3125 応答曲面近似・データマイニングを併用した高効率多目的ロバスト設計最適化(J03-1 解析・設計の高度化・最適化(1),J03 解析・設計の高度化・最適化)

A new approach for multi-objective robust design optimization was proposed and applied to a practical design problem with a large number of objective functions. The present approach is assisted by response surface approximation and visual data-mining, and resulted in two major gains regarding computational time and data interpretation. The Kriging model for response surface approximation can markedly reduce the computational time for predictions of robustness. In addition, the use of self-organizing maps as a data-mining technique allows visualization of complicated design information between optimality and robustness in a comprehensible two-dimensional form. Therefore, the extraction and interpretation of trade-off relationships between optimality and robustness of design, and also the location of sweet spots in the design space, can be performed in a comprehensive manner.

In this paper, a multi-objective optimization of a transonic axial fan to enhance aerodynamic stability has been conducted using three-dimensional Reynolds-Averaged Navier-Stokes equations, surrogate modeling and multi-objective genetic algorithm (MOGA). Hub radius and first rotor chord length of the axial fan were chosen as design variables for the optimization. Peak adiabatic efficiency of the axial fan and stall margin at 60% of the designed rotational speed, were used as objective functions. Latin Hypercube Sampling (LHS) method was used to select design points in the design space. The objective functions were formulated using the response surface approximation (RSA) model. Three LHS samples with different distributions of twelve design points were tested to study their effects on prediction accuracy of the RSA model and optimization results. MOGA with the RSA models based on the best LHS sample, was used to obtain the Pareto-optimal front. As a result of optimization, an improvement of 17.2% in the stall margin at 60% of the designed rotational speed and 2.96% in peak adiabatic efficiency were obtained compared to the reference design. It was also found that distribution of the design points generated by LHS affects the effectiveness of the surrogate-based optimization.

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

In this study, high efficient design tool is developed with several informatics approaches for Multidisciplinary Design Optimization (MDO) and knowledge discovery of supersonic wing design. In this design, Multi-Objective Genetic Algorithm (MOGA) is applied as an optimizer, while Kriging model is also used to reduce computational cost. To obtain the information of the design space, functional ANalysis Of VAriance (ANOVA) and Parallel Coordinate Plot (PCP) is applied. For Kriging model construction, 107 sample points are evaluated. This tool is applied to the multidisciplinary design problem of supersonic wing. The objective functions are to maximize lift to drag ratio and to minimize sonic boom intensity at supersonic cruise, and to minimize wing weight. According to the results, there are trade-off relationships among three objective functions. The ANOVA results indicate that the cambers of the wing section at the root and the kink have an influence on the lift to drag ratio, the inner wing sweep back angle affects the sonic boom intensity, and the camber of wing section at the kink and aspect ratio affect the wing weight. The design space information could be visualized quantitatively from the sampling results with PCP technique. Since the design space exploration using MOGA is carried out based on Kriging surrogate models, the proposed MDO process is effective in terms of computational cost.

The so-called Green Engine architectures are deeply investigated by the scientific community with the aim of reducing fuel consumption and noise emissions by 50%, and pollutants by 80%, environmental targets established by the Advisory Council for Aeronautical Research in Europe to be achieved by 2020. Low pressure turbine improvements will be important to increase the efficiency of the two most innovative propulsive architectures, the Geared Turbofan and the Open Rotor Engine. The low pressure turbine is released from the fan and can rotate at higher speed values, implying a reduction in fuel consumption. Due to a higher rotational speed, low pressure turbine disks design needs careful considerations due to their higher stress level and reduced burst limit. This paper presents a multi-objective hybrid optimization methodology designed to study high speed low pressure turbine disks. The presented study falls within the preliminary design phase, thus a code based on finite differences was used to perform an optimization study of high speed low pressure turbine disks. The objective functions of the constrained multi-objective optimization were the minimization of the disks weight and the maximization of the burst speed, and a hybrid approach was pursued to better investigate the design space and find the optimum. Then a surrogate-model-based hybrid optimization was conducted to reduce computational time while ensuring the analysis accuracy. A trade-off of most common approximation strategies was conducted. Distributed computing was used involving three national research centers, and parallel computing was adopted to spread the calculation tasks on local workstations. Numeric and Finite-Element-Methodology-based validations followed. This study provides an innovative approach to design such critical components by reducing disks weight by 15% and computational time by 30% if compared to traditional design methodologies. Furthermore, a good match between optimal solutions was found, thus justifying a surrogate-model-based-approach that led to further gains in computational time.

There are two general methods of robust design optimization (RDO) and reliability-based robust design optimization (RBRDO) for the optimal design of structures with non-deterministic variables. In the problem-solving process of both RDO and RBRDO, assessing the probabilistic constraints of the problem and the standard deviation of the structural responses is time-consuming and costly. In this study, by presenting a multi-step approach, for a probable optimal solution, the deterministic constraints are first investigated. Then the limit state functions related to probabilistic constraints are computed based on the mean value of random variables (in the RBRDO problem) and in the step of uncertainties effects simulation on the response of the structure, probabilistic constraints are evaluated (in the RBRDO problem). Designs that not meeting the deterministic constraints or in the unsafe area for the mean values of the random variables are not included in calculating the first and second terms of the objective function and reliability assessment. This leads to reduce the volume of calculations. The Monte Carlo simulation method is used to assess the probabilistic constraints, and the EVPS metaheuristic algorithm is used for the optimization process. Three benchmark trusses of 10, 25, and 72 bars were studied to assess the efficiency of the proposed approach. The first objective function in these problems was the mean weight of trusses and the second objective function was the standard deviation of the displacement of a specific node in a certain direction.

Multi-objective optimization of flexible pavement design from an environmental and economic perspective

Robust multi-objective optimization for sustainable design of distributed energy supply systems

The main concern of this research is to control traffic flow and monitor highways by installing wireless sensors. Therefore, a new multi-objective model is proposed to find the optimal location of wireless sensors along highways. The sensors are paired and each pair of sensors communicates and interacts with each other to receive information from passing cars. The speed estimation of the vehicles passing through this pair of sensors must have the minimum deviation from the actual speed that is obtained by an accurate measurement. This deviation is called measurement error, which is minimized in the first objective function. In this research when traffic jams happens, some sensors located in proper distance with enough energy, move into the traffic area to reduce the measurement error which is caused by traffic congestion. In fact, for each traffic area a new location problem should be solved to relocate sensors so that the maximum decrease in error rate happens. The second objective maximizes the error reduction resulted from sensors movement. In this paper, movement of sensors is considered based on the amount of solar energy stored in the sensor at that moment. Finally, the third objective function maximizes the benefits resulted from detecting the bottlenecks in highways. Since some parameters of the objective functions such as error rates, error reduction resulted from movement of sensors and benefits are uncertain, this research employs a multi-objective robust optimization approach which results in a traffic control plan which is less sensitive to the realization of uncertain parameters.

The data mining has been performed for the aerodynamic design optimization result of two-stage-to-orbit reusable launch vehicle flyback booster wing. Three data mining techniques were used such as self-organizing map, functional analysis of variance, and rough set theory. The optimization problem had four aerodynamic objective functions and 71 design variables regarding wing shape. The optimization obtained the result as the hypothetical design database with 302 all solutions including the 102 non-dominated solutions. Consequently, the knowledge in the design space was acquired regarding the correlation between objective functions, and the influence of the design variables to the objective function, for non-dominated and all evaluated solutions, respectively. The features of three data mining techniques were revealed. Although the combination among three techniques discovered detailed design knowledge, self-organizing map was especially a key technique for knowledge discovery. Moreover, design knowledge from all solutions conserved the information from non-dominated solutions. Data mining was essential to solve multi-objective optimization problem.

A preliminary design optimization approach of axial flow compressors is developed. Loss correlations associated with airfoil geometry are introduced to relax the stringent requirement for the designer to prescribe the stage efficiency. In face of the preliminary design complexity resulted from the large number of design variables together with their stringent variation ranges and multiple design goals, the multi-objective optimization algorithm is incorporated. With such a developed preliminary design optimization method, the design space can be then explored extensively and the optimum designs of both high level overall efficiency and wide stall margin can be readily achieved. The preliminary design optimization method is validated in two steps. Firstly, an existing 5-stage compressor is redesigned without optimization. The obtained geometries and flow parameters are compared to the existing data and a good consistency is achieved. Then, the redesigned compressor is used as initial design and optimized by the developed multi-objective preliminary design optimization method, and significant performance gains are obtained, which demonstrates the effectiveness of the developed optimization methods.

A computationally efficient technique for multiobjective design optimization of narrowband antennas is presented. In our approach, the corrected low-fidelity antenna model [obtained through coarse-discretization electromagnetic (EM) simulations] is enhanced using frequency scaling and response correction, sampled, and utilized to obtain a fast response surface approximation (RSA) antenna surrogate. The RSA model is constructed in the reduced design space. The initial set of Pareto-optimal designs is then utilized to confine the design space further by identifying designs that satisfy minimum requirements with respect to antenna reflection response. The updated RSA model set up in the confined space is subsequently optimized to yield the final Pareto set at the low computational cost.

Purpose This paper aims to investigate different multi-objective optimization (MOO) approaches for design and control of electromagnetic devices. The main goal of MOO is to find the set of design variables or control parameters which will provide the best possible values of typical conflicting objective functions. Design/methodology/approach In the research studies, standard genetic algorithm (GA), non-dominated sorting GA (NSGA-II), migration NSGA algorithm and alternance method of optimal control theory are discussed and compared. Findings The test practical problems of multi-criteria optimization of induction heating processes with respect to chosen quality criteria confirm the effectiveness of application of considered MOO approaches both for the problems of design and control. Originality/value This paper represents and investigates different MOO approaches for design and control of electrotechnological systems.

This paper addresses the critical issue of effectiveness, efficiency, and reliability in simulation-based design optimization under surrogate model uncertainty. Specifically, it presents a novel method to build surrogate models iteratively with sufficient fidelity for accurately capturing global optimal design solutions at a minimal cost. The salient feature of the proposed method lies in its unique preference of focusing necessarily high fidelity at potential global optimal regions of surrogate models. The proposed method is the synergic integration of the multiple preference point method, which updates surrogate model at current local optimal points predicted with data-mining techniques in genetic algorithm setup, and the maximum variance point method, which updates surrogate model at the point associated with the maximum prediction variance. Through illustrative comparison studies on thirty different optimization scenarios derived from 15 different test functions, the proposed method demonstrates the tangible reliability advancement. The experimental results indicate that the proposed method can be a reliable updating method in surrogate-model-based design optimization for efficiently locating the global optimal point/points in various kinds of optimization scenarios featured by single/multiple global optimal point/points that may exist at the corners of design space, inside design space, or on the boundaries of design space.

By having accurate knowledge of the magnetic field distribution and the thrust calculation in linear synchronous motors, assessing the performance and optimization of the motor design are possible. In this paper, after carrying out a performance analysis of a single-sided wound secondary linear synchronous motor by varying the motor design parameters in a layer model and a d-q model, machine single- and multi-objective design optimizations are carried out to improve the thrust density of the motor based on the motor weight and the motor efficiency multiplied by its power factor by defining various objective functions including a flexible objective function. A genetic algorithm is employed to search for the optimal design. The results confirm that an overall improvement in the thrust mean, efficiency multiplied by the power factor, and thrust to the motor weight ratio are obtained. Several design conclusions are drawn from the motor analysis and the design optimization. Finally, a finite element analysis is employed to evaluate the effectiveness of the employed machine models and the proposed optimization method.