结构系统可靠性优化设计的神经网络方法

针对具有非正态随机参数的可靠性(优化)设计,提出了随机摄动-Edgeworth级数方法,采用该方法将可靠性概率约束转化为等价的确定型约束,可以迅速准确地获得优化设计信息。针对具有多失效模式的结构系统可靠性优化设计,提出了随机模拟一神经网络方法(MCS—NN),将随机模拟方法与神经网络技术有机结合,为结构系统可靠性优化设计提供了一种新方法。     

结构稳健性设计与考虑不确定因素的优化设计的比较

用典型的三杆桁架结构设计问题，进行了结构稳健性设计与考虑不确定因素的优化设计的比较，通过用蒙特卡罗模拟法对设计结果的结构可靠性计算，表明两种设计在提高结构可靠性上是一致的，但结构稳健性设计更具有有效控制结构特性散布的优点。     

结构随机动力稳定性的定量分析方法

提出了结构随机动力稳定性的定量分析方法,讨论了经典的随机动力稳定性概念,指出结构动力稳定性不仅与结构参数有关,也与作用在结构上的外部载荷密切相关,据此引入了一种判定结构动力稳定性的新准则,明确了结构随机动力稳定性的基本涵义.在概率守恒原理基础上,推导了概率耗散系统的广义概率密度演化方程.引入结构动力失稳的物理机制作为引起概率耗散的驱动力,利用概率耗散系统概率密度演化方程、可以方便获得结构响应的概率密度演化过程,从而定量求解结构的动力稳定概率.据此,可以定量评价结构系统依概率为1或依给定概率意义上的结构随机动力稳定性.采用本文所建议方法对典型结构动力系统进行了随机动力稳定性分析,并与蒙特卡洛方法计算结果进行对比.数值结果表明了所建议方法的有效性.      

Combined interval analysis - Monte Carlo simulation approach for the analysis of uncertainties in parallel manipulators

The quantification of the impact of uncertainties may increase the reliability and robustness of parallel manipulators. Monte Carlo simulation (MCS) and interval analysis are among the most common techniques used in uncertainty quantification. Interval analysis provides guaranteed performance since the interval evaluation of a function always contains the exact result. Nevertheless, interval analysis estimations are very conservative, frequently yielding overestimated results. Conversely, Monte Carlo Simulation avoids overestimation, but does not provide guaranteed performance. This paper proposes a novel hybrid algorithm combining the best features of interval analysis and Monte Carlo simulation for estimating probabilities of failure in the positioning error of parallel manipulators. A 3RRR manipulator is employed as case-study. The hybrid approach provides information on the bounds (minimum and maximum values) and estimated values of failure probabilities. The simulations herein compare the hybrid approach with pure interval analysis and pure Monte Carlo simulation. The results reveal that the hybrid technique may estimate not only the probability of failure in a continuous region, but also the worst and best case probabilities, much faster than interval analysis based approaches.

     

随机和区间非齐次线性哈密顿系统的比较研究及其应用

随着计算机技术的飞速发展,更高效、更稳定和长时间模拟能力更强的数值算法需求迫切.哈密顿系统辛算法与传统算法相比在稳定性和长期模拟方面具有显著优越性.但动力系统中不可避免地存在大量不同程度的不确定性,动力学分析中需要考虑这些不确定性的影响以确保合理有效性. 然而,目前考虑参数不确定性的哈密顿系统响应分析的研究基础还比较薄弱. 为此,本文考虑随机和区间参数不确定性,对两种不确定性非齐次线性哈密顿系统分析计算结果进行了比较研究,从而突破了传统哈密顿系统的局限性, 并应用于结构动力响应评估中. 首先,针对确定性非齐次线性哈密顿系统, 提出了考虑确定性扰动的参数摄动法;在此基础上, 分别提出了随机、区间非齐次线性哈密顿系统的参数摄动法,得到了它们响应界限的数学表达; 随后,用数学理论推导得到了区间响应范围包含随机响应范围的相容性结论; 最后,两个数值算例在较小时间步长下验证了所提方法在结构动力响应中的可行性和有效性,体现了随机、区间哈密顿系统响应结果之间的包络关系,并在较大时间步长下与传统方法相比较凸显了哈密顿系统辛算法的数值计算优势、与蒙特卡洛模拟方法相比较验证了所提方法的精度.      

Nonlinear Random Response of Ocean Structures Using First- and Second-Order Stochastic Averaging

This paper deals with the dynamic response of nonlinear elastic structure subjected to random hydrodynamic forces and parametric excitation using a first- and second-order stochastic averaging method. The governing equation of motion is derived by using Hamilton's principle, taking into account inertia and curvature nonlinearities and work done due to hydrodynamic forces. Within the framework of first-order stochastic averaging, the system response statistics and stability boundaries are obtained. Unfortunately, the effects of nonlinear inertia and curvature are not reflected in the final results, since the contribution of these nonlinearities is lost during the averaging process. In the absence of hydrodynamic forces, the method fails to give bounded response statistics, and the analysis yields stability conditions. It is the second-order stochastic averaging which can capture the influence of stiffness and inertia nonlinearities that were lost in the first-order averaging process. The results of the second-order averaging are compared with those predicted by Gaussian and non-Gaussian closures and by Monte Carlo simulation. In the absence of parametric excitation, the non-Gaussian closure solutions are in good agreement with Monte Carlo simulation. On the other hand, in the absence of hydrodynamic forces, second-order averaging gives more reliable results in the neighborhood of stochastic bifurcation. However, under pure parametric random excitation, the stochastic averaging and Monte Carlo simulation predict the on-off intermittency phenomenon near bifurcation point, in addition to stochastic bifurcation in probability.     

不确定结构时域响应分析的多项式维数分解法

针对具有不确定参数结构,提出时域不确定性传播和量化的多项式维数分解法,确定了结构响应统计量的演变过程.首先,采用参数概率模型来描述结构参数的不确定性,建立结构动力学方程,将结构响应表达为不确定参数的函数;进一步,将所关心的结构响应采用成员函数进行维数分解,并利用正交多项式基底对成员函数进行Fourier展开;最后,应用降维积分方法进行展开系数的求解,给出了响应均值和标准差的计算表达式.在数值算例中,将本文方法与蒙特卡洛方法进行对比,结果表明所建立方法具有较高的求解效率和计算精度.     

Probabilistic sensitivity of the limit states of structures using Monte Carlo simulation

The paper presents the concept of probabilistic sensitivity of structural limit states with respect to given design variables. A general idea is presented, illustrated by a simple case solved in an analytical way. More general approach is presented for the engineering structures, in this case a dedicated Monte Carlo simulation procedure is involved as part of the methodology. Illustration of the engineering case is done, by means of the computational method, the results are estimators of the probability density functions of the limit state of a structure, with respect to a given parameter. The proposed definition of probabilistic sensitivity is based on the problem-oriented numerical algorithm, thus it can be included into the class of computational methods.     

基于Chebyshev展开的区间穿孔板超材料分析

目前对于声学超材料的传输特性分析和优化大多是基于确定的数值和确定的模型,然而在实际工程和结构设计中存在大量材料自身特性和几何物理参数的不确定性.如果忽略这些不确定变量对声学超材料传输特性分析和优化过程的影响,得到的结果可能不正确.针对这一现状,拟将切比雪夫区间模型引入多层穿孔板超材料,提出多层穿孔板超材料声学透射率的区间切比雪夫展开-蒙特卡洛模拟法(interval Chebyshev expansionMonte Carlo simulation method,ICE-MCSM).该方法采用截断切比雪夫多项式近似拟合多层穿孔板超材料的声学透射率响应曲线,构造声学透射率响应曲线的切比雪夫代理模型;然后采用蒙特卡洛模拟法(Monte Carlo simulation method,MCSM)随机生成一定数量的不确定区间变量的样本数据点,并将生成的不确定区间变量样本数据点代入切比雪夫代理模型,预测单个不确定区间变量和多个不确定区间变量条件下的多层穿孔板超材料声学透射率区间的上界和下界.数值分析结果表明,ICE-MCSM预测的声学透射率变化区间的上界和下界与直接蒙特卡洛法(direct Monte Carlo simulation method,DMCSM)预测的声学透射率上界和下界的结果非常接近.与DMCSM相比,ICE-MCSM具有更高的计算效率.因此,ICE-MCSM可有效且高效地分析不确定区间变量条件下多层穿孔板超材料声学透射率传输特性,具有良好的工程应用前景.     

Kepler’s equation and limit cycles in a class of PWM feedback control systems

The aim of this paper is to point out some new results concerning the ripple instability in the closed-loop control system using pulse width modulators (PWM), with natural sampling, as power amplifier. The presented analysis, based on the dual-input describing function method and the theoretical framework of Kepler’s problem, shows an equivalence between the computation of switching instants of the PWM and the eccentric anomaly of the planet orbit around the sun, giving a simple stability criterion and a sufficient condition for the absence of solutions of the harmonic balance equation and, therefore, the probable absence of limit cycles of a period of a multiple of that characteristic of the modulator. The derived stability criterion, by using the describing function method, is successively compared with the local stability of the closed-loop PWM system for first- and second-order plants. In the first case it has been formally proved that the proposed criterion ensures the local stability of an equilibrium point, while in the second one a Monte Carlo simulation has confirmed that the selection of the modulator parameters, according to the proposed criterion, gives an effective method to avoid limit cycles and to ensure the local stability.     

随机响应面法最优概率配点数目分析

系统地研究随机响应面法采用线性无关原则选取概率配点的优越性,给出了基于线性无关原则选取概率配点的流程图,比较了基于回归方法和基于线性无关原则选取概率配点的优缺点。算例结果表明,基于回归方法选取概率配点时,配点数目应保证Hermite系数矩阵达到满秩,此时随机响应面法的计算精度才能得到保证,计算效率也远远高于传统的蒙特卡洛模拟方法。基于线性无关原则选取概率配点的随机响应面法在保证计算精度的同时,其计算效率远远高于基于回归方法选取概率配点的随机响应面法,它是结构可靠度分析一种有效的方法,尤其适用于极限状态方程不能用显式函数表达的复杂结构可靠度问题。研究成果为随机响应面法最优概率配点数目的确定奠定了一定的基础。     

对区间不确定性问题的可靠性度量的探讨

实际工程中大量存在不确定性因素,处理不确定性因素的可靠性逐渐成为科学和工程中一个非常重要的概念。区间不确定性是继随机性和模糊性之后被人们研究的又一种不确定性。区间不确定性一般可由区间变量或凸集合模型来描述。近年来,有些文献针对区间不确定性提出了计算非概率可靠性的方法。本文对这些方法进行比较和讨论,并和假定各区间不确定参量在允许取值区间内为具有熵最大的矩形分布,采用概率可靠度的理论来处理问题得到的结果进行了比较。     

剪切型钢筋混凝土柱临界斜裂缝倾角的概率模型

对于剪切型钢筋混凝土(RC)柱,传统的确定性临界斜裂缝倾角模型难以有效考虑其材料参数、几何尺寸和边界约束条件等方面不确定性因素的影响,导致计算精度有限,且离散性较大。鉴于此,本文研究建立了剪切型RC柱临界斜裂缝倾角的概率模型。首先,基于变角桁架模型理论,建立了剪切型RC柱临界裂缝倾角的确定性模型;然后,考虑主观不确定性和客观不确定性因素的影响,结合贝叶斯理论和马尔可夫链蒙特卡洛(MCMC)法,建立了剪切型RC柱临界斜裂缝倾角的概率模型,并推导了均值和方差的解析表达式,从而能够合理描述临界斜裂缝倾角的概率分布特性;最后,利用试验数据对比验证了该模型的有效性,并校准了现有确定性模型的置信水平,进而确定了不同置信水平下剪切型RC柱临界斜裂缝倾角的概率特征值。     

钢筋混凝土柱抗弯承载力的概率模型与校准分析

为了克服传统确定性抗弯承载力模型和校准方法无法合理考虑不确定性所存在的缺陷,分别建立了钢筋混凝土(RC)柱的概率抗弯承载力模型与概率校准方法。首先,基于RC柱正截面受弯承载力的基本假定,结合偏心受压RC柱的截面内力平衡条件,分别建立了大(小)偏心受压RC柱的确定性抗弯承载力模型;然后,综合考虑固有不确定性和认知不确定性的影响,分别建立了大(小)偏心受压RC柱概率抗弯承载力模型的解析表达式,进而结合贝叶斯理论和MCMC法确定了概率模型参数的后验分布信息,从而建立了RC柱的概率抗弯承载力模型;最后,基于概率抗弯承载力模型所确定的概率密度函数、置信区间和置信水平,提出了传统确定性抗弯承载力模型的概率校准方法。研究结果表明,所建立的概率抗弯承载力模型不仅可以合理描述RC柱抗弯承载力的概率分布特性,而且可以校准传统确定性抗弯承载力模型的计算精度和置信水平。     

一种分析区间参数结构可靠性的减基快速计算方法

将减基法与蒙特卡洛模拟结合,提出了一种快速计算区间不确定结构可靠性的方法。该方法分为离线和在线计算两个阶段,离线阶段利用减基法建立减基空间,进而形成减缩模型;而在线阶段则将减缩模型融入蒙特卡洛方法,进而快速求解区间失效概率及相应的区间参数失效域。该方法在减基空间而非有限元空间中分析区间结构的可靠性,减少了求解时间,提高了计算效率,通过算例验证了该方法的可行性和有效性。     

Dynamic stability of a viscoelastic rotating shaft under parametric random excitation

This paper deals with dynamic stability of a viscoelastic rotating shaft subjected to a parametric random axial compressive thrust, by using moment Lyapunov exponents and the largest Lyapunov exponents as indicators. The equation of motion for the shaft is derived, which is a system of gyroscopic stochastic differential equations. The method of stochastic averaging is used to decouple the governing equations into Itô equations, from which the moment Lyapunov exponent is obtained by using mathematical transformations only. The largest Lyapunov exponent is obtained through its relation with moment Lyapunov exponents. The effects of various parameters on the stochastic dynamic stability are discussed. The approximate analytical results are confirmed by Monte Carlo simulation.     

An efficient 3D stochastic finite element method

Real life structural systems are characterized by their inherent or externally induced uncertainties in the design parameters. This study proposes a stochastic finite element tool efficient to take account of these uncertainties. Here uncertain structural parameter is modeled as homogeneous Gaussian stochastic field and commonly used two-dimensional (2D) local averaging technique is extended and generalized for 3D random field. This is followed by Cholesky decomposition of respective covariance matrix for digital simulation. By expanding uncertain stiffness matrix about its reference value, the Neumann expansion method is introduced blended with direct Monte Carlo simulation. This approach involves decomposition of stiffness matrix only once for the entire simulated structure. Thus substantial saving of CPU time and also the scope of tackling several stochastic fields simultaneously are the basic advantages of the proposed algorithm. Accuracy and efficiency of this method with reference to example problem is also studied here and numerical results validate its superiority over direct simulation method or first-order perturbation approach.     

Dynamics analysis of slender vehicle influenced by random factors

In this paper, the aeroelastic problems of slender vehicles under the influence of random factors and thrust are studied. An aeroelastic dynamic model of a free-free Euler–Bernoulli beam considering thrust and aerodynamic forces is established based on Hamilton’s principle of nonconservative systems. On this basis, considering the influence of random factors, the elastic modulus and viscous drag are regarded as one-dimensional continuous stationary random fields and discretized. The stochastic finite element method is used to solve the dynamic model, and the results are compared with the Monte Carlo simulation results. Then, the influence of the correlation of the random field on the elastic displacement is further analyzed. The following simulation results are obtained: (1) the stochastic factor analysis model established in this paper can reflect the statistical characteristics of aeroelastic response well; (2) the stronger the correlation of the random field is, the greater the expectation of elastic displacement, but as the correlation increases, the expectation tends to be constant; and (3) it is necessary to choose the discrete length of the random field reasonably, and the discrete length depends on the correlation characteristics of the random field studied.     

基于凸集合模型的非概率可靠性研究

研究了结构不确定参量用超椭球凸集描述情况下的非概率可靠性问题,提出了一个可靠性指标,可用于度量超椭球凸集模型与区间变量共存情况下的结构安全程度;给出了该指标的求解算法;设计了超椭球凸集模型的Monte Carlo仿真算法,通过算例比较了该指标与传统概率可靠性指标之异同。