Multidisciplinary Design Optimization Algorithm Research Articles

Towards an efficient global multidisciplinary design optimization algorithm

This article proposes a new surrogate-based multidisciplinary design optimization algorithm. The main idea is to replace each disciplinary solver involved in a non-linear multidisciplinary analysis by Gaussian process surrogate models. Although very natural, this approach creates difficulties as the non-linearity of the multidisciplinary analysis leads to a non-Gaussian model of the objective function. However, in order to follow the path of classical Bayesian optimization such as the efficient global optimization algorithm, a dedicated model of the non-Gaussian random objective function is proposed. Then, an Expected Improvement criterion is proposed to enrich the disciplinary Gaussian processes in an iterative procedure that we call efficient global multidisciplinary design optimization (EGMDO). Such an adaptive approach allows to focus the computational budget on areas of the design space relevant only with respect to the optimization problem. The obtained reduction of the number of solvers evaluations is illustrated on a classical MDO test case and on an engineering test case.

Multidisciplinary design optimization of dental implant based on finite element method and surrogate models

This study aims to propose a Multidisciplinary design optimization (MDO) approach for dental implant based on Finite element method (FEM), surrogate model and a new MDO algorithm. FEM is used to calculate the stress at the implant-bone interface first. Two surrogate models, Support vector regression (SVR) and Kriging (KRG) are built to replace FEM in the following MDO of dental implant, and their verifications indicate their accuracies. A new multidisciplinary design optimization algorithm, named as Homogenization-target-values MDO algorithm (HTV-MDO), is established and first tested by a numerical example to demonstrate its effectiveness. After that, it is applied to the MDO of dental implant based on the SVM and KRG. The results indicate that the new MDO approach proposed in this study can effectively deal with the MDO of dental implant. The stress is reduced greatly with other characteristics of dental implant (contact area and volume of implant in this study) optimizing or slightly deteriorating. This approach can be expanded to other MDO of different bio-implants.

A new approach in multidisciplinary design optimization of upper-stages using combined framework

Optimum design of an upper-stage with bipropellant propulsion system consists of optimization of three major subsystems including thruster, feeding subsystem, and propellant tanks. Optimization of such a complex system involved in optimization of many disciplines including structure, heat transfer, aerothermodynamics, guidance and control, trajectory and propulsion. Hard coupling of the disciplines increase the optimization processing times. Multidisciplinary design optimization algorithm can derive the optimum configuration but more elapsed time is needed for single-level methods such as all at once (AAO) and lower feasibility occurred in multi-level methods such as collaborative optimization (CO). In this paper, a new multidisciplinary design optimization framework is proposed for such coupled disciplines with concentrating on the propulsion system. The proposed framework uses Combined Single-level and Bi-level Optimizations (CSBO) frameworks to minimize numbers of design variables and system constraints when feasibility is increased. For this goal, modeling of every discipline is introduced and the design algorithm validated by redesigning of two real bipropellant thrusters. Three MDO frameworks are applied for our problem including AAO, CO and CSBO. Comparisons between the results show that CSBO can find the optimum solution in shorter elapsed time with lower F-count. Therefore, CSBO is more efficient for complex systems with coupled disciplines.

Heat Transfer Modeling of Bipropellant Thrusters for using in Multidisciplinary Design Optimization Algorithm

Heat Transfer Modeling of Bipropellant Thrusters for using in Multidisciplinary Design Optimization Algorithm

Implementation of set-based design in multidisciplinary design optimization

Set-based design is a design approach where feasible regions for the design variables are determined from different disciplines, with the goal of locating and working with the areas of feasible overlap. During the process the constraints are adjusted in order to accommodate conflicting requirements between disciplines. The main objective of set-based design is to narrow the design space, while delaying the pursuit of a single point design as much as possible. This process avoids finalizing decisions early and allows for flexibility in dealing with requirement creep. This paper presents the development and application of a new multidisciplinary design optimization (MDO) algorithm inspired by the principles of set-based design. The new MDO algorithm was developed with the core concept of describing the design using sets to incorporate features of set-based design and achieve greater flexibility than with a single-point optimization. The MDO algorithm was applied to a ship design problem and the ship design application demonstrated the value of utilizing set-based design as a space-reducing technique before approaching the problem with a point-based optimization. Furthermore, incorporating flexibility in the constraints allowed the optimization to handle a problem with very strict constraints in a rational manner and minimize the necessary constraint violation.

Development of a Multi-objective Genetic Algorithm for MDO Problem

Engineering systems have become quite complicated in recent days. The requirements of design are complex and it is hard to meet them by considering only one discipline. In this paper, we suggest a hybrid Multi-objective Genetic Algorithm (MOGA) for a Multidisciplinary Design Optimization (MDO) model in engineering design. In order to get Pareto optimal solutions, we use local search to enhance the efficiency and effectiveness. We solve a problem of airplane wings optimization using MOGA. After compared with other MDO algorithms, we find the result shows that the proposed algorithm’s performance has an advantage over previous work for these MDO problems. As the algorithm is evaluated based on practical data, we show that the approach can be used to solve MDO problems in the real world.

Reliability-Based Multidisciplinary Design Optimization Using Probabilistic Gradient-Based Transformation Method

Recently, solving the complex design optimization problems with design uncertainties has become an important but very challenging task in the communities of reliability-based design optimization (RBDO) and multidisciplinary design optimization (MDO). The MDO algorithms decompose the complex design problem into the hierarchical or nonhierarchical optimization structure and distribute the workloads to each discipline (or subproblem) in the decomposed structure. The coordination of the local responses is crucial for the success of finding the optimal design point. The problem complexity increases dramatically when the existence of the design uncertainties is not negligible. The RBDO algorithms perform the reliability analyses to evaluate the probabilities that the random variables violate the constraints. However, the required reliability analyses build up the degree of complexity. In this paper, the gradient-based transformation method (GTM) is utilized to reduce the complexity of the MDO problems by transforming the design space to multiple single-variate monotonic coordinates along the directions of the constraint gradients. The subsystem responses are found using the monotonicity principles (MP) and then coordinated for the new design points based on two general principles. To consider the design uncertainties, the probabilistic gradient-based transformation method (PGTM) is proposed to adapt the first-order probabilistic constraints from three different RBDO algorithms, including the chance constrained programming (CCP), reliability index approach (RIA), and performance measure approach (PMA), to the framework of the GTM. PGTM is efficient because only the sensitivity analyses and the reliability analyses require function evaluations (FE). The optimization processes of monotonicity analyses and the coordination procedures are free of function evaluations. Several mathematical and engineering examples show the PGTM is capable of finding the optimal solutions with desirable reliability levels.

On the use of geometry design variables in the MDO analysis of wing structures with aeroelastic constraints on stability and response

A Multidisciplinary-Design-Optimization (MDO) approach for the initial design of wing structures based on the integrated modeling of structures, aerodynamics, flight dynamics, and aeroelasticity, has been developed. The procedure is based on the use of a standard numerical optimizer which employs structural, aeroelastic, and aerodynamic analyzers (a finite-element analyzer for structures, panel method analyzer for aerodynamics, and a longitudinal trim analyzer for flight mechanics) in the MDO process. The space discretizations of the numerical models – namely, the structural and aerodynamic meshes – are dynamically updated as function of wing-structure geometry variables during the optimization process. The geometric-updating procedure has been validated using available analytical solutions for a structural optimization problem. The obtained MDO solutions are essentially based on a first-principle formulation but, in the meanwhile, they do not result to be computationally expansive. Moreover, in order to make the implemented MDO algorithm more computationally efficient and effective, an analytical method based on Matched-Filter Theory (MFT) has been used to evaluate the worst aeroelastic-response case due to a gust input having an assigned energy level with the purpose of obtaining a final design also optimizing the gust-response performance. The optimization capabilities of using geometry design variables vs the standard structural design variables in the MDO process have been highlighted. Moreover, the use of a composite objective function, combining structure and aerodynamic issues, has been shown further capabilities of the presented MDO procedure. Finally, some results are also presented for a benchmark regional aircraft wing to show the potentiality of the approach.

Trends, features, and tests of common and recently introduced global optimization methods

Global optimization techniques have been used extensively due to their capability in handling complex engineering problems. In addition to a number of well known global optimization techniques, many new methods have been introduced recently for various optimal design applications. In this work, a number of representative, well known and recently introduced global optimization techniques are closely examined and compared. The historical development, special features and trends on the development of global optimization algorithms are reviewed. Special attention is devoted to the recent developments of multidisciplinary design optimization algorithms based on effective metamodelling techniques. Commonly used benchmark optimization problems are used as test examples to reveal the pros and cons of these global optimization methods. A new meta-model based global optimization search method, introduced and improved recently by the authors, is also included in the tests and comparison.

Application of the multidisciplinary design optimization algorithm to the design of a belt-integrated seat while considering crashworthiness

Multidisciplinary design optimization based on independent subspaces (MDOIS), which is a multidisciplinary design optimization (MDO) algorithm, has been recently proposed. Since MDOIS is relatively simple compared with other MDO algorithms, it is easy to apply MDOIS to practical engineering problems. In this research, an MDO problem is defined for the design of a belt-integrated seat (BIS) while considering crashworthiness. The crash model consists of an airbag, a BIS, an energy-absorbing steering system, and a safety belt. It is found that the current design problem has two disciplines - structural non-linear analysis and occupant analysis. The interdisciplinary relationship between the disciplines is identified. Interdisciplinary variables between the two disciplines are stiffness of the seat back frame and the belt load. The interdisciplinary relationship is addressed in the system analysis step in MDOIS. Prior to each independent subspace design, values of interdisciplinary variables at a given design point are determined in the system analysis step. The determined values are passed to corresponding subspaces, and the subspaces treat the received values of the interdisciplinary variables as constant parameters throughout the subspace design. For the present example, the belt load is passed to the structural analysis subspace and the stiffness of the seat back frame is passed to the occupant analysis subspace. Determined design variables in each subspace are passed to the system analysis step. In this way, the design process iterates until the convergence criterion is satisfied. As a result of the design, the weight of the BIS and the head injury criterion (HIC) of an occupant are reduced while the specified constraints are satisfied. Since the system analysis cannot be formulated in an explicit form in the current example, an optimization problem is formulated to solve the system analysis. The results from MDOIS are discussed.

Validating the Need to Validate Code

I am also concerned with the issues raised by Douglass Post and Lawrence Votta. A great deal of computational physics involves fitting parameters—for example, some turbulence constants and grid design parameters. Fifty physics models put together, each with a couple of free parameters, could yield 100 parameters that can be used to fit the code to whatever verification and validation tests it needs to pass. Yet we know that an interpolation function fitted to a bunch of points can be wildly wrong between them. This concerns me, before we even start extrapolating the code to regions where its performance is completely untested.The problem the article highlighted is serious. People who know the issues involved in computational physics are essential. Unfortunately, these days universities turn out users who employ codes as black boxes but do not understand what they do or when their results can be trusted. Moreover, analysis codes are often incorporated into multidisciplinary design optimization algorithms—for example, to design a better aircraft—but the optimization process drives the codes beyond any reasonable applicability. Expert guidance is usually needed to stay within implicit constraints of analysis codes.Rigorous component testing, although necessary, is not sufficient. Software components can be combined, but their combination could be wrong even though the components test well individually. A combination that is insensitive to minor component errors could still give invalid results. Each component has an unstated region of applicability that is often horribly complicated to describe, yet the combination could unexpectedly exceed individual component limits.© 2005 American Institute of Physics.

충돌을 고려한 안전띠 일체형 의자의 다분야 통합최적설계

Recently Multidisciplinary Design Optimization Based on Independent Subspaces (MDOIS), an MDO (multidisciplinary design optimization) algorithm, has been proposed. In this research, an MDO problem is defined for design of a belt integrated seat considering crashworthiness, and MDOIS is applied to solve the problem. The crash model consists of an airbag, a belt integrated seat (BIS), an energy absorbing steering system, and a safety belt. It is found that the current design problem has two disciplines - structural nonlin- ear analysis and occupant analysis. The interdisciplinary relationship between the disciplines is identified and is addressed in the system analysis step in MDOIS. Interdisciplinary variables are belt load and stiffness of the seat, which are determined in system analysis step. The belt load is passed to the structural analysis subspace and stiffness of the seat back frame to the occupant analysis subspace. Determined design vari- ables in each subspace are passed to the system analysis step. In this way, the design process iterates until the convergence criterion is satisfied. As a result of the design, the weight of the BIS and Head Injury Crite- rion (HIC) of an occupant are reduced with specified constraints satisfied at the same time. Since the system analysis cannot be formulated in an explicit form in the current example, an optimization problem is formu - lated to solve the system analysis. The results from MDOIS are discussed.

Multidisciplinary design optimization based on independent subspaces

Optimization has been successfully applied to systems with a single discipline. Since many disciplines are involved in a coupled fashion in modern engineering, multidisciplinary design optimization (MDO) technology has been developed. MDO algorithms are designed to solve the coupled aspects generated from the interdisciplinary relationship. In a general MDO algorithm, a large design problem is decomposed into smaller ones which can be easily solved. Although various methods have been proposed for MDO, research is still in the early stage. This study proposes a new MDO method which is named MDO based on independent subspaces (MDOIS). Many real engineering problems consist of physically separate components and they can be independently designed. The inter-relationship occurs through coupled physics. MDOIS is developed for such problems. In MDOIS, a large system is decomposed into small subsystems. The coupled aspects are solved via system analysis which solves the coupled physics. The algorithm is mathematically validated by showing that the solution satisfies the Karush–Kuhn–Tucker condition. Copyright © 2005 John Wiley & Sons, Ltd.

독립적 하부 시스템에 의한 다분야 통합 최적설계

Optimization has been successfully applied to systems with a single discipline. As many disciplines are involved in coupled fashion, MDO (multidisciplinary design optimization) technology has been developed. MDO algorithms are trying to solve the coupled aspects generated from interdisciplinary relationship. In a general MDO algorithms, a large design problem is decomposed into small ones which can be easily solved. Although various methods have been proposed for MDO, the research is still in the early stage. This research proposes a new MDO method which is named as MDOIS (Multidisciplinary Design Optimization Based on Independent Subspaces). Many real engineering problems consist of physically separate components and they can be independently designed. The inter-relationship occurs through coupled physics. MDOIS is developed for such problems. In MDOIS, a large system is decomposed into small subsystems. The coupled aspects are solved via system analysis which solves the coupled physics. The algorithm is mathematically validated by showing that the solution satisfies the Karush-Kuhn-Tucker condition.