Multi-objective Multidisciplinary Design Optimization Research Articles

High Aspect Ratio Composite Wings: Geometrically Nonlinear Aeroelasticity, Multi-Disciplinary Design Optimization, Manufacturing, and Experimental Testing

In the field of aerospace engineering, the design and manufacturing of high aspect ratio composite wings has become a focal point of innovation and efficiency. These long, slender wings, constructed with advanced materials such as carbon fiber and employing efficient manufacturing methods such as vacuum bagging, hold the promise of significantly lighter aircraft, reduced fuel consumption, and enhanced overall performance. However, to fully realize these benefits, it is imperative to address a multitude of structural and aeroelastic constraints. This research presents a novel aeroelastically tailored Multi-objective, Multi-disciplinary Design Optimization (MMDO) approach that seamlessly integrates numerical optimization techniques to minimize weight and ensure structural integrity. The optimized wing configuration is then manufactured, and a Ground Vibration Test (GVT) and static deflection analysis using the Digital Image Correlation (DIC) system are used to validate and correlate with the numerical model. Within the fully automated in-house Nonlinear Aeroelastic Simulation Software (NAS2) package (version v1.0), the integration of analytical tools offers a robust numerical approach for enhancing aeroelastic and structural performance in the design of composite wings. Nonlinear aeroelastic analyses and tailoring are included, and a population-based stochastic optimization is used to determine the optimum design within NAS2. These analytical tools contribute to a comprehensive and efficient methodology for designing composite wings with improved aeroelastic and structural characteristics. This comprehensive methodology aims to produce composite wings that not only meet rigorous safety and performance standards but also drive cost-efficiency in the aerospace industry. Through this multidisciplinary approach, the authors seek to underscore the pivotal role of tailoring aeroelastic solutions in the advanced design and manufacturing of high aspect ratio composite wings, thereby contributing to the continued evolution of aerospace technology.

Multi-objective multidisciplinary design optimization of liquid-propellant engines thrust chamber based on a surrogate model

The design of liquid-propellant engines (LPEs) has several challenges in setting the performance parameters. Accordingly, optimizing the design of a thrust chamber is of considerable importance that has been considered in several research projects. Previous research has focused on multidisciplinary design optimization (MDO). However, despite these efforts, the main issues remain. The present paper proposes a multi-objective multidisciplinary design optimization based on an efficient adaptive surrogate model of the thrust chamber to address these issues. The proposed method introduces a practical multidisciplinary optimization method based on an adaptive surrogate model that uses the moving least squares methodology, CCM, sensitivity analysis, and the elite multi-objective genetic algorithm (NSGAII). Due to the high importance of specific impulse and thrust-to-weight ratio, these two functions were used as target functions and in the NSGAII framework, the Pareto frontier was drawn for them. The proposed method is applied to a thrust-chamber engine test case. The results show that the target performance of the engine is improved, the specific impulse value is increased by 3.4 s, and the thrust-to-weight ratio is increased by 4%. These values represent significant advances in LPE engine design. The results obtained in this study indicate the potential of the proposed method in solving large-scale thrust-chamber design optimization problems.

Multi-Objective Multidisciplinary Design Optimization of a Robotic Fish System

Biomimetic robotic fish systems have attracted huge attention due to the advantages of flexibility and adaptability. They are typically complex systems that involve many disciplines. The design of robotic fish is a multi-objective multidisciplinary design optimization problem. However, the research on the design optimization of robotic fish is rare. In this paper, by combining an efficient multidisciplinary design optimization approach and a novel multi-objective optimization algorithm, a multi-objective multidisciplinary design optimization (MMDO) strategy named IDF-DMOEOA is proposed for the conceptual design of a three-joint robotic fish system. In the proposed IDF-DMOEOA strategy, the individual discipline feasible (IDF) approach is adopted. A novel multi-objective optimization algorithm, disruption-based multi-objective equilibrium optimization algorithm (DMOEOA), is utilized as the optimizer. The proposed MMDO strategy is first applied to the design optimization of the robotic fish system, and the robotic fish system is decomposed into four disciplines: hydrodynamics, propulsion, weight and equilibrium, and energy. The computational fluid dynamics (CFD) method is employed to predict the robotic fish’s hydrodynamics characteristics, and the backpropagation neural network is adopted as the surrogate model to reduce the CFD method’s computational expense. The optimization results indicate that the optimized robotic fish shows better performance than the initial design, proving the proposed IDF-DMOEOA strategy’s effectiveness.

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.

Optimal two-stage parachute and retro motor sizing for launch vehicle stage recovery

A deceleration system consisting of staged parachute clusters and retro thrusters is optimized for the recovery of the first stage of a launch vehicle on sea. Optimal mass as well as reduction in speed by each parachute cluster and the retro thrusters is essential to minimize the inherent payload loss due to inclusion of additional systems. Three disciplines are involved in the study, namely parachute design, grain design and Three Degrees of Freedom (3-DOF) trajectory simulations. Parachute components are sized and their masses are estimated using a parachute design code. It computes the number of parachutes in the cluster, their sizes and opening loads for multiple reefing stages. Solid motor grain design is carried out, using high burn rate propellant, to provide high thrust to decelerate the launch vehicle stage to a near-zero descent rate at touchdown. A Multiobjective Multidisciplinary Design Optimization ( $$\text{M}^{2}$$ DO) problem has been formulated to minimize the mass of the deceleration system and minimize the touchdown speed of the recovered stage, subject to constraints on Maximum Expected Operating Pressure (MEOP), feasibility, etc. The optimization is carried out and the Pareto optimal front is obtained using an in-house multi-objective optimization algorithm, Attractor Anchored Multi-objective Evolutionary Algorithm (A $$^2$$ -MOEA). A total of twenty-five design variables are considered including initial conditions for each deceleration stage, size of parachute cluster components for both drogue and main parachutes, and the size and shape of the solid motor grain for retro rockets. It is seen that the two objectives are conflicting. The Pareto optimal designs are discussed and the variation of design variables is presented.

Multi-Objective Multidisciplinary Design Optimization Approach for Partially Reusable Launch Vehicle Design

Reusability of the first stage of launch vehicles may offer new perspectives to lower the cost of payload injection into orbit if sufficient reliability and efficient refurbishment can be achieved. One possible option that may be explored is to design the vehicle first stage for both reusable and expendable uses, in order to increase the flexibility and adaptability to different target missions. This paper proposes a multilevel multidisciplinary design optimization (MDO) approach to design aerospace vehicles addressing multimission problems. The proposed approach is focused on the design of a family of launchers for different missions sharing commonalities using multi-objective MDO to account for the computational cost associated with the discipline simulations. The multimission problem addressed considers two missions: 1) a reusable configuration for a sun synchronous orbit with a medium payload range and recovery of the first stage using a gliding-back strategy; 2) an expendable configuration for a medium payload injected into a geostationary transfer orbit. A dedicated MDO formulation introducing couplings between the missions is proposed in order to efficiently solve such a coupled problem while limiting the number of calls to the exact multidisciplinary analysis thanks to the use of Gaussian processes and multi-objective efficient global optimization.

An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.

Multi-objective multidisciplinary design analyses and optimization of high altitude airships

High Altitude Airships (HAAs) offer tremendous potential as long-endurance relocatable aerial platforms for several strategic and commercial applications. Design, analyses, and optimization of HAAs involves a complex interplay of various disciplines, and hence a multidisciplinary approach is essential. This paper describes a methodology to obtain the optimal design of an HAA meeting the requirements of onboard payload and power. The methodology couples six mutually interacting disciplines, viz., Environment, Geometry, Energy, Structure, Aerodynamics, and Thermal. The design problem is posed in a multidisciplinary optimization framework involving eleven design variables drawn from these six disciplines, and optimal solutions are obtained using Genetic Algorithm. The methodology obtains the optimal envelope shape, layout of the solar array, and altitude of operation, and determines the most critical day of operation. To demonstrate the efficacy of methodology, the optimal solutions are obtained for five different geographical locations of deployment, and compared with those for a standard envelope shape. A comparative study of these solutions is carried out to highlight the importance of thermal considerations in design optimization. Since the problem involves mutually conflicting disciplines; a multi-objective optimization involving Aerodynamics and Structures are also carried out. It is noticed that operating parameters and thermal behavior have a significant effect on design.

Computational Design for Sport Buildings

The design of sport buildings has great impact on top-sport as well as on recreational sport-activities. It implies challenging tasks in meeting the performance-requirements. This includes the control of factors like daylight/lighting, air flow, thermal conditions, just to name a few. Such factors impact the performance of athletes and are hard to control in large sport halls; their control is even harder when the public/audience is located within the halls and require different climate conditions. While mechanical installations are often needed during competitions in order to guarantee constant conditions, relaying on mechanical installations during the daily and recreational use of the venues challenges their medium/long term sustainability. Computational form finding approaches can favour the achievement of high-performing and sustainable sport buildings. In this light, the paper tackles the use of Multi-objective and Multidisciplinary design optimization. The paper presents the concept of Multi-objective Multidisciplinary design optimization techniques to support trade-off decisions between multiple conflicting design objectives and interdisciplinary design methodology, during the conceptual design of sport buildings. The proposed method is based on parametric modelling, performance simulation tools and algorithms for computational optimization, for which the paper tackles three specific aspects. First of all, due to the complexity of large sport buildings, the formulation of the optimization and the screening of the related design variables is crucial in order to obtain a meaningful design space, which helps reducing unnecessary computational burden. Secondly, assessing performance based on measurements and analyses is crucial and can be supported by performance simulations tools; however effectively integrating performance simulations tools in the early phase of the design requires new tools. In this light, a customized computational process for the rapid assessment of temperature and airflow patterns is presented. Thirdly, the process requires the combination of design optimization and design exploration, while searching for well-performing solutions. The importance of design exploration is emphasized also for sub-optimal solutions. In order to facilitate the design exploration, the combination of optimization algorithms, multi-variate analysis algorithms and options for exploring design solutions via an interactive dashboard connected to a database are presented. To exemplify the method, specific case studies are developed as collaboration between Delft university of Technology and South China university of Technology.

A new methodology for multi-objective multidisciplinary design optimization problems based on game theory

The design of engineering systems often involves multiple disciplines and competing objectives, which requires coordination, information exchange and share amongst the disciplines. However, in practical design environments, designers have to make decisions in isolation due to organization barriers, time schedules and geographical constraints. This paper will propose a new approach for the multi-objective multidisciplinary design optimization (MDO) problems in non-cooperative environments based on gene expression programming (GEP) and Nash equilibrium in the game theory. In this approach, the GEP method is used as a surrogate to construct the approximate rational reaction sets (RRSs) in the Nash model. The effectiveness of the proposed method is demonstrated by the design of a thin-walled pressure vessel and the hull form parameter design of a small waterplane area twin hull (SWATH) ship. The results show that this approach can fully explore and provide the explicit functional relationship between the strategy of an isolated player and the control variables of the other players, thus able to obtain a better Nash equilibrium solution.

An uncertain multidisciplinary design optimization method using interval convex models

This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss–Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.

On Maximizing Solution Diversity in a Multiobjective Multidisciplinary Genetic Algorithm for Design Optimization

This article presents a new method for multiobjective multidisciplinary design optimization. The method obtains an estimate of the Pareto frontier with maximum solution diversity using a quality index, referred to as entropy index. Unlike previous methods that maintain diversity in the solution set heuristically, our method improves overall quality of solutions by explicitly optimizing the entropy index at every system-level iteration, and then using this information to bias the search process toward obtaining a solution set with maximum diversity. Our method utilizes a multiobjective genetic algorithm as an optimizer in each subproblem of a multidisciplinary optimization problem. To demonstrate the proposed approach, we applied our method to a mechanical design problem of a speed reducer and the results are compared with those obtained by a few other multiobjective optimization methods. A minimal set of quality indexes is used to compare the diversity and optimality of the obtained solution sets from the different methods on a quantitative basis.

Integrating linear physical programming within collaborative optimization for multiobjective multidisciplinary design optimization

Multidisciplinary design optimization (MDO) is a concurrent engineering design tool for large-scale, complex systems design that can be affected through the optimal design of several smaller functional units or subsystems. Due to the multiobjective nature of most MDO problems, recent work has focused on formulating the MDO problem to resolve tradeoffs between multiple, conflicting objectives. In this paper, we describe the novel integration of linear physical programming within the collaborative optimization framework, which enables designers to formulate multiple system-level objectives in terms of physically meaningful parameters. The proposed formulation extends our previous multiobjective formulation of collaborative optimization, which uses goal programming at the system and subsystem levels to enable multiple objectives to be considered at both levels during optimization. The proposed framework is demonstrated using a racecar design example that consists of two subsystem level analyses — force and aerodynamics — and incorporates two system-level objectives: (1) minimize lap time and (2) maximize normalized weight distribution. The aerodynamics subsystem also seeks to minimize rearwheel downforce as a secondary objective. The racecar design example is presented in detail to provide a benchmark problem for other researchers. It is solved using the proposed formulation and compared against a traditional formulation without collaborative optimization or linear physical programming. The proposed framework capitalizes on the disciplinary organization encountered during large-scale systems design.

Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms

SUMMARY A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensional Helmholtz equation which is obtained using a fictitious domain method. Numerical experiments illustrate the above evolutionary methodology on an IBM SP2 parallel computer. Copyright © 1999 John Wiley & Sons, Ltd.

Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms

A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensional Helmholtz equation which is obtained using a fictitious domain method. Numerical experiments illustrate the above evolutionary methodology on an IBM SP2 parallel computer. Copyright © 1999 John Wiley & Sons, Ltd.