Inverse modelling of multi-objective thermodynamically optimized turbojet engines using GMDH-type neural networks and evolutionary algorithms

A novel approach is presented in this article for obtaining inverse mapping of thermodynamically Pareto-optimized ideal turbojet engines using group method of data handling (GMDH)-type neural networks and evolutionary algorithms (EAs). EAs are used in two different aspects. Firstly, multi-objective EAs (non–dominated sorting genetic algorithm-II) with a new diversity preserving mechanism are used for Pareto-based optimization of the thermodynamic cycle of ideal turbojet engines considering four important conflicting thermodynamic objectives, namely, specific thrust ({ST}), specific fuel consumption ({SFC}), propulsive efficiency (η_p), and thermal efficiency (η_t). The best obtained Pareto front, as a result, is a data table representing data pairs of non-dominated vectors of design variables, which are Mach number and pressure ratio, and the corresponding four objective functions. Secondly, EAs and singular value decomposition are deployed simultaneously for optimal design of both connectivity configuration and the values of coefficients, respectively, involved in GMDH-type neural networks which are used for the inverse modelling of the input–output data table obtained as the best Pareto front. Therefore, two different polynomial relations among the four thermo-mechanical objectives and both Mach number and pressure ratio are searched using that Pareto front. The results obtained in this paper are very promising and show that such important relationships may exist and could be discovered using both multi-objective EAs and evolutionarily designed GMDH-type neural networks.     

Radial basis functional model for multi-objective sheet metal forming optimization

Fracture and wrinkling are two major defects in sheet metal forming and can be eliminated via an appropriate drawbead design. This article proposes to adopt a multi-objective particle swarm optimization (MOPSO) approach, which differs from traditional multi-objective optimization with construction of a single cost function. MOPSO shows a certain advantage over other single cost function or population-based algorithms. While radial basis function (RBF) has shown considerable promise in highly non-linear problems, there has been no report in sheet metal forming design. Here RBF is attempted to establish the metamodels for fracture and wrinkling criteria in sheet metal forming design. In this article, a sophisticated automobile inner stamping case is exemplified, which demonstrated that RBF provides a better surrogate accuracy and MOPSO is more effective than the other methods studied. The use of RBF driven MOPSO procedure significantly improved the formability and can be recommended for sheet metal process design.     

Design and analysis adaptivity in multiresolution topology optimization

Multiresolution topology optimization (MTO) methods involve decoupling of the design and analysis discretizations, such that a high-resolution design can be obtained at relatively low analysis costs. Recent studies have shown that the MTO method can be approximately 3 and 30 times faster than the traditional topology optimization method for two-dimensional (2D) and three-dimensional (3D) problems, respectively. To further exploit the potential of decoupling analysis and design, we propose a dp-adaptive MTO method, which involves locally increasing/decreasing the polynomial degree of the shape functions (p) and the design resolution (d). The adaptive refinement/coarsening is performed using a composite refinement indicator that includes criteria based on analysis error, presence of intermediate densities, as well as the occurrence of design artifacts referred to as QR-patterns. While standard MTO must rely on filtering to suppress QR-patterns, the proposed adaptive method ensures efficiently that these artifacts are suppressed in the final design, without sacrificing the design resolution. The applicability of the dp-adaptive MTO method is demonstrated on several 2D mechanical design problems. For all the cases, significant speedups in computational time are obtained. In particular for design problems involving low material volume fractions, speedups of up to a factor of 10 can be obtained over the conventional MTO method.     

Dual-mode nested search method for categorical uncertain multi-objective optimization

Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.     

基于速度交流的多种群多目标粒子群算法研究

为提高多目标优化算法的收敛精度和搜索性能,提出一种基于速度交流的多种群多目标粒子群算法。算法引入速度交流机制,将种群划分为多个子种群以实现速度信息共享,改善粒子单一搜索模式,提高算法的全局搜索能力。采用混沌映射优化惯性权重,提高粒子搜索遍历性和全局性,为降低算法在运行后期陷入局部最优Pareto前沿的可能性,对各个子种群执行不同的变异操作。将算法与NSGA-Ⅱ、SPEA2、AbYSS、MOPSO、SMPSO和GWASF-GA先进多目标优化算法进行对比,实验结果表明:该算法得到的解集具有更好的收敛性和分布性。     

飞机总体设计中的一种多目标鲁棒优化方法

 提出一种基于灵敏度的多目标鲁棒优化方法。针对各维设计变量存在扰动的情况,在原约束多目标优化模型上,附加偏差目标函数,并采用最差估计法对约束条件进行鲁棒可行性调整。采用全局敏度方程方法来计算目标函数和约束函数对设计变量的敏度,进而采用Pareto遗传算法搜索约束多目标优化问题的非劣解集,设计者可以根据不同的设计准则从中选择合适的设计点。将上述方法用于飞机总体参数优化设计,并与采用常规优化方法所得的优化结果进行了分析和比较。     

Pricing and location decisions in multi-objective facility location problem with M/M/m/k queuing systems

This article presents a new multi-objective model for a facility location problem with congestion and pricing policies. This model considers situations in which immobile service facilities are congested by a stochastic demand following M/M/m/k queues. The presented model belongs to the class of mixed-integer nonlinear programming models and NP-hard problems. To solve such a hard model, a new multi-objective optimization algorithm based on a vibration theory, namely multi-objective vibration damping optimization (MOVDO), is developed. In order to tune the algorithms parameters, the Taguchi approach using a response metric is implemented. The computational results are compared with those of the non-dominated ranking genetic algorithm and non-dominated sorting genetic algorithm. The outputs demonstrate the robustness of the proposed MOVDO in large-sized problems.     

Optimization of composite stiffened panels under mechanical and hygrothermal loads using neural networks and genetic algorithms

The present work develops an optimization procedure for a geometric design of a composite material stiffened panel with conventional stacking sequence using static analysis and hygrothermal effects. The procedure is based on a global approach strategy, composed by two steps: first, the response of the panel is obtained by a neural network system using the results of finite element analyses and, in a second step, a multi-objective optimization problem is solved using a genetic algorithm. The neural network implemented in the first step uses a sub-problem approach which allows to consider different temperature ranges. The compression load and relative humidity of the air are assumed to be constants throughout the considered temperature range.     

RDS-NSGA-II: a memetic algorithm for reference point based multi-objective optimization

Reference point based optimization offers tools for the effective treatment of preference based multi-objective optimization problems, e.g. when the decision-maker has a rough idea about the target objective values. For the numerical solution of such problems, specialized evolutionary strategies have become popular, despite their possible slow convergence rates. Hybridizing such evolutionary algorithms with local search techniques have been shown to produce faster and more reliable algorithms. In this article, the directed search (DS) method is adapted to the context of reference point optimization problems, making this variant, called RDS, a well-suited option for integration into evolutionary algorithms. Numerical results on academic test problems with up to five objectives demonstrate the benefit of the novel hybrid (i.e. the same approximation quality can be obtained more efficiently by the new algorithm), using the state-of-the-art algorithm R-NSGA-II for this coupling. This represents an advantage when treating costly-to-evaluate real-world engineering design problems.     

Multiobjective crashworthiness optimization design of functionally graded foam-filled tapered tube based on dynamic ensemble metamodel

Foam-filled thin-walled structures have recently gained attention with increasing interest due to their excellent energy absorption capacity. In this study, a new type of foam-filled thin-walled structure called as functionally graded foam-filled tapered tube (FGFTT) is proposed. FGFTT consists of graded density foam and thin-walled tapered tube. In order to investigate the energy absorption characteristics of FGFTTs, the numerical simulations for two kinds of FGFTTs subjected to axial dynamical loading are carried out by nonlinear finite element code LS-DYNA. In addition, a new kind of multiobjective crashworthiness optimization method employing the dynamic ensemble metamodeling method together with the multiobjective particle swarm optimization (MOPSO) algorithm is presented. This new kind of multiobjective crashworthiness optimization method is then used to implement the crashworthiness optimization design of FGFTTs. Meanwhile, the crashworthiness optimization designs of FGFTTs are implemented by using traditional multiobjective crashworthiness optimization method, which employs metamodels such as polynomial response surface (PRS), radial basis function (RBF), kriging (KRG), support vector regression (SVR) or the ensemble with the static design of experiment (DOE). Finally, by comparing the optimal designs of FGFTTs obtained by using the new multiobjective crashworthiness optimization method and the traditional one, the results show that the proposed new crashworthiness optimization method is more feasible.     

结构动力鲁棒优化设计方法综述

如何提高结构动力学性能的鲁棒性,以减小各种不确定性因素对设计结果的影响是当前学术界和工程界研究和关注的热点问题之一。该文阐述了结构动力鲁棒优化设计的基本概念,从基于Taguchi的方法、基于多目标优化的方法和基于响应面建模的方法三个方面对结构动力鲁棒优化设计的研究进行了综述。以双转子为例,从结构的动力响应要求出发,采用响应面建模、多目标优化的方法进行了设计并与采用Taguchi方法得到的结果进行比较。结果表明,基于响应面建模、多目标优化的方法能够获得多个具有鲁棒性的设计方案,在处理具有不确定性的结构动力学问题时有着很大的应用潜力。最后,对当前方法和后续研究内容作了简要总结和展望。     

Multi-objective robust optimization design of a front-end underframe structure for a high-speed train

A multi-objective robust design optimization of a front-end underframe structure for application in high-speed trains is proposed and the structural parameter uncertainty is considered. A finite element model of the structure is developed and verified by dynamic impact experiments. The sensitivity analysis demonstrates that the thicknesses of the centre sill have significant influences on structural crushing behaviours. The specific energy absorption and the initial peak crushing force (F_p) are taken as optimization objectives. Compared with the baseline structure, the 6-sigma robust design shows that the F_p and the structural mass are reduced by 54.86% and 13.06%, respectively, and the robust optimum is more reliable. The 6-sigma robust optimal solution has an efficient energy-absorbing capacity while satisfying the design constraint. Thus, 6-sigma robust optimization can be applied for high-speed trains.     

Multi-objective optimization of engineering systems using game theory and particle swarm optimization

This study proposes particle swarm optimization (PSO) based algorithms to solve multi-objective engineering optimization problems involving continuous, discrete and/or mixed design variables. The original PSO algorithm is modified to include dynamic maximum velocity function and bounce method to enhance the computational efficiency and solution accuracy. The algorithm uses a closest discrete approach (CDA) to solve optimization problems with discrete design variables. A modified game theory (MGT) approach, coupled with the modified PSO, is used to solve multi-objective optimization problems. A dynamic penalty function is used to handle constraints in the optimization problem. The methodologies proposed are illustrated by several engineering applications and the results obtained are compared with those reported in the literature.     

VIS: An artificial immune network for multi-objective optimization

The aim of this work is to propose and validate a novel multi-objective optimization algorithm based on the emulation of the behaviour of the immune system. The rationale of this work is that the artificial immune system has, in its elementary structure, the main features required by other multi-objective evolutionary algorithms described in the literature, such as diversity preservation, memory, adaptivity, and elitism. The proposed approach is compared with three multi-objective evolutionary algorithms that are representative of the state of the art in multi-objective optimization. Algorithms are tested on six standard problems (both unconstrained and constrained) and comparisons are carried out using three different metrics. Results show that the proposed approach has very good performances and can become a valid alternative to standard algorithms for solving multi-objective optimization problems.     

Multi-objective planning of a multiple geostationary spacecraft refuelling mission

The multi-objective optimization of multiple geostationary spacecraft refuelling is investigated in this article. A servicing spacecraft (SSc) and a propellant depot (PD), both parked initially in geostationary Earth orbit (GEO), are utilized to refuel multiple GEO targets of known propellant demand. The capacitated SSc is expected to rendezvous with fuel-deficient GEO targets or the PD for the purpose of refuelling or getting refuelled. The multiple geostationary spacecraft refuelling problem is treated as a multi-variable combinatorial optimization problem with the principal objective of minimizing the propellant consumption and the mission duration. A two-level optimization model is built, and the design variables are the refuelling order X, the refuelling time T and the binary decision variable S. The non-dominated sorting genetic algorithm is employed to solve the up-level optimization problem. For the low-level optimization, an exact algorithm is proposed. Finally, numerical simulations are presented to illustrate the effectiveness and validity of the proposed approach.     

卫生型离心泵水力性能的参数化研究

为给卫生型离心泵过流部件结构的优化设计提供依据,采用CFD分析软件Fluent对卫生型离心泵内部流场流动进行了数值模拟和水力性能的参数化分析.给出了建模和流场分析方法,分析了泵内流体速度和压力的分布特性,基于流动模拟结果预测了水力性能.性能预测结果与试验结果吻合较好.关键结构参数对水力性能影响的计算结果表明,叶轮轴向间隙、叶片宽度、叶轮与蜗壳直径比等参数均存在最优值.研究结果对卫生型离心泵的结构改进和性能提高具有参考价值.     

A novel evolutionary meta-heuristic for the multi-objective optimization of real-world water distribution networks

Genetic algorithms are currently one of the state-of-the-art meta-heuristic techniques for the optimization of large engineering systems such as the design and rehabilitation of water distribution networks. They are capable of finding near-optimal cost solutions to these problems given certain cost and hydraulic parameters. Recently, multi-objective genetic algorithms have become prevalent in the water industry due to the conflicting nature of these hydraulic and cost objectives. The Pareto-front of solutions can aid decision makers in the water industry as it provides a set of design solutions which can be examined by experienced engineers. However, multi-objective genetic algorithms tend to require a large number of objective function evaluations to arrive at an acceptable Pareto-front. This article investigates a novel hybrid cellular automaton and genetic approach to multi-objective optimization (known as CAMOGA). The proposed method is applied to two large, real-world networks taken from the UK water industry. The results show that the proposed cellular automaton approach can provide a good approximation of the Pareto-front with very few network simulations, and that CAMOGA outperforms the standard multi-objective genetic algorithm in terms of efficiency in discovering similar Pareto-fronts.     

Crushing analysis and multi-objective optimization design for bionic thin-walled structure

Thin-walled structure has gained increasing attention and been widely used in the field of mechanical engineering due to their extraordinary energy absorption capacity and light weight. In this paper, we introduced a new energy absorbed structure named as bionic thin-walled structure (BTS) based on the structural characteristics of horsetails. In this study, six kinds of BTSs with different cross-sectional configurations under lateral loading conditions were investigated using nonlinear finite element method through LS-DYNA. According to the numerical results, it can be found that the cell number, inner wall diameter and wall thickness of the BTS had significant effect on the crashworthiness of the structure. In order to obtain the optimal design among the six kinds of BTSs, the six BTSs were optimized using a metamodel-based multi-objective optimization method which was developed by employing polynomial regression (PR) metamodel and multi-objective particle swarm optimization (MOPSO) algorithm. In the optimization process, we aimed to achieve maximum value of specific energy absorption (SEA) and minimum value of maximum impact force (MIF). Meanwhile, we also optimized the traditional thin-walled structures, i.e., the circular and square tubes. Based on the comparison of the Pareto fronts obtained by the multi-objective optimizations, we found that the crashworthiness of the BTSs was better than that of the circular and square tubes and the best BTS among the six kinds of BTSs was different when the limit of MIF was different. And, the optimal designs of the BTSs were found to have excellent energy absorption capacity under lateral impact and could be used in the future vehicle body.     

Aging process optimization for a copper alloy considering hardness and electrical conductivity

A multi-objective optimization methodology for the aging process parameters is proposed which simultaneously considers the mechanical performance and the electrical conductivity. An optimal model of the aging processes for Cu–Cr–Zr–Mg is constructed using artificial neural networks and genetic algorithms. A supervised artificial neural network (ANN) to model the non-linear relationship between parameters of aging treatment and hardness and conductivity properties is considered for a Cu–Cr–Zr–Mg lead frame alloy. Based on the successfully trained ANN model, a genetic algorithm is adopted as the optimization scheme to optimize the input parameters. The result indicates that an artificial neural network combined with a genetic algorithm is effective for the multi-objective optimization of the aging process parameters.