稀疏偏最小二乘回归-多项式混沌展开代理模型方法EI北大核心CSCD

为解决传统多项式混沌展开方法在高维全局灵敏度和结构可靠度分析当中存在的维数灾难与多重共线性问题,该文提出一种稀疏偏最小二乘回归-多项式混沌展开代理模型方法。该方法首先采用偏最小二乘回归技术得到多项式混沌展开系数的初步估计,然后根据回归误差阈值允许下的最大稀疏度原则,采用带有惩罚的矩阵分解技术自适应地保留与结构响应相关性强的多项式,并采用偏最小二乘回归得到多项式混沌展开系数的更新估计。通过对展开系数进行简单后处理即可得到Sobol灵敏度指数。在此基础上保留重要输入变量并按新方法重新进行回归可实现对代理模型的精简,从而在不增加计算代价的情况下实现高精度结构可靠度分析。算例结果表明在保证精度的情况下,采用新方法进行全局灵敏度和结构可靠度分析比传统方法在计算效率方面有显著优势。     

基于修正混沌控制的一次二阶矩可靠度算法

在结构可靠度指标的求解中,HL-RF迭代算法由于其格式简单,效率高被广泛应用到一次二阶矩计算中。然而该方法仅适用于功能函数非线性程度低的情况,当功能函数非线性程度较高时,HL-RF算法常会出现混沌、振荡和周期解的现象,甚至导致不收敛。该文在混沌控制理论的基础上提出了一种新的修正的混沌控制算法来控制迭代过程中产生的振荡。该方法在保留基于混沌控制方法稳健性的同时提高了计算效率,并对迭代过程中振荡现象引入了一种新的判据。当迭代过程逐渐收敛到最可能失效点时,采用经典的HL-RF算法;当检测到振荡时,采用基于修正混沌控制的迭代算法。算例结果表明:基于修正混沌控制的迭代算法能有效解决迭代中的振荡问题,与经典的HL-RF算法相比,该算法具备效率和稳健性方面的优势。     

稀疏偏最小二乘回归-多项式混沌展开代理模型方法

为解决传统多项式混沌展开方法在高维全局灵敏度和结构可靠度分析当中存在的维数灾难与多重共线性问题,该文提出一种稀疏偏最小二乘回归-多项式混沌展开代理模型方法。该方法首先采用偏最小二乘回归技术得到多项式混沌展开系数的初步估计,然后根据回归误差阈值允许下的最大稀疏度原则,采用带有惩罚的矩阵分解技术自适应地保留与结构响应相关性强的多项式,并采用偏最小二乘回归得到多项式混沌展开系数的更新估计。通过对展开系数进行简单后处理即可得到Sobol灵敏度指数。在此基础上保留重要输入变量并按新方法重新进行回归可实现对代理模型的精简,从而在不增加计算代价的情况下实现高精度结构可靠度分析。算例结果表明在保证精度的情况下,采用新方法进行全局灵敏度和结构可靠度分析比传统方法在计算效率方面有显著优势。     

归一化小波熵与RVM的滚动轴承运行可靠度预测

针对传统可靠度评估和预测方法难以实现对正在服役中的单台机械设备进行可靠度评估和预测的问题。设计了一种基于归一化小波包信息熵与相关向量机的滚动轴承运行可靠度预测方法;该方法主要包括确立运行可靠度指标以及构建相关向量机预测模型,通过试验测取滚动轴承运行过程中的振动信号,利用小波包分解,提取反映滚动轴承运行状态的特征频带能量,基于信息熵理论建立运行可靠度指标;构建相关向量机预测模型,准确预测正在服役中的滚动轴承运行可靠度指标及其变化趋势。试验结果表明,采用归一化小波包信息熵与相关向量机的可靠度预测模型,能有效克服传统基于概率统计数据的平均可靠度计算问题,并且相关向量机的可靠度预测精度更高。     

随机区间模糊混合参数结构可靠性分析

研究同时存在随机、区间、模糊变量的混合参数结构可靠性问题。利用广义密度函数法将模糊变量转化为当量随机变量,基于随机概率可靠性分析方法,获得概率可靠度指标表达式。考虑可靠度指标具有的区间性,利用区间数运算法则及区间截断法对所得可靠度指标区间进行计算、重置,获得混合参数结构可靠度区间表达。通过两算例验证该方法的可行性及有效性。     

锈蚀钢筋混凝土结构可靠度评估

钢筋锈蚀是混凝土结构破坏最主要的原因之一,目前钢筋混凝土结构可靠度研究大多数没有考虑锈蚀的影响。提出了锈蚀钢筋混凝土结构可靠度评估方法。首先分析大气环境下和氯离子环境下钢筋锈蚀的模型,然后考虑钢筋面积和粘结强度的降低,建立锈蚀钢筋混凝土结构抗力的随机模型,最后采用一次二阶矩实用分析法计算可靠度指标,以评估大气环境下和氯离子环境下混凝土结构可靠度。两个算例表明,该方法可用于锈蚀钢筋混凝土结构可靠度评估。     

基于响应面法和Morgenstern-Price法土坡可靠度计算方法

基于响应面法,建立了一种高效的边坡可靠度指标和失效概率近似计算方法。该法在构造响应面函数时,抽样点计算采用Morgenstern-Price法取代传统费时的有限单元法,大大降低了计算工作量。利用Monte-Carlo随机抽样原理,提出了一种能同时确定边坡最危险非圆弧滑动面和最小可靠度指标的随机搜索新算法。该文给出的两个算例验证了方法的实用性和可靠性,其计算结果同时表明:当分别以最小可靠度指标和最小中值安全系数为目标函数时,搜索到的边坡最危险滑动面相差较大。最后,探讨了土性指标(c,φ)的分布概型及相关性对边坡可靠度计算结果的影响。     

改进响应面法计算钢筋混凝土框架体系可靠度

钢筋混凝土框架结构体系可靠度是评定结构抗震性能的重要指标,也是对既有结构进行加固的评估基础。以框架底层柱端极限弯矩承载力作为参考变量可有效评估框架结构体系可靠度,该方法采用Pushover静力推覆分析,通过研究框架结构底层柱端极限弯矩承载能力对Pushover曲线的影响规律,由Pushover曲线上的基准点推广得到结构失效响应面,从而计算出结构体系可靠度。应用该方法对一榀钢筋混凝土框架进行了体系可靠度计算,计算结果与直接响应面法和蒙特卡洛法分析结果进行对比,结果表明,该方法计算快捷,且能够很好地评估出框架体系抗震可靠度。     

二次序列响应面法分析重力坝的动力可靠度

提出了用二次序列响应面法分析重力坝可靠度的方法。该方法用界面元法对重力坝进行确定性计算,在适当的区间内用统计的方法确定各变量的样本点,经过若干次重复计算,由界面元法的计算结果可以得到该结构的响应面函数,然后由这一函数算出重力坝可靠度的近似值。用同样方法可得第二、第三个响应面函数,并使可靠度计算结果逐渐达到良好的精度要求。这一方法与统计可靠度分析方法相比可以减少大量的计算工作量。对于包含混凝土特性和坝上游水位等随机变量的重力坝,本文用上述方法计算了一些关键时刻重力坝抗裂的动力可靠度,并据此分析了在整个地震过程中该坝抗裂可靠指标β（t）随时间t的变化规律。     

MTMD控制下随机结构的动力可靠度分析

考虑到实际工程结构的不确定性，基于遗传优化的神经网络响应面法，进行了MTMD控制下随机结构的动力可靠度分析，并对TMD及MTMD控制下结构的动力可靠度进行对比。该方法不仅具有传统神经网络响应面法的特性，而且引进了遗传算法的全局随机搜索的优点，可以精确地逼近随机结构的功能函数表达式，有效地减少用JC法求解可靠度指标的迭代次数，节省时间。算例分析表明了本文方法的有效性和准确性，对于随机结构，MTMD比TMD能更好地提高结构的动力可靠度。     

A time-variant reliability analysis method for structural systems based on stochastic process discretization

In this paper, we propose a new method for analyzing time-variant system reliability based on stochastic process discretization, which provides an effective tool for reliability design of many relatively complex structures considering the whole lifecycle. Within a design lifetime, the stochastic process is discretized into a series of random variables, and meanwhile, we can derive a time-invariant limit-state function in each time interval; the discretized random variables from the stochastic processes and the original random variables are transformed to the independent normal space, and a conventional time-invariant system reliability problem is derived through the linearization to each discretized limit-state functions; by solving this time-invariant system reliability problem, we can obtain the structural reliability or failure probability within the design lifetime. Finally, in this paper, we provide four numerical examples to verify the effectiveness of the method.     

Reliability analysis of structures based on a probability‐uncertainty hybrid model

The traditional reliability analysis method based on probabilistic method requires probability distributions of all the uncertain parameters. However, in practical applications, the distributions of some parameters may not be precisely known due to the lack of sufficient sample data. The probabilistic theory cannot directly measure the reliability of structures with epistemic uncertainty, ie, subjective randomness and fuzziness. Hence, a hybrid reliability analysis (HRA) problem will be caused when the aleatory and epistemic uncertainties coexist in a structure. In this paper, by combining the probability theory and the uncertainty theory into a chance theory, a probability‐uncertainty hybrid model is established, and a new quantification method based on the uncertain random variables for the structural reliability is presented in order to simultaneously satisfy the duality of random variables and the subadditivity of uncertain variables; then, a reliability index is explored based on the chance expected value and variance. Besides, the formulas of the chance theory‐based reliability and reliability index are derived to uniformly assess the reliability of structures under the hybrid aleatory and epistemic uncertainties. The numerical experiments illustrate the validity of the proposed method, and the results of the proposed method can provide a more accurate assessment of the structural system under the mixed uncertainties than the ones obtained separately from the probability theory and the uncertainty theory.     

用Lagrange乘子法求解结构可靠指标

本文用Ｌａｇｒａｎｇｅ乘子法把求解结构可靠指标的条件极值问题转化为无条件极值问题，对目前已被应用的迭代公式给出了理论证明；同时指出，对于随机变量为一般分布情况下的结构可靠指标的计算，把原来非正态分布随机变量用当量正态分布随机变量代替时，为了保证收敛，迭代过程中当量正态分布随机变量的均值和标准差必须有足够的精度。文中的几个算例表明，采用的计算方案具有较快的收敛速度和计算精度。     

自适应遗传算法用于机械零件的可靠性设计

目的　探索机械零件可靠性优化设计的一种新方法 .方法　在造价、体积、强度和重量等约束条件下 ,机械零件的可靠性优化设计问题是一个具有多局部极值、非线性及具有整数和实数变量的混合优化问题 .本文以发动机气门弹簧为例 ,应用遗传算法建立了机械零件可靠性优化设计的一种新方法 .结果　应用自适应遗传算法建立的新方法比常规优化方法更适合于并行处理优化计算 .结论　将自适应遗传算法用于机械零件的可靠性设计效果是明显的     

Reliability‐based topology optimization against geometric imperfections with random threshold model

This paper develops a new reliability‐based topology optimization framework considering spatially varying geometric uncertainties. Geometric imperfections arising from manufacturing errors are modeled with a random threshold model. The projection threshold is represented by a memoryless transformation of a Gaussian random field, which is then discretized by means of the expansion optimal linear estimation. The structural response and their sensitivities are evaluated with the polynomial chaos expansion, and the accuracy of the proposed method is verified by Monte Carlo simulations. The performance measure approach is adopted to tackle the reliability constraints in the reliability‐based topology optimization problem. The optimized designs obtained with the present method are compared with the deterministic solutions and the reliability‐based design considering random variables. Numerical examples demonstrate the efficiency of the proposed method.     

随机结构在随机载荷下的动力可靠度分析

提出了综合考虑动载荷和结构参数双重随机性的动力可靠度分析方法.首先基于随机振动的首次超越破坏准则,参照随机变量功能函数模式,建立了随机结构动力可靠度功能函数;然后引入序列响应面法,对功能函数进行拟合;最后用JC法求解可靠指标.算例分析验证了本文方法具有较好的计算精度和计算效率,尤其在复杂工程结构的动力可靠度分析中有广阔的应用前景.     

模糊可靠度隶属函数求解的迭代线抽样法

针对同时存在随机基本变量和模糊基本变量的结构,提出了一种模糊可靠度隶属函数求解的迭代线抽样方法.所提方法首先求得给定隶属度水平下模糊基本变量的取值域.然后通过优化建模和迭代策略,求得使功能函数取最值的模糊基本变量取值点,并求得对应的缩减后的随机变量空间内功能函数的设计点.最后基于功能函数最值对应的模糊基本变量取值点及其...     

A new reliability analysis method for uncertain structures with random and interval variables

In this paper, a new reliability analysis method is developed for uncertain structures with mixed uncertainty. In our problem, the uncertain parameters with sufficient information are treated by random distributions, while some ones with limited information can only be given variation intervals. A complex nesting optimization will be involved when using the existing methods to compute such a hybrid reliability, which will lead to extremely low efficiency or instable convergence performance. In this paper, an equivalent model is firstly created for the hybrid reliability, which is a conventional reliability analysis problem with only random variables. Thus only through computing the reliability of the equivalent model the original hybrid reliability can be easily evaluated. Based on the above equivalent model, an algorithm with high efficiency and robust convergence performance is then constructed for computation of the above hybrid reliability with both random and interval variables. Two numerical examples are provided to demonstrate the effectiveness of the present method.     

Reliability-based evaluation of automotive wind noise quality

This paper proposes an efficient method for the reliability analysis of a vehicle body–door subsystem with respect to an important quality issue—wind noise. A nonlinear seal model is constructed for the automotive wind noise problem and the limit state function is evaluated using finite element analysis. A multi-modal adaptive importance sampling (AIS) method is developed for reliability analysis at system level, to improve the efficiency of the Monte Carlo simulation. The method can easily handle implicit and time-dependent limit-state functions, with variables of any statistical distributions. Existing analytical as well as simulation-based methods are also investigated to solve the car door wind noise problem. It is demonstrated through this industrial application problem that the multi-modal AIS method is superior to existing methods in terms of efficiency and accuracy. A generalized framework for reliability estimation is then established for series system reliability problems with large numbers of random variables and complicated, implicit limit states.     

分数布朗运动环境下亚式期权定价的新方法

本文考虑分数布朗运动环境下几何平均型亚式期权定价问题,给出了一种基于可靠性数学思想的期权定价的新方法.首先,通过It5公式推导出亚式期权所满足的概率密度转移函数.其次,类比可靠性数学中求平均寿命的方法,用无套利定价方法给出了分数布朗运动环境下几何平均型亚式看涨期权定价公式.结果表明该方法同样适用于其它类型欧式期权.