Integrating subset simulation with probabilistic re-analysis to estimate reliability of dynamic systems

It is often expensive to estimate the failure probability of highly reliable systems by Monte Carlo simulation. Subset Simulation breaks the original problem of estimating a small probability into the estimation of a sequence of large conditional probabilities, which is more efficient. The conditional probabilities are estimated by Markov Chain simulation. Uncertainty in the power spectral density of the excitation makes it necessary to re-evaluate the reliability for many power spectral densities that are consistent with the evidence about the system excitation. Subset Simulation is more efficient than Monte Carlo simulation, but still requires a new simulation for each admissible power spectral density. This paper presents an efficient method to re-evaluate the reliability of a dynamic system under stationary Gaussian stochastic excitation for different load spectra. We accomplish that by re-weighting the results of a single Subset Simulation. This method is applicable to both linear and nonlinear systems provided that all of the spectra contain the same amount of energy. The authors are currently working on an extension of the method to nonlinear systems, even when the sampling and true power spectral density functions contain different amounts of energy.     

Computer simulation and field measurement of dynamic pavement loading

Two methods, i.e. computer simulation and field measurement, are used in this paper to investigate dynamic pavement loading (DPL) generated by vehicle–pavement interaction. A profilometer is used for measuring road surface roughness. Based on the power spectral density of the measured surface roughness, a computer simulation program is developed using quarter vehicle model. In field measurement methods, an experiment is designed to gain the time history of DPL. An IVECO vehicle is taken as a test vehicle and eight vibration cells were used to pick up vertical accelerations of vehicle body and axle. The test data are collected and recorded while the test vehicle is moving along 11 different pavement sections of highway and bridge at six different speeds. Statistical characteristics of vertical accelerations and DPL of the test vehicle are obtained and analyzed by means of random process theory. The result of computer simulation matches the result of field measurement very well. It is found that DPL is primarily concentrated between 1.8 and 14.8 Hz and coefficient of variation of DPL falls into the range of 5–35% of static vehicle load. An approximate relationship between coefficient of variation of DPL and vehicle speed and road surface roughness is established.     

群决策中随机信息的贝叶斯集结与统计模拟方法

针对方案属性值和权重都为随机变量的群决策问题,结合贝叶斯理论和随机模拟,提出一种集成专家主观概率分布集结和随机多属性决策方案选优的方法.该方法首先构建一个多元正态集结模型,将多个专家估计的属性值分布集结成单一分布,然后用随机模拟算法,生成不完全权重信息,并通过计算各方案获得特定排名的可信度因子,以及反映决策者风险偏好的整体排名可信度因子,得到各方案排序.实例分析验证了方法的有效性.     

含混合储能微网对配电网可靠性的影响

混合储能可快速平滑微网中分布式电源出力的随机性,从而提升配电网可靠性。提出了一种基于网络划分的蒙特卡洛模拟法,定量研究了含混合储能微网对配电网可靠性的影响。首先建立蓄电池与超级电容组成的混合储能系统模型并制定其充放电策略;在设备发生故障后,根据系统区域划分和负荷削减模型,确定负荷停电原则,采用序贯蒙特卡洛模拟法计算可靠性指标。以改进的IEEE RBTS BUS6系统为算例,对比分析了不同储能方式的微网接入前后的系统可靠性指标,结果表明：含混合储能微网接入配电网,能提高配电网供电的可靠性。     

On wavelet-based testing for serial correlation of unknown form using Fan’s adaptive Neyman method

Test procedures for serial correlation of unknown form with wavelet methods are investigated. A new test statistic is motivated using a canonical multivariate normal hypothesis testing model. It relies on empirical wavelet coefficients of a wavelet-based spectral density estimator. The choice of the Haar wavelet function is advocated, since evidence demonstrates that the choice of the wavelet function is not critical. Under the null hypothesis of no serial correlation, the asymptotic distribution of a vector of empirical wavelet coefficients is derived, which is asymptotically a multivariate normal distribution. A test statistic is proposed based on that asymptotic result, which presents the serious advantage to be completely data-driven or adaptive, avoiding the selection of any smoothing parameters. Furthermore, under a suitable class of fixed alternatives, the wavelet-based method is consistent against serial correlation of unknown form. The test statistic is expected to exhibit good power properties when the true spectral density displays significant spatial inhomogeneity, such as seasonal or business cycle periodicities. However, the convergence of the test statistic towards its asymptotic distribution is relatively slow. Thus, Monte Carlo methods based on random samples are suggested to determine the corresponding critical values. In a simulation study, the new methodology is compared with several test statistics, with respect to their exact levels and powers. The robustness properties of the spectral methods based on Monte Carlo critical values are also investigated empirically, when the error terms are weak white noises.     

An algorithm to study non-stationary random vibrations of vehicle–bridge systems

An efficient algorithm is proposed for non-stationary random vibration of vehicle–bridge systems. The pseudo excitation method (PEM) is extended to handle the random analysis of time-dependent vehicle–bridge systems, for which the statistical characteristics of dynamic responses are computed. A vehicle–bridge interaction element is adopted to reduce the computational effort. In the numerical examples, the proposed method is justified by comparing with Monte Carlo simulation results. Also, a method to estimate maximum responses is suggested. Examples include a train moving across both simply supported and three-span continuous bridges and some observed phenomena are discussed.     

An adaptive coherence filter

This paper derives an adaptive coherence filter for canceling interference from a signal of interest whose power spectral density is symmetric. A basic property of the Fourier transform of real signals is that their spectra are Hermitian symmetric. This property is exploited to determine which part of a spectrum is interference and which part is the signal of interest. An unconstrained Wiener filter is derived that exploits the frequency domain symmetry of the signal of interest. While the adaptive coherence filter is based on the Fourier transform property of real signals, an extension of the algorithm is provided so the filter can be used on any signal that displays spectral symmetry. A practical method for implementing the filter is provided. The filter has application in the area of telecommunications, but is applicable in wireless communication applications where a signal, that displays spectral symmetry, is corrupted by interfering signals within the signal of interest's bandwidth.     

Combining the Hanning windowed interpolated FFT in both directions

The interpolated fast Fourier transform (IFFT) has been proposed as a way to eliminate the picket fence effect (PFE) of the fast Fourier transform. The modulus based IFFT, cited in most relevant references, makes use of only the 1st and 2nd highest spectral lines. An approach using three principal spectral lines is proposed. This new approach combines both directions of the complex spectrum based IFFT with the Hanning window. The optimal weight to minimize the estimation variance is established on the first order Taylor series expansion of noise interference. A numerical simulation is carried out, and the results are compared with the Cramer-Rao bound. It is demonstrated that the proposed approach has a lower estimation variance than the two-spectral-line approach. The improvement depends on the extent of sampling deviating from the coherent condition, and the best is decreasing variance by 2/7. However, it is also shown that the estimation variance of the windowed IFFT with the Hanning is significantly higher than that of without windowing.     

Dynamic response of highway girder bridges

The objective of the paper is to investigate the variation of dynamic loading of girder bridges with different girder number and span length due to several vehicles moving across rough bridge decks. Nine girder bridges with girder number ranging from four to eight and span length changing from 40 to 120 ft are designed based on the AASHTO standard highway bridges and modeled as grillage beam systems. The vehicle is simulated as a nonlinear vehicle model with 11 d.f. according to the HS20-44 truck design loading contained in the AASHTO specifications. Four types of road surface roughness generated from power spectral density function for very good, good, average and poor roads in accordance with International Organization for Standardization (ISO) specifications are used in this study. The maximum impact factors of different girders of bridges are obtained for different number of loading trucks (side by side), road surface roughnesses, transverse loading positions and the vehicle speeds changing from 15 to 75 mph. The conclusions reached in this study are useful in the further study of the impact of highway bridges and for practical bridge design engineers.     

Computer simulation of the skin reflectance spectra

The reflectance spectra of the human skin in visible and near-infrared (NIR) spectral region have been calculated using the Monte Carlo technique, and the specular and internal reflection on the medium surface is taken into account. Skin is represented as a complex inhomogeneous multi-layered highly scattering and absorbing medium. The model takes into account variations in spatial distribution of blood, index of blood oxygen saturation, volume fraction of water and chromophores content. The simulation of the skin tissues optical properties and skin reflectance spectra are discussed. Comparison of the results of simulation and in vivo experimental results are given.     

1/2分数阶线性随机动力系统的非平稳响应解析解

提出随机激励作用下1/2分数阶线性系统非平稳响应解析解的一种新方法.首先,利用特征向量展开得到1/2分数阶阻尼系统的脉冲响应函数解析表达;之后,基于Laplace变换计算得到响应功率谱密度的解析表达式和系统均方响应.通过白噪声、调制白噪声和调制修正金井清谱三种不同随机激励类型的数值算例,利用与蒙特卡洛模拟所得结果对比证明该方法的准确性和适用性.     

Impact in a railway truss bridge

The aim was to investigate the dynamic interactions between an open deck steel truss bridge and a moving freight train. A non-linear, 100-ton (gross weight 131.5 tons), freight car vehicle model and the 200-ft, open deck, Warren-type steel bridge model were used in this study. Equations of motion for the vehicle, bridge, and bridge/vehicle interactions were also presented. The track irregularities on the approach and the bridge were generated from power spectral density functions for Federal Railroad Administration (FRA) class 4 track (maximum speed 60 mph). Both zero and two percent of the critical damping were assumed for the bridge. Impact percentages in the bridge due to a three, 100-ton freight car train operating at 20, 40, and 60 mph were calculated. These were compared with the data obtained from an earlier field investigation and those specified by the American Railway Engineering Association (AREA) specifications.     

The effect of material and thickness variability on the buckling load of shells with random initial imperfections

The effect of material and thickness imperfections on the buckling load of isotropic shells is investigated in this paper. For this purpose, the concept of an initial ‘imperfect’ structure is introduced involving not only geometric deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticity as well as the thickness of the shell. The initial geometric imperfections are described as a two-dimensional uni-variate (2D-1V) stochastic field with statistical properties that are either based on an available data bank of measured initial imperfections or assumed, in cases where no experimental data is available. In order to describe the non-homogeneous characteristics of the initial imperfections, the spectral representation method is used in conjunction with an autoregressive moving average model with evolutionary power spectra based on a statistical analysis of the experimentally measured imperfections. In cases where no experimental results is available, the initial imperfections are assumed to be homogeneous and their impact on the buckling load is investigated on the basis of ‘worst’-case scenarios with respect to the correlation length parameters of the stochastic fields. The elastic modulus and the shell thickness are described as 2D-1V non-correlated homogeneous stochastic fields, while the stochastic stiffness matrix of the shell elements is formulated using the local average method. The Monte Carlo Simulation method is used to calculate the variability of the buckling load, while for the determination of the limit load of the shell, a stochastic formulation of the elastoplastic and geometrically non-linear TRIC facet triangular shell element is implemented.     

On testing for serial correlation of unknown form using wavelet thresholding

Omnibus procedures for testing serial correlation are developed, using spectral density estimation and wavelet shrinkage. The asymptotic distributions of the wavelet coefficients under the null hypothesis of no serial correlation are derived. Under some general conditions on the wavelet basis, the wavelet coefficients asymptotically follow a normal distribution. Furthermore, they are asymptotically uncorrelated. Adopting a spectral approach and using results on wavelet shrinkage, new one-sided test statistics are proposed. As a spatially adaptive estimation method, wavelets can effectively detect fine features in the spectral density, such as sharp peaks and high frequency alternations. Using an appropriate thresholding parameter, shrinkage rules are applied to the empirical wavelet coefficients, resulting in a non-linear wavelet-based spectral density estimator. Consequently, the advocated approach avoids the need to select the finest scale J, since the noise in the wavelet coefficients is naturally suppressed. Simple data-dependent threshold parameters are also considered. In general, the convergence of the spectral test statistics toward their respective asymptotic distributions appears to be relatively slow. In view of that, Monte Carlo methods are investigated. In a small simulation study, several spectral test statistics are compared, with respect to level and power, including versions of these test statistics using Monte Carlo simulations.     

Estimating pedestrian delays at signalized intersections in developing cities by Monte Carlo method

This paper proposes a Monte Carlo model to estimate pedestrian delays at signalized intersections adopting pre-timed two-phase control in developing cities like Xi’an, China. In the model, the signal cycle is divided into a series of subphases, and each subphase lasts 1 s. The model includes four parts: vehicle generator, pedestrian generator, pedestrian model, and statistical module. Vehicle generator is used to generate a vehicle sequence traversing the crosswalk. Pedestrian generator is used to generate a pedestrian sequence arriving at the crosswalk. Pedestrian model includes a set of rules pedestrians follow at signalized intersections. And statistical module calculates the average delay of pedestrians arriving during each subphase, and the overall average delay as well. Finally, field data collected from an intersection in Xi’an are used to validate the model, and the validation results indicate that the proposed model is able to estimate accurately the average delay of pedestrians arriving during each subphase.     

换电站对配网无功优化的影响研究

换电站作为电动汽车的主要充电基础设施,随着电动汽车的普及也将大规模建设。为了分析大规模换电站接入配网对无功优化产生的影响,提出了以换电站充电负荷对配网无功优化的影响为研究对象。首先基于力帆换电站的历史数据分析了换电站充电负荷影响因素的分布规律,然后采用蒙特卡洛仿真模拟建立了换电站的充电负荷模型。还建立了配网无功优化的数学模型,采用禁忌搜索算法求解数学模型。考虑到换电站充电负荷为概率模型,采用基于蒙特卡洛模拟的随机潮流进行潮流计算。最后从换电站充电负荷的渗透率角度分析了对配网无功优化的影响,得出的结论是换电站充电负荷的渗透率为一定值时,相比未接入换电站充电负荷的情况,可以降低电容器的投切次数,延长电容器的使用寿命。     

基于全相位频谱校正的TMBOC信号的捕获

针对使用传统部分匹配滤波器（PMF）结合快速傅里叶变换（FFT）无法精确捕获时分复用二进制偏移载波（TMBOC）调制信号的问题,提出一种基于全相位频谱校正的捕获方法。首先通过PMF过程对接收信号进行部分相关运算,再使用全相位快速傅里叶变换（apFFT）算法对多普勒效应进行补偿,最后结合全相位频谱校正技术对功率谱进行校正。仿真结果表明,在同一条件下,该算法比PMF-FFT加窗算法检测概率提高了3 dB左右,并有效缩短了捕获时间。该算法可比PMF-FFT加窗算法更精确捕获TMBOC信号。     

电能质量监测中频谱泄露检测方法研究

为了提高电能质量算法的精确度,需要检测傅里叶变换(FFT)时的频谱泄露程度,尽可能地抑制频谱泄露现象。详细分析了频谱泄露的机理,在此基础上提出了一种基于调制波的频谱泄露检测方法,在源信号上叠加调制波,根据连续十周波电压测量值,计算出波动频率下的频谱泄露系数,从而判断信号的频谱泄露情况。使用该方法对比分析了通过两种不同加窗方式进行FFT的结果,实验结果验证了频谱泄露系数及其约束条件的可行性,该检测方法简单易操作,能够有效地检测频谱泄露现象,为检测电能质量监测终端的电压计算方法提供了新思路。     

整车路面不平度激励的仿真方法研究

分析了路面不平度对三轴式整车的随机激励输入,利用白噪声法和传递函数法推导 得出整车六轮路面不平度输入的状态方程。在Matlab/Simulink 中搭建二维路面不平度数学模型, 并与标准路面不平度进行了比较和验证,说明了搭建模型的准确性。通过整车状态方程搭建六轮 路面不平度数学模型,仿真结果说明了同车桥的左右两车轮的功率密度谱差异较大,同侧前后车 轮的功率密度谱差异较小,比较符合多车桥式重卡的实际情况,且均在标准路面不平度功率密度 谱的标准范围内。为了进一步验证仿真结果,对整车六轮的路面不平度互相关系数进行了分析, 分析结果与上述结论吻合。