objective optimization method based on Kriging surrogate model was proposed to decrease the dogboning effect and the radial elastic recoil of stents to improve stent expansion properties and thus reduce the risk of vascular in-stent restenosis injury. Integrating design of experiment methods and Kriging surrogate model were employed to construct the relationship between measures of stent dilation performance and geometric design parameters. Expected improvement, an infilling sampling criterion, was employed to balance local and global search with the aim of finding the global optimal design. A typical diamond-shaped coronary stent-balloon system was taken as an example to test the effectiveness of the optimization method. Finite element method was used to analyze the stent expansion of each design.Results27 iterations were needed to obtain the optimal solution. The absolute values of the dogboning ratio at 32 and 42 ms were reduced by 94.21 and 89.43%, respectively. The dogboning effect was almost eliminated after optimization. The average of elastic recoil was reduced by 15.17%.ConclusionThis article presents FEM based multi-objective optimization method combining with the Kriging surrogate model to decrease both the dogboning effect and radial elastic recoil of stents. The numerical results prove that the proposed optimization method effectively decreased both the dogboning effect and radial elastic recoil of stent. Further investigations containing more design goals and more effective multidisciplinary design optimization method are warranted.

Multidisciplinary reliability design optimization under time-varying uncertainties

Degradation failure is one of the main reasons for complex mechanical systems losing their functions. Research on multidisciplinary design optimization under uncertainties should shift from static uncertainties to time-varying uncertainties. Aiming at time-varying uncertainties in mechanical systems, we put forward a multidisciplinary reliability design optimization method using stochastic process theory. First, we investigated the characteristics of time-varying uncertainties in complex mechanical systems, and then utilized stochastic process theory to quantify time-varying uncertainties. Second, through combining the multidisciplinary simultaneous analysis and design optimization method, the model of multidisciplinary design optimization under time-varying uncertainties is established. Moreover, a mathematical problem and an engineering example are provided to illustrate the accuracy and effectiveness of the proposed method.

Multidisciplinary design optimization to identify additive manufacturing resources in customized product development

Abstract Additive manufacturing (AM) techniques are ideal for producing customized products due to their high design flexibility. Despite the previous studies on specific additive manufactured customized products such as biomedical implants and prostheses, the simultaneous optimization of components, materials, AM processes, and dimensions remains a challenge. Multidisciplinary design optimization (MDO) is a research area of solving complex design problems involving multiple disciplines which usually interact with each other. The objective of this research is to formulate and solve an MDO problem in the development of additive manufactured products customized for various customers in different market segments. Three disciplines, i.e. the customer preference modeling, AM production costing, and structural mechanics are incorporated in the MDO problem. The optimal selections of components, materials, AM processes, and dimensional parameters are searched with the objectives to maximize the functionality utility, match individual customers' personal performance requirements, and minimize the total cost. A multi-objective genetic algorithm with the proposed chromosome encoding pattern is applied to solve the MDO problem. A case study of designing customized trans-tibial prostheses with additive manufactured components is presented to illustrate the proposed MDO method. Clusters of multi-dimensional Pareto-optimal design solutions are obtained from the MDO, showing trade-offs among the objectives. Appropriate design decision can be chosen from the clusters based on the manufacturer's market strategy. Highlights An optimization problem for additive manufactured customized products is solved. Three disciplines are incorporated in multidisciplinary design optimization (MDO). The selection of component, material, additive manufacturing process and dimensions are optimized. A multiobjective genetic algorithm is applied to solve the MDO problem. Pareto-optimal solutions with different utilities and costs are obtained.

Multidisciplinary design optimization of the diesel particulate filter in the composite regeneration process

In our previous works, the diesel particulate filter (DPF) using a new composite regeneration mode by coupling microwave and ceria-manganese base catalysts is verified as an effective way to reduce the particulate matter emission of the diesel engine. In order to improve the overall performance of this DPF, its multidisciplinary design optimization (MDO) model is established based on objective functions such as pressure drop, regeneration performance, microwave energy consumption, and thermal shock resistance. Then, the DPF is optimized by using MDO method based on adaptive mutative scale chaos optimization algorithm. The optimization results show that with the help of MDO, DPF’s pressure drop is decreased by 14.5%, regeneration efficiency is increased by 17.3%, microwave energy consumption is decreased by 17.6%, and thermal deformation is decreased by 25.3%. The optimization results are also verified by experiments, and the experimental results indicate that the optimized DPF has larger filtration efficiency, better emission performance and regeneration performance, smaller pressure drop, lower wall temperature and temperature gradient, and lower microwave energy consumption.

A non-nested collaborative optimization method for multidisciplinary design optimization and its application in satellite designs

As a decomposition-based multidisciplinary design optimization (MDO) method, collaborative optimization (CO) has been widely applied in aerospace design systems. During the execution process of CO method, subsystem optimizations are nested into the system optimization, and numerous subsystem analyses are thus required to achieve the consistency for entire system. For this problem, a non-nested collaborative optimization (NNCO) method is presented in this paper. In this method, system and subsystem optimizations are conducted sequentially and repeatedly, and system consistency is then coordinated with the use of a loop process by updating penalty parameters. The feasibility of this method was firstly tested in solving common analytical problems, and it was further applied in two MDO problems of an observation satellite as well as a maneuver satellite. All of the results have demonstrated the efficacy of this proposed NNCO method, which indicates that it is effective and suitable for dealing with practical multidisciplinary design problems.

Multiple objective multidisciplinary design optimization of heavier-than-water underwater vehicle using CFD and approximation model

As ocean resources received considerable attention, the autonomous underwater vehicle (AUV) has been more widely applied due to its excellent flexibility and adaptability, and the optimization design of AUV has becoming a more important issue. The heavier-than-water underwater vehicle (HUV) is a new conceptual AUV, and its design is a typical multidisciplinary problem, but heavily dependent on the experience with naval architects at the present engineering design. To realize the optimization design of HUV, the multidisciplinary design optimization (MDO) method is applied to the multiple objective MDO design of an HUV. In this paper, a system synthesis model of the HUV has been set up. To predict the hydrodynamic characteristics accurately, the computational fluid dynamics (CFD) method is used. In the MDO process, the all-in-one (AIO) method has been adopted with non-dominated sorting genetic algorithms (NSGA)-II and a Kriging model for constructing global approximations to reduce the cost of the CFD numerical simulation. According to the multiple objective MDO design, the Pareto-optimal solutions are analyzed and verified by the numerical simulation, and it is found that the optimal design of HUV has better performance than that of prototype.

Multidisciplinary design optimization of tunnel boring machine considering both structure and control parameters under complex geological conditions

A Tunnel Boring Machine (TBM) is an extremely large and complex engineering machine that usually works under a complicated geological environment to excavate tunnel underground. Considering the large number of sub-systems that usually belong to different disciplines, it is a challenging task to define, model, and optimize the whole TBM from the perspective of system engineering. Also, due to the complex mechanism and geological environment, the flexibility and efficiency of existing TBM excavation strategies are generally limited. To address these challenges, a multidisciplinary modeling is presented so that corresponding analytical or empirical models of each sub-system are formulated, and a multidisciplinary design optimization (MDO) method is applied to the TBM system optimization. Four excavation strategies are studied and compared, including: (i) two existing excavation strategies, and (ii) two new proposed excavation strategies by making control and/or structure parameters adaptive to geological conditions. Two case studies with these four excavation strategies are presented to illustrate the effectiveness and benefits of designing TBM using MDO methodologies. Wherein, Case I aims to minimize the construction period taking into account the restriction of sub-systems, and Case II simultaneously minimizes construction period, cost, and energy consumption. Since the resulting MDO formulation is straightforward to be solved as a single problem, the All-At-Once (AAO) method is utilized in this paper. The optimization results obtained by modeling the problem as MDO show that the excavation strategy with adaptive control and structure parameters can significantly reduce the total construction time, with lower cost and energy consumption.

Multiparametric optimization for multidisciplinary engineering design

The area of Multiparametric Optimization (MPO) solves problems that contain unknown problem data represented by parameters. The solutions map parameter values to optimal design and objective function values. In this paper, for the first time, MPO techniques are applied to improve and advance Multidisciplinary Design Optimization (MDO) to solve engineering problems with parameters. A multiparametric subgradient algorithm is proposed and applied to two MDO methods: Analytical Target Cascading (ATC) and Network Target Coordination (NTC). Numerical results on test problems show the proposed parametric ATC and NTC methods effectively solve parametric MDO problems and provide useful insights to designers. In addition, a novel Two-Stage ATC method is proposed to solve nonparametric MDO problems. In this new approach elements of the subproblems are treated as parameters and optimal design functions are constructed for each one. When the ATC loop is engaged, steps involving the lengthy optimization of subproblems are replaced with simple function evaluations.

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.

Evaluation of Multidisciplinary Design Optimization Methods and Applying Single Level Frameworks in Unmanned Aerial Vehicle (UAV) Design

Objectives: Evaluation of Multidisciplinary Design Optimization (MDO) methods, comparison of advantages and disadvantages of them by applying single level frameworks in design of UAVs using genetic algorithm optimization and Sequential Quadratic Programming (SQP). Methods/Statistical Analysis: Multidisciplinary design optimization methods are divided into 2 overall single level and multilevel frameworks, mathematically. Frameworks under investigation here are: Multi Disciplinary Feasibility (MDF), All At Once (AAO) as single level frameworks and Collaborative Optimization (CO) in addition to Bi-Level Integrated System Synthesis (BLISS) as bi-level frameworks. Selection criteria of appropriate design framework include simplicity of algorithm, quick response as well as degree of convergence in finding optimal answers. Findings: in accordance with the aforementioned criteria, single level methods are superior to multilevel ones. Anyway, no method or framework could be considered as superior; instead, appropriate design framework according to each application should be selected. Finally, single level methods have been used in UAVs design according to which, MDF framework holds higher convergence capability than AAO, though with higher run time in comparison to AAO. Applications /Improvements: single level methods have been used in UAVs design and Global Hawk (RQ-4B) is redesigned for implementation and comparison.

Decoupled Multidisciplinary Design Optimization Formulation for Interdisciplinary Coupling Satisfaction Under Uncertainty

At early design phases, taking into account uncertainty in the optimization of a multidisciplinary system is essential to assess the optimal characteristics and performance. Uncertainty multidisciplinary design optimization methods aim at efficiently organizing not only the different disciplinary analyses, the uncertainty propagation, and the optimization but also the handling of interdisciplinary couplings under uncertainty. A new decoupled uncertainty multidisciplinary design optimization formulation (named Individual Discipline Feasible/Polynomial Chaos Expansion) ensuring the coupling satisfaction for all the realizations of the uncertain variables is presented in this paper. Coupling satisfaction in realizations is necessary to maintain the equivalence between the coupled and decoupled uncertainty multidisciplinary design optimization formulations, and therefore to ensure the physical relevance of the obtained designs. The proposed approach relies on the iterative construction of Polynomial Chaos Expansions in order to represent, at the convergence of the optimization problem, the functional couplings between the disciplines. The proposed formulation is tested on an analytic problem and on the design of a two-stage launch vehicle.

Reevaluating conceptual design fidelity: An efficient supersonic air vehicle design case

Multifidelity and multidisciplinary design optimization (MDO) results for an efficient supersonic air vehicle (ESAV) are presented. This work builds upon previous published work that created a multifidelity and multidisciplinary analysis and design optimization framework. Based on the usual aircraft conceptual design assumption that low-fidelity analyses are capable of converging upon a design through MDO that would at least be representative of that which would be predicted by higher fidelity methods, a process is created to allow low-fidelity multidisciplinary analysis runs to guide the higher fidelity optimization in an effort to reduce the total required computational expense. Due to disparate physical simulation results between the different fidelity levels, the expected reduction in computational effort was not realized. A separate low-fidelity optimization and a higher fidelity optimization were then subsequently performed. A MDO method that required an order of magnitude fewer objective function evaluations than the low-fidelity MDO method was developed to perform the more computationally expensive higher fidelity MDO in the full ESAV design space. Although optimal low-fidelity and higher fidelity ESAV configurations are identified, the low-fidelity optimal solution is infeasible when analyzed with the higher fidelity framework, and vice versa. This was a surprising and unexpected result as these two fidelity level model suites were developed by the same team for the same aircraft. The common assumption that low-fidelity MDO design methods will find a feasible design close to the eventual higher fidelity design did not hold for the ESAV case. Sensitivity studies were performed around the optimal design to gain insight into this important region of the design space with respect to the particular fidelity level models used.

Uncertainty-based MDO for aircraft conceptual design

Purpose – The purpose of this paper is to study the consideration of uncertainty from analysis modules for aircraft conceptual design by implementing uncertainty-based design optimization methods. Reliability-Based Design Optimization (RBDO), Possibility-Based Design Optimization (PBDO) and Robust Design Optimization (RDO) methods were developed to handle uncertainties of design optimization. The RBDO method is found suitable for uncertain parameters when sufficient information is available. On the other hand, the PBDO method is proposed when uncertain parameters have insufficient information. The RDO method can apply to both cases. The RBDO, PBDO and RDO methods were considered with the Multidisciplinary Design Optimization (MDO) method to generate conservative design results when low fidelity analysis tools are used. Design/methodology/approach – Methods combining MDO with RBDO, PBDO and RDO were developed and have been applied to a numerical analysis and an aircraft conceptual design. This research eva...

An application of multidisciplinary design optimization to the hydrodynamic performances of underwater robots

Multidisciplinary Design Optimization (MDO) is proposed for the design of the lines of an underwater robot. Hydrodynamic performances of the underwater robot are concerned about in the design, including the resistance and the manoeuvrability. A method of MDO, Collaborative Optimization (CO), is adopted. To improve the efficiency of optimization, approximate models are established in sub-disciplines. Also, an artificial intelligent technique, Particle Swarm Optimization (PSO), is incorporated into the CO framework. The optimization design of the lines of the underwater robot is carried out on an Isight platform, an automatic integration optimization platform. Through the platform, the optimization design of the lines and the analysis of the hydrodynamic performances can be achieved automatically with high efficiency. An autonomous underwater vehicle (AUV), SUBOFF, is taken as a verification model. For different lines, CFD calculation is performed to analyze the resistance and manoeuvrability. By comparison, the optimal lines of the hull and the fairwater are determined.

Multidisciplinary design optimization of a human occupied vehicle based on Bi-Level integrated system collaborative optimization

The design of Human Occupied Vehicle (HOV) is a typical multidisciplinary problem, but heavily dependent on the experience of naval architects at present engineering design. In order to relieve the experience dependence and improve the design, a new Multidisciplinary Design Optimization (MDO) method “Bi-Level Integrated System Collaborative Optimization (BLISCO)” is applied to the conceptual design of an HOV, which consists of hull module, resistance module, energy module, structure module, weight module, and the stability module. This design problem is defined by 21 design variables and 23 constraints, and its objective is to maximize the ratio of payload to weight. The results show that the general performance of the HOV can be greatly improved by BLISCO.