Effect of Variable Selection on Multidisciplinary Design Optimization: a Flight Vehicle Example

The optimal design of multidisciplinary systems under uncertainty involves three types of iterative analyses- multidisciplinary analyses, reliability analyses, and optimization. If these processes are carried out in a nested manner in reliability based multidisciplinary design optimization (RBMDO), the computational expense can be enormous. Computationally efficient simultaneous analysis and design (SAND) or All-AtOnce methods have been developed earlier for deterministic MDO. Single loop RBDO methods have also been developed to integrate reliability analysis and optimization in a single loop. This paper develops a novel formulation of RBMDO problems with both system and component level reliability constraints. The formulation allows for solution with a single design optimization loop by using the KKT optimality conditions of the first-order reliability method (FORM) as constraints in the design optimization along with disciplinary consistency constraints. Alternative solution processes which remove the FORM MPP’s from the decision space and many constraints from the problem are developed. The alternative solution methods are more efficient and more robust than using nonlinear programming to solve the single loop formulation. A numerical example is solved with the two proposed solution algorithms. I. Introduction In the design of multidisciplinary systems it is often necessary to make decisions under uncertainty. This requires that multidisciplinary systems modeling be integrated with uncertainty analysis and optimization. A common example of such an engineering design application would be the design of an aircraft wing under uncertain aerodynamic loading conditions, with multiple structural components with uncertain capacities, such that the entire structural system achieves a prescribed level of reliability. The problem has coupled physics, in that the pressure distribution is dependent upon the deflection, and the deflection is dependent on the pressure distribution. Such designs have been performed using multidisciplinary optimization (MDO). Other examples where MDO may be applied include electronics packaging, in which the disciplines of heat transfer and circuit analysis are coupled, the design of new types of aircraft and integrating them into an existing fleet of aircraft, and even the management of interconnected homeland infrastructures. While MDO has matured with the development of different types of algorithms for various types of problems and design organizations, there has been little work to incorporate reliability analysis into MDO. However, system and component reliabilities are often a major concern in the design of multidisciplinary systems. MDO can be computationally expensive due to the need to achieve consistency across multiple disciplinary analysis codes; each disciplinary analysis code may be computationally expensive to run. Further, the optimal design of multidisciplinary systems under uncertainty involves three types of iterative procedures- multidisciplinary analyses, reliability analyses, and optimization. The integration of these three procedures is referred to in this paper as reliability based multidisciplinary design optimization (RBMDO). If these processes are carried out simultaneously, the computational expense can be enormous. Computational savings can often be achieved with simultaneous analysis and design (SAND) or All-At-Once methods, which allow for the solution of the multidisciplinary analyses and the optimization in one single loop. Single loop RBDO methods allow for the integration of reliability analysis and optimization in a single loop. Applying SAND and single-loop RBDO together may allow for large computational savings when applied to problems in RBMDO. This paper develops a novel formulation of RBMDO problems with both system and component level reliability constraints based on the SAND method for MDO and by use of the KKT conditions of the first order reliability method (FORM). The resulting formulation may be solved as a standard nonlinear programming problem. While the single loop formulation presented in this paper is a solution of the RBMDO problem, robustness and efficiency are improved through two improved algorithms which can remove the MPP’s from the decision space, thereby significantly reducing the optimizer’s workload.

The design of complex aerospace systems is a multidisciplinary design optimization (MDO) problem involving the interaction of multiple disciplines. However, because of the necessity of evaluating expensive black-box simulations, the enormous computational cost of solving MDO problems in aerospace systems has also become a problem in practice. To resolve this, metamodel-based design optimization techniques have been applied to MDO. With these methods, system models can be rapidly predicted using approximate metamodels to improve the optimization efficiency. This paper presents an overall survey of metamodel-based MDO for aerospace systems. From the perspective of aerospace system design, this paper introduces the fundamental methodology and technology of metamodel-based MDO, including aerospace system MDO problem formulation, metamodeling techniques, state-of-the-art metamodel-based multidisciplinary optimization strategies, and expensive black-box constraint-handling mechanisms. Moreover, various aerospace system examples are presented to illustrate the application of metamodel-based MDOs to practical engineering. The conclusions derived from this work are summarized in the final section of the paper. The survey results are expected to serve as guide and reference for designers involved in metamodel-based MDO in the field of aerospace engineering.

Multidisciplinary design optimization of long-range slender guided rockets considering aeroelasticity and subsidiary loads

<div class="section abstract"><div class="htmlview paragraph">The design of drive units in electric vehicles (EVs) presents challenges due to the need to pass multiple linear and non-linear load cases. This can result in inefficient design. Therefore, optimization plays a critical role in improving the design efficiency. However, setting up the optimization process itself can be challenging, especially when dealing with complex design variables and different load cases that require the use of various computer-aided engineering (CAE) solvers. The drive unit, being a casting component, presents additional challenges in setting up Multidisciplinary Design Optimization (MDO) process. This paper introduces an efficient process for addressing these challenges by presenting a sample Multidisciplinary Design Optimization (MDO) problem. The problem involves the manipulation of discrete design variables, such as the number of ribs, and incorporates five different load cases that require the utilization of different CAE solvers. The proposed process demonstrates a streamlined approach that can be completed in less than one week. It showcases the steps involved in setting up the optimization process, including defining the design variables, selecting appropriate load cases, and integrating different CAE solvers. By following this process, engineers can effectively optimize the design of drive units in EVs, leading to improved mass efficiency. Overall, this paper highlights the importance of optimization in addressing the challenges associated with the design of drive units in EVs. It presents a practical and efficient process that can be implemented within a short timeframe, allowing engineers to achieve optimal design solutions. By leveraging this approach, manufacturers can enhance the performance and efficiency of EV drive units, contributing to the advancement of electric mobility.</div></div>

Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to the organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Decomposition algorithms reformulate the MDO problem as a set of independent subproblems, one per discipline, and a coordinating master problem. A popular approach to MDO problems is bilevel decomposition algorithms. These algorithms use nonlinear optimization techniques to solve both the master problem and the subproblems. In this paper, we propose two new bilevel decomposition algorithms and analyze their properties. In particular, we show that the proposed problem formulations are mathematically equivalent to the original problem and that the proposed algorithms converge locally at a superlinear rate. Our computational experiments illustrate the numerical performance of the algorithms.

Model-Based Systems Engineering (MBSE) supports the system-level design of complex products effectively. Currently, system design and optimization for complex products are two distinct processes that must be executed using different software or platforms, involving intricate data conversion processes. Applying multidisciplinary optimization to validate system optimization often necessitates remodeling the optimization objects, which is time-consuming, labor-intensive, and highly error-prone. A critical activity in systems engineering is identifying the optimal design solution for the entire system. Multidisciplinary Design Optimization (MDO) and reliability analysis are essential methods for achieving this. This paper proposes a SysML-based multidisciplinary reliability design optimization modeling method. First, by analyzing the definitions and mathematical models of multidisciplinary reliability design optimization, the SysML extension mechanism is employed to represent the optimization model based on SysML. Next, model transformation techniques are used to convert the SysML optimization model generated in the first stage into an XML description model readable by optimization solvers. Finally, the proposed method’s effectiveness is validated through an engineering case study of an in-vehicle environmental control integration system. The results demonstrate that this method fully utilizes SysML to express MDO problems, enhancing the efficiency of design optimization for complex systems. Engineers and system designers working on complex, multidisciplinary projects can particularly benefit from these advancements, as they simplify the integration of design and optimization processes, facilitating more reliable and efficient product development.

5 - Multidisciplinary Design and Optimization Methods

on multidisciplinary design optimization (MDO) of truss-braced wing airplanes. The primary focus has been to include utter constraints for structural sizing of the wing. The structural sizing uses a gradient-based optimization procedure along with an analytically calculated response function sensitivity with respect to the thickness design variables. It is shown that using the updated routine leads to lower structural mass in comparison with the fully-stressed structural design procedure used in the previous MDO studies. The primary reasons for the lower mass is that inertial weight relief due to secondary structure is now included in the sizing process, and the buckling analysis is now based on a linearized eigenvalue problem, as opposed to a simple beam Euler buckling criteria used for the previous study which was signicantly conservative. However, the results show that for a wing with lower mass the utter constraint becomes active for both strut-braced and truss-braced wing congurations. Hence, it is important to include those in the MDO studies to maintain feasibility of designs. Two challenges encountered during the process of including structural optimization with the utter constraint within the system-level MDO architecture are discussed along with the strategies devised to overcome them: convergence of structural optimization and the resulting numerical noise. A response surface methodology is used to integrate the structural optimization and system-level MDO and some initial results for the design of a truss-braced wing transonic transport airplane for minimum fuel consumption and emissions are presented.

Multidisciplinary design optimization (MDO) is expected to play a major role in the competitive transportation industries of tomorrow, i.e., in the design of aircraft and spacecraft, of high speed trains, boats, and automobiles. All of these vehicles require maximum performance at minimum weight to keep fuel consumption low and conserve resources. Here, MDO can deliver mathematically based design tools to create systems with optimum performance subject to the constraints of disciplines such as structures, aerodynamics, controls, etc. Although some applications of MDO are beginning to surface, the key to a widespread use of this technology lies in the improvement of its efficiency. This aspect is investigated here for the MDO subset of structural optimization, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures (here, statically indeterminate trusses and beams for proof of concept) is performed. In the system level optimization, the design variables are the coefficients of assumed displacement functions, and the load unbalance resulting from the solution of the stiffness equations is minimized. Constraints are placed on the deflection amplitudes and the weight of the structure. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. This approach is expected to prove very efficient, especially for complex structures, since the design task is broken down into a large number of small and efficiently handled subtasks, each with only a small number of variables. This partitioning will also allow for the use of parallel computing, first, by sending the system and subsystems level computations to two different processors, ultimately, by performing all subsystems level optimizations in a massively parallel manner on separate processors. It is expected that the subsystems level optimizations can be further improved through the use of controlled growth, a method which reduces an optimization to a more efficient analysis with only a slight degradation in accuracy. The efficiency of all proposed techniques is being evaluated relative to the performance of the standard single level optimization approach where the complete structure is weight minimized under the action of all given constraints by one processor and to the performance of simultaneous analysis and design which combines analysis and optimization into a single step. It is expected that the present approach can be expanded to include additional structural constraints (buckling, free and forced vibration, etc.) or other disciplines (passive and active controls, aerodynamics, etc.) for true MDO.

Satellite constellation system design is a challenging and complicated multidisciplinary design optimization (MDO) problem involving a number of computation-intensive multidisciplinary analysis models. In this paper, the MDO problem of a constellation system consisting of small observation satellites is investigated to simultaneously achieve the preliminary design of constellation configuration and the satellite subsystems. The constellation is established based on Walker-? configuration considering the coverage performance. Coupled with the constellation configuration, several disciplines including payload, power, thermal control, and structure are taken into account for satellite subsystems design subject to various constraints (i.e., ground resolution, power usage, natural frequencies, etc.). Considering the mixed-integer and time-consuming behavior of satellite constellation system MDO problem, a novel sequential radial basis function (RBF) method using the support vector machine (SVM) for discrete-continuous mixed variables notated as SRBF-SVM-DC is proposed. In this method, a discrete-continuous variable sampling method is utilized to handle the discrete variables, i.e., the number of orbit planes and number of satellites, in the satellite constellation system MDO problem. RBF surrogates are constructed and gradually refined to represent the time-consuming simulations during optimization, which can efficiently lead the search to the optimum. Finally, the proposed SRBF-SVM-DC utilized to solve the satellite constellation system MDO problem is compared with a conventional integer coding based genetic algorithm (ICGA). The results show that SRBF-SVM-DC significantly decreases the system mass by about 28.63% subject to all the constraints, which greatly reduces the cost of the satellite constellation system. Moreover, the computational budget of SRBF-SVM-DC is saved by over 85% compared with ICGA, which demonstrates the effectiveness and practicality of the proposed surrogate assisted optimization approach for satellite constellation system design.

<p>Multidisciplinary design optimization (MDO) refers to the process of designing systems characterized by the interaction of multiple interconnected disciplines. High-fidelity MDO usually requires large computational resources due to the computational cost of achieving multidisciplinary consistent solutions by coupling high-fidelity physics-based solvers. Gradient-based minimization algorithms are generally applied to find local minima, due to their efficiency in solving problems with a large number of design variables. This represents a limitation to performing global MDO and integrating black-box type analysis tools, usually not providing gradient information. The latter issues generally inhibit a wide use of MDO in complex industrial applications.</p><p>An architecture named multi-criterion adaptive sampling MDO (MCAS-MDO) is presented in the current research for complex simulation-based applications. This research aims at building a global derivative-free optimization tool able to employ high-fidelity/expensive black-box solvers for the analysis of the disciplines. MCAS-MDO is a surrogate-based architecture featuring a variable level of coupling among the disciplines and is driven by a multi-criterion adaptive sampling (MCAS) assessing coupling and sampling uncertainties. MCAS uses the dynamic radial basis function surrogate model to identify the optimal solution and explore the design space through parallel infill of new solutions.</p><p>The MCAS-MDO is tested versus a global derivative-free multidisciplinary feasible (MDF) approach, which solves fully-coupled multidisciplinary analyses, for two analytical test problems. Evaluation metrics include number of function evaluations required to achieve the optimal solution and sample distribution. The MCAS-MDO outperforms the MDF showing a faster convergence by clustering refined function evaluations in the optimum region.</p><p>The architecture is applied to a steady fluid-structure interaction (FSI) problem, namely the design of a tapered three-dimensional carbon fiber-reinforced plastic hydrofoil for minimum drag. The objective is the design of shape and composite material layout subject to hydrodynamic, structural, and geometrical constraints. Experimental data are available for the original configuration of the hydrofoil and allow validating the FSI analysis, which is performed coupling computational fluid dynamics, solving the Reynolds averaged Navier-Stokes equations, and finite elements, solving the structural equation of elastic motion. Hydrofoil forces, tip displacement, and tip twist are evaluated for several materials providing qualitative agreement with the experiments and confirming the need for the two-way versus one-way coupling approach in case of significantly compliant structures.</p><p>The free-form deformation method is applied to generate shape modifications of the hydrofoil geometry. To reduce the global computational expense of the optimization, a design space assessment and dimensionality reduction based on the Karhunen–Loève expansion (KLE) is performed off-line, i.e. without the need for high-fidelity simulations. It provides with a selection of design variables for the problem at hand through basis rotation and re-parametrization. By using the KLE, an efficient design space is identified for the current problem and the number of design variables is reduced by 92%.</p><p>A sensitivity analysis is performed prior to the optimization to assess the variability associated with the shape design variables and the composite material design variable, i.e. the fiber orientation. These simulations are used to initialize the surrogate model for the optimization, which is carried out for two models: one in aluminum and one in composite material. The optimized designs are assessed by comparison with the original models through evaluation of the flow field, pressure distribution on the body, and deformation under the hydrodynamic load. The drag of the aluminum and composite material hydrofoils is reduced by 4 and 11%, respectively, increasing the hydrodynamic efficiency by 4 and 7%. The optimized designs are obtained by evaluating approximately 100 designs. The quality of the results indicates that global derivative-free MDO of complex engineering applications using expensive black-box solvers can be achieved at a feasible computational cost by minimizing the design space dimensionality and performing an intelligent sampling to train the surrogate-based optimization.</p>

Response surface methods have been used for a variety of applications in aerospace engineering, particularly in multidisciplinary design optimization. We investigate the use of kriging models as alternatives to traditional second-order polynomial response surfaces for constructing global approximations for use in a real aerospace engineering application, namely, the design of an aerospike nozzle. Our objective is to examine the difeculties in building and using kriging models to create accurate global approximations to facilitate multidisciplinary design optimization. Error analysis of the response surface and kriging models is performed, along with a graphical comparison of the approximations. Four optimization problems are also formulated and solved using both sets of approximation models to gain insight into their use for multidisciplinary design optimization. We end that the kriging models, which use only a constant “global” model and a Gaussian correlation function, yield global approximations that are slightly more accurate than the response surface models.

Design engineers and decision-makers across various fields are constantly working to make optimal design decisions for multidisciplinary engineering systems in an effort to improve performance and reduce costs. The multiple disciplines that decision-makers are forced to consider can range from different physical components of a system, to competing physical phenomena influencing a component (e.g. flow forces and structural strength), to completely separate models of interest to a system (e.g. engineering performance and lifecycle cost). The common element that all these decision-making scenarios share is the presence of couplings between the considered disciplines (or subsystems). How the values for these coupling parameters are determined within a decision-making or optimization framework is the subject of countless research efforts. At present the multidisciplinary design optimization (MDO) community has settled on a few proven techniques such Collaborative Optimization (CO) and Analytic Target Cascading (ATC). However, current MDO techniques have issues that limit their effectiveness in solving various MDO problems. Many of these strategies require close coordination between subsystem optimization solvers, require significant effort by decision-makers to pose their problems in a suitable format, and/or can have large computational efficiency problems due to the fact that they involve solving nested optimization problems. In an effort to alleviate some of these issues and make MDO easier to implement and more computationally efficient, a new sequential MDO algorithm called Cooperative Design Optimization (CDO) is proposed. The CDO approach functions through a series of subsystem optimizations using a successively smaller cooperation space. The cooperation space is analogous to the design space of a traditional optimization problem, but includes only the coupling parameters that are a factor in multiple subsystems. A single iteration of the approach can be thought of as a negotiation between all of the subsystems regarding the boundaries of the cooperation space. To facilitate this cooperation, each subsystem optimization problem is restructured as a multi-objective optimization problem so that a Pareto set of optimal solutions, or agreeable design alternatives, are produced. As a result, after all subsystem optimizations are accomplished, each subsystem’s obtained Pareto optimal solution sets are compared with respect to the coupling parameters and new bounds in the cooperation space are determined for the next iteration. This process allows each subsystem to be optimized completely independently within the boundaries of the agreed upon cooperation space while coordination is achieved through an analysis of obtained optimal solutions for each subsystem. Iterations, or negotiations, are repeated until an acceptable solution or set of solutions is obtained for all included subsystems through this cooperative process.

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.

It is necessary to employ the Multidisciplinary Design Optimization (MDO) method in the design process of automatic weapon, because the process in itself is related to many disciplines and their couplings. The knowledge structure of MDO is analyzed, which includes mathematic modeling, system decomposition, optimization framework, approximation model, sensitivity analysis, optimization method, software integration, and etc.. The idea of using MDO in the design process of individual soldier automatic weapon is also explored. Based on the software package of iSIGHT, the primary multidisciplinary integration is carried out. Current research work will be helpful for further research on integrating MDO into the design of automatic weapon.