离散复合形法的改进及应用研究

在工程设计中,复合形法是求解约束非线性规划的一种直接方法.它计算简单、适用性强,是解决工程技术问题的常用方法.通常情况下,复合形法多用于连续变量优化设计问题的求解,但在工程实际中还存在大量的离散变量优化问题.为此,我们在连续变量复合形算法的基础上,采用平均值舍入法获取离散点,并改进了复合形迭代过程和停机准则,使之成为一种能直接求解离散变量优化解的方法.几个典型工程离散变量优化设计算例的计算结果表明,我们提出的方法十分有效.     

模糊变量与随机变量组合时模糊可靠度计算方法研究

对现有的随机应力、模糊强度可靠度计算方法进行了系统的分析研究,将其分成模糊变量直接转化为随机变量、由模糊强度的隶属函数直接构造模糊失效事件的隶属函数、可能度法和实用计算法四类,根据模糊失效概率的属性又可分成定量计算法和模糊计算法两类;得到了在定量计算方法中,广义密度函数法与面积法等价,当量密度函数法与截集法等价,真正独立的主要方法为广义密度函数法、当量密度函数法和直接转化法三种等结果;对强度模糊隶属函数为线性、正态分布情况推导了有关公式;通过算例给出了各主要方法的计算结果,其值相差较大,因此,哪种方法更合理还必须作进一步研究。     

在高等数学中如何巧用变量代换法求解

在高等数学解题中,变量代换法是一种简单而重要的解题方法,对变量代换法在高等数学中各部分的应用做简单的总结,以方便学生在学习高等数学时会灵活运用"变量代换法"求解,提高学生的解题能力。     

混合离散变量模拟退火方法及其应用

基于海洋工程中存在的设计变量为离散型和连续型的混合离散变量的情况,探讨了一种优化设计问题的方法———混合离散模拟退火法.该方法相对常规模拟退火方法有一定改进并且针对混合离散变量进行了特定处理.实际算例计算表明,该方法可用于海洋工程优化设计中,其结果不需圆整,而且其解题可靠性和效率相当高.     

基于SA算法的行星齿轮减速器离散变量优化设计

考虑制造工艺要求,将所有设计变量均视为离散变量,包括一般离散变量和伪离散变量,并就这两种情况下状态产生函数的设计原理进行深入研究,解决了将模拟退火算法用于离散变量函数优化的关键技术问题,介绍了一种基于模拟退火算法的离散变量函数优化的新方法。行星齿轮传动中各齿轮的齿数受传动比条件、同轴条件和装配条件的限制而不能任意取值,齿轮的模数也要受国家标准的制约只能取一些离散值,用以数学规划理论为基础的经典约束优化方法求解效果很差,用基于模拟退火算法的离散变量优化设计方法则可以方便快捷地获得满足各方面要求的最优设计方案。     

新高阶多变量马尔可夫模型

本文提出了一种新高阶多变量马尔可夫模型,并对其收敛性进行了分析.给出了模型的参数估计方法.数值实验表明在预测精度方面新高阶多变量马尔可夫模型比高阶多变量马尔可夫模型更加有效.     

分数阶导数系统非平稳随机振动灵敏度分析的时域显式方法EI北大核心CSCD

分数阶导数模型是描述黏弹性材料本构关系的理想模型。进行了分数阶导数线性系统非平稳随机振动的灵敏度分析。建立分数阶导数系统动力响应的时域显式表达式;采用灵敏度分析的直接求导法或伴随变量法,推导系统动力响应灵敏度的时域显式表达式;提出分数阶导数系统响应统计矩灵敏度高效计算的时域显式方法。所提出的基于直接求导法和伴随变量法的时域显式方法,分别适用于少设计变量和多设计变量两种情况下的响应统计矩灵敏度分析。以非平稳地震激励下设置分数阶导数黏弹性阻尼器的层剪切结构为数值算例,验证了所提方法的计算精度和计算效率。     

闪光X光噪声图象的局部统计滤波

本文介绍一种噪声图象的滤波方法 ,它不需要先验的图象模型 ,而且也不会损伤边界和细小的细节 ,在相加性和相乘性噪声的情况下 ,计算与边界方向有关的子集的局部平均值和方差 ,相应地沿着边界方向的噪声就被去掉 ,同时对边界有一定的增强效果     

基于变量选择的电站燃煤锅炉NO_(x)排放浓度预估北大核心CSCD

针对电站燃煤锅炉NOx排放浓度存在测量迟延的情况,提出了基于互信息和长短期记忆神经网络相结合的电站燃煤锅炉NO_(x)排放浓度预测模型。首先,利用互信息计算出候选输入变量与输出变量NO_(x)浓度之间的延迟时间,并引入最大相关最小冗余算法,筛选出最优特征子集,将最优特征子集作为LSTM模型的输入,建立了锅炉NO_(x)排放浓度预测模型。仿真结果表明,所建模型的测试集均方根误差为4.626 mg/m^(3),平均绝对误差为3.836 mg/m^(3),与未经变量选择和未考虑时延的LSTM模型相比,预测精度显著提高。     

模糊结构有限元分析的一种新方法

本文利用信息熵的概念,将模糊变量转变为随机变量,将模糊结构视为随机结构进行处理,从而提出了模糊结构有限元分析的一种新方法。当模糊结构转换的随机变量处于小扰动情况下,利用摄动法得到有限元递归方程组,解之可以得到响应量的均值和方差。     

随机结构反应概率密度演化分析的切球选点法

发展了随机结构反应概率密度演化分析中随机参数空间的切球选点法。密度演化方法是一类直接获取随机结构动力反应概率密度函数及其演化过程的有效方法。在多个随机变量时，随机变量空间中的离散代表点选点规则直接关系到密度演化方法的精度和效率。本文构造了平面内等半径相切圆圆心分布定位的算法，以此为基础，建立了三维空间中等半径相切球球心坐标定位的计算公式。从而给出随机变量空间中的离散代表点及其赋得概率。计算表明，基于空间切球法的选点规则具有良好的精度和效率，在2个和3个随机变量情况下是较为理想的选点方法。     

Hybrid reliability analysis with uncertain statistical variables,sparse variables and interval variables

There are differences among sampling data and representation types of uncertain statistical variables, sparse variables and interval variables, which increase the complexity of structure reliability analysis. Therefore, a hybrid first order reliability analysis method considering the three types of uncertain variables is demonstrated in this article. First, distribution types and distribution parameters of sparse variables are identified and probabilistically estimated. Secondly, interval variables are transformed into probabilistic types using a uniformity approach. Thirdly, a unified hybrid reliability calculation method considering these uncertain variables simultaneously is demonstrated. The most probable point (MPP) is searched for using the first order reliability method, and then a linear approximation function of performance function is constructed in the neighbourhood of the MPP. Finally, the belief and plausibility measures of the reliability index are efficiently calculated using the theoretical analytical method. Three examples are investigated to demonstrate the effectiveness of the proposed method.     

Some properties of beta functions and the distribution for the product of independent beta random variables

Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this article we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration, the exact null density of Wilks’A for testing linear hypothesis in the real Gaussian case is derived. Furthermore, it will be shown that this method is applicable also to problems of a more general nature.     

Canonical Correlation Analysis of Formulation Optimization Experiments

Formulation optimization experiments are primarily composed of two groups of variables, a set of independent variables and a set of dependent variables. Simultaneous consideration of all the variables in a single analysis is desirable since it provides an opportunity to study the interrelationships of all variables, independent as well as dependent at the same time and imparts an in-depth insight into the entire system as a whole. A multivariate statistical analysis, known as canonical correlation analysis, has indeed this capability. In addition, the analysis has the capacity of extracting the maximum possible correlation, called canonical correlation, between the variables of the two sets. The larger the value of the canonical correlation (0.90 or above), the higher is the predictability of one set from the other set. The analysis produces two composite canonical functions, one for each set. They can be used to streamline the subsequent search process associated with the full-fledged optimization analysis. The analysis also has the cardinal property to rank-order the variables in each set according to their relative contributions to the canonical prediction function, and to delineate the most important variable in each set. This information can be useful in monitoring the future performance of the formulation in a time-and-cost effective manner and in selecting variables for future experiments. All the relevant features of the analysis have been depicted in this paper in the context of a mobile phase composition optimization experiment.     

计量抽样检查程序设计

计量抽样检查是对产品质量特性进行检查,以确定一批产品是否接收的统计方法。本文论述了不合格品率计量抽样方案的原理。给出了国家标准GB6378的程序,通过计算机处理和示例分析,说明这种方法的应用。     

Ordered Samples Control Charts for Ordinal Variables

The paper presents a new method for statistical process control when ordinal variables are involved. This is the case of a quality characteristic evaluated by an ordinal scale. The method allows a statistical analysis without exploiting an arbitrary numerical conversion of scale levels and without using the traditional sample synthesis operators (sample mean and variance). It consists of a different approach based on the use of a new sample scale obtained by ordering the original variable sample space according to some specific ‘dominance criteria’ fixed on the basis of the monitored process characteristics. Samples are directly reported on the chart and no distributional shape is assumed for the population (universe) of evaluations. Finally, a practical application of the method in the health sector is provided. Copyright © 2005 John Wiley & Sons, Ltd.     

AN INDEPENDENT VARIABLE CONTROLLED GREY FUZZY LINEAR PROGRAMMING APPROACH FOR WASTE FLOW ALLOCATION PLANNING

This paper proposes an independent variable controlled grey fuzzy linear programming (IVC-GFLP) approach to address uncertainty in optimization processes. The IVC-GFLP method improves upon established grey linear programming (GLP) and ordinary grey fuzzy linear programming (GFLP) methods by introducing independent control variables into model formulations. These variables enable the model to address the independent characteristics of constraint uncertainty well. In this paper, the IVC-GFLP approach is applied to a hypothetical case study of municipal solid waste management. Included comparisons between the IVC-GFLP and GLP/GFLP solutions indicate that the IVC-GFLP approach can provide more realistic and applicable solutions than its counterparts.     

Weak atomicity: A helpful notion in the construction of atomic shared variables

A new class of 1-writer shared variables, calledweakly atomic variables, is defined, and an elegant general method of constructing atomic variables from weakly atomic ones is presented in this paper. Four examples of atomic variable constructions that use this method are described. Two of these constructions are new. Weak atomicity provides an intermediate step between regularity and atomicity. In addition to enabling new constructions, this concept helps to derive simple correctness proofs of the constructions.     

Efficient Calculation of All Possible Regressions

When the number of contemplated independent variables in a regression analysis is reasonably small, an alternative to the use of step-wise procedures for selecting variables is to base the selection on the calculation of all possible regressions.

This paper describes efficient computational procedures for calculating all possible 2 ^{k ? 1} regressions of a dependentv ariable upon subsets of k independent variables, and provides efficiency comparisons among five different procedures.