Multidisciplinary Design Optimization Method Research Articles

A reliability-based multidisciplinary design parallel optimization method based on double-layer approximation model for nuclear fuel assembly bottom nozzle

The design of intricate systems such as the nuclear fuel assembly necessitates elevated levels of multi-disciplinary performance and reliability. In current reliability-based multidisciplinary design optimization methods, the decoupling strategy between optimization and reliability assessment involves sequential optimization and reliability assessment, with reliability serving as a constraint for optimization. This approach often suffers failure in locating the global optimal solution. In light of this issue, a reliability-based multidisciplinary design parallel optimization method based on double-layer approximation model is hereby proposed, achieving parallel separation and global efficient optimization of deterministic disciplinary performances and reliability, while performing efficient and accurate calculation on the multi-disciplinary reliability numerical solution. This method has been implemented for the multi-disciplinary uncertain optimization of the nuclear fuel assembly bottom nozzle. In comparison to conventional optimization methods, this approach demonstrates enhanced global optimization effectiveness.

Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance

Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance

Solid-State Electroaerodynamic Aircraft Design Using Signomial Programming

Electroaerodynamics (EAD) is a form of airbreathing electric propulsion that uses high voltages to produce and accelerate ions, generating thrust without any moving parts. This method of solid-state propulsion is nearly silent and produces no direct combustion emissions. This paper describes a program for designing and optimizing fixed-wing solid-state aircraft propelled solely using EAD. Signomial programming (SP), an emerging method of efficient multidisciplinary design optimization, is employed. The program incorporates performance models for state-of-the-art EAD thrusters, and for custom high-voltage power electronics. It can be used to generate vehicle specifications, or to assess the effect of technological improvements on vehicle performance. The program was used to design and build a flight demonstrator aircraft, based on a goal of achieving steady level flight. In 2017–2018, the demonstrator successfully achieved steady level flight, a first for a fixed-wing electric aircraft with solid-state propulsion. The unproven nature of the EAD propulsion system necessitated a design philosophy centered around minimal technical risk, affecting configuration selection and choice of objective function. A similar design philosophy may prove useful for other design projects with unproven propulsion systems. Finally, endurance values greater than 30 min are achievable with recent improvements in EAD thruster and battery technology.

Multi-Objective, Multi-Disciplinary Design Optimization and Multi-Attribute Evaluation of Hybrid Rocket Motors Used for Manned Lunar Lander

This paper proposed a multi-objective, multi-disciplinary design optimization and multi-attribute evaluation method for the manned lunar lander descent stage. A system design model is established considering multiple disciplines such as propulsion, structure, trajectory and cost. With the goal of minimizing mass, minimizing cost and maximizing velocity increment, the overall scheme for hybrid rocket motors was optimized by altering various grain shapes and feed systems, acting as an alternative propulsion scheme for the manned lunar lander. Under the same design conditions, the optimal scheme of hybrid rocket motors considering continuous and discrete attributes was studied and compared with that of liquid rocket engines to elucidate the characteristics of the hybrid rocket motors for deep space exploration. The results showed that the evaluation results obtained by considering only continuous attributes were different from those by considering both continuous and discrete attributes. The liquid propulsion scheme with liquid oxygen/kerosene is superior to the hybrid propulsion schemes due to its excellent cost and specific impulse performance when only continuous attributes are considered. However, hybrid rocket motors have shown good performance in terms of operability, manufacturability, safety and environmental protection. So, after introducing discrete attributes, the hybrid propulsion schemes show greater potential. In brief, based on the multi-attribute evaluation method considering comprehensive attributes, the hybrid rocket motor provided with tube grain and gas pressure feed system was considered as the optimal propulsion system for the lunar lander. Furthermore, the parametric analysis showed that the fuel grain outside diameter, the initial design thrust and the initial oxygen-to-fuel ratio had a significant influence on the performance of the hybrid rocket motor for the lunar lander, and in particular, the effect of the fuel grain outside diameter was more than 50%.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization (RBMDO) of engineering structures, the saddlepoint approximation (SA) method can be utilized to enhance the accuracy and efficiency of reliability evaluation. However, the random variables involved in SA should be easy to handle. Additionally, the corresponding saddlepoint equation should not be complicated. Both of them limit the application of SA for engineering problems. The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments. However, the traditional moment matching method is not very accurate generally. In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization, a fourth-moment saddlepoint approximation (FMSA) method is introduced into RBMDO. In FMSA, the approximate cumulative generating functions are constructed based on the first four moments of the limit state function. The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function. Furthermore, the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment, which is based on the performance measure approach strategy. Two engineering examples are introduced to verify the effectiveness of proposed method.

Multidisciplinary Design Optimization of a Re-Entry Spacecraft via Radau Pseudospectral Method

The design and optimization of re-entry spacecraft or its subsystems is a multidisciplinary or multiobjective optimization problem by nature. Multidisciplinary design optimization (MDO) focuses on using numerical optimization in designing systems with several subsystems or disciplines that have interactions and independent actions. In the present paper, the system-level optimizer, trajectory, geometry and shape, aerodynamics, and aerothermodynamics differential equations, are converted to algebraic equations using the Radau pseudospectral method (RPM) since a spacecraft is a nonlinear, extensive, and sparse system. The solution to the problem with the help of MDO is reached by iterating all the disciplines together; one can simultaneously enhance the design, decrease the time and cost of the entire design cycle, and minimize the structural mass of a re-entry spacecraft. Considering various methods presented in earlier research works, a combined and innovative all-at-once (AAO), RPM-based MDO method, including the key subsystems in the design process of a re-entry capsule-shape spacecraft with a low lift-to-drag ratio (L/D), is presented. Considering the applicable state and control variables, various constraints, and parameters applied to several geometric shapes of a blunt capsule and using Apollo’s aerodynamic and aerothermodynamic coefficients, the optimized dimensions for a re-entry spacecraft are presented. The introduced optimization scheme led to a 17% mass reduction compared to the original mass of the Apollo vehicle. Fast computing and simplified models are used together in this method to analyze a wide range of vehicle shapes and entry types during conceptual design.

A Dimension Reduction-Based Multidisciplinary Design Optimization Method for High Pressure Turbine Blades

Abstract The complex aero-thermal coupling between fluid and solid regions within high-pressure turbines makes it important to perform multidisciplinary design optimization of high-pressure turbine blades. However, most published works failed to consider the correlations between blade profiles and cooling structures that could best compromise the aerodynamic and thermal performance of high-pressure turbine blades, and the related optimization problems were so far limited to single- or bi-objective ones. The critical drawbacks of these available studies are mainly due to the reduced accuracies of the adopted methods when dealing with large numbers of design variables and objectives. To tackle these difficulties, a dimension reduction-based multidisciplinary design optimization method is proposed and validated through an aero-thermal design optimization of the NASA-C3X vane with a total of 39 design variables and five performance objectives. The main novelties of this proposed method lie in a hybrid dimension reduction of design space by means of the proper orthogonal decomposition and global sensitivity analysis methods, as well as the integration of the ensemble surrogate model and the reference vector evolutionary algorithm for optimal solutions. The results show that the prediction accuracy of the ensemble surrogate model for each performance objective is enhanced, even though the dimensionalities of design space are reduced. Complicated compromises exist among the five performance objectives under consideration. For NASA-C3X vane, the optimal design helps reduce irreversible flow losses especially wake losses while reducing the volumes with high-temperature and high-temperature gradient near the trailing edge is mainly responsible for the reduced irreversible losses due to heat transfer. The outcomes of this work are particularly relevant for the advanced design optimization methods for high pressure turbines.

All-At-Once formulation integrating pseudo-spectral optimal control for launch vehicle design and uncertainty quantification

Launch vehicle design is a multidisciplinary process involving different disciplines such as aerodynamics, structure, propulsion and trajectory. This latter is a key discipline in the design process as it is used to assess the overall performance of the vehicle by solving of an optimal control problem involving a system of nonlinear ordinary differential equations. Usual Multidisciplinary Design Optimization methods for launch vehicle design consider the trajectory design discipline as an auxiliary embedded optimization problem to find the optimal trajectory control. In this paper, a multidisciplinary approach is proposed relying on an All-At-Once formulation by using Gauss–Lobatto collocation technique to solve the optimal control problem. The problem is solved using a gradient-based optimizer. Furthermore, based on this framework, an uncertainty quantification technique using post-optimality analysis is derived to perform sensitivity analysis. This allows to analyze the influence of modeling uncertainty on the optimal launch vehicle performance in the early design phases. The efficiency of the proposed approach is illustrated on the optimization and uncertainty quantification of a representative Two-Stage-To-Orbit launch vehicle design problem.

Data-Driven Set Based Concurrent Engineering Method for Multidisciplinary Design Optimization

<div class="section abstract"><div class="htmlview paragraph">In the development of multi-disciplinary systems, many experts in different discipline fields need to collaborate with each other to identify a feasible design where all multidisciplinary constraints are satisfied. This paper proposes a novel data-driven set-based concurrent engineering method for multidisciplinary design optimization problems by using machine learning techniques. The proposed set-based concurrent engineering method has two advantages in the concurrent engineering process. The first advantage is the decoupling ability of multidisciplinary design optimization problems. By introducing the probabilistic representation of multidisciplinary constraint functions, feasible regions of each discipline sub-problem can be decoupled by the rule of product. The second advantage is an efficient concurrent study to explore feasible regions. A batch sampling strategy is introduced to find feasible regions based on Bayesian Active Learning (BAL). In the batch BAL, Gaussian Process models of each multi-disciplinary constraint are trained. Based on the posterior distributions of trained Gaussian Process models, an acquisition functions that combine Probability of Feasibility and Entropy Search are evaluated. In order to generate new sampling points in and around feasible regions, optimization problems to maximize the acquisition function are solved by assuming that the constraint function is Lipschitz continuous. To show the effectiveness of the proposed method, a practical numerical example of a multi-disciplinary vehicle design problem is demonstrated.</div></div>

A novel polynomial chaos expansion-based method for feedback-coupled multidisciplinary design optimization under metamodel uncertainty

A novel polynomial chaos expansion-based method for feedback-coupled multidisciplinary design optimization under metamodel uncertainty

Certification-Driven Platform for Multidisciplinary Design Space Exploration in Airframe Preliminary Design

Airworthiness certification is a mandatory but expensive process in aircraft development. To reduce certification cost, it is desired to incorporate certification considerations into aircraft early design stages. The tradeoff between performance and certification constraints and the interactions between the behind-the-scene disciplines require a multidisciplinary design optimization (MDO) method implemented to incorporate certification considerations. Several MDO frameworks currently exist with mixing levels of fidelity and multidisciplinary coupling. However, few of them capture the impacts of certification constraints on the overall aircraft performance. Moreover, preceding MDO studies have mostly focused on optimizing a single design point, whereas little attention is paid to design space exploration. To fill these gaps, this paper proposes a certification-driven platform for airframe early preliminary design. With statistical methods applied, this platform allows efficient design space exploration and multi-objective optimization. To demonstrate the capabilities of this platform, a test case of preliminary horizontal tail design of a large twin-aisle aircraft is performed. The feasibility test and multi-objective optimization conducted in the test case prove that certification constraints play a critical role in the design space exploration at the early preliminary stage.

Reliability-based multidisciplinary concurrent design optimization method for complex engineering systems

Reliability-based multidisciplinary design optimization (RBMDO) has been considered as an efficient technology for addressing complex engineering design optimization problems under uncertainties. Current RBMDO methods, however, perform design optimization either in a sequential manner or in an all-at-once manner, which does not support design autonomy in various disciplines and has low computational efficiency. In this article, a reliability-based multidisciplinary concurrent design optimization (RBMCDO) method is proposed to solve the problems of lack of design autonomy and low computational efficiency in current RBMDO methods. In RBMCDO, the multidisciplinary reliability constraints are first transformed into deterministic constraints using the multidisciplinary probabilistic constraint transformation method, developed in this work based on the performance measure approach and Karush–Kuhn–Tucker conditions. The RBMDO problem is then decomposed into several optimization problems of a single discipline, which are solved in parallel based on the collaborative optimization strategy. Two examples are used to verify the proposed method.

Multidisciplinary design for structural integrity using a collaborative optimization method based on adaptive surrogate modelling

As one of the multidisciplinary design optimization methods, the collaborative optimization (CO) can enjoy a high degree of discipline autonomy. It has received extensive attention and been used in the modern engineering design process. However, the original CO is low optimization accuracy and efficiency for the design of high-dimensional nonlinearity systems because of the involved compatibility constraints. To solve this problem, an enhanced CO method based on the adaptive surrogate model is proposed in this study. The strategy of the proposed method includes the following steps. Firstly, the traditional surrogate models of system objective and performance function are constructed by the Latin hypercube sampling and the Kriging method. Then, the expected improvement function and the self-cycling optimization strategy are utilized to modify the traditional surrogate models into the corresponding adaptive surrogate models. Finally, the original objective and constraints at the system level and disciplinary level are replaced by their adaptive surrogate models, respectively. Consequently, the formulation of CO based on the adaptive surrogate model can be obtained. In the proposed method, the accuracy of the non-linear region of the response surface can be enhanced efficiently. An engineering structure design problem is introduced to show the effectiveness of the proposed method.

Discrete structural optimization of a passenger car rear seat frame using aluminium alloy

To reduce the weight and improve the structural performances of a passenger car rear seat frame, this study uses a discrete structural optimization method to design an aluminium alloy seat frame to replace the original steel one. The optimization problem aims to minimize the total mass, manufacturing cost, the maximum displacements and tensile stresses under certain load conditions and maximize the first order natural frequency. The cross-sectional dimensions and material types of members in the seat frame are considered as the design variables. A modified non-dominated sorting genetic algorithm, the third version (mNSGA-III) which is adapted at handling problems with four or more objective functions, is used to solve the optimization problem. To benchmark the performance of the proposed method, a multidisciplinary design optimization (MDO) method is also utilized to solve the optimization problem. The comparison between the solutions obtained by the proposed method and the MDO method shows that the accuracy and the effectiveness of the proposed method are better. A weight saving of 35.1% is achieved by the aluminium alloy seat frame as compared to the original steel seat frame.

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

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

An uncertainty-based design optimization strategy with random and interval variables for multidisciplinary engineering systems

Generally, the traditional uncertainty-based multidisciplinary design optimization (UBMDO) methods are based on the probability distribution information of random design variables and parameters. However, the probability distribution information needs to be obtained based on a large number of sample points. In many engineering structure design problems, for some uncertainties, it is difficult to obtain enough experimental samples to construct their accurate probability distribution, only the variation interval of them can be known. In this situation, mixed uncertainties exist in the engineering systems. Furthermore, with the increase in the complexity of engineering systems, these mixed uncertainties will even produce cumulative effects along with the internal coupling of the systems themselves. To tackle these challenges, the random and interval variables (RIV) are considered and a strategy of UBMDO with RIV (UBMDO-RIV) is proposed in this study. In the given method, the evaluation of uncertainty constraints is performed in the worst case scenario due to interval uncertainties. Meanwhile, the classic decoupling strategy for UBMDO, the framework of sequential design and uncertainty evaluation (SDUE), is introduced into UBMDO-RIV to reduce the computational burden. The engineering case study is utilized to illustrate the application of the proposed strategy.

Multidisciplinary Design Optimization of Low-Boom Supersonic Aircraft with Mission Constraints

Conceptual design of low-boom supersonic aircraft is heavily dictated by aircraft volume and lift distributions. These unique design characteristics make it a challenge to enforce mission requirements (such as static margins and trim requirements) during design optimization. This low-boom design challenge is resolved by using reversed equivalent area targets for low-fidelity low-boom inverse design and a block coordinate optimization (BCO) method for multidisciplinary design optimization (MDO). The corresponding low-boom MDO problem includes aircraft mission constraints on ranges, cruise speeds, trim for low-boom cruise, static margins for takeoff/cruise/landing, takeoff/landing field lengths, approach velocity, and tail rotation angles for trim at takeoff/landing, as well as fuselage volume constraints for passengers and main gear storage. The BCO method is developed to optimally resolve the conflicts between the low-boom inverse design objective and other design constraints. This method is successfully applied to design a low-boom supersonic configuration that carries 40 passengers, flies a low-boom mission with cruise Mach of 1.6 and range of 2500 nm, and cruises overwater at Mach 1.8 with range of 3600 nm. The generated configuration satisfies all specified mission constraints and has the potential to match a reversed equivalent area target with ground noise level below 70 PLdB.

Multidisciplinary design optimization of an electric propulsion system of a hybrid UAV considering wind disturbance rejection capability in the quadrotor mode

The electric propulsion system (EPS) of a quadrotor fixed-wing hybrid unmanned aerial vehicle (QFHUAV) has important effects on its time of endurance and wind disturbance rejection capability in the quadrotor mode. Currently, the design methods of most QFHUAV EPSs are to design the quadrotor propulsion system and fixed-wing propulsion system independently. The wind disturbance rejection capability in the quadrotor mode is not considered in these methods. The multidisciplinary design optimization (MDO) method can reduce design time and cost by integrating all the disciplines involved in the design process. The MDO solutions are generally more optimal with respect to standard optimal sequential solutions. This paper proposes an MDO for a QFHUAV EPS considering the wind disturbance rejection capability in the quadrotor mode. The analysis modules of the propeller/rotor discipline, brushless direct current motor discipline, electronic speed control discipline, lithium polymer battery discipline, time of endurance discipline, mass discipline, and wind disturbance rejection capability in the quadrotor mode discipline are modeled. The MDO process of a QFHUAV EPS is constructed according to the transfer process and coupling relations among the discipline parameters. Based on the mission profile, the flight performance and mission requirements of the QFHUAV are created and a multi-objective optimization design model of the QFHUAV EPS is modeled. The Multidisciplinary feasible approach is implemented to decompose the mass coupling variables between the EPS component analysis modules and the mass analysis module effectively. A multi-objective evolutionary algorithm named NSGA-II is used to discover the full Pareto front for the multi-objective problem. The proposed MDO method is used to design the EPS of a self-developed QFHUAV. The optimal combination of QFHUAV EPS components is determined based on the optimization results. A comparison between the optimization results and the actual flight performance of the QFHUAV shows that the flight performance is in good agreement with the optimization results, which indicates that the MDO method proposed in this paper is feasible and reasonable.

A Reliability based Multidisciplinary Design Optimization Method with Multi-Source Uncertainties

The complexity of engineering systems is increasing greatly, and more coupled disciplines and multi-source uncertainties are involved in the design and development of complex engineered systems (CESs). Actually, uncertainties are ubiquitous in design of CESs, which can be mainly classified into alteatory uncertainty (AU) and epistemic uncertainty (EU). To gain high reliability and safety of CESs, the Reliability-based MDO (RBMDO) which considers uncertainties of design variables and parameters has become a hot research topic. In this paper, the quantification of aleatory and epistemic uncertainties based on the probability theory and convex set-theory, multidisciplinary comprehensive reliability evaluation index, adaptive collaborative optimization strategy based on the intelligent optimization algorithm, sequential multidisciplinary reliability analysis method based on the concurrent subspace optimization (CSSO) and performance measure approach (PMA), and hierarchical and hybrid sequential optimization and reliability assessment (HSORA) RBMDO strategy under multi-source uncertainties have been researched. All of the researches can expand and improve the RBMDO theoretical system, and also provide the effective method for the design and optimization of CESs under multi-source uncertainties.

Uncertainty analysis and design optimization of solid rocket motors with finocyl grain

The traditional multidisciplinary design optimization (MDO) method for the conceptual design of the solid rocket motor (SRM) is usually deterministic and seldom focuses on systematic design optimization. This paper develops a systematic design model of the SRM with a finocyl grain and proposes an approach for uncertainty analysis and design optimization of SRM. The mean value and standard deviation of the target function, as well as the probability that the constraints can be met, are calculated using Monte Carlo simulation (MCS) analysis. The uncertainty-based multidisciplinary design optimization (UMDO), together with the deterministic multidisciplinary design optimization (DMDO), is applied to the conceptual design of SRM based on the third-stage engine ZEFIRO9 of the Vega launch vehicle. By main effect diagrams and Pareto diagrams, the most influential design variables and standard deviation of uncertain parameters are obtained, which can help designers understand more of the uncertainty relationships between parameters and system performance.