非线性隐式极限状态方程失效概率计算的组合响应面法

提出组合响应面的新方法,用以计算设计点附近非线性程度较大的隐式极限状态方程的失效概率。该方法用主响应面和多个次响应面近似对失效概率贡献较大的区域,其响应面函数形式为不含交叉的二次多项式。主响应面依据传统响应面法通过选择适当的插值点和迭代运算获得,其设计点为主设计点。延坐标轴正负方向偏移主设计点得到拟均值点。以拟均值点为基础得到一组次响应面和次设计点。通过主次响应面在各自设计点处的切平面建立组合响应面近似原隐式极限状态方程,并计算其失效概率。算例结果说明所提方法具有较高精度。     

基于支持向量机的非概率可靠性分析

针对具有隐式极限状态函数的不确定性结构的非概率可靠性分析,提出一种基于支持向量机回归的不确定性结构非概率可靠性分析方法,并给出了该方法的分析流程.抽取数据样本,优化支持向量机回归参数,使用训练后的支持向量机替代隐式极限状态函数.利用非概率集合理论中的区间分析法,引入尺寸比例因子,构造合适的不确定性结构非概率可靠性指标迭...     

基于切平面布点的一种改进响应面方法

基于合理选择试验点的位置,该文提出一种改进响应面方法。该方法首先在经过设计点的切平面上布置试验点,然后沿切平面法向量方向移动试验点,并利用设计点和先前试验点的信息布置加强试验点。所布置的试验点既对设计点附近区域给予足够重视,同时又考虑极限状态函数在设计点附近区域的变化趋势,进而提高响应面函数在设计点附近区域的拟合精度。在响应面函数的拟合过程中,该文方法能够保证响应面函数在设计点处是无误差的,进一步提高失效概率的评估精度。算例表明,对于显式和隐式极限状态函数,该方法均具有较好的效率和精度。     

基于马尔科夫链模拟的支持向量机可靠性分析方法

针对实际工程中可靠性分析设计的极限状态方程为隐式的情况,提出了一种基于马尔科夫链模拟的支持向量机可靠性分析方法.所提方法采用改进的马尔科夫链来产生极限状态重要区域上的样本点,再采用支持向量机方法求得相应的函数替代模型来进行可靠性分析.由于马尔科夫链能够自适应的模拟极限状态重要失效区域附近的样本,并且由于采用马尔科夫链备...     

结构非概率可靠性分析的支持向量机分类方法

利用支持向量机分类技术解决隐式极限状态结构的非概率可靠性问题。基于未确知信息的分段描述模型,设计了训练样本抽取策略,将基本变量区域中的样本等效转化为标准区间变量域中的样本,统一了尺度,有效保证了支持向量机训练的稳定性,并使蒙特卡洛模拟更易实现,有效解决了隐式极限状态结构的非概率可靠性分析问题。通过2 个算例对文中方法的精度和可行性进行了验证。     

基于ELM的可折支撑锁机构可靠性及其敏感度分析

 针对大多可靠性工程问题中机构极限状态函数为隐式的情况,提出了一种基于极限学习机（ELM）回归近似极限状态方程的可靠性及灵敏度分析的新方法.通过极限学习机与蒙特卡洛法相结合,利用极限学习机快速学习的能力,将复杂或隐式极限状态方程近似等价为显式极限状态方程,运用蒙特卡洛法计算出机构的失效概率,然后由高精度的显式极限状态方程进行各随机变量参数的灵敏度分析.该方法采用了基于单隐层前馈神经网络极限学习算法,因而在拟合非线性极限状态方程上表现优越,计算精度和效率高.最后以某型起落架中可折支撑锁机构为对象,进行了机构的可靠性及敏感度分析.结果表明：该方法具有高精度和高效率的优点,在工程应用上具有一定的价值．     

考虑状态模糊性时广义失效概率计算的矩方法

针对失效状态和安全状态具有模糊性的广义可靠性分析问题,提出了一种广义失效概率计算的矩方法。所提方法首先将广义失效概率的积分区域依据功能函数的取值离散化,在离散化的积分区域中,极限状态函数对模糊失效域的隶属函数近似保持为常数,从而将模糊可靠性问题转化为一般的随机可靠性问题,进而可以利用近似的矩方法求得广义失效概率。该文给出了所提方法的实现步骤和原理,算例结果表明所提方法对于中低维问题具有很高的精度和效率。     

基于频响函数截断奇异值响应面的有限元模型修正

考虑由于模型参数误差造成的有限元模型偏差的问题,提出一种基于频响函数截断奇异值响应面的模型修正方法。利用傅里叶反变换将结构频响函数变换为时域内的脉冲响应函数,通过延迟坐标法重构脉冲响应函数的相空间矩阵,进而对相空间矩阵进行截断奇异值分解,提取有限个较大的奇异值作为频响函数的特征量。以待修正模型参数为样本集输入,截断的奇异值为样本集输出,建立支持向量机响应面模型并进行训练,以逼近模型待修正参数与频响函数的特征量之间的非线性映射关系。以目标频响函数的特征量与支持向量机响应面模型输出的特征量之间的差值最小化为目标,利用遗传算法通过优化求解参数修正量。仿真计算表明:支持向量机的保留奇异值响应面能准确预报训练集以外样本的保留奇异值,具有较强的泛化能力;结合遗传优化算法能获得准确的参数修正量,算法对噪声有较强的鲁棒性。     

基于支持向量机的卫星动力学多目标优化

针对实际工程中优化大规模结构耗时长问题,采用支持向量机与遗传算法相结合的优化方法。基于支持向量机建立结构近似模型,代替耗时长的有限元分析并应用遗传算法进行结构优化,形成省时、精度高、适应性强的优化方法。以某卫星整星结构动力学多目标优化为例,建立支持向量机近似模型模拟卫星蜂窝板、碳纤维框架结构设计参数与加速度频率响应、应力响应等非线性映射关系,选用二阶响应面模型作对比。计算结果表明,支持向量机与遗传算法组合优化方法不仅能降低耗时成本,且具精度良好。     

柔性机构时变可靠性分析的时变随机响应面法

针对柔性机构极限状态函数的时变、非线性和隐式问题,提出了柔性机构时变可靠性分析的一种新响应面法——时变随机响应面法。将模态综合法与广义混沌多项式方法相结合,建立时变随机响应面,用以描述在随机参数和刚柔耦合影响下,系统响应随时间变化的规律,并得到系统响应的统计特征。与仅用混沌多项式拟合系统响应相比,提高了计算效率。建立系统运动可靠性的时变可靠性模型,给出了时变可靠度的蒙特卡罗计算方法。以两连杆柔性机械臂为例,对方法的有效性进行了验证,结果与蒙特卡罗法相比,具有较高的计算精度。     

A new artificial neural network-based response surface method for structural reliability analysis

This paper presents a new artificial neural network-(ANN)based response surface method in conjunction with the uniform design method for predicting failure probability of structures. The method involves the selection of training datasets for establishing an ANN model by the uniform design method, approximation of the limit state function by the trained ANN model and estimation of the failure probability using first-order reliability method (FORM). In the proposed method, the use of the uniform design method can improve the quality of the selected training datasets, leading to a better performance of the ANN model. As a result, the ANN dramatically reduces the number of required trained datasets, and shows a good ability to approximate the limit state function and then provides a less rigorous formulation in the context of FORM. Results of three numerical examples involving both structural and non-structural problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure. Compared with the conventional ANN-based response surface method, the proposed method is much more economical to achieve reasonable accuracy when dealing with problems where closed-form failure functions are not available or the estimated failure probability is extremely small. Finally, several important parameters in the proposed method are discussed.     

Enhanced high‐dimensional model representation for reliability analysis

This paper presents a new and alternative computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry based on high‐dimensional model representation (HDMR) generated from low‐order function components. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high‐dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher‐order variable correlations are weak, allowing the physical model to be captured by the lower‐order terms and facilitating lower‐dimensional approximation of the original high‐dimensional implicit limit state/performance function. When first‐order HDMR approximation of the original high‐dimensional implicit limit state/performance function is not adequate to provide the desired accuracy to the predicted failure probability, this paper presents an enhanced HDMR (eHDMR) method to represent the higher‐order terms of HDMR expansion by expressions similar to the lower‐order ones with monomial multipliers. The accuracy of the HDMR expansion can be significantly improved using preconditioning with a minimal number of additional input–output samples without directly invoking the determination of second‐ and higher‐order terms. The mathematical foundation of eHDMR is presented along with its applicability to approximate the original high‐dimensional implicit limit state/performance function for subsequent reliability analysis, given that conventional methods for reliability analysis are computationally demanding when applied in conjunction with complex finite element models. This study aims to assess how accurately and efficiently the eHDMR approximation technique can capture complex model output uncertainty. The limit state/performance function surrogate is constructed using moving least‐squares interpolation formula by component functions of eHDMR expansion. Once the approximate form of implicit response function is defined, the failure probability can be obtained by statistical simulation. Results of five numerical examples involving elementary mathematical functions and structural/solid‐mechanics problems indicate that the failure probability obtained using the eHDMR approximation method for implicit limit state/performance function, provides significant accuracy when compared with the conventional Monte Carlo method, while requiring fewer original model simulations. Copyright © 2008 John Wiley & Sons, Ltd.     

An optimization method for learning statistical classifiers in structural reliability

Monte Carlo simulation is a general and robust method for structural reliability analysis, affected by the serious efficiency problem consisting in the need of computing the limit state function a very large number of times. In order to reduce this computational effort the use of several kinds of solver surrogates has been proposed in the recent past. Proposals include the Response Surface Method (RSM), Neural Networks (NN), Support Vector Machines (SVM) and several other methods developed in the burgeoning field of Statistical Learning (SL). Many of these techniques can be employed either for function approximation (regression approach) or for pattern recognition (classification approach). This paper concerns the use of these devices for discriminating samples into safe and failure classes using the classification approach, because it constitutes the core of Monte Carlo simulation as applied to reliability analysis as such. Due to the flexibility of most SL methods, a critical step in their use is the generation of the learning population, as it affects the generalization capacity of the surrogate. To this end it is first demonstrated that the optimal population from the information viewpoint lies around in the vicinity of the limit state function. Next, an optimization method assuring a small as well as highly informative learning population is proposed on this basis. It consists in generating a small initial quasi-random population using Sobol sequence for triggering a Particle Swarm Optimization (PSO) performed over an iteration-dependent cost function defined in terms of the limit state function. The method is evaluated using SVM classifiers, but it can be readily applied also to other statistical classification techniques because the distinctive feature of the SVM, i.e. the margin band, is not actively used in the algorithm. The results show that the method yields results for the probability of failure that are in very close agreement with Monte Carlo simulation performed on the original limit state function and requiring a small number of learning samples.     

Effect of blow-holes on reliability of cast component

This paper presents a study on the effect of blow-holes on the reliability of a cast component. The most probable point (MPP) based univariate response surface approximation is used for evaluating reliability. Crack geometry, blow-hole dimensions, external loads and material properties are treated as independent random variables. The methodology involves novel function decomposition at a most probable point that facilitates the MPP-based univariate response surface approximation of the original multivariate implicit limit state/performance function in the rotated Gaussian space. Once the approximate form of the original implicit limit state/performance function is defined, the failure probability can be obtained by Monte Carlo simulation (MCS), importance sampling technique, and first- and second-order reliability methods (FORM/SORM). FORTRAN code is developed to automate calls to ABAQUS for numerically simulating responses at sample points, to construct univariate response surface approximation, and to subsequently evaluate the failure probability by MCS, importance sampling technique, and FORM/SORM.