Limit theorems for supremum of Gaussian processes over a random interval

Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.

Non-Stationary Random Process for Large-Scale Failure and Recovery of Power Distribution

This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe weather. Large-scale power failures often occur, resulting in millions of people without electricity for days. However, the problem of large-scale power failure, recovery and resilience has not been formulated rigorously nor studied systematically. This work studies the resilience of power distribution from three aspects. First, we derive non-stationary random processes to model large-scale failures and recoveries. Transient Little’s Law then provides a simple approximation of the entire life cycle of failure and recovery through a queue at the network-level. Second, we define time-varying resilience based on the non-stationary model. The resilience metric characterizes the ability of power distribution to remain operational and recover rapidly upon failures. Third, we apply the non-stationary model and the resilience metric to large-scale power failures caused by Hurricane Ike. We use the real data from the electric grid to learn time-varying model parameters and the resilience metric. Our results show non-stationary evolution of failure rates and recovery times, and how the network resilience deviates from that of normal operation during the hurricane.

Numerical Approximation of Fractal Dimension of Gaussian Stochastic Processes

In this paper we propose a numerical method to estimate the fractal dimension of stationary Gaussian stochastic processes using the random Euler numerical scheme and based on an analytical formulation of the fractal dimension for filtered stochastic signals. The discretization of continuous time processes through this random scheme allows us to find, numerically, the expected value, variance and correlation functions at any point of time. This alternative method for estimating the fractal dimension is easy to implement and requires no sophisticated routines. We use simulated data sets for stationary processes of the type Random Ornstein Uhlenbeck to graphically illustrate the results and compare them with those obtained whit the box counting theorem.

基于高斯过程回归的主动配电网负荷控制优化方法

以需求响应为核心进行配电网负荷控制优化时,节能百分比较低。因此,提出基于高斯过程回归的主动配电网负荷控制优化方法。依托于随机森林算法,判断所有输入变量的重要性,明确主动配电网负荷影响变量。运用高斯过程回归原理,应用负荷预测算法,准确得出主动配电网需求侧未来一段时间内的负荷要求。在此基础上,以直接负荷控制为核心,建立负荷控制协调优化模型,再应用遗传算法求解最优负荷控制优化方案。算例分析结果表明:所提优化方法的节能百分比达到6.23%,说明该方法达到了节能的目的。

TVAR Time-frequency Analysis for Non-stationary Vibration Signals of Spacecraft

Predicting the time-varying auto-spectral density of a spacecraft in high-altitude orbits requires an accurate model for the non-stationary random vibration signals with densely spaced modal frequency. The traditional time-varying algorithm limits prediction accuracy, thus affecting a number of operational decisions. To solve this problem, a time-varying auto regressive （TVAR） model based on the process neural network （PNN） and the empirical mode decomposition （EMD） is proposed. The time-varying system is tracked on-line by establishing a time-varying parameter model, and then the relevant parameter spectrum is obtained. Firstly, the EMD method is utilized to decompose the signal into several intrinsic mode functions （IMFs）. Then for each IMF, the PNN is established and the time-varying auto-spectral density is obtained. Finally, the time-frequency distribution of the signals can be reconstructed by linear superposition. The simulation and the analytical results from an example demonstrate that this approach possesses simplicity, effectiveness, and feasibility, as well as higher frequency resolution.

非线性随机响应单侧尾部分布的代理模型算法

对于大型复杂结构的非线性随机响应,随机模拟法是较为实用的工程分析方法。然而对于需要大量样本的尾部概率估计,高昂的计算成本限制了该类方法的应用。为了降低计算成本,开发了基于主动学习的高斯过程代理模型算法,但其主动学习优化策略仍需进一步完善,以满足工程中对单侧尾部概率分布估计精度的需求。为此提出了一种具有智能关注功能的搜索函数,构建了针对工程中事故风险极高的单侧尾部的算法。以地铁隧道环梁和衬砌间复杂粘结滑移行为为例,验证了该算法的有效性。相比原有算法,本文算法对单侧尾部概率的估计误差降低了30%。本文算法能更精确地估计复杂结构随机响应分布的单侧尾部概率,进而估计极端事故的发生概率,为风险测度和防灾管理决策提供量化分析依据。

车削加工随机切削力建模与预测研究

针对车削材料的非均匀性和多模态加工系统等实际加工条件,提出了一种预测随机切削力的模型。将确定性模型中的常数切削系数转化为平稳的高斯过程,采用随机模型对刀具振动和未切削切屑厚度进行了建模。通过实验估计了随机切削系数,并在任意时间尺度下利用随机微分方程进行有效模拟。结合随机模型与多模态动力学方程,对随机切削力进行了数值预测。为此建立了三模态加工系统,并对不同金属合金的工件进行了测试。结果表明估计的随机切削系数对切削参数不敏感,预测结果与实验结果在时域和统计域上具有较好的吻合性。在切削力无法在线测量的情况下,该模型可为刀具状态监测提供参考。

基于高斯过程回归模型对一回路泄漏率的预测

工况的剧烈变化可能导致一回路系统中法兰连接部位、泵的密封面等处发生泄漏。针对准确的泄漏物理模型很难建立的实际情况,在对不可测的温度应力参数进行正态随机游走的基础上,以高斯过程回归模型为替代模型对一回路泄露率进行预测,并对替代模型的不确定性进行定量分析。结果表明,高斯过程回归模型能够方便地实现对替代模型的不确定性评估,并且在小样本容量的情况下,能够实现对一回路泄漏率较准确的预测。

基于改进T-B法的宽带高斯过程疲劳损伤分析

针对宽带高斯随机应力过程造成的疲劳损伤问题,本文提出一种基于改进Tovo-Benasciutti(T-B)法的疲劳损伤频域分析方法。通过不同参数形式的功率谱进行时域的疲劳损伤分析,针对T-B法中的关键参数bTB提出一个新的非线性函数模型。与原T-B法相比,新提出的函数模型bMTB可以考虑S-N曲线斜率参数m的影响,并以此为基础提出基于改进T-B法的疲劳损伤分析方法。以时域的雨流计数法结果作为基准,分别采用参数化功率谱和真实响应谱进行数值试验,并与现有的多种宽带高斯疲劳损伤分析方法进行对比,验证本文所提出的改进T-B法的准确性和适用性。

考虑特征选择的短期光伏功率组合预测模型

针对光伏功率预测中特征因素太多、关键特征与功率间映射关系难以有效挖掘和预测精度不高的问题,提出一种基于随机森林RF(random forest)算法特征选择和灰狼优化算法GWO(grey wolf optimizer)优化高斯过程回归GPR(Gaussian process regression)模型相结合的组合预测模型。首先,采用皮尔逊和斯皮尔曼相关系数对特征进行相关性分析,并进行初步筛选;接着,基于随机森林算法对特征进行重要性评价,并选取最优特征子集;然后,采用灰狼优化算法对高斯过程回归模型进行优化;最后,将最优特征子集输入到组合预测模型RFGWO-GPR中进行短期光伏功率预测。应用某光伏电站实测数据的仿真实验结果表明,提出的模型在不同天气条件下可以对特征进行有效选择,与未进行特征选择的单一模型相比,预测精度显著提高,并且明显优于其他优化算法与GPR模型组成的组合预测模型。

CFAR DETECTORS FOR HIGH RESOLUTION RADAR IN NON-GAUSSIAN CLUTTER

For high resolution radar, the echoes of target come from several points rather than one point as in low resolution radar. In this case the target is called an extended target. This paper presents two CFAR detectors for such a target in non Gaussian clutter, which are CA CFAR and OS CFAR detectors. The detection performances of the two detectors are evaluated.

Existence and joint continuity of local time of multi-parameter fractional Lévy processes

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.

Parameters Identification of Stochastic Nonstationary Process Used in Earthquake Modelling

This paper proposes a new deterministic envelope function to define non-stationary stochastic processes modeling seismic ground motion accelerations. The proposed envelope function modulates the amplitude of the time history of a stationary filtered white noise to properly represent the amplitude variations in the time histories of the ground motion accelerations. This function depends on two basic seismological indices: the Peak Ground Acceleration (PGA) and the kind of soil. These indices are widely used in earthquake engineering. Firstly, the envelope function is defined analytically from the Saragoni Hart’s function. Then its parameters are identified for a set of selected real records of earthquake collected in PEER Next Generation Attenuation database. Finally, functions of the parameters depending on the Peak Ground Acceleration and the kind of soil are defined from these identified values of the parameters of the envelope function through a regression analysis.

水平集高斯过程的非星凸形扩展目标跟踪算法

针对复杂环境下的非星凸形不规则形状扩展目标跟踪问题,该文提出基于能量泛函的水平集高斯过程扩展目标跟踪算法。首先,利用水平集随机超曲面模型(Level-Set RHM)通过多边形方法对形状内部进行建模。然后,用高斯过程(GP)学习Level-Set建模输入与输出的非线性映射关系,以求得边界函数最大值,并进一步推导Level-Set与GP相融合的非线性量测方程。在最优非线性滤波的框架下,最终推导得到水平集高斯过程(Level-Set GP)算法,并利用面积差作为不规则形状扩展目标形状估计的评价指标。仿真实验表明了所提算法对非星凸形不规则形状扩展目标形状估计的有效性。

改进的复合高斯型杂波模拟方法

零记忆非线性变换(ZMNL)方法和球不变随机过程(SIRP)是模拟复合高斯型杂波的主要方法.针对基于传统ZMNL与SIRP方法中的K与Pareto分布雷达杂波仿真中存在的形状参数只能为整数或半整数的问题,通过增加支路利用Gamma函数第二参数的可加性,提出将Gamma函数的概率密度函数(PDF)转化为二阶非线性常微分方程,并求解产生任意参数下的Gamma分布随机数,从而将复合高斯型分布杂波的形状参数扩展到一般实数.仿真实验表明:提出的方法不仅适用于非整数或非半整数形状参数值的杂波仿真,而且进一步提高了拟合度.

基于随机森林贝叶斯优化的机械臂运动参数优化研究

机械臂作为生产系统中的重要物流设备之一,在新产品投产前,需要对其未知的上下料轨迹及其运动参数进行寻优配置或整定,以找到适应于该产品的最优物流参数配置方案;但目前在机械臂的运动参数优化方面仍存在着优化时间成本较高、优化效果欠佳的问题。面向机械臂安装燃料电池极板工作场景,以机械臂的运动平稳性、绝对定位精度、物流效率的综合归一值为优化目标,采用基于随机森林概率代理模型的贝叶斯优化算法,以ABB IRB 1410机械臂为例,对其关键运动参数进行寻优。将其与高斯过程代理的贝叶斯算法在相同条件下所得实验结果进行了对比。实验表明,在机械臂运动参数优化问题上,随机森林贝叶斯算法相较于高斯贝叶斯算法,综合效果提升了15%。

The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index

Let {X（t）, t ≥ 0} be a standard（zero-mean, unit-variance） stationary Gaussian process with correlation function r（·） and continuous sample paths. In this paper, we consider the maxima M（T） = max{X（t）, t∈ [0, T ]} with random index TT, where TT /T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M（TT） exists under some additional conditions related to the correlation function r（·）.

Almost Sure Asymptotics for Extremes of Non-stationary Gaussian Random Fields

In this paper, the authors prove an almost sure limit theorem for the maxima of non-stationary Caussian random fields under some mild conditions related to the covariance functions of the Gaussian fields. As the by-products, the authors also obtain several weak convergence results which extended the existing results.

一种新的高斯双模态随机疲劳损伤分析方法

为能够准确地对高斯双模态随机过程的疲劳损伤进行评估,提出了一种名为改进频带法的疲劳损伤频域计算方法。该方法从功率谱分割的角度出发,首先分别将低频模态和高频模态的功率谱密度函数分割成很多份极窄的频带,利用损伤等效原则进行等效转换,得到相应的等效窄带过程。然后,将高频等效窄带过程向低频等效窄带过程再次进行等效转换。在此过程中,为考虑低频模态与高频模态之间的相互作用,引入与一个高、低频模态频率比、能量比以及S-N曲线材料参数m有关的修正因子对总零阶谱矩进行修正。最后,利用窄带过程疲劳损伤解析解即可计算高斯双模态过程的总疲劳损伤。以时域雨流计数法计算的疲劳损伤结果作为基准,分别采用理想矩形双模态谱和真实双模态谱进行数值试验,将该方法与多种现有频域疲劳损伤分析方法进行了对比。研究结果表明,提出的改进频带法与传统频域方法相比,具有计算精度更高并且易于编程的优点,该方法在实际工程应用中将具有很大的潜力。

MINIMUM ENTROPY DECONVOLUTION OF ONE-AND MULTI-DIMENSIONAL NON-GAUSSIAN LINEAR RANDOM PROCESSES

The minimum entropy deconvolution is considered as one of the methods for decomposing non-Gaussian linear processes. The concept of peakedness of a system response sequence is presented and its properties are studied. With the aid of the peakedness, the convergence theory of the minimum entropy deconvolution is established. The problem of the minimum entropy deconvolution of multi-dimensional non-Gaussian linear random processes is first investigated and the corresponding theory is given. In addition, the relation between the minimum entropy deconvolution and parameter method is discussed.