脉冲噪声下基于Myriad滤波及分形盒维数的频谱感知

为了实现脉冲噪声背景下频谱感知,本文提出基于Myriad滤波及分形盒维数的频谱感知方法。Alpha稳定分布噪声影响信号的分形盒维数值。由于Myriad滤波可以抑制Alpha稳定噪声,所以先对接收信号Myriad滤波,再计算其分形盒维数值作为检验统计量。仿真结果表明,该方法在Alpha稳定分布噪声下具有良好的频谱感知性能     

任意分布随机序列的产生方法

随机序列已经被广泛地使用在信号处理中。通常都是由已知概率密度得到分布函数,通过分布函数产生随机序列。然而在难以通过概率密度求得分布函数时,产生随机序列则变得十分困难。提出了一种随机数生成的新方法——基于频数的随机重构方法,即由已知的概率密度直接产生随机序列;以K分布概率密度产生随机序列为例,并用K分布的特征函数以及特征函数的标准差进行验证,通过仿真分析证明该方法的正确性。最后通过统计对比,此方法不仅简捷,而且解决了传统方法的一些局限性。     

一种非白非高斯数据的数值仿真方法

使用复合抽样法,可以产生具有指定概率密度形式的加性分布非高斯序列。通过在极零图上直接指定数对极零点,可以实现定性色化低阶自回归滤波器设计。把非高斯激励序列通过自回归滤波器,即可得到非高斯信号处理仿真研究中频繁使用的非高斯有色序列。结合一组混合高斯有色数据数值仿真实例,演示了这一由复合抽样法加定性色化构成的非白非高斯数据快捷数值仿真方法的有效性。     

混合高斯概率密度模型动态簇算法参数估计

混合高斯概率密度模型可以很好地拟合样本的概率密度。在各高斯分量概率密度互不重叠的条件下，使用动态簇算法可以快速而精确地估计出混合高斯概率密度模型参数。这是一种基于最小均方差原则的递推算法，在正向推导出各种可能簇边界后，再根据确定的最末边界值逆向推定各前导簇边界，从而得到混合高斯概率密度模型参数估计值。算法介绍之后，给出了两个拥有不同概率密度分布的仿真建模实例．最后总结分析了该算法的优劣，并简介了算法的推广．     

混合高斯参数估计的动态簇算法

混合高斯概率密度模型可以很好地拟合非高斯样本的概率密度。在各高斯分量概率密度互不重叠的条件下,使用动态簇算法可以快速而精确地估计出混合高斯概率密度模型参数。这是一种基于最小均方差原则的递推算法,在正向推导出各种可能的簇边界后,再根据确定的最末边界值逆向推定各前导簇边界,从而得到混合高斯概率密度模型参数估计值。描述模型及参数估计问题之后,动态簇算法被推导出来。然后深入探讨了该算法的实质及适用条件。最后结合数值仿真实例,分析了动态簇算法的估计性能。     

随机结构复合随机振动分析的概率密度演化方法

提出了随机结构复合随机振动分析的概率密度演化方法。通过引入扩展状态向量,构造具有随机初始条件的状态方程,导出了复合随机振动反应的概率密度演化方程。结合精细时程积分方法和Lax-Wendroff差分格式对概率密度演化方程提出了数值求解方法。进行了八层层间剪切框架结构复合随机振动反应的概率密度演化分析,证明提出的方法具有计算高效、收敛性稳定与精度高的特点。研究表明随着时间的增长,复合随机振动反应概率密度曲线趋于复杂,基于正态分布假定的二阶矩分析方法可能造成可靠度分析结果的显著偏差。与仅考虑结构参数随机性和仅考虑输入随机性时的结构反应相比,复合随机振动反应概率密度曲线峰值降低、分布变宽,且随机涨落显著增强。     

非瑞利混响背景下接收机工作特性曲线仿真

介绍了高分辨主动声呐的非瑞利分布混响的产生原因及几种典型的混响概率密度分布函数,并通过对混响概率密度分布函数的拖尾分析及其高阶统计量的比较,分析了检测过程中虚警概率增大的原因。此外,在窄带信号检测条件下,利用蒙特卡洛方法对瑞利分布和非瑞利分布混响背景下的接收机工作特性曲线进行了仿真。     

安全性第一准则下的组合贷款模型

提出了一种在概率准则意义下的组合贷款模型,并设计了基于随机模拟的混合优化算法进行求解。 该算法突破了各种贷款收益率必须服从正态分布的假定,可对贷款收益率是任意分布形式的模型进行求解。 经数值仿真,验证了算法的可行性。     

尾矿坝属性参数概率分布类型及变化趋势研究

现有研究认为大多数坝体属性参数服从中心极限分布,但由于属性参数实际取值范围有限,导致采用中心极限分布不足以表征参数的非正态分布特性,造成所拟合分布模型与实际参数分布区间契合度低等问题.考虑到坝体属性参数具有非负值,且存在偏度,首先用"3σ"准则结合样本数据的偏度确定样本分布取值范围;根据参数偏度特征利用改进的经典分布拟合法拟合出不同分布概率密度曲线和累积概率函数曲线,从而对参数概率分布模型进行推断,并根据卡方检验法、K-S检验法进行检验;在确定参数分布类型后,利用曼-肯德尔法对参数变化趋势作出分析.研究结果表明:固结排水剪切试验中粘聚力分布取值表现出左偏态特征,其他实验下参数取值均表现出右偏态;固结排水剪切和不排水剪切实验中粘聚力服从极值I型分布,内摩擦角服从对数正态分布;固结不排水剪切实验中粘聚力和内摩擦角均服从正态分布;固结排水剪切和不排水剪切实验中粘聚力在经历波动期后均表现出下降趋势,而3组实验中内摩擦角整体在经历波动期后均呈现显著上升趋势.     

失配误差的计算机辅助分析与评定

失配误差是无线电测量中的一项主要误差,通常认为它服从反正弦分布。本文利用计算机仿真技术研究了失配误差的分布形式,仿真结果表明失配误差只在反射参数的测量误差可以忽略的情形下服从反正弦分布,因而工程估算法存在一定的误差。同时研究了矢量修正后失配误差的分布形式及修正结果引入的不确定度。     

基于预测模型的虚拟试验不确定性分析方法

 工程系统中不可避免地存在各种参数不确定性,利用数值计算模型对系统进行虚拟试验时应进行不确定性分析.大型耗时计算模型的不确定性分析将面临严重的的计算复杂性问题,为此,针对工程应用中耗时计算模型,提出一种基于贝叶斯预测模型的不确定性分析仿真方法,采用概率分布为参数不确定性建模,研究系统响应预测不确定性的概率特征.泰勒杆撞击实例验证了该方法的高效性.     

Digital simulation of an arbitrary stationary stochastic process by spectral representation

In this paper we present a straightforward, efficient, and computationally fast method for creating a large number of discrete samples with an arbitrary given probability density function and a specified spectral content. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In contrast to previous work, where the analyses were limited to auto regressive and or iterative techniques to obtain satisfactory results, we find that a single application of the inverse transform method yields satisfactory results for a wide class of arbitrary probability distributions. Although a single application of the inverse transform technique does not conserve the power spectra exactly, it yields highly accurate numerical results for a wide range of probability distributions and target power spectra that are sufficient for system simulation purposes and can thus be regarded as an accurate engineering approximation, which can be used for wide range of practical applications. A sufficiency condition is presented regarding the range of parameter values where a single application of the inverse transform method yields satisfactory agreement between the simulated and target power spectra, and a series of examples relevant for the optics community are presented and discussed. Outside this parameter range the agreement gracefully degrades but does not distort in shape. Although we demonstrate the method here focusing on stationary random processes, we see no reason why the method could not be extended to simulate non-stationary random processes.     

Voltage stability analysis considering the uncertainties of dynamic load parameters

Many uncertainties exist in power systems and they will affect the stability analysis results. Voltage stability considering uncertainty in load parameters will be discussed. With the assumption that parameter variation is normal distribution, the probabilistic characteristics of eigenvalues under the uncertainties of dynamic load parameters can be obtained. Distribution of the critical eigenvalue will determine the stability probability of a power system. The stability margin can be inferred from the probabilistic critical load level, which is the maximal load level where system is `probabilistically` stable. Case studies on three test systems illustrate that the stability margin will be reduced with load uncertainty. The proposed probabilistic results are validated using deterministic method of Monte Carlo on multi 10`000 sample studies.     

Probability of liquefaction spread

In order to predict the potential of liquefaction spread for sandy soil surface ground, a methodology is presented which evaluates probability of fraction of liquefaction spread for a zone under study, conditional on earthquake hazard. The SPT values are considered variables which are spatially correlated. The method which is used on this study is a Monte Carlo simulation based on a disjoint set of sampling density functions to make easy the sampling of random variables which are, otherwise, to be sampled from a joint probability density function of general distribution.The ground is modelled to consist of three dimensional discrete semi-zones having discrete elements in the vertical direction.A liquefaction potential index that is widely used in the design practice in Japan to account for the distribution of the safety factor in the soil-column direction, is employed as the performance function for the probability of liquefaction spread, and the numerical results are presented as a fragility curve of liquefaction spread.     

横浪中船舶的随机混沌运动

采用概率密度函数和数值模拟的方法研究随机横浪中船舶的混沌运动特性和发生混沌运动的临界参数条件。综合考虑非线性阻尼、非线性恢复力矩以及白噪声横浪激励,建立了船舶的横摇非线性随机微分方程。用随机Melnikov均方准则确定混沌运动的系统参数域后,应用路径积分法求解随机微分方程得到了响应的概率密度函数。研究发现:当噪声强度大于混沌临界值时,船舶出现随机混沌运动;对于高的白噪声激励强度,系统响应有两种较大可能的状态并在这两个状态间随机跳跃,这时船舶的运动不稳定并可能发生倾覆。     

Dynamic response and reliability analysis of structures with uncertain parameters

An original approach for dynamic response and reliability analysis of stochastic structures is proposed. The probability density evolution equation is established which implies that incremental rate of the probability density function is related to the structural response velocity. Therefore, the response analysis of stochastic structures becomes an initial‐value partial differential equation problem. For the dynamic reliability problem, the solution can be derived through solving the probability density evolution equation with an initial value condition and an absorbing boundary condition corresponding to specified failure criterion. The numerical algorithm for the proposed method is suggested by combining the precise time integration method and the finite difference method with TVD scheme. To verify and validate the proposed method, a SDOF system and an 8‐storey frame with random parameters are investigated in detail. In the SDOF system, the response obtained by the proposed method is compared with the counterparts by the exact solution. The responses and the reliabilities of a frame with random stiffness, subject to deterministic excitation or random excitation, are evaluated by the proposed method as well. The mean, the standard deviation and the reliabilities are compared, respectively, with the Monte Carlo simulation. The numerical examples verify that the proposed method is of high accuracy and efficiency. Moreover, it is found that the probability transition of structural responses is like water flowing in a river with many whirlpools, showing complexity of probability transition process of the stochastic dynamic responses. Copyright © 2004 John Wiley & Sons, Ltd.     

An RKPM-based formulation of the generalized probability density evolution equation for stochastic dynamic systems

In the stochastic dynamic analysis, the probability density evolution method (PDEM) provides an optional way to capture the complete probability distribution of the stochastic response of general nonlinear systems. In the PDEM, the key point is to solve the generalized probability density evolution equation (GDEE), which governs the evolution of the joint probability density function (PDF) of the response and the randomness. In this paper, a new numerical method based on the reproducing kernel particle method (RKPM) is proposed. The GDEE can be approximated through the RKPM. By some particles in the response domain, the instantaneous PDF and its partial derivative with respect to response are smoothly expressed. Then, the approximated GDEE can be discretized directly at the collocation points in the response domain. At the same time, discretization in the time domain is achieved by the difference scheme. Therefore, the RKPM-based formulation to obtain the numerical solution of GDEE is formed. The implementation procedure of the proposed method is given in detail. The accuracy and efficiency of this method are illustrated with some numerical examples. Some details of parameter analysis are also discussed.     

Reliability–sensitivity analysis using dimension reduction methods and saddlepoint approximations

Reliability–sensitivity, which is considered as an essential component in engineering design under uncertainty, is often of critical importance toward understanding the physical systems underlying failure and modifying the design to mitigate and manage risk. This paper presents a new computational tool for predicting reliability (failure probability) and reliability–sensitivity of mechanical or structural systems subject to random uncertainties in loads, material properties, and geometry. The dimension reduction method is applied to compute response moments and their sensitivities with respect to the distribution parameters (e.g., shape and scale parameters, mean, and standard deviation) of basic random variables. Saddlepoint approximations with truncated cumulant generating functions are employed to estimate failure probability, probability density functions, and cumulative distribution functions. The rigorous analytic derivation of the parameter sensitivities of the failure probability with respect to the distribution parameters of basic random variables is derived. Results of six numerical examples involving hypothetical mathematical functions and solid mechanics problems indicate that the proposed approach provides accurate, convergent, and computationally efficient estimates of the failure probability and reliability–sensitivity. Copyright © 2012 John Wiley & Sons, Ltd.