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1.
In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory.  相似文献   

2.
Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator (LQR) approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.  相似文献   

3.
Based on the random perturbation technique for reliability sensitivity design,some realistic reliability-based sensitivity issues are discussed,some of which have a structure of high nonlinear performance functions.Combining the related theories of the moment method of the reliability analysis,the matrix differential,and the Kronecker algebra,the reliability-based sensitivity method based on the perturbation method is modified if the first four moments of random variables are given.Meanwhile,a reliability-based sensitivity computation method is proposed.Some examples are used to show that using this method can effectively improve the accuracy of the reliability-based sensitivity computation and offer a reliable theoretic basis in engineering.  相似文献   

4.
An improved Monte-Carlo method for the failure calculation of structureis proposed.The present method can determine whether some sample points are in thesafe region without doing structural analysis,so the calculation work is greatly reducedcompared with the ordinary M-C method.Finally,the new M-C method is applied toreliability analysis of frame and the torsional buckling reliability analysis of cylindricalshells.  相似文献   

5.
The purpose of this paper is to analyse theoretically and numerieally the coupled vibration of an ideal fiuid with a linear elastie structure.It is proved in the paper that the natural frequencies of the coupled vibration do exist and are all real positive. The paper presents an efficient method to transform a coupled fluid-structure system to the structure with added mass and the ribrational analysis of the former is replaced by the latter in vacuum only. Numerical solution is outlined for the transformed problem and a compact frequecy equation is derived in which fluid variables do not appear. This simplifies the analysis significanily. A convergent proof has been given to guarantee the reliability of the solution. The paper also offers a general algorithm combined with Ritz method, boundary element method, and finite element method to analyse the transformed problem. Based on this algorithm, one can apply a known structural analysing program, with a little modification, to solve many different kinds  相似文献   

6.
In order to improve the efficiency of the support vector machine (SVM) for classification to deal with a large amount of samples, the least squares support vector machine (LSSVM) for classification methods is introduced into the reliability analysis. To reduce the coraputational cost, the solution of the SVM is transformed from a quadratic programming to a group of linear equations. The numerical results indicate that the reliability method based on the LSSVM for classification has higher accuracy and requires less computational cost than the SVM method.  相似文献   

7.
A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.  相似文献   

8.
In this paper, the hierarchical approach is adopted for series representation of the stochastic nodal displacement vector using the hierarchical basis vectors, while the Karhunen-Lòeve series expansion technique is employed to discretize the random field into a set of random variables. A set of hierarchical basis vectors are defined to approximate the stochastic response quantities. The stochastic variational principle instead of the projection scheme is adopted to develop a hierarchical stochastic finite element method (HSFEM) for stochastic structures under stochastic loads. Simplified expressions of coefficients of governing equations and the first two statistical moments of the response quantities in the schemes of the HSFEM are developed, so that the time consumed for computation can be greatly reduced. Investigation in this paper suggests that the HSFEM yields a series of stiffness equations with similar dimensionality as the perturbation stochastic finite element method (PSFEM). Two examples are presented for numerical study on the performance of the HSFEM in elastic structural problems with stochastic Young’s Modulus and external loads. Results show that the proposed method can achieve higher accuracy than the PSFEM for cases with large coefficients of variation, and yield results agreeing well with those obtained by the Monte Carlo simulation (MCS).  相似文献   

9.
Based on the classical response surface method (RSM), a novel RSM using improved experimental points (EPs) is presented for reliability analysis. Two novel points are included in the presented method. One is the use of linear interpolation, from which the total EPs for determining the RS are selected to be closer to the actual failure surface; the other is the application of sequential linear interpolation to control the distance between the surrounding EPs and the center EP, by which the presented method can ensure that the RS fits the actual failure surface in the region of maximum likelihood as the center EPs converge to the actual most probable point (MPP). Since the fitting precision of the RS to the actual failure surface in the vicinity of the MPP, which has significant contribution to the probability of the failure surface being exceeded, is increased by the presented method, the precision of the failure probability calculated by RS is increased as well. Numerical examples illustrate the accuracy and efficiency of the presented method.  相似文献   

10.
The problem of magnetohydrodynamic (MHD) flow on a moving surface with the power-law velocity and special injection/blowing is investigated. A scaling group transformation is used to reduce the governing equations to a system of ordinary differen- tial equations. The skin friction coefficients of the MHD boundary layer flow are derived, and the approximate solutions of the flow characteristics are obtained with the homotopy analysis method (HAM). The approximate solutions are easily computed by use of a high order iterative procedure, and the effects of the power-law index, the magnetic parameter, and the special suction/blowing parameter on the dynamics are analyzed. The obtained results are compared with the numerical results published in the literature, verifying the reliability of the approximate solutions.  相似文献   

11.
This is the second paper of our work on structural reliability analysis for implicit performance function. The first paper proposed structural reliability analysis methods using multilayer perceptron artificial neural network [Deng, J., Gu, D.S., Li, X.B., Yue, Z.Q., 2005. Structural reliability analysis for implicit performance function using artificial neural network. Structural Safety 25 (1), 25–48]. This paper presents three radial basis function network (RBF) based reliability analysis methods, i.e. RBF based MCS, RBF based FORM, and RBF based SORM. In these methods, radial basis function network technique is adopted to model and approximate the implicit performance functions or partial derivatives. The RBF technique uses a small set of the actual data of the implicit performance functions, which are obtained via physical experiments or normal numerical analysis such as finite element methods for the complicated structural system, and are used to develop a trained RBF generalization algorithm. Then a large number of the function values and partial derivatives of implicit performance functions can be readily obtained by simply extracting information from the established and successfully trained RBF network. These function values and derivatives are used in conventional MCS, FORM or SORM to constitute RBF based reliability analysis algorithms. Examples are presented in the paper to illustrate how the proposed RBF based methods are used in structural reliability analysis. The results are well compared with those obtained by the conventional reliability methods such as the Monte-Carlo simulation, multilayer perceptrons networks, the response surface method, the FORM method 2, and so on. The examples showed the proposed approach is applicable to structural reliability analysis involving implicit performance functions.  相似文献   

12.
响应面法是解决隐式极限状态方程结构可靠度分析问题比较理想的方法,其关键问题是响应面函数的重构。根据响应面方法经验点集的小样本特点,利用支持向量机(SVM)对小样本数据良好的学习和泛化能力,用SVM重构结构响应面方程,建立了基于SVM的隐式极限状态方程结构可靠度分析的响应面方法。在此基础上,文中提出了改进SVM响应面方法,改进的方法充分利用每次有限元计算成果,大幅减少了有限元计算次数。算例表明本文方法具有很好的计算精度和计算效率。  相似文献   

13.
Fuzzy reliability analysis can be implemented using two discrete optimization maps in the processes of reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative reliability methods are two main factors in the fuzzy-based reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy reliability analysis, the first-order reliability method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size method for fuzzy structural reliability analysis, namely Fuzzy conjugate relaxed-finite step size method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural reliability method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for reliability analysis using proposed conjugate relaxed-finite step size method. The fuzzy CRS and fuzzy HL-RF methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based reliability analysis of the nonlinear structural reliability problems.  相似文献   

14.
建立了基于支持向量机回归算法和分类算法的替代模型可靠性分析方法,与蒙特卡罗法结合,采用拉丁超立方抽样技术,进行隐式极限状态函数的可靠度计算。讨论了相关参数对支持向量机模型性能的影响,并通过遗传算法进行参数优化,为支持向量机模型的参数选择提供了依据。研究了不同训练样本数量对支持向量机模型预测值精度的影响,进一步证实了支持...  相似文献   

15.
结构可靠度FORM方法的混沌动力学分析   总被引:9,自引:1,他引:8  
杨迪雄  许林  李刚 《力学学报》2005,37(6):799-804
引入混沌动力学理论讨论了FORM收敛失败的非线性动力学根源. 给出了几个典 型函数在参数区间上的可靠指标分岔图,展示了极限状态函数经过FORM迭代成为 非线性映射后计算结果的周期振荡、分岔和混沌等复杂动力学现象,计算了非线性映射的 Lyapunov指数. 结果表明,极限状态函数设计点的曲率大小与FORM的收敛性没有简单的联 系,判别FORM迭代计算收敛性的指标是非线性映射的Lyapunov指数.  相似文献   

16.
基于支持向量机回归的结构系统可靠性及灵敏度分析方法   总被引:3,自引:0,他引:3  
提出了一种基于支持向量机回归近似极限状态方程的系统可靠性分析方法,所提方法首先由支持向量机拟合系统各失效模式的极限状态方程,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,然后根据系统各个失效模式的逻辑结构,由高精度的显式极限状态方程方法计算系统的失效概率和参数灵敏度.与线性展开和响应面法近似极限状态方程相比,文中方法由于采用了基于结构风险最小化原理的支持向量机回归,因而在拟合非线性极限状态方程上表现优越,计算精度高.与直接蒙特卡洛模拟相比,由于该方法采用较少的样本即可近似出概率等价的显式极限状态方程,因而计算效率大幅提高.工程实例表明:所提方法可以处理串联、并联和混合系统的可靠性与可靠性灵敏度分析,具有工程运用价值.  相似文献   

17.
结合鞍点概率分布估计和传统线抽样方法的优点,提出了非正态变量可靠性分析的鞍点线抽样方法.传统的线抽样方法对非正态变量可靠性问题进行分析时需将非正态变量等价转换为标准正态变量,这种非线性转换将增加响应功能函数的非线性程度,进而加大了转换后响应函数失效概率估计的难度.所提鞍点线抽样方法则无需将非正态变量转化为标准正态变量,它利用鞍点概率分布估计方法可以直接估计非正态变量空间中线性响应函数概率分布的特点,并利用线抽样方法可以将非线性功能函数的失效概率转化为一系列线性功能函数失效概率平均值进行估计的优点,实现了非正态变量空间非线性功能函数失效概率的高精度估计.鞍点线抽样方法使用前需将变量进行标准化变换,这种变换是线性的,通过对变量的标准化变换可以消除变量的量纲,从而使得标准化变量空间概率分布更具规律性.理论推导可以证明:鞍点线抽样方法在基本变量服从正态分布时将退化为传统的线抽样方法.算例验证结果表明:针对非线性功能函数的可靠性问题,鞍点线抽样方法比传统的直接鞍点估计具有更高的精度,比直接Monte Carlo模拟有更高的效率.  相似文献   

18.
结构可靠度分析FORM迭代算法的混沌控制   总被引:1,自引:1,他引:0  
杨迪雄 《力学学报》2007,39(5):647-654
利用混沌控制原理对FORM收敛失败进行控制. 理清了全局性和局部性两类混沌反馈 控制各种方法的内在联系,说明稳定转换法和自适应调节法属于全局混沌反馈控制 方法,自适应调节法可视为稳定转换法的特例. 参 数调节混合法不过是松弛牛顿法的另一种表达形式,它们都属于局部混沌反馈控制方法. 阐 明了混沌反馈控制表达式与工程力学收敛控制迭代算法的对应关系. 也揭示了这些迭代算法 收敛控制措施的功效和局限性. 提出了一个以稳定转换法为主联合松弛牛顿法的混 沌反馈控制方法,对可靠度分析FORM迭代算法实现了周期振荡、分岔和混沌控制.  相似文献   

19.
基于主动学习Kriging模型的可靠性分析   总被引:1,自引:0,他引:1  
论文采用Kriging模型代替结构真实功能函数,引入主动学习函数,序列选择最佳样本点,在每次迭代中加入最佳样本点更新Kriging模型.与直接的蒙特卡洛方法相比,主动学习Kriging模型仅需要少量的结构分析就能够得到精度较高的可靠度结果,适用于实际工程具有隐式功能函数的结构可靠性分析.论文通过三个数学算例,从最佳样本点的分布情况、功能函数的拟合程度及可靠度计算结果出发对四种学习函数进行对比研究,最后对具有隐式功能函数的悬臂板进行可靠度分析.结果表明,主动学习函数的引入,合理选择了Kriging模型所需的样本,提高了计算效率,同时,学习函数的选择对结构可靠性分析结果也存在影响.  相似文献   

20.
提出了一种针对一般非线性极限状态方程的时变结构可靠度分析方法. 该方法首先将时变功能函数中的随机过程进行离散,获得多个不同时间段的静态功能函数. 之后,将各功能函数在最大可能点处进行线性化,并运用全概率公式将其化简为一新的静态可靠度分析模型,该模型可运用传统的一次二阶矩方法进行高效求解.最后通过管状悬臂梁、十杆桁架、汽车发动机主轴3 个算例验证了该方法的有效性.  相似文献   

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