Multidisciplinary Design Optimization Method Research Articles

Multidisciplinary Design Optimization of Turbine Disks Based on ANSYS Workbench Platforms

The design of aero engine turbine disks, which are working under high thermal and centrifugal loads, is an interactive and multidisciplinary process that includes several disciplines, such as aerodynamics, structural analysis, mechanical design, and heat transfer etc. Considering the actual aero-thermal-structure coupled environment, the main challengefor the designersis to produce an optimum design that satisfies all the design criteria such as weight, life, efficiency and reliability.Especially, problems of overweight and maximum localized stress have been always encountered for designers in the preliminary design phase. Therefore, there exist contradictions for the design parameters fromdifferent disciplines, and then multidisciplinary design optimization method could be a very valuableand efficient strategy tosolve the problem.In this paper, based on the platforms of ANSYS workbench software, the aero-thermal-structure coupled analysis of a high pressure turbine disk had been conducted. Then, the parameters of width and height of the disk bore were selected as the design variables, and multidisciplinary design optimization of turbine disk had been done. As a result, with the constraints on strength criteria, the objective function of disk weight had been decreased by 6 percents which achieved the expected goal and significantly reduced the design and research time.

An integrated multidisciplinary design optimization method for computer numerical control machine tool development

Computer numerical control machine tool is a typical complex product related with multidisciplinary fields, complex structure, and high-performance requirements. It is difficult to identify the overall optimal solution of the machine tool structure for their multiple objectives. A new integrated multidisciplinary design optimization method is then proposed by using a Latin hypercube sampling, a Kriging approximate model, and a multi-objective genetic algorithm. Design space and parametric model are built by choosing appropriate design variables and their value ranges. Samples in design space are generated by optimal Latin hypercube method, and design variable contributions for design performance are discussed for aiding the designer’s judgments. The Kriging model is built by using polynomial approximation according to the response outputs of these samples. The multidisciplinary design model is established based on three optimization objectives, that is, setting mass, optimum deformation, and first-order natural frequency, and two constraints, that is, second-order natural frequency and third-order natural frequency. The optimal solution is identified by using a multi-objective genetic algorithm. The proposed method is applied in a multidisciplinary optimization case study for a typical computer numerical control machine tool. In the optimal solution, the mass decreases by 3.35% and the first-order natural frequency increases by 4.34% in contrast to the original solution.

Differential geometry tools for multidisciplinary design optimization, part II: application to QSD

Having previously developed a differential geometry framework for analyzing and conceptualizing Multidisciplinary Design Optimization (MDO) problems and methods, we now apply that framework to consider the Quasi-Separable Decomposition (QSD) architecture. Based on our theoretical investigations, we predict that QSD will fail to return feasible designs for MDO problems. In the same vein, we analyze the Individual Discipline Feasible (IDF) architecture, predict that IDF will converge to feasible designs, and propose a modified version of QSD which we believe will also output feasible design points. To test these predictions, we run all three architectures on a well-known analytical MDO problem. Our predictions regarding feasibility prove to be accurate: QSD does not return any feasible points, whereas all of the final design points from IDF and the modified QSD are feasible. Now that convergence to feasibility has been established, the next step is to investigate the optimization performance of various QSD modifications.

Differential geometry tools for multidisciplinary design optimization, Part I: Theory

Analysis within the field of Multidisciplinary Design Optimization (MDO) generally falls under the headings of architecture proofs and sensitivity information manipulation. We propose a differential geometry (DG) framework for further analyzing MDO systems, and here, we outline the theory undergirding that framework: general DG, Riemannian geometry for use in MDO, and the translation of MDO into the language of DG. Calculating the necessary quantities requires only basic sensitivity information (typically from the state equations) and the use of the implicit function theorem. The presence of extra or non-differentiable constraints may limit the use of the framework, however. Ultimately, the language and concepts of DG give us new tools for understanding, evaluating, and developing MDO methods; in Part I, we discuss the use of these tools and in Part II, we provide a specific application.

Robust design of Mars entry micro-probe with evidence theory and multi-fidelity strategies

Purpose – A multi-disciplinary robust design optimization method for micro Mars entry probe (no more than 0.8 m in diameter) is proposed. The purpose of this paper is to design a Mars entry probe, not only the geometric configuration, but the trajectory and thermal protection system (TPS). In the design optimization, the uncertainties of atmospheric and aerodynamic parameters are taken into account. The probability distribution information of the uncertainties are supposed to be unknown in the design. To ensure accuracy levels, time-consuming numerical models are coupled in the optimization. Multi-fidelity approach is designed for model management to balance the computational cost and accuracy. Design/methodology/approach – Uncertainties which cannot defined by usual Gaussian probability distribution are modeled with degree of belief, and optimized through with multiple-objective optimization method. The optimization objectives are set to be the thermal performance of the probe TPS and the corresponding b...

Aerodynamic configuration optimization by the integration of aerodynamics, aerothermodynamics and trajectory for hypersonic vehicles

The problem of aerodynamic configuration design optimization is a multidisciplinary design optimization (MDO) problem, and recently the MDO method is widely adopted in the field of hypersonic vehicle configuration design. From the aerodynamic point of view, the aerodynamics, aerothermodynamics and trajectory are considered in this paper. Generally speaking, the aerodynamic characteristics, aerodynamic heating and trajectory are determined by the aerodynamic configuration and the design of flight trajectory. The design method considering these three disciplines is proposed. The parametric geometrical configurations are proposed, and the aerodynamic characteristics are predicted by the rapid and effective engineering method. The optimization of aerodynamic configuration considering the integration of aerodynamics, aerothermodynamics and trajectory is investigated based on the parametric geometrical configuration. Maximum lift-to-drag ratio, maximum range of the trajectory and minimum total heat load of the stagnation point are chosen as the three optimal goals. The detailed research indicates that the optimal configurations and trajectories with different weighting factors can be obtained by the optimization, and there are obvious differences between them. The optimal configuration and flight trajectory obtained by the optimization can be used as the feasible schemes in the future work.

Method of Optimization Design of Permanent Magnet Retarder

This paper introduced the method of multidisciplinary design optimization. The conceptual model of permanent magnet retarder was developed to maximize the brake torque of the permanent magnet retarder. The influences of magnetic field parameters, structural design parameters, rotor parameters and permanent magnet temperature parameters on the behaviors performance of the permanent magnet retarder were discussed. The design variables included the radial width and the axis length of permanent magnet, the number of permanent magnet, the radius of rotor, the thickness of rotor, and the air gas. The multidisciplinary design optimization in this paper is an effective method for the global design optimization of the permanent magnet retarder.

Carbody structural lightweighting based on implicit parameterized model

Most of recent research on carbody lightweighting has focused on substitute material and new processing technologies rather than structures. However, new materials and processing techniques inevitably lead to higher costs. Also, material substitution and processing lightweighting have to be realized through body structural profiles and locations. In the huge conventional workload of lightweight optimization, model modifications involve heavy manual work, and it always leads to a large number of iteration calculations. As a new technique in carbody lightweighting, the implicit parameterization is used to optimize the carbody structure to improve the materials utilization rate in this paper. The implicit parameterized structural modeling enables the use of automatic modification and rapid multidisciplinary design optimization (MDO) in carbody structure, which is impossible in the traditional structure finite element method (FEM) without parameterization. The structural SFE parameterized model is built in accordance with the car structural FE model in concept development stage, and it is validated by some structural performance data. The validated SFE structural parameterized model can be used to generate rapidly and automatically FE model and evaluate different design variables group in the integrated MDO loop. The lightweighting result of body-in-white (BIW) after the optimization rounds reveals that the implicit parameterized model makes automatic MDO feasible and can significantly improve the computational efficiency of carbody structural lightweighting. This paper proposes the integrated method of implicit parameterized model and MDO, which has the obvious practical advantage and industrial significance in the carbody structural lightweighting design.

Multidisciplinary design optimization of offshore wind turbines for minimum levelized cost of energy

This paper presents a method for multidisciplinary design optimization of offshore wind turbines at system level. The formulation and implementation that enable the integrated aerodynamic and structural design of the rotor and tower simultaneously are detailed. The objective function to be minimized is the levelized cost of energy. The model includes various design constraints: stresses, deflections, modal frequencies and fatigue limits along different stations of the blade and tower. The rotor design variables are: chord and twist distribution, blade length, rated rotational speed and structural thicknesses along the span. The tower design variables are: tower thickness and diameter distribution, as well as the tower height. For the other wind turbine components, a representative mass model is used to include their dynamic interactions in the system. To calculate the system costs, representative cost models of a wind turbine located in an offshore wind farm are used. To show the potential of the method and to verify its usefulness, the 5 MW NREL wind turbine is used as a case study. The result of the design optimization process shows 2.3% decrease in the levelized cost of energy for a representative Dutch site, while satisfying all the design constraints.

Redundancy Transmission System Based on Multidisciplinary Object Compatibility Design Optimization

In studying multidisciplinary design optimization method for non-hierarchic system, Multidisciplinary Object Compatibility Design Optimization method based on simulated annealing algorithm is presented. In order to coordinate the independent optimization of subsystems, the compatibility constraint in system level and compatibility objective in subsystem work together. As optimization process continued, the coupling relationship between system level and different subsystems is gradually improved by state accepting function which is embedded in compatibility constraint. In this way, abnormal program termination and premature convergence will be avoided and ideal global optimal solution will be achieved effectually. Then the method is used in the optimization design of TR-B triple-redundancy transmission system. The multidisciplinary object compatibility design optimization model is established and the comprehensive optimal solution is obtained which meets the matching relationship of gear teeth, strength requirement and dynamic requirement, etc

小卫星用反作用飞轮系统设计

According to the requirement of reaction flywheels in small satellites for small sizes, the design method for an armature size was proposed when the electrical motor was at a minimal volume, and a stator coreless reaction flywheel system was designed based on the method. To avoid the magnetic saturation, the multidisciplinary design optimization method was applied to the design of flywheel rotor and magnetic field of the motor. A optimization strategy combined with Exterior Penalty(EP) function and Sequential Quadratic Programming(SQP) was proposed to optimize the system as well. With optimization, the minimum mass and maximum air-gap magnetic flux density of the rotor were chosen as the objects, respectively, and the maximum equivalent stress, resonance frequency, the polar moment of inertia and the magnetic saturation were taken as constrains. Then, the software iSIGHT with finite element analysis (ANSYS) were integrated to achieve the optimization. Finally, a flywheel prototype was designed based on the optimal results. The results indicate that the total mass of the flywheel rotor has been decreased from 0.73 kg to 0.67 kg (reduced by 8.22%) and the flux density has been increased from 0.376 T to 0.401 T (increased by 6.65%). The optimal design method can improve the rationality of flywheel design, and will promote the progress of the miniaturization investigation of flywheel systems.

Multi-disciplinary design optimization and performance evaluation of a single stage transonic axial compressor

The multidisciplinary design optimization method, which integrates aerodynamic performance and structural stability, was utilized in the development of a single-stage transonic axial compressor. An approximation model was created using artificial neural network for global optimization within given ranges of variables and several design constraints. The genetic algorithm was used for the exploration of the Pareto front to find the maximum objective function value. The final design was chosen after a second stage gradient-based optimization process to improve the accuracy of the optimization. To validate the design procedure, numerical simulations and compressor tests were carried out to evaluate the aerodynamic performance and safety factor of the optimized compressor. Comparison between numerical optimal results and experimental data are well matched. The optimum shape of the compressor blade is obtained and compared to the baseline design. The proposed optimization framework improves the aerodynamic efficiency and the safety factor.

The multidisciplinary design optimization method of aero engine fan blade based on the airworthiness compliance and approximation model

PurposeThe purpose of this paper is to introduce the multidisciplinary design optimization method using approximation model for the aircraft engine fan blade based on the airworthiness compliance such as stress, vibration, and bird impact.Design/methodology/approachFirstly, the airworthiness analysis of the typical fan blade was carried out based on the numerical simulation. Secondly, the design of experiment (DOE) was utilized to construct the approximation model of the fan blade. Finally, the airworthiness optimization of fan blade was carried out based on Kriging approximation model.FindingsThe numerical simulation result shows that the analysis method can show the airworthiness compliance in the design stage. And the optimization result shows that structure, bird impact and vibration characteristics improve obviously, satisfying the constraints conditions of optimization.Originality/valueThe multidisciplinary design optimization method of fan blade based on the airworthiness and approximation model is presented and achieved.

Enhance Derivative Design Considering Global Sensitivity of Design Parameters

An engineering product design considers derivatives to reduce the life cycle cost and to increase the efficiency on operation when it has new demands. The proposed design process in this study obtains derivative designs based on sensitivity of design variable. The efficiency and accuracy of the derivative design process can be enhanced by implementing global sensitivity analysis. Sensitivity analysis sensors the design variables accordingly and variables with low sensitivity for objective function can be neglected, since computational effort and time is not necessary for a design with less priority. In this research, e-FAST method code for global sensitivity analysis module was developed and implemented on Multidisciplinary Design Optimization (MDO) problem. The wing design was considered for MDO problem that used aerodynamics and structural disciplines. The global sensitivity analysis method was applied to reduce the number of design variables and Collaborative Optimization (CO) was used as MDO method. This research shows the efficiency of reduction of dimensionality of complex MDO problem by using global sensitivity analysis. In addition, this result shows important design variables for design requirement to student when they solving design problem.

Multidisciplinary design optimization on production scale of underground metal mine

In order to ensure overall optimization of the underground metal mine production scale, multidisciplinary design optimization model of production scale which covers the subsystem objective function of income of production, safety and environmental impact in the underground metal mine was established by using multidisciplinary design optimization method. The coupling effects from various disciplines were fully considered, and adaptive mutative scale chaos immunization optimization algorithm was adopted to solve multidisciplinary design optimization model of underground metal mine production scale. Practical results show that multidisciplinary design optimization on production scale of an underground lead and zinc mine reflect the actual operating conditions more realistically, the production scale is about 1.25 Mt/a (Lead and zinc metal content of 160 000 t/a), the economic life is approximately 14 a, corresponding coefficient of production profits can be increased to 15.13%, safety factor can be increased to 5.4% and environmental impact coefficient can be reduced by 9.52%.

Multidisciplinary design optimization of a milling cutter for high-speed milling of stainless steel

The milling cutter’s fracture strength is more important than its chemical stability and thermal conductivity in high-speed milling. The multidisciplinary design optimization (MDO) method is employed to optimize the fracture-resistant performance of a milling cutter in this work. An experimental study on high-speed milling of the martensitic stainless steel 0Cr13Ni4Mo is conducted. The cutting forces and cutting temperature in the milling process are measured to provide initial data for the structural optimization of the milling cutter. The mathematical models of cutting force and cutting temperature are studied. Considering that the induced stress in the milling cutter is generated by thermomechanical coupling, the thermoelastic–plastic governing equation in the milling process is introduced in this work. The sensitivity of the structural parameters to the maximum equivalent stress of the milling cutter is calculated, and the structural parameters that have the greatest effects on the maximum equivalent stress are determined as design variables for the cutters’ optimization. The MDO procedure for the cutter’s optimization consists of updating of solid model, finite element analysis of thermomechanical coupling, postprocessing, and optimization algorithm. The MDO results show that the optimized milling cutter has a better fracture-resistant performance than the initial one. The maximum deformation, overall equivalent stress, and deformation are decreased.

Sequential optimisation and reliability assessment for multidisciplinary design optimisation under hybrid uncertainty of randomness and fuzziness

For engineering product design under uncertainty, it is important to guarantee the reliability and safety, especially for complex and coupled systems design problems, using multidisciplinary design optimisation (MDO). Due to the different cognitive levels to various uncertain parameters, it is necessary to include the mixed uncertain parameters such as the random parameters and fuzzy parameters into consideration simultaneously. The design problem under hybrid uncertainty of randomness and fuzziness presents a challenge. However, little attention has been paid to solve hybrid uncertainty problems until now. This study constructs the formulation of fuzzy random uncertainty-based MDO (FRMDO), and proposes a method to solve the FRMDO problems within the framework of sequential optimisation and reliability assessment (SORA), called the FRMDO–SORA approach. The FRMDO–SORA approach can be applied both in single-level and multi-level MDO methods, and can effectively solve MDO problems, where fuzzy, random and fuzzy-random uncertainties coexist. Case studies are given to demonstrate the efficiency and feasibility of the proposed FRMDO–SORA approach.

Comparison of MDO Methods for an Earth Observation Satellite

It is shown in this paper the application of several multidisciplinary design optimization (MDO) methods for an earth observation satellite to optimize the performance of the earth observation. Based on the best earth observation criteria, a mathematical model of the satellite is proposed, which involves design variables, coupling variables and constraint functions. The analysis models of each subsystem are given, including the payload, attitude control, propulsion, power, and structure subsystem. The optimization is conducted by utilizing three MDO methods. Moreover the comparison among these methods is given to show the different features of these methods.

Design of the Reaction Flywheel System Based on Axial-flux Motor

To satisfy the requirements of miniaturization for attitude control unit in distributed small satellite system(DSSS),a reaction flywheel system based on axial-flux motor is presented.The three-dimensional distribution of air-gap magnetic field is analyzed by using the finite element method(FEM).A computational model for back-EMF of the motor is established based on the printed circuit board(PCB) winding.The multidisciplinary design optimization method is applied to optimize the main structure size of the flywheel rotor to minimize the weight of the flywheel system while meeting the requirements of strength,stiffness and the air-gap flux density under the premise of using sequential quadratic programming(NLPQL).The total mass of the flywheel rotor is decreased from 0.899 kg to 0.741 kg(namely reduced by 17.6%) after optimization.A flywheel prototype is designed based on the optimal results and the no-load performance is tested.The results show that the maximum error between the calculated and measured values of back-EMF is 9.7%,which verifies the correctness of the design method and provides an important reference in the miniaturization design of reaction flywheel system.

A gradient-based transformation method in multidisciplinary design optimization

Multidisciplinary design optimization (MDO) has become essential for solving the complex engineering design problems. The most common approach is to "divide and conquer" the MDO problem, that is, to decompose the complex problem into several sub-problems and to collect the local solutions to give a new design point for the original problem. In 1990s, researchers have developed some decomposition strategies to find or synthesize the optimal model of the optimization structure in order to evenly distribute the computational workloads to multiple processors. Several MDO methods, such as Collaborative Optimization (CO) and Analytical Target Cascading (ATC), were then developed to solve the decomposed sub-problems and coordinate the coupling variables among them to find the optimal solution. However, both the synthesis of the decomposition structure and the coordination of the coupling variables require additional function evaluations, in terms of evaluating the functional dependency between each sub-problem and determining the proper weighting coefficients between each coupling functions respectively. In this paper, a new divide-and-conquer strategy, Gradient-based Transformation Method (GTM), is proposed to overcome the challenges in structure synthesis and variable coordination. The proposed method first decomposes the MDO problem into several sub-systems and distributes one constraint from the original problem to each sub-system without evaluating the dependency between each sub-system. Each sub-system is then transformed to the single-variate coordinate along the gradient direction of the constraint. The total function evaluations equal the number of constraints times the number of variables plus one in every iteration. Due to the monotonicity characteristics of the transformed sub-problems, they are efficiently solved by Monotonicity Analyses without any additional function evaluations. Two coordination principles are proposed to determine the significances of the responses based on the feasibility and activity conditions of every sub-problem and to find the new design point at the average point of the most significant responses. The coordination principles are capable of finding the optimal solution in the convex feasible space bounded by the linearized sub-system constraints without additional function evaluations. The optimization processes continue until the convergence criterion is satisfied. The numerical examples show that the proposed methodology is capable of effectively and efficiently finding the optimal solutions of MDO problems.