Vector outcrossing probabilities by Monte Carlo

An exact method for calculating the probability that a vector-valued Gaussian stationary process will cross out of a safe set in a given time, is presented. It is based on representing the process by a random trigonometric polynomial and then calculating the probability by directional simulation. Exact bounds for the error can be calculated, giving a predetermined accuracy. A numerical example relating to the response of a structure to wind excitation is given.     

Response level crossing rate of a linear system excited by a partially specified Gaussian load process

The problem of determining the maximum mean response level crossing rate of a linear system driven by a partially specified Gaussian load process has been considered. The partial specification of the load is given only in terms of its total average energy. The critical input power spectral (PSD) function, which maximizes the mean response level crossing rate, is obtained. The critical input PSD turns out to be highly narrow-banded which fails to capture the erratic nature of the excitation. Consequently, the trade-off curve between the maximum mean response level crossing rate and the maximum disorder in the input process, quantified in terms of its entropy rate, has been generated. The method of Pareto optimization is used to tackle the conflicting objectives of the simultaneous maximization of the mean response level crossing rate and the input entropy rate. The non-linear multi-objective optimization has been carried out using a recently developed multi-criteria genetic algorithm scheme. Illustrative example of determining the critical input of an axially vibrating rod, excited by a partially specified stationary Gaussian load process, has been considered.     

Multivariate non-Gaussian process simulation based on HPM-JTM hybrid model

For the simulation of wind field or wind load, the Gaussian assumption is not applicable in some situations. Hence the simulation of non-Gaussian process becomes significant. In order to avoid the iteration and maintain a wide application range, a HPM-JTM hybrid model is proposed based on translation process. During the simulation, the correlation function of the related Gaussian process can be solved by analytical or numerical expression. Through a numerical example, the application of the model is presented. Results show that the model provides a reasonable estimation for the target case, which can be regarded as an appropriate candidate for the simulation of multivariate non-Gaussian process.     

朱-王-唐非线性粘弹性本构模型在有限元分析中的实现及其应用

LS-DYNA可以满足用户对某些材料本构关系子程序开发的要求.本文首先编制了各向同性线弹性材料本构模型子程序,计算单轴拉伸作用,得到材料子程序开发的可行性;另外主要编制了飞机风挡材料采用的具有应变率效应的非线性粘弹性朱-王-唐本构模型,结果能很好地对朱-王-唐模型进行描述,特别是应变率对该模型的影响.并用于真实风挡的计算,得到的数值结果与试验值比较吻合.     

An analysis of the viscoelastic fracture toughness and crack growth in ice

In this paper, a numerical model is presented to predict the viscoelastic fracture toughness and crack growth in ice under different loading conditions. It is assumed that ice is a homogeneous, linear, and isotropic material. The model can predict the viscoelastic response of small ice samples under constant cross-head speed, constant strain rate, and constant stress rate loading conditions. The effect of different parameters such as test temperature, test sample size, and rate of loading is also investigated.     

Real-time reliability estimation for serviceability limit states in structures with uncertain dynamic excitation and incomplete output data

A novel technique is presented for indirectly monitoring threshold exceedance in a sparsely-instrumented structure represented by a linear dynamic model subject to uncertain excitation modeled as a Gaussian process. The goal is to answer the following question: given incomplete output data from a structure excited by uncertain dynamic loading, what is the probability that any particular unobserved response of the structure exceeds a prescribed threshold? It is assumed that a good linear dynamic model of the target structure has previously been identified using dynamic test data. The technique is useful for monitoring the serviceability limit states of a structure subject to unmeasured “small-amplitude” ambient excitation (e.g. wind excitation or non-damaging earthquake ground motions), or for monitoring the damage status of equipment housed in the structure that is vulnerable to such excitation. The ISEE algorithm developed by Au and Beck in 2000 is used to efficiently estimate the threshold exceedance (first-passage) probability by stochastic simulation. To improve computational efficiency for the monitoring problem, a new state-space version of ISEE is developed that incorporates state-estimation and a newly-developed state-sampling technique. The computational efficiency of the proposed technique is demonstrated through two numerical examples that show that it is vastly superior to Monte Carlo simulation in estimating the first-passage probability. Moreover, the approach produces useful by-products, including estimates for the model state and the uncertain excitation.     

Numerical calculation for first excursion probabilities of linear systems

A numerical method is proposed to calculate the first excursion probability that the linear system response to non-stationary random excitation exceeds in magnitude its respective threshold level within a specified time interval. Its derivation is carried through three steps. First, the numerical expression for the first excursion probability, based on the modification of the level crossing rates, is developed. Secondly, the time domain expressions for the first three order spectral moments of the response are given, from which the level crossing rates can be computed. Thirdly, it is then demonstrated how Simpson’s rule of numerical integration can be applied to the approximate computation of the first three order spectral moments. It is shown by examples that both numerical accuracy and efficiency of this method are apparently very high.     

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called “ensemble-crossing rate” approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings.     

多自由度结构动力可靠度分析的小波方法

该文发展了基于小波分析的局部平稳法在多自由度结构动力可靠度中的应用。首先,基于广义谐和小波和随机过程的局部平稳小波模型,发展了线性多自由度结构系统在各时间-频率子域上激励功率谱与响应功率谱之间的关系,并计算得到了在一般随机动力激励下结构随机动力响应功率谱密度和各阶谱矩。随后,根据随机动力激励和响应的高斯假定及超越过程的Markov假定,得到了线性多自由度结构在均匀/非均匀调制随机激励下层间位移的动力可靠度指标。结构动力可靠度的Monte Carlo模拟显示了所提方法的可靠性与计算高效性。     

高斯/非高斯混合随机风压场的模拟方法

针对作用于屋盖结构随机风压场样本的统计特性要求,基于零记忆非线性转化法的理论,给出了随机风压场的具体模拟过程。其中,解决了两个关键问题：（1）推导了服从对数正态分布和韦布尔分布的多点非高斯随机过程向量的标准化协方差,与相应高斯随机过程向量的标准化协方差的函数转化关系;（2）提出了分解谱密度函数修正法,解决利用谐波合成法模拟多点高斯随机过程向量时,功率谱密度函数矩阵在某些频率点出现负定的问题。经过具体算例表明,所提出的方法能生成合乎风洞实验数据统计特性要求的随机风压场样本。     

Wedge simulation method for calculating the reliability of linear dynamical systems

In this paper the problem of calculating the probability of failure of linear dynamical systems subjected to random excitations is considered. The failure probability can be described as a union of failure events each of which is described by a linear limit state function. While the failure probability due to a union of non-interacting limit state functions can be evaluated without difficulty, the interaction among the limit state functions makes the calculation of the failure probability a difficult and challenging task. A novel robust reliability methodology, referred to as Wedge-Simulation-Method, is proposed to calculate the probability that the response of a linear system subjected to Gaussian random excitation exceeds specified target thresholds. A numerical example is given to demonstrate the efficiency of the proposed method which is found to be enormously more efficient than Monte Carlo Simulations.     

风浪联合作用下海上风力涡轮机的碰撞阻尼减振控制

提出利用碰撞调谐质量阻尼器(Pounding Tuned Mass Damper,PTMD)控制近海单桩风力涡轮机塔身在风浪联合作用下的结构振动.为此,利用拉格朗日方程推导风浪联合作用下风机与PTMD 的耦合动力方程并据此分析了相关控制效果.具体而言,结构模型方面,以美国国家可再生能源实验室(NREL)的5 MW基准单...     

Wave analysis by Slepian models

Ocean waves exhibit more or less a Gaussian distribution for the instantaneous water surface height, and there is a need to develop simple models for generation of the characteristic non-Gaussian statistics, namely the asymmetric distributions of water surface height and wave slope. We argue that a simple class of non-linear oscillators can reproduce some of the characteristic features of random water wave processes and linear or non-linear response to ocean waves. We describe the Slepian model for the Gaussian case, and explain the use of the regression approximation for level crossing distances and associated variables, such as wave period and amplitude. Finally we speculate about a generalization of the regression technique to the non-linear Markov process case.     

桅杆风振试验研究

基于风洞模型试验的方法,对桅杆的风振响应进行了试验研究。研究表明:① 桅杆的自振频率相当密集,其风振响应亦具有明显的宽带特征;② 桅杆风振响应频谱随风速的增大由多频离散谱向连续谱转变,在大风条件下位移谱上的频率成份大量增多,振动显现出混沌特征,此时基于振型叠加法的分析结果误差较大;③ 桅杆动位移响应在风速较大时不宜采用零均值假设,但在可靠性分析中仍可采用按动位移均值平移后的Gauss分布假设;④ 桅杆横风振动主要源于顺、横风向振动间能量的转移,应通过在前两阶自振频率处增设VED或TSD装置加以控制。     

Calculations of Sobol indices for the Gaussian process metamodel

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well-known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling.     

A different view of ridge analysis from numerical optimization

This research falls into the gap between applied statistics and numerical optimization in a specific topic—Ridge Analysis (RA). This article proposes using the trust-region (TR) methods in numerical optimization to solve the RA problem, arising from the literature of response surface methodology (RSM) in applied statistics, where its goal is to help engineers for ‘process improvement’ to find the better response value of the predicted response function within the boundary of experimentation. In the field of numerical optimization, as the family of TR approaches always exhibits excellent mathematical properties during optimization steps, thus the algorithm presented in this study guarantees global optima for the RA problem. Two examples found in the RSM literature are included to illustrate the algorithm, demonstrating its capability of locating better operating conditions than existing computing methods and pointing out particular circumstances (termed the ‘hard case’) where the classical RA procedure fails. An important application to the response modeling problem arising from the philosophy of Taguchi's quality engineering illustrates the hard case. Finally, the utility of the presented TR algorithm is demonstrated through a sequential framework with iterative updates of the TR model under local approximation provided that the predicted response model is a high-order or even non-polynomial function.     

Semi-active control of wind excited building structures using MR/ER dampers

A semi-active control strategy for building structures subject to wind loading and controlled by MR/ER dampers is proposed. The power spectral density (PSD) matrix of the fluctuating part of wind velocity vector is diagonalized in the eigenvector space. Each element of the diagonalized PSD matrix is modeled as a set of second-order linear filter driven by white noise. A Bingham model for MR/ER dampers is used. The forces produced by MR/ER dampers are split into passive and active parts and the passive part is combined with structural damping forces. A set of partially averaged Itô equations for controlled modal energies are derived by applying the stochastic averaging method for quasi-integrable-Hamiltonian systems. The optimal control law is then determined by using the stochastic dynamical programming principle and the cost function is so selected that the optimal control law can be implemented by the MR/ER dampers. The response of semi-active controlled structures is predicted by using the reduced Fokker–Planck–Kolmogorov equation associated with fully averaged Itô equations of the controlled structures. A comparison with clipped linear quadratic Gaussian (LQG) control strategy, for an example, shows that the proposed semi-active control strategy for MR/ER dampers is superior to clipped LQG control strategy.     

Compressive strengths and dynamic response of corrugated metal sandwich plates with unfilled and foam-filled sinusoidal plate cores

The compressive strengths and dynamic response of corrugated sandwich plates with unfilled and foam-filled sinusoidal plate cores are investigated. The “effective” compressive strengths of the unfilled and foam-filled sinusoidal plate cores are derived and numerically analyzed. Finite element method is employed to analyze the dynamic response of fully clamped metal sandwich plates with unfilled and foam-filled sinusoidal plate cores subjected to impulsive loading. Moreover, a simplified plastic-string model is developed to analytically predict the large deflection and time responses of the clamped sandwich plates under impulsive loading. One can see a good agreement between the analytical and numerical predictions. It can be seen that the present analytical procedure is efficient and simple to evaluate the dynamic response of corrugated sandwich plates.     

Multiple timescale spectral analysis

Spectral analysis is a classical tool for the structural analysis of structures subjected to random excitations. The most common application of spectral analysis is the determination of the steady-state second order cumulant of a linear oscillator, under the action of a stationary loading prescribed by means of its power spectral density. There exists however a broad variety of such similar problems, extending the concept to multi degree-of-freedom systems, non Gaussian excitation, slightly nonlinear oscillators or even transient excitations. In this wide class of problems, the cumulants of the response are obtained as the result of the integral of corresponding spectra over the frequency space, which is possibly multidimensional. Application of standard numerical integration techniques may be prohibitive, a reason why the spectral approach is often left aside. Besides, many engineering problems involve a clear timescale separation, usually of those pertaining to the loading and to the mechanical behavior of the system. In these problems, a proper consideration of the timescale separation results in dropping the order of integration by one, at least. This offers the possibility to derive analytical solutions, whenever the order of integration drops to zero, or to make numerical integration competitive. The paper presents this general method, together with some applications in wind and marine engineering.     

线性轮廓滤波器的不确定度传递规律研究

基于新一代产品几何规范（GPS）标准体系的线性轮廓滤波器的基本原理,提出一种线性轮廓滤波器的不确定度传递规律的计算方法,从而可以由输入轮廓的不确定度计算出经过滤波后的输出轮廓的不确定度。最后给出一个高斯滤波器的测量实例。