Reliability‐based design optimization with equality constraints

Equality constraints have been well studied and widely used in deterministic optimization, but they have rarely been addressed in reliability‐based design optimization (RBDO). The inclusion of an equality constraint in RBDO results in dependency among random variables. Theoretically, one random variable can be substituted in terms of remaining random variables given an equality constraint; and the equality constraint can then be eliminated. However, in practice, eliminating an equality constraint may be difficult or impossible because of complexities such as coupling, recursion, high dimensionality, non‐linearity, implicit formats, and high computational costs. The objective of this work is to develop a methodology to model equality constraints and a numerical procedure to solve a RBDO problem with equality constraints. Equality constraints are classified into demand‐based type and physics‐based type. A sequential optimization and reliability analysis strategy is used to solve RBDO with physics‐based equality constraints. The first‐order reliability method is employed for reliability analysis. The proposed method is illustrated by a mathematical example and a two‐member frame design problem. Copyright © 2007 John Wiley & Sons, Ltd.     

A level set approach for topology optimization with local stress constraints

The purpose of this work is to present a level set‐based approach for the structural topology optimization problem of mass minimization submitted to local stress constraints. The main contributions are threefold. First, the inclusion of local stress constraints by means of an augmented Lagrangian approach within the level set context. Second, the proposition of a constraint procedure that accounts for a continuous activation/deactivation of a finite number of local stress constraints during the optimization sequence. Finally, the proposition of a logarithmic scaling of the level set normal velocity as an additional regularization technique in order to improve the minimization sequence. A set of benchmark tests in two dimensions achieving successful numerical results assesses the good behavior of the proposed method. In these examples, it is verified that the algorithm is able to identify stress concentrations and drive the design to a feasible local minimum. Copyright © 2014 John Wiley & Sons, Ltd.     

Truss optimization on shape and sizing with frequency constraints based on genetic algorithm

Truss optimization on shape and sizing with frequency constraints are highly nonlinear dynamic optimization problems. Coupling of two different types of design variables, nodal coordinates and cross-sectional areas, often lead to divergence while multiple frequency constraints often cause difficult dynamic sensitivity analysis. So optimal criteria method and mathematical programming, which need complex dynamic sensitivity and are easily trapped into the local optima, are difficult to solve the problems. To solve the truss shape and sizing optimization simply and effectively, a Niche Hybrid Genetic Algorithm (NHGA) is proposed. The objective of NHGA is to enhance the exploitation capacities while preventing the premature convergence simultaneously based on the new hybrid architecture. Niche techniques and adaptive parameter adjustment are used to maintain population diversity for preventing the premature convergence while simplex search is used to enhance the local search capacities of GAs. The proposed algorithm effectively alleviates premature convergence and improves weak exploitation capacities of GAs. Several typical truss optimization examples are employed to demonstrate the validity, availability and reliability of NHGA for solving shape and sizing optimization of trusses with multiple frequency constraints.     

放疗床多目标协调机构参数优化研究

随着精确放疗技术在肿瘤治疗中的广泛应用,放疗床的研发也受到人们越来越多的关注.为了达到使放疗床的工作空间和结构尺寸能够满足实际使用要求的目的,提出针对6-HTRT并联构型放疗床的一种多目标协调的机构参数优化方法.研究过程中首先对放疗床进行了运动学分析,结合运动学逆解约束条件,对双端虎克铰形式的并联放疗床进行工作空间的精确分析,并得到工作空间随各结构参数的变化规律,为放疗床的参数优化提供依据.其次,针对提高虎克铰强度及刚度问题,提出了一种虎克铰初始安装角度优化方法.之后考虑工作空间、放疗床受力、雅可比矩阵条件数,同时构建关于条件数全域均值、条件数波动情况的目标函数,对放疗床进行参数的具体优化.最终得到了放疗床各结构参数,经验证使得放疗床的雅可比矩阵条件数在工作空间内较小且分布均匀.由上述可知,所研究的放疗床多目标协调机构参数优化方法在一定范围内可以减小雅克比矩阵条件数,使经过参数优化后的放疗床得到合理的工作空间和结构尺寸,满足实际使用的要求.     

Soil parameter determination for deep excavation analysis by optimization

Abstract

This paper presents an efficient method of determining soil parameters for finite element analysis of deep excavation. Due to the limitation of soil tests, field measurements are often used to calibrate in‐situ soil properties. This process is time consuming and computationally cumbersome. In this paper, nonlinear optimization techniques are applied to determine the unknown parameters of an objective function, which is defined as the sum of the square of differences between observed and predicted values. The convergence and stability of the optimization algorithm are confirmed by three well‐known mathematical functions and a hypothetical excavation case under varied ground conditions. Finally, a case study is presented to show the reliability of the proposed soil parameter determination procedure.     

An alternating optimization approach for mixed discrete non-linear programming

This article contributes to the development of the field of alternating optimization (AO) and general mixed discrete non-linear programming (MDNLP) by introducing a new decomposition algorithm (AO-MDNLP) based on the augmented Lagrangian multipliers method. In the proposed algorithm, an iterative solution strategy is proposed by transforming the constrained MDNLP problem into two unconstrained components or units; one solving for the discrete variables, and another for the continuous ones. Each unit focuses on minimizing a different set of variables while the other type is frozen. During optimizing each unit, the penalty parameters and multipliers are consecutively updated until the solution moves towards the feasible region. The two units take turns in evolving independently for a small number of cycles. The validity, robustness and effectiveness of the proposed algorithm are exemplified through some well known benchmark mixed discrete optimization problems.     

Constrained optimization using a multipoint type chaotic Lagrangian method with a coupling structure

This article proposes a new constrained optimization method using a multipoint type chaotic Lagrangian method that utilizes chaotic search trajectories generated by Lagrangian gradient dynamics with a coupling structure. In the proposed method, multiple search points autonomously implement global search using the chaotic search trajectory generated by the coupled Lagrangian gradient dynamics. These points are advected to elite points (which are chosen by considering their objective function values and their feasibility) by the coupling in order to explore promising regions intensively. In this way, the proposed method successfully provides diversification and intensification for constrained optimization problems. The effectiveness of the proposed method is confirmed through application to various types of benchmark problem, including the coil spring design problem, the benchmark problems used in the special session on constrained real parameter optimization in CEC2006, and a high-dimensional and multi-peaked constrained optimization problem.     

基于演化算法的带频率约束的桁架结构形状和尺寸优化

具有频率约束的桁架结构形状和尺寸优化设计是一个难度大的非线性动力优化问题。形状和尺寸变量的耦合通常导致收敛困难,而频率约束则使得动力灵敏度分析困难,传统的优化准则法和数学规划法难于求解。将单纯形算法、子空间变维技术、均匀变异有机融入郭涛算法,提出一种混合演化算法,避开繁琐的动力灵敏度分析,简单、有效地求解这类桁架形状和尺寸优化问题。典型的桁架算例验证了算法的有效性和可靠性。     

Groundwater optimization and parameter estimation by genetic algorithm and dual reciprocity boundary element method

Genetic algorithms have been applied with great success in a number of fields as a tool for optimization. This paper explores their application in the groundwater field. The dual reciprocity boundary element method with global interpolation functions is employed as the computational tool. Two optimization problems are investigated: a pumping management problem in a homogeneous aquifer, and a parameter estimation problem in a heterogeneous aquifer. The initial findings about the effectiveness of the algorithms are encouraging.     

Bi-level heat exchanger network synthesis with evolution method for structure optimization and memetic particle swarm optimization for parameter optimization

The synthesis of heat exchanger networks (HENs) is a complex problem because of the nonlinearity that results from the integer and continuous variables. Here, a bi-level algorithm for the optimal design of a HEN is proposed that attempts to optimize separately the integer and continuous variables on two levels. The master level is a problem-oriented evolution method generating new candidate HEN structures. The slave level is a memetic particle swarm optimization, an improved particle swarm optimization combined with a local search component, improvement of neighbourhood topologies and control parameter preference. The slave level minimizes the total annual cost (TAC) of a given structure received from the master level, and then sends this value back to the master level for structure evolution. The proposed bi-level method is applied to several cases taken from the literature, which demonstrate its reliable search ability in both structure space and continuous variable space and its ability to optimize the system, producing generally lower TACs than previously used methods.     

基于AFSA-SimpleMKL对振动筛建模及筛机优化

针对目前振动筛筛分性能差及筛分理论不完善,亟待建立筛机参数与筛分效率间综合数学模型来指导振动筛的设计.基于离散单元法(Discrete Element Method,DEM)的筛分仿真实验解决筛分过程的复杂性和筛分数据难获得等问题,用可调参数的振动筛对仿真实验进行验证.筛分效率与筛分参数之间的数学关系是一个复杂的非线性问题,由于传统的回归算法对筛分数学模型预测精度低,利用能有效解决小样本问题和基于统计学理论的简单多核支持向量机(Simple Multiple Kernel Learning,SimpleMKL)对仿真实验获得的数据建立回归模型.但其模型是多极值且不可微分的多参数大规模计算问题,借用鲁棒性强和全局收敛性好的人工鱼群优化算法(Artificial Fish Swarm Algorithm,AFSA)对由SimpleMKL建立的筛分回归模型进行参数寻优,得出筛机振动和结构参数:振幅为2.5mm,振动频率为22Hz,振动方向角为50°,筛孔大小为0.9mm,筛丝直径为0.4mm,筛面倾角为21.6°.提高了振动筛的筛分效率,为振动筛的设计和制造提供了新思路.     

不等式约束优化问题的Hestenes-Powell增广拉格朗日函数的精确性质

增广拉格朗日函数法是用无约束极小化技术求解约束优化问题的一类重要方法.本文对不等式约束优化问题的Hestenes-Powell增广拉格朗日函数(简记为HP-ALF)的精确性质作了详尽讨论.在适当的假设下,建立了原不等式约束优化问题的极小点和HP-ALF在原问题变量空间或者原问题变量空间与乘子变量空间的积空间上的无约束极小点之间的相互对应关系;获得了关于HP-ALF的精确性的许多新结果.本文给出的性质说明HP-ALF是一个连续可微的精确乘子罚函数,且用经典的乘子法可求得不等式约束优化问题的最优解和对应的拉格朗日乘子值.     

Hybrid evolutionary multi-objective optimization and analysis of machining operations

Evolutionary multi-objective optimization (EMO) has received significant attention in recent studies in engineering design and analysis due to its flexibility, wide-spread applicability and ability to find multiple trade-off solutions. Optimal machining parameter determination is an important matter for ensuring an efficient working of a machining process. In this article, the use of an EMO algorithm and a suitable local search procedure to optimize the machining parameters (cutting speed, feed and depth of cut) in turning operations is described. Thereafter, the efficiency of the proposed methodology is demonstrated through two case studies – one having two objectives and the other having three objectives. Then, EMO solutions are modified using a local search procedure to achieve a better convergence property. It has been demonstrated here that a proposed heuristics-based local search procedure in which the problem-specific heuristics are derived from an innovization study performed on the EMO solutions is a computationally faster approach than the original EMO procedure. The methodology adopted in this article can be used in other machining tasks or in other engineering design activities.     

Wind farm layout design optimization through multi-scenario decomposition with complementarity constraints

This article presents a multi-scenario decomposition with complementarity constraints approach to wind farm layout design to maximize wind energy production under region boundary and inter-turbine distance constraints. A complementarity formulation technique is introduced such that the wind farm layout design can be described with a continuously differentiable optimization model, and a multi-scenario decomposition approach is proposed to ensure efficient solution with local optimality. To combine global exploration and local optimization, a hybrid solution algorithm is presented, which combines the multi-scenario approach with a bi-objective genetic algorithm that maximizes energy production and minimizes constraint violations simultaneously. A numerical case study demonstrates the effectiveness of the proposed approach.     

基于粒子群算法的改进模态参数识别方法

针对一类多模态振动衰减信号的模态参数识别,结合奇异值分解(singular value decomposition,SVD)、解析模态分解(analytical mode decomposition,AMD)、自回归功率谱和粒子群优化(particle swarm optimization,PSO)算法,提出了一种改进...     

On parameter design optimization procedures

The Taguchi idea of parameter design has received considerable attention from statisticians and engineers. However, it is only recently that some of the underlying principles of his ideas have been clarified and other alternative procedures have been proposed. This paper reviews the currently available procedures for parameter design in terms of minimizing expected loss. Advantages and disadvantages of each procedure are discussed for the three types of performance characteristics, and guidelines are provided for the choice of an appropriate procedure for a given parameter design problem.     

基于ADAMS与CPSO算法的火炮结构参数优化设计研究

针对火炮动力学模型是多部件、强非线性的系统,直接在ADAMS环境下对火炮结构参数进行优化,可能存在实现难度大、迭代次数过多、优化效果不明显等问题,提出了基于ADAMS与CPSO算法相结合的火炮结构参数优化设计方法.在利用Pro/E与ADAMS建立火炮虚拟样机并进行仿真试验的基础上,采用混沌粒子群算法对火炮结构参数进行优化,从而获得火炮结构参数和炮口扰动优化结果.根据优化值与初始值的对比分析,证明了文中所提优化设计方法合理可行.     

Technologic parameter optimization of gas quenching process using response surface method

A step function model with time is presented in the paper, and an axisymmetric component is regarded as the study objective in this model. The heat transfer coefficient during the gas quenching process is described as a function of time in this model, and five design variables are selected to do the design of Box–Behnken experiment with five factors and three levels. The levels of design variables that attain from the result of Box–Behnken experiment design are regard as the technical parameters of gas quenching to simulate the gas quenching process using the FEM software developed in the paper. Some mathematical models of response surface are gained by the mixed regression method and response surface method. These mathematical models show the dependencies of distortion, surface average equivalent residual stress, standard deviation of equivalent residual stress, average surface hardness and standard deviation of surface hardness with respect to the design variables. The optimization model is presented with the distortion as the optimization objective, and the model is optimized with an upper limit, a lower limit and the constraint function by the non-linear method and the Lagrange multiplier method.     

A method for structural dynamic contact problems with friction and wear

A method for structural dynamic contact problems with friction and wear is suggested. The method is obtained by including wear in the non‐smooth contact dynamics method of Moreau. A comparison of the method to the discrete energy‐momentum method of Simo and Tarnow is also outlined briefly. The fully discrete equations are treated using the augmented Lagrangian approach, where a non‐smooth Newton method is used as the equation solver. Two two‐dimensional examples are solved by the method. It is investigated how solutions of contact, friction and wear are influenced by inertia. It is shown that the quasi‐static assumption might be questionable for solving contact problems with friction and wear. Copyright © 2003 John Wiley & Sons, Ltd.     

冗余约束多刚体系统摩擦碰撞问题的数值求解方法

针对冗余约束多刚体系统的摩擦碰撞问题,以牛顿恢复系数作为碰撞终止条件,以离散化的系统动力学方程和线性规划理论为基础,建立了相应的混合互补模型。为有效求解该模型,利用最小二乘法和线性化方法,将混合互补模型转化为标准的线性互补模型,用线性互补模型的求解算法进行数值求解。接着,提出一种直接投影修正算法对碰撞计算过程进行修正,有效防止了碰撞加剧约束违约的现象。最后,通过一个算例,验证了数值求解方法和修正算法的有效性。