混沌优化算法在土质边坡稳定性分析中的应用

确定边坡最危险滑动面并计算与之相对应的安全系数是边坡支护的重要任务。本文结合简化Bishop法,用一种新的智能优化算法——混沌优化算法来搜索全局最优解。该方法利用混沌运动本身具有遍历性、随机性、“规律性”等内在特点,能在一定范围内按其自身“规律”不重复地遍历所有状态,易于跳出局部最优解,具有很强的全局搜索能力。通过坡高为12.3m的某电厂三层土质边坡的典型算例分析,并和遗传算法、枚举法计算结果对比可知,计算结果超于一致,其差值接近于0,因此混沌优化算法能在很高精度下搜索到全局最优解,能很好地解决边坡稳定性分析中的优化问题。     

改进PSO算法在结构作动器位置优化中的应用

针对空间结构振动主动控制中的作动器位置优化问题, 提出了一种改进的粒子群(PSO) 优化方法, 以系统总能量为性能指标进行优化; 应用改进PSO方法对算例结构进行了计算, 并与其他算法的优化结果进行了对比; 结果表明: 几种优化方法计算结果相符; 且 PSO优化算法能更有效快速地解决复杂优化问题, 从而有效地进行结构的振动控制.     

两种高分辨率数值方法计算波前有非均匀流的变截面管内激波传播规律的比较

本文采用两种对间断解具有高分辨率的数值方法基于推广Riemann问题解的二阶Godunov型有限差分法和分裂算子的随机选取法,计算了微波在波前有非均匀定常流的一维变截面管道中的传播和波后流场特征,得到一致结果,用数值模拟方法揭示了这类运动的一些特殊规律。对比两种方法的计算过程和结果,可以看出,二阶Godunov型方法明显优于随机选取法。     

基于差分进化和RBF响应面的混合优化算法

针对气动优化等昂贵优化问题,提出了一种基于差分进化和RBF响应面的混合优化算法HSADE,该方法结合了差分进化算法的强全局寻优能力和RBF响应面方法的快速局部搜索能力,能够同时有效地提高算法的局部搜索效率和全局寻优能力.对各子算法中的策略和逻辑进行了多项改进,提出和应用了基于双败淘汰赛的竞赛赛制和参数自适应等改进策略.对HSADE使用多个典型算例进行了测试,并横向对比了NSGA-II,MOPSO和多目标差分进化算法.测试结果表明,在大多数问题中HSADE在以世代距离表征的局部搜索效率和以超体积比表征的全局寻优能力两项指标上都优于其他算法,证实了以上混合策略及算法改进的有效性.将该算法应用于一个翼型优化问题和一个二维超声速喷管膨胀面优化问题,并横向对比未经改良的差分进化算法DE和另一种混合算法NARSGA,结果表明在接近1 000次的函数评估下,HSADE能相对其他算法进一步对翼型减阻0.5 count,在喷管优化中HSADE得到的结果也好于其他两种算法,表明该方法具有较强工程应用价值.     

随机有限元分析的二级区域分解并行求解算法

采用蒙特卡罗模拟(MCS)和加权积分法对二维问题进行随机有限元分析。尽管MCS方法对任何有确定解的问题都具有求解精度高的优点,但由于求解所需的计算量巨大使其应用受到限制。利用并行求解技术可有效地处理这种密集型计算问题。基于有限元分裂对接法(FETI)的并行特性并利用预处理共轭梯度法(PCG)的求解高效性,结合整体子区域实现(GSI-PCG)和FETI法,提出二级求解算法,并在工作站机群上实现了数值算例。算例计算结果表明本文GSI(PCG)-FETI算法具有较高的并行加速比和并行效率,具有良好的性能,可有效地进行二维问题的随机有限元分析。     

工程结构优化的进化策略-高斯过程协同优化方法

针对采用仿生全局优化方法进行复杂工程结构优化时数值计算量浩大导致的计算代价过高的公开问题,将自适应协方差矩阵进化策略(CMAES)全局优化算法、高斯过程(GP)机器学习技术与有限元方法相结合,提出了基于自适应协方差矩阵进化策略-高斯过程协同优化算法(CMAES-GP)的结构优化方法。该方法利用全局寻优性好且寻优效率高的CMAES算法进行全局最优搜索,当搜索进入局部寻优阶段时,采用回归性能优秀的GP模型对适应度函数进行动态拟合,进而利用GP模型替代有限元分析进行个体适应度评价,以减小局部寻优阶段的有限元重分析次数,从而实现有效降低工程结构优化计算代价的目的。算例研究表明,与传统结构优化方法相比较,本文方法具有全局性好、计算效率高的优点。     

基于微分进化算法的深空轨道全局优化设计

针对多目标多任务的深空探测轨道设计问题,提出一种新的将探测目标、探测方式、探测顺序以及发射窗口同时作为优化变量, 并采用微分进化算法进行全局优化的设计方法. 使用该方法在只考虑太阳中心引力作用的二体模型下,基于圆锥曲线拼接法建立第三届全国深空轨道设计竞赛问题的优化模型并进行求解. 最后利用该方法求解ESA的ACT研究团队的深空探测任务算例并对结果进行对比分析. 结果表明, 提出的全局优化设计方法对解决多目标、多任务深空探测轨道优化设计问题是可行和有效的.      

基于优化算法的串联体系可靠度分析

结构体系的失效概率数学上可以表示为结构体系失效域上联合概率密度函数的积分，一般情况下很难直接积分求解。近几十年来，结构体系可靠度分析一直是可靠度领域的一个研究热点，人们提出许多方法，如：Monte—Carlo法、重要性抽样法与界限法和概率网络估算技术等，这些算法在求解精度、计算效率、收敛性和易使用性等方面是不同的。本文采用优化算法(改进的可行方向法、序列线性规划和序列二次规划法)进行串联体系可靠度分析，并且与其他算法(HL—RF法、Monte—Carlo法和重要性抽样法)的结果以及一些精确解进行了比较。结果表明，相对于其他算法，基于优化算法的可靠度分析适用性广，在收敛性和健实性等方面具有明显的优势。     

基于Kriging代理模型的两类全局优化算法比较

代理模型在结构优化领域中的应用逐渐增多。相对传统优化方法,代理模型方法在处理带有噪音或仿真模拟十分耗时的问题时有明显优势。加点准则是代理模型技术的一个关键,为了避免陷入局部最优解,加点准则需要同时考虑局部搜索(exploitation)和全局搜索(exploration)两部分并加以平衡。本文在Kriging代理模型基础上提出一种基于几何全局搜索的全局优化算法MSG(Multi-start Local Search with Geometrical Exploration),通过数值算例将其与基于不确定性全局搜索的有效全局优化算法EGO(Efficient Global Optimization)进行比较,研究了MSG算法参数的影响,并讨论了MSG与EGO各自的特点和适用范围。     

面向工程全局优化的混沌优化算法研究进展

近年来,基于混沌的初值敏感性、伪随机性、遍历性以及自相似分形等非线性动力学特性所发展的混沌优化方法,是一种有潜力的工程全局优化新工具,已广泛应用于科学与工程技术的各学科领域。根据混沌优化方法的发展历程,以算法基本思想和工程应用研究状况为重点,评述了混沌神经网络优化方法、第一类混合混沌优化算法(基于混沌搜索)、第二类混合混沌优化算法(混沌序列代替随机序列)以及混沌分形优化四种主要混沌优化算法。混沌映射最早被引入神经网络,发展了混沌神经网络优化方法,可解决复杂的组合优化等全局优化问题。遗传算法及粒子群等启发式随机算法虽具全局搜索能力,但易出现早熟并陷入局部最优。然后,出现了混沌搜索的概念,研究者将其嵌入启发式算法建立了第一类混合混沌优化算法,可有效克服原启发式算法早熟收敛的缺点。随后,利用混沌映射产生的混沌序列代替启发式算法中的随机参数形成了第二类混合混沌优化算法。混合混沌优化算法有益于实现快速全局收敛和提高计算精度。最后,利用混沌分形特性,从分形理论出发提出一类新颖的混沌分形优化算法,可搜索到优化问题的所有全局最优解。此外,对混沌优化算法研究的几个发展方向进行了展望,诸如加强混沌优化算法的参数设计、处理大规模优化、多目标优化问题以及使用代理模型等。     

A domain decomposition method for stochastic analysis of acoustic fields with hybrid and localized uncertainties

An efficient domain decomposition method (DDM) is proposed for the dynamic analysis of stochastic acoustic fields with hybrid and localized uncertainties. The hybrid and localized uncertainties refer to the parameters that are associated with local properties of the acoustic fields and meanwhile are subjected to different kinds of randomness. To take advantage of the locally distributed feature of uncertain parameters, the full acoustic domain is divided into several sub-domains, along with each localized uncertain parameter being assigned to one specific sub-domain. In each sub-domain, the deterministic Helmholtz equation is transformed to a weak integral form and the discretized governing equation is obtained by employing Chebyshev orthogonal polynomials as admissible functions. The random or interval perturbation technique is applied to the individual governing equation according to the respective uncertainty type, whereby the stochastic governing equation is established. The original acoustic field is eventually recovered by the introduction of penalty functions to impose sound pressure continuity on the interfaces of sub-domains, and the (intervals of) sound pressure, together with its expectation and variance, can be subsequently obtained. The accuracy and efficiency of the proposed method are verified in several numerical examples by comparisons with the results given by brute force Monte Carlo simulations, and the DDM-based independent way of modelling and analysis proves to be quite effective and flexible for uncertainty quantification in acoustic fields.     

面向工程全局优化的混沌优化算法研究进展Research advances of chaos optimization algorithms for engineering global optimization

近年来,基于混沌的初值敏感性、伪随机性、遍历性以及自相似分形等非线性动力学特性所发展的混沌优化方法,是一种有潜力的工程全局优化新工具,已广泛应用于科学与工程技术的各学科领域。根据混沌优化方法的发展历程,以算法基本思想和工程应用研究状况为重点,评述了混沌神经网络优化方法、第一类混合混沌优化算法（基于混沌搜索）、第二类混合混沌优化算法（混沌序列代替随机序列）以及混沌分形优化四种主要混沌优化算法。混沌映射最早被引入神经网络,发展了混沌神经网络优化方法,可解决复杂的组合优化等全局优化问题。遗传算法及粒子群等启发式随机算法虽具全局搜索能力,但易出现早熟并陷入局部最优。然后,出现了混沌搜索的概念,研究者将其嵌入启发式算法建立了第一类混合混沌优化算法,可有效克服原启发式算法早熟收敛的缺点。随后,利用混沌映射产生的混沌序列代替启发式算法中的随机参数形成了第二类混合混沌优化算法。混合混沌优化算法有益于实现快速全局收敛和提高计算精度。最后,利用混沌分形特性,从分形理论出发提出一类新颖的混沌分形优化算法,可搜索到优化问题的所有全局最优解。此外,对混沌优化算法研究的几个发展方向进行了展望,诸如加强混沌优化算法的参数设计、处理大规模优化、多目标优化问题以及使用代理模型等。     

基于遗传算法的低压液压管路模型参数识别

为了合理预测伴随气泡和气穴的低压液压管路压力瞬态脉动,提出了用改进遗传算法对低压液压管路压力瞬态脉动模型进行参数辨识的新方法.给出了用来描述管路流动特性的瞬态脉动数学模型,建立了用来计算伴随气泡和气穴的液压管路瞬态下气泡体积和气穴体积的数学模型.构造了基于最小二乘法的适应度模型,探讨了遗传操作方式及算法终止准则,采用了算术交叉同线性逼近相结合的改进算术交叉算子进行交叉操作,给出了模型参数寻优的算法流程.实现了对低压液压管路压力瞬态脉动数学模型的参数识别,得到了参数优化后的低压液压管路压力瞬态脉动模型.仿真结果与实验数据的比较表明在低压液压管路瞬态模型中,用改进遗传算法来识别模型中的未知参数的方法是可行的、有效的.     

演化算法求解桁架多目标拓扑优化的收敛速度研究

演化算法能够同时满足结构拓扑优化的前沿领域对全局优化、黑箱函数优化、组合优化和多目标优化的需求,但采用此类算法的可行性与必要性由其收敛性与计算效率决定。本文以应力约束桁架多目标拓扑优化问题为求解对象,致力于揭示在收敛性与计算效率两方面具有竞争力的算法。首先提出评估演化算法求解拓扑优化问题收敛性与计算效率的通用方法,采用穷举法严格推导了典型桁架多目标拓扑优化问题的全局最优解,并采用超体积指标定义了多层次收敛性能准则。最后通过比较研究得到不同收敛性需求下具有最快收敛速度的演化算法,并揭示了具有竞争力的算法机制。本研究为演化算法求解多目标拓扑优化问题的收敛速度奠定了理论基础,同时为高效求解实际工程拓扑优化问题提供算法支持。     

Hybrid genetic algorithms and artificial neural networks for complex design optimization in CFD

The present paper is devoted to the study of design optimization strategies in the particular framework of complex computational fluid dynamics. Genetic algorithms are chosen as the optimization strategy, thanks to their robustness and flexibility. Two ways are explored to improve the behaviour of genetic algorithms in order to increase the efficiency of the search. First, approximated pre‐evaluations based on artificial neural networks are used to benefit from the knowledge acquired from the problem and to reduce the number of expensive evaluations by the flow solver required at each generation. Then, a hybridization technique is proposed for the final local search, which is performed by a deterministic method. These approaches are validated and applied on two‐ and three‐dimensional problems, involving Reynolds‐averaged Navier–Stokes computations with near‐wall turbulence modeling. Copyright © 2004 John Wiley & Sons, Ltd.     

Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

     

Dynamic 3D axisymmetric problems in continuously non-homogeneous piezoelectric solids

The meshless local Petrov-Galerkin (MLPG) method is used to analyze transient dynamic problems in 3D axisymmetric piezoelectric solids with continuously inhomogeneous material properties. Both mechanical and thermal loads are considered here. A 3D axisymmetric body is created by rotation of a cross section around an axis of symmetry. Axial symmetry of geometry and boundary conditions reduces the original 3D boundary value problem into a 2D problem. The cross section is covered by small circular sub-domains surrounding nodes randomly spread over the analyzed domain. A unit step function is chosen as test function, in order to derive local integral equations on the boundaries of the chosen sub-domains, called local boundary integral equations (LBIE). These integral formulations are either based on the Laplace transform technique or the time-difference approach. The local integral equations are non-singular and take a very simple form, despite of inhomogeneous and anisotropic material behaviour across the analyzed structure. Spatial variation of all physical fields (or of their Laplace transforms) at discrete time instants are approximated on the local boundary and in the interior of the sub-domain by means of the moving least-squares (MLS) method. The Stehfest algorithm is applied for the numerical Laplace inversion, in order to retrieve the time-dependent solutions.     

Multi-swingby optimization of mission to Saturn using global optimization algorithms

Based on the trajectory design of a mission to Saturn, this paper discusses four different trajectories in various swingby cases. We assume a single impulse to be applied in each case when the spacecraft approaches a celestial body. Some optimal trajectories ofEJS, EMS, EVEJS and EVVEJS flying sequences are obtained using five global optimization algorithms： DE, PSO, DP, the hybrid algorithm PSODE and another hybrid algorithm, DPDE. DE is proved to be supe- rior to other non-hybrid algorithms in the trajectory optimi- zation problem. The hybrid algorithm of PSO and DE can improve the optimization performance of DE, which is vali- dated by the mission to Saturn with given swingby sequences. Finally, the optimization results of four different swingby sequences are compared with those of the ACT of ESA.     

Local and parallel finite element algorithms for time-dependent convection-diffusion equations

Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel proce- dures. Hence, these local and parallel algorithms only involve one small original problem on the coarse mesh and some correction problems on the local fine grid. One technical tool for the analysis is the local a priori estimates that are also obtained. Some numerical examples are given to support our theoretical analvsis.