随机法

Firstly, the article expatiates the concept of fuzzy reliability and the relation between random and fuzzy. It presents a list of random-finite element formula that is suitable for the reliability analysis for mechanical rigid frame system. Secondly, it presents two arrangements' reliability analysis methods that fit for component and fabric system. Finally, according to the characteristic of engineering mechanical, the article first brings forward half random-half fuzzy"stress-intensity intermeddle model"for mechanical intensity analysis, and according to Gerber equation for weariness intensity calculation, the article presents fuzzy number's calculating principle and the fuzzy reliability analysis method for engineering structure weariness intensity.

首先阐述了模糊可靠性概念、随机性与模糊性的关系；在导出摄动随机有限元法随机变量的变分原理、随机有限元控制方程和递归方程组基础上，给出了适合于工程机械刚架系统可靠性分析的随机有限元列式；给出了构件和结构体系两个层次的可靠性分析方法；根据工程机械的特点，首次提出机械强度分析的半随机半模糊"应力-强度干涉模型"，并依据疲劳强度计算的Gerber方程，给出了模糊强度的模糊数运算法则及工程结构疲劳强度模糊可靠性分析计算方法，该方法具有简便实用的特点和普遍意义。

In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis.

传统的最佳化演算法中迭代的计算和分析是确定的，与之相比，随机方法依靠随机过程和乱数字/向量的生成作为演算法和演算法分析的一部分。

Quasi Hamiltonian system; nonlinear stochastic optimal control; robustness; robust control; parametric uncertainty; uncertain disturbance; Bouc-Wen hysteretic system; Preisach hysteretic system; minimax optimal control; stochastic stabilization; stochastic averaging method; stochastic dynamical programming principle; stochastic differential game; maximal Lyapunov exponent

国家自然科学基金；拟Hamilton系统；非线性随机最优控制；鲁棒性；鲁棒控制；参数不确定性；不确定扰动； Bouc-Wen滞迟系统； Preisach滞迟系统；极小极大最优控制；随机稳定化；随机平均法；随机动态规划原理；随机微分对策；最大Lyapunov指数

The local averaging method is used to discretize the random field, correlated random variables are transformed to a set of uncorrelated normalized random variables, combining viscoelastic stochastic finite element method with H-L algorithm, the reliability of solid propellant grain is studied with different random parameters.

为了讨论各类随机因素对药柱结构可靠性的影响，采用局部平均法离散参数随机场，并通过相关结构分解成归一化的独立随机变量，将可靠度指标算法和粘弹性随机有限元法相结合，进行了固体推进剂药柱的结构可靠性分析。

The article first theoretically analyzes the principle that microcavity reduces threshold 、changes resonant modes of output light and enhances unidirection of the random laser.Then study the structure parameters of different microcavity by transfer matrix.Based on the theory of Maxwell equations and the rate equations, analyze the principle that microcavity reduces the threshold by FDTD method: Changing the confined position,reducing relaxation time and increasing reversing particles, also simultaneously study the influences of the threshold and output light modes by different microcavities and random intensity of random medium.

首先从理论上分析了利用微腔降低随机激光器阈值、改变出射光振荡模式、提高出射光准直性的原理，然后利用传输矩阵法模拟研究了不同的微腔应具有的结构参数，最后以麦克斯韦方程和速率方程理论为基础，利用时域有限差分法分析了利用微腔降低阈值的原理：改变局域化位置、缩短弛豫时间及增大粒子数反转，同时也模拟研究了微腔、随机介质的随机强度对阈值及出射光波模式的影响。

The FEM, whose process is very *** and is fit to deal with complex boundary condition, is used to simulate the frequency-domain IP. Studying the characters and laws of IP\'parameters under different measuring devices and undulate topography will provide scientific references and basis and reduce the multiplicities of interpretation. It is will be an attempt and exploration.Because of the frequency of the exciting currents is usually between 10-2～102 Hz, the vector A can be seen is not change with the time and the EM effect can be ignored in the low frequency.

双频以及伪随机三频激电法以它特有的轻便、快捷、高效率等特点在有色金属矿躲勘探领域里获得了广泛的应用，运用有限单元法的推导过程简单、适合处理复杂几何外形等特点来对双频以及伪随机三频激电法进行正演数值模拟，分析和研究了激电参数在不同丈量装置、模型参数和起伏地形情况下的特点和规律，为后续的资料解释提供科学的依据和参考，为减少地球物理中的多解性做一些有益的探索和尝试。

Pseudo-random multi-frequency signal is invented and named by academician He Jishan. The bandwidth of PRMF signal is controllable, it's energy concentrates on several frequencies, which are equally spaced on log scale coordinates. It is ideal excitation source for electrical exploration.

中文题名伪随机多频电磁法观测系统研究副题名外文题名 The study on pseudo-random multi-frequency electromagnetic prospecting system 论文作者陈儒军导师何继善学科专业地球探测与信息技术研究领域\研究方向学位级别博士学位授予单位中南大学学位授予日期2003 论文页码总数165页关键词电法勘探电磁法伪随机多频信号馆藏号BSLW /2003 /P631.3 /4 伪随机多频信号由何继善院士发明和命名，该信号带宽可控，其能量集中在数个在对数坐标上呈等间距分布的频率上，是电法勘探的理想场源。

Simulation results prove that symmetry algorithm is applicable for generating the long periodic hopping pattern used in valid data communications, while random shift replace algorithm is proper for the short periodic pattern with the good balance in the range of maximum effective length, and it can be used in the situations of short-cycle emergency communications.

仿真结果表明，对偶法在长周期条件下的性能优于随机平移法，适用于产生正常通信使用的调制跳变图案；随机平移法在最大有效周期长度范围内具有很好的均衡性，适用于短周期突发通信。

Throughout comparing the above estimating methods, we have the following results: the estimators of the moments of the errors does not depend on the random effects, and that of the random effects does not depend on the errors, and then the corresponding asymptotic variances are very simple and optimal; when the random effects are multivariate, we can not construct different estimating equations for the random effects and errors respectively, which results that the asymptotic covariances of estimation are very complex and then the estimating efficiency is bad.

比较上述两种估计法，我们发现：当随机效应是一维的时侯，误差的各阶矩的估计不依赖不可观测的随机效应，随机效应的估计也不依赖误差，因此，估计的渐近方差结构特别简单也是最优的；而当随机效应是多维的，因为随机效应的协变量的影响，我们没有办法针对随机效应和误差的各阶矩分别建立估计方程，这导致所得的估计的渐近方差或者协方差矩阵特别复杂，从而估计的效果不是很好。

In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis.

传统的最佳化演算法中迭代的计算和分析具有确定性，与之相比，随机方法依靠随机过程和乱数字/向量的生成作为演算法和演算法分析的一部分。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。