函数变量

PSO is a population-based optimization algorithm, which mimics the social behavior of animals in a flock. It makes use of individual and group memory to update each particle position allowing global and local search optimization. The objective function considered was the total weight of the structure subjected to stresses, displacements and forces constraints. The effects of the parameters were investigated as well and such combination of tuning parameters promote a better global search behavior avoiding premature convergence while rapidly converging to the optimal solution. Results showed the effectiveness of the proposed method by comparing with ANSYS Design Optimization Tool (zero-order method). The PSO with the tuning parameters makes it an ideal method for offshore wind turbines foundations optimization tasks.(2) A reliability analysis method for pile foundation bearing axial loads based PSOThe performance function of pile foundation's axially bearing capacity sometimes is nonlinear and complex, on the basis of geometric meaning of structural reliability index, an optimum model with PSO for structural reliability analysis under arbitrary random variables was established, The PSO algorithm is very efficient to solve global optimization problemsIts use in structural reliability field presents not only the advantage of its facility of implementation, but also the possibility to obtain the design point and the failure probability with a good accuracy. In addition, PSO is a zero order algorithm, for no derivative is necessary for its implementation.

本文的研究针对桩式海上风机基础结构的特点，在国内外有关研究成果的基础上对海上风机基础结构优化设计理论和可靠度方法一些相关问题进行了较为深入的研究，具体做了以下几个方面的工作：(1)基于粒子群优化的桩式海上风机基础确定性优化设计方法桩式海上风机基础的优化设计是一个复杂的、非线性约束的优化问题，针对传统的基于梯度信息的优化方法在处理非线性问题中易陷入局部最优解的问题，本文将一种耦合惩罚函数的PSO算法引入到海上风机基础结构概念设计中，PSO算法是从群体动物聚集觅食这一活动中受到启发而发展的，该算法利用个体和群体的信息共享不断改进自身的位置从而进行局部和全局最优搜索，本文中以桩和三脚架连接段直径及壁厚为设计变量，以基础总重量作为优化的目标函数，在给定的约束条件下建立了三脚架基础优化数学模型，另外本文还研究了PSO参数变化对结果的影响，协调的参数组合可以避免陷入早熟收敛而能够快速的获得全局的最优解，通过与ANSYS优化模块的计算结果比较验证了该方法的有效性，本方法为海上风机基础的确定性设计提供了一条有效的途径。

All sets of constraint function are the linear function of design variables and the feasible region is a convex set according to this formulation.

模型中所有的约束函数都是设计变量的线性函数，可行域是一个凸域。

The first level and the lower level both have their objective functions and constraint conditions, the objective function and constraint conditions of the first level not only have relations with the upper decision variable, but also depends on the optimal value of the lower level.

上层和下层各有目标函数和约束条件，上层问题的目标函数和约束条件，不仅与上层决策变量有关，而且还依赖于下层问题的最优解或最优值。

Chapter six presents such new concepts as margin utility contribution force, profit-risk exchange rate, state-expectation-variance utility function, long-term expectation-variance utility curve and optimal portfolio expansion curve. The state-expectation-variance analytical method is developed from the expectation-variance analytical method. The changing rate of profit-risk exchange rate to state variable is used to define and distinguish the decreasing, constant and increasing relative risk aversion. A decomposition formula about the margin contribution force of holding wealth to state-expectation-variance utility function is displayed. The decomposition formula demonstrates that the contribution force of investors' holding wealth to their utility is composed of the pure contribution force of holding wealth and the investment contribution force bronght about through investment portfolio.

第六章提出了边际效用贡献力、收益—风险替换率、状态—期望—方差效用函数、长期期望—方差效用曲线、最优证券组合扩展线等新概念；把期望—方差分析方法发展成状态—期望—方差分析方法；用收益—风险替换率对状态变量ω的变化率来定义和区分递减、定常、递增相对风险厌恶；获得了持有财富对状态—期望—方差效用函数的边际贡献力的分解式，该分解公式表明投资者的持有财富对他的效用的贡献力由持有财富本身的纯贡献力和持有财富通过投资证券组合所产生的投资贡献力所组成。

The approximation of field variable by RPIM is performed in a parameter domain. The shape function of RPIM possess Delta function's property.

该方法利用径向点插值方法，在参数域对每一个非样本点的支持域进行过点插值，构造出具有Delta函数性质的插值函数，能够实现参数域场变量的快速插值近似。

We get to the conclusion that the function set of DCRBFN is dense in a varible-decomposable function set. The result shows that DCRBFN has excellent approximation ability.

DCRBFN系统的逼近能力分析，我们得到DCRBFN的函数集在变量可分离函数集中稠密的结果，因此DCRBFN具有良好的逼近能力。

And had proven the essence of submit function on geo-technical material is under certain stress condition between the second deviator stress tensor invariant and the own attribute functional relation of materials.

证明了岩土类介质屈服函数的实质是在一定应力状态下偏应力张量第二不变量与材料自身属性之间的函数关系。

Based on the ICMmethod,the discrete topological optimization problem about spot-weld's existence or not is transformed into the continuous optimization problem on[0,1].The optimization model is founded with maximizing the structural stiffness as objective and structural strength as constraints.The problem of multi-objectives and multi-constraints is transformed into the problem of single-objective and single-constraint with the K-S function.The displacement and stress are transformed into the explicit function of design variables with the Response Surface Methodology.The optimization model is solved with Sequential Quadratic Program.

基于ICM（Independent Continuous Mapping，即独立、连续、映射）方法，将焊点有无的离散拓扑优化问题转化为[0，1]区间上的连续优化问题；建立了以结构刚度最大为目标、结构强度为约束的连续拓扑优化模型；采用K-S函数将多目标和多约束问题转化为单目标和单约束问题；运用响应面方法将位移和应力转化为设计变量的显式函数，采用序列二次规划方法求解优化模型。

The Mixed Discrete variable Complex Programming method is used to solute the mathematical model of oil pipeline.

该方法可以根据所求解问题的规模、目标函数和约束函数的形态和复杂程度，在运算过程中对所输出的信息进行人工干预或改变计算策略，把程序的机械运行和使用者的智慧融合在一起，有效灵活地解决离散变量约束非线性

In chapter 2 the strong deviation theorems for functions of series of discrete random variables are given. Here we construct a moment generating function and a convergent martingale .

本文第二章用矩母函数构造一收敛鞅，利用截尾法和单调函数的性质，证明了离散型随机变量序列泛函的强偏差定理。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。