Multi-objective Structural Optimization Research Articles

Response surface model and genetic algorithm-based multi-objective optimization of stator structures of hollow-type traveling wave ultrasonic motors

The stators of hollow-type traveling wave ultrasonic motors have certain problems stemming from their complex and hollow structures, significant differences between the two orthogonal modal frequencies, incomplete separation of the design model and interferential model, low-vibration amplitude, and significant localized inner stress during vibration, etc. In this paper, a dimensional parameterized finite elemental model for the motor was established by utilizing the finite elemental method. Afterwards, modal assurance criteria were used to identify the vibration models with various objectives for optimization established from this and integrating multiple objectives for optimization into a single optimization objective. Then a response surface model was established in the design space the Latin-hypercube random sampling method. Finally, a globally optimal solution was obtained according to the self-adaptive genetic algorithm and the response surface model. In order to prove the reasonableness of the optimized result, the stators are processed according to the sizes determined before and after the optimization. This paper describes the vibration of stators tested by a Doppler vibration tester. The Z-direction amplitude of the optimized stator changed from 1.0 µm to 2.5 µm. According to the testing results, the structural optimization plan used in this paper is reasonable and obviously helpful for vibration optimization of the stator.

Crash performance and multi-objective optimization of a gradual energy-absorbing structure for subway vehicles

To improve the crash performance of subway vehicles, this study presents an investigation of a newly designed gradual energy-absorbing structure subjected to impact loads using a test trolley for experimental and numerical simulations, as referenced in EN15227:2008. The structure is composed of a front-end beam, rear-end plate, outer-side beams, inner-side beams, cross beams and longitudinal beams. In this work, a finite element model (FEM) was established and effectively verified using experimental data. To evaluate the effect of the thicknesses of the longitudinal beams (t1), outer-side beams (t2) and inner-side beams (t3) on the energy absorption (EA) and peak crushing force (Fp), sensitivity study was performed using extreme difference (R) analysis. Then, a polynomial response surface method (PRSM) was employed to formulate the output responses of EA and Fp with the input parameters of t1, t2 and t3. In order to optimize the crash performance of the structure, a Non-dominated Sorting Genetic Algorithm (NSGA) was used in a multi-objective optimization to achieve the maximum EA and minimum Fp values. The optimal EA and Fp with the associated thickness parameters (t1, t2, and t3) of the gradual energy-absorbing structure were obtained in the form of Pareto fronts. Additionally, the Pareto solutions derived from the surrogate models of the quadratic, cubic and quartic polynomials eventually converge at intersection D (i.e., Fp=7.2940×103kN, EA=1.3511×103kJ).

Multidisciplinary Design Optimization of Crankshaft Structure Based on Cooptimization and Multi-Island Genetic Algorithm

The feasibility design method with multidisciplinary and multiobjective optimization is applied in the research of lightweight design and NVH performances of crankshaft in high-power marine reciprocating compressor. Opt-LHD is explored to obtain the experimental scheme and perform data sampling. The elliptical basis function neural network (EBFNN) model considering modal frequency, static strength, torsional vibration angular displacement, and lightweight design of crankshaft is built. Deterministic optimization and reliability optimization for lightweight design of crankshaft are operated separately. Multi-island genetic algorithm (MIGA) combined with multidisciplinary cooptimization method is used to carry out the multiobjective optimization of crankshaft structure. Pareto optimal set is obtained. Optimization results demonstrate that the reliability optimization which considers the uncertainties of production process can ensure product stability compared with deterministic optimization. The coupling and decoupling of structure mechanical properties, NVH, and lightweight design are considered during the multiobjective optimization of crankshaft structure. Designers can choose the optimization results according to their demands, which means the production development cycle and the costs can be significantly reduced.

Multiobjective Antenna Design By Means of Sequential Domain Patching

A simple yet robust methodology for rapid multiobjective design optimization of antenna structures has been presented. The key component of our approach is sequential domain patching of the design space, which is a stencil-based search that aims at creating a path that connects the extreme Pareto-optimal designs, obtained by means of single-objective optimization runs. The patching process yields the initial approximation of the Pareto set representing the best possible tradeoffs between conflicting design objectives. It is realized-for the sake of computational efficiency-at the level of coarse-discretization electromagnetic (EM) simulation model. The final Pareto front is subsequently obtained using surrogate-assisted optimization where the EM simulation data acquired at the initial design stage is reused.

Study on Multi-objective Optimization of Energy Structure in China Based on Improved Genetic Algorithm

Study on Multi-objective Optimization of Energy Structure in China Based on Improved Genetic Algorithm

Multi-objective structural robust optimization under stress criteria based on mixed plate super-elements and genetic algorithms

This paper presents a methodology for the multi-objective (MO) robust optimization of plate structures under stress criteria, based on Mixed Super-Elements (MSEs). The optimization is performed with a classical Genetic Algorithm (GA) method based on Pareto-optimal solutions. It considers antagonist objectives among them stress criteria and thickness parameters distributed along the plate. This work aims at providing fast and efficient objective calculations. Our method is based on the implementation of MSEs for each zone of the plate featured by its own thickness. They are constructed with a Mixed Finite Element Model (MFEM) based on a displacement-stress mechanical formulation, and is enhanced with a sub-structuring modal reduction method in order to reduce the size of each constant thickness MSE. Those methods combined enable a fast and stress-wise efficient structure analysis, which improves the performance of the repetitive GA. A few cases minimizing the mass and the maximum Von Mises stress within a plate structure under dynamic loads put forward the relevance of our method with promising results. For the sake of robustness, both discrete frequencies and frequency bands are studied. The MO optimization is able to satisfy multiple damage criteria with different thickness distributions. It brings simplicity, saves computational time and the Pareto-front presentation with stress objective provides a good overview of the possibilities for the designers.

Multi-objective geometry optimization of the Fish Bone Active Camber morphing airfoil

This work presents the development of a design optimization code for the geometry of the Fish Bone Active Camber morphing airfoil concept, which has been under development at Swansea University. This concept employs a biologically inspired architecture to provide highly anisotropic structural compliance, which creates smooth and continuous camber changes of large magnitude. Previous work has shown that this concept is capable of large lift coefficient control authority and significant reductions in drag over traditional trailing edge flaps. Further development of the concept requires a more robust design methodology that allows for an automated and thorough search of the available design space in order to optimize the aero-structural and system-level performance of the concept. To this end, this research extends a previously developed fluid–structure interaction analysis into a useful design tool by embedding it within a multi-objective structural optimization routine based on a genetic algorithm. The three objective functions of aerodynamic drag, added mass, and actuation energy are minimized concurrently. Example results from a specific operating condition are shown. Examination of the Pareto frontiers and the objective values of the population at large give insight into the structural behavior of the morphing concept. The objectives of mass and energy are found to be strongly competing, but good compromise points exist. The drag objective is found to be less sensitive than the others, with low drag being achievable across a range of designs with both low mass and low energy requirements, although the Pareto frontiers formed are not as well populated with regard to drag.

Multiobjective optimization of complex antenna structures using response surface models

A very efficient multiobjective (MO) design technique for complex antenna structures involving a large number of design parameters is presented. This design technique, multiobjective-fractional factorial design (MO-FFD), is very different from conventional Pareto-based MO algorithms, which take a great deal of effort to balance the trade-off between all the design specifications. By performing one single combination of simulations, all the response surface models of design goals are simultaneously built, and Derringer's desirability functions are readily applied to these models so that the optimum structure is obtained. Compared to classical MO algorithms such as Strength Pareto Evolutionary Algorithm 2, nondominated sorting particle swarm optimizer, and cultural MO particle swarm optimization, MO-FFD yields more desirable performances yet the required number of simulations is reduced by 97%. This article thoroughly illustrates the mathematical development of MO-FFD, deriving a novel application of ultrawideband (UWB) antennas because of its MO optimization capability. More explicitly, MO-FFD overcomes all the design challenges of dual band-notched UWB antennas including desired impedance characteristics, enhanced fidelity factors, and uniform peak gains over the passband, which are what conventional Pareto-based algorithms cannot attain. The measured results show that all the performance criteria are met; especially, the time-domain signal distortion is minimized. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:62–71, 2016.

Recent developments in simulation-driven multi-objective design of antennas

Abstract This paper addresses computationally feasible multi-objective optimization of antenna structures. We review two recent techniques that utilize the multi-objective evolutionary algorithm (MOEA) working with fast antenna replacement models (surrogates) constructed as Kriging interpolation of coarse-discretization electromagnetic (EM) simulation data. The initial set of Pareto-optimal designs is subsequently refined to elevate it to the high-fidelity EM simulation accuracy. In the first method, this is realized point-by-point through appropriate response correction techniques. In the second method, sparsely sampled high-fidelity simulation data is blended into the surrogate model using Co-kriging. Both methods are illustrated using two design examples: an ultra-wideband (UWB) monocone antenna and a planar Yagi-Uda antenna. Advantages and disadvantages of the methods are also discussed.

Derivative-Free Techniques for Multiobjective Structural Optimization: A Review

Derivative-Free Techniques for Multiobjective Structural Optimization: A Review

Aerodynamic shape optimization of civil structures: A CFD-enabled Kriging-based approach

In the case of mega-structures such as tall buildings and long-span bridges, the mitigation of the intensity of the wind excitation through aerodynamic tailoring of the external shape can be fundamental for meeting the performance goals. The search for the best performing shape through an automatic CFD-enabled optimization methodology is potentially less expensive, less time-consuming and more thorough than the common trial-and-error approach based on wind tunnel test results, therefore very attractive. This paper investigates the possibility of carrying out the multi-objective aerodynamic shape optimization of civil structures through an approach in which evolutionary algorithms are used in synergy with ordinary Kriging surrogates. A specifically developed strategy is adopted to update the Kriging models making efficient use of additional CFD runs. Shell scripting, parallelized computations and mesh morphing algorithms are exploited for enhancing the framework's efficiency and consistency. As a case study, the optimization of the shape of a tall building cross-section in terms of both the lift and the drag coefficient is considered.

Um algoritmo baseado em evolução diferencial para problemas de otimização estrutural multiobjetivo com restrições

Structural optimization problems aim at increasing the performance of the structure while decreasing its costs guaranteeing, however, the applicable safety requirements. As these aspects are conflicting, the formulation of the structural optimization problem as multiobjective is natural but uncommon, and has the advantage of presenting a diverse set of solutions to the decision maker(s). The literature shows that Evolutionary Algorithms (EAs) are effective to obtain solutions in multiobjective optimization problems, and that the Differential Evolution (DE) based ones are efficient when solving structural mono-objective structural optimization problems, specially those with a real encoding of the design variables. On the other hand, one can note that DE has not yet been applied to the multiobjective version of these problems. This article presents a performance analysis of a DE-based algorithm in five multiobjective structural optimization problems. The obtained results are compared to those found in the literature, and the comparisons indicate the potential of the proposed algorithm.

Multi-objective shape optimization of plate structure under stress criteria based on sub-structured mixed FEM and genetic algorithms

This paper presents a methodology for the multi-objective (MO) shape optimization of plate structure under stress criteria, based on a mixed Finite Element Model (FEM) enhanced with a sub-structuring method. The optimization is performed with a classical Genetic Algorithm (GA) method based on Pareto-optimal solutions and considers thickness distributions parameters and antagonist objectives among them stress criteria. We implement a displacement-stress Dynamic Mixed FEM (DM-FEM) for plate structure vibrations analysis. Such a model gives a privileged access to the stress within the plate structure compared to primal classical FEM, and features a linear dependence to the thickness parameters. A sub-structuring reduction method is also computed in order to reduce the size of the mixed FEM and split the given structure into smaller ones with their own thickness parameters. Those methods combined enable a fast and stress-wise efficient structure analysis, and improve the performance of the repetitive GA. A few cases of minimizing the mass and the maximum Von Mises stress within a plate structure under a dynamic load put forward the relevance of our method with promising results. It is able to satisfy multiple damage criteria with different thickness distributions, and use a smaller FEM.

Multi-Objective Structural Design Optimization using Fuzzy Optimization Programming based on T-Norm

In this paper we propose an approach to solve multi-objective structural design problem using basic t-norm based fuzzy optimization programming technique. Here a planer truss structural model in fuzzy environment has been developed. In this structural model formulation, the objective functions are the weight of the truss and the vertical deflection of loaded joint; the design variables are the cross-sections of the truss members; the constraints are the stresses in members. A classical truss optimization example is presented here in to demonstrate the efficiency of our propose optimization approach. The test problem includes a three-bar planar truss subjected to a single load condition. This approximation approach is used to solve this multi-objective structural optimization model. The model is illustrated with numerical examples.

Multi-objective Structural Optimization Using Fuzzy and Intuitionistic Fuzzy Optimization Technique

In this paper, we develop an intuitionistic fuzzy optimization (IFO) approach for optimizing the design of plane truss structure with multiple objectives subject to a specified set of constraints. In this optimum design formulation, the objective functions are the weight of the truss and the deflection of loaded joint; the design variables are the cross-sections of the truss members; the constraints are the stresses in members. A classical truss optimization example is presented here in to demonstrate the efficiency of the Intuitionistic fuzzy optimization approach. The test problem includes a three-bar planar truss subjected to a single load condition. This multi- objective structural optimization model is solved by fuzzy optimization approach as well as intuitionistic fuzzy optimization approach. Numerical example is given to illustrate our approach. The result shows that the IFO approach is very efficient in finding the best discovered optimal solutions..

A Hybrid Method for Structural System Reliability-Based Design Optimization and its Application to Trusses

Most research studies on structural optimum design have focused on single-objective optimization of deterministic structures, while little study has been carried out to address multi-objective optimization of random structures. Statistical parameters and redundancy allocation problems should be considered in structural optimization. In order to address these problems, this paper presents a hybrid method for structural system reliability-based design optimization (SRBDO) and applies it to trusses. The hybrid method integrates the concepts of the finite element method, radial basis function (RBF) neural networks, and genetic algorithms. The finite element method was used to compute structural responses under random loads. The RBF neural networks were employed to approximate structural responses for the purpose of replacing the structural limit state functions. The system reliabilities were calculated by Monte Carlo simulation method together with the trained RBF neural networks. The optimal parameters were obtained by genetic algorithms, where the system reliabilities were converted into penalty functions in order to address the constrained optimization. The hybrid method applied to trusses was demonstrated by two examples which were a typical 10-bar truss and a steel truss girder structure. Detailed discussions and parameter analysis for the failure sequences such as web-bucking failure and beam-bending failure in the SRBDO were given. This hybrid method provides a new idea for SRBDO of trusses. Copyright © 2015 John Wiley & Sons, Ltd.

Multi-Objective Design Optimization of Planar Yagi-Uda Antenna Using Physics-Based Surrogates and Rotational Design Space Reduction

A procedure for low-cost multi-objective design optimization of antenna structures is discussed. The major stages of the optimization process include: (i) an initial reduction of the search space aimed at identifying its relevant subset containing the Pareto-optimal design space, (ii) constructionusing sampled coarse-discretization electromagnetic (EM) simulation dataof the response surface approximation surrogate, (iii) surrogate optimization using a multi-objective evolutionary algorithm, and (iv) the Pareto front refinement. Our optimization procedure is demonstrated through the design of a planar quasi Yagi-Uda antenna. The final set of designs representing the best available trade-offs between conflicting objectives is obtained at a computational cost corresponding to about 172 evaluations of the high-fidelity EM antenna model.

Multi-Objective Evolutionary Optimization of Sandwich Structures: An Evaluation by Elitist Non-dominated Sorting Evolution Strategy

In this study, an application of evolutionary multi-objective optimization algorithms on the optimization of sandwich structures is presented. The solution strategy is known as Elitist Non-Dominated Sorting Evolution Strategy (ENSES) wherein Evolution Strategies (ES) as Evolutionary Algorithm (EA) in the elitist Non-dominated Sorting Genetic algorithm (NSGA-II) procedure. Evolutionary algorithm seems a compatible approach to resolve multi-objective optimization problems because it is inspired by natural evolution, which closely linked to Artificial Intelligence (AI) techniques and elitism has shown an important factor for improving evolutionary multi-objective search. In order to evaluate the notion of performance by ENSES, the well-known study case of sandwich structures are reconsidered. For Case 1, the goals of the multi-objective optimization are minimization of the deflection and the weight of the sandwich structures. The length, the core and skin thicknesses are the design variables of Case 1. For Case 2, the objective functions are the fabrication cost, the beam weight and the end deflection of the sandwich structures. There are four design variables i.e., the weld height, the weld length, the beam depth and the beam width in Case 2. Numerical results are presented in terms of Paretooptimal solutions for both evaluated cases.

W122002 構造最適化に多目的最適化は必要か?もし必要とすればどのような方法で可能となるか?

In this talk, I will discuss the idea of applying multiobjective optimization techniques to structural optimization. First, recent developments in structural optimization techniques are briefly reviewed in terms of their problem formulations and their applications. Next, the concept of multiobjective optimization to obtain a Pareto optimal solution set is introduced, and I'll show the potential requirements of multiobjective optimization in structural optimization problems for use in design processes, such as trade-off analysis. Finally, I'll briefly review multiobjective optimization techniques and discuss several of the features required in solvers applied in multiobjective structural optimization problems.

Intuitionistic Fuzzy Goal Programming Technique for Solving Non-Linear Multi-objective Structural Problem

This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.