比较函数

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。

We also introduce and compare different methods of parameters estimates and the methods of choosing the best Copula function.

对Copula函数参数估计的不同方法和最优Copula函数的选择方法进行了介绍和比较。

Three methods for the computation of the isotropic tensor function,spectral decomposition method,eigenprojection operator method and representation theorem method,are compared.Different approaches to calculate the eigenvalues and their corresponding eigenvectors are also discussed.As an example,the exponent tensor function is calculated.

对计算各向同性对称张量函数的3种方法(谱分解法、特征投影算子法和表示定理法)进行了分析比较，同时也对如何计算特征根与特征向量的技巧进行了探讨，并利用3种方法对指数张量函数进行了实例计算。

A new growth model is derived from the logarithmic function and the power law.

通过对幂函数和对数函数的比较分析，本文构建了新的词汇增长模型，并应用此模型推导出科技英语的理论词汇增长曲线及其95%双向置信区间。

They give accurate energies andoverlappings compared with the results of exact diagonalization in both field-free andmagnetic field conditions.

与精确对角化的结果相比较，试探波函数在无磁场和有磁场的情况下均能给出准确的能级，并且二者的波函数接近重合。

In the first four sections of this paper, these basic knowledge and calculational methods for the study of potential energy function are simply introduced. 9-parameter Murrell-Sorbie analytical potential energy function that can accurately describe especial potential energy function of diatomic molecule is obtained through calculations and analysis for the first time.

本文前面部分在简单介绍与分子势能函数研究相关基础理论知识和计算方法的基础上，通过计算、分析比较，首次得到了能够正确描述双原子分子特殊势能曲线的九参数Murrell-Sorbie解析势能函数。

Based on the comparison of fixing discount factor method with the parameter e-valuation method, the heterogeneity function method is presented to determine the discount factor .

在比较固定贴现因子法及参数评估法的基础上，提出了用异质偏好函数法来确定贴现因子，并用实际的数据库验证了异质偏好函数法确定贴现因子在消费者行为模型的适应性方面比前两种方法优越，还讨论了三种方法的使用原则。

During the phase of iris recognition, we put forward the match judgement evaluation function—energy junction factor diversity function, and contrast it with existed methods.

在虹膜识别阶段，我们提出了匹配判决评价函数——能量结点因子相异函数，并与现有方法比较。

Extended elliptic function expansion method is applied to construct the explicit exact solutions of the Zakharov Equation.

将改进的Jacobi椭圆函数展开法应用到Zakharov方程，比较方便地得到新的解析周期解(包含冲击波解、孤波解和双曲函数解)。这种方法也适用于其他非线性方程或方程组

Because the mathematical expressions of the software development process cost function are so complicated and Gamma function is usually applied in statistic theory, so we can deal with this kind of model easily.

由于软件开发中的过程成本函数一般具有比较复杂的数学形式，采用统计理论中常用的Gamma函数形式可以使得这种模型在数学上更为容易处理。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。