Developing theory of probability density function for stochastic modeling of turbulent gas-particle flows

Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.

Auxiliary error and probability density function based neuro-fuzzy model and its application in batch processes

This paper focuses on resolving the identification problem of a neuro-fuzzy model(NFM) applied in batch processes. A hybrid learning algorithm is introduced to identify the proposed NFM with the idea of auxiliary error model and the identification principle based on the probability density function(PDF). The main contribution is that the NFM parameter updating approach is transformed into the shape control for the PDF of modeling error. More specifically, a virtual adaptive control system is constructed with the aid of the auxiliary error model and then the PDF shape control idea is used to tune NFM parameters so that the PDF of modeling error is controlled to follow a targeted PDF, which is in Gaussian or uniform distribution. Examples are used to validate the applicability of the proposed method and comparisons are made with the minimum mean square error based approaches.

Identification of Neuro-Fuzzy Hammerstein Model Based on Probability Density Function

A new identification method of neuro-uzzy Hammerstein model based on probability density function(PDF) is presented,which is different from the idea that mean squared error(MSE) is employed as the index function in traditional identification methods.Firstly,a neuro-fuzzy based Hammerstein model is constructed to describe the nonlinearity of Hammerstein process without any prior process knowledge.Secondly,a kind of special test signal is used to separate the link parts of the Hammerstein model.More specifically,the conception of PDF is introduced to solve the identification problem of the neuro-fuzzy Hammerstein model.The antecedent parameters are estimated by a clustering algorithm,while the consequent parameters of the model are identified by designing a virtual PDF control system in which the PDF of the modeling error is estimated and controlled to converge to the target.The proposed method not only guarantees the accuracy of the model but also dominates the spatial distribution of PDF of the model error to improve the generalization ability of the model.Simulated results show the effectiveness of the proposed method.

A NEW DATA ASSOCIATION ALGORITHM USING PROBABILITY HYPOTHESIS DENSITY FILTER

Probability Hypothesis Density (PHD) filtering approach has shown its advantages in tracking time varying number of targets even when there are noise,clutter and misdetection. For linear Gaussian Mixture (GM) system,PHD filter has a closed form recursion (GMPHD). But PHD filter cannot estimate the trajectories of multi-target because it only provides identity-free estimate of target states. Existing data association methods still remain a big challenge mostly because they are com-putationally expensive. In this paper,we proposed a new data association algorithm using GMPHD filter,which significantly alleviated the heavy computing load and performed multi-target trajectory tracking effectively in the meantime.

MULTITARGET STATE AND TRACK ESTIMATION FOR THE PROBABILITY HYPOTHESES DENSITY FILTER

The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existing approaches combine the data association step to solve this problem. This paper proposes an algorithm which does not need the association step. Our basic ideal is based on the clustering algorithm of Finite Mixture Models (FMM). The intensity distribution is first derived by the particle-PHD filter, and then the clustering algorithm is applied to estimate the multitarget states and tracks jointly. The clustering process includes two steps: the prediction and update. The key to the proposed algorithm is to use the prediction as the initial points and the convergent points as the es- timates. Besides, Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) ap- proaches are used for the FMM parameter estimation.

A novel refined dynamic model of high-speed maglev train-bridge coupled system for random vibration and running safety assessment

Running safety assessment and tracking irregularity parametric sensitivity analysis of high-speed maglev train-bridge system are of great concern,especially need perfect refinement models in which all properties can be well characterized based on various stochastic excitations.A three-dimensional refined spatial random vibration analysis model of high-speed maglev train-bridge coupled system is established in this paper,in which multi-source uncertainty excitation can be considered simultaneously,and the probability density evolution method(PDEM)is adopted to reveal the system-specific uncertainty dynamic characteristic.The motion equation of the maglev vehicle model is composed of multi-rigid bodies with a total 210-degrees of freedom for each vehicle,and a refined electromagnetic force-air gap model is used to account for the interaction and coupling effect between the moving train and track beam bridges,which are directly established by using finite element method.The model is proven to be applicable by comparing with Monte Carlo simulation.By applying the proposed stochastic framework to the high maglev line,the random dynamic responses of maglev vehicles running on the bridges are studied for running safety and stability assessment.Moreover,the effects of track irregularity wavelength range under different amplitude and running speeds on the coupled system are investigated.The results show that the augmentation of train speed will move backward the sensitive wavelength interval,and track irregularity amplitude influences the response remarkably in the sensitive interval.

Multiple model PHD filter for tracking sharply maneuvering targets using recursive RANSAC based adaptive birth estimation

An algorithm to track multiple sharply maneuvering targets without prior knowledge about new target birth is proposed. These targets are capable of achieving sharp maneuvers within a short period of time, such as drones and agile missiles.The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems. However, the standard PHD filter operates on the single dynamic model and requires prior information about target birth distribution, which leads to many limitations in terms of practical applications. In this paper,we introduce a nonzero mean, white noise turn rate dynamic model and generalize jump Markov systems to multitarget case to accommodate sharply maneuvering dynamics. Moreover, to adaptively estimate newborn targets’information, a measurement-driven method based on the recursive random sampling consensus (RANSAC) algorithm is proposed. Simulation results demonstrate that the proposed method achieves significant improvement in tracking multiple sharply maneuvering targets with adaptive birth estimation.

Probability Distribution of the Hull Motion and Mooring Line Tension of Two Floating Systems

The statistical and distribution characteristics of the responses of a floater and its mooring lines are essential in designing floating/mooring systems.In general,the dynamic responses of offshore structures obey a Gaussian distribution,assuming that the structural system,and sea loads are linear or weakly nonlinear.However,mooring systems and wave loads are considerably nonlinear,and the dynamic responses of hull/mooring systems are non-Gaussian.In this study,the dynamic responses of two types of floaters,semi-submersible and spar platforms,and their mooring lines are computed using coupled dynamic analysis in the time domain.Herein,the statistical characteristics and distributions of the hull motion and mooring line tension are discussed and compared.The statistical distributions of the dynamic responses have strong non-Gaussianity and are unreasonably fitted by a Gaussian distribution for the two floating and mooring systems.Then,the effects of water depth,wave parameters,and low-frequency and wave-frequency components on the non-Gaussianity of the hull motion,and mooring line tension are investigated and discussed.A comparison of the statistical distributions of the responses with various probability density functions,including the Gamma,Gaussian,General Extreme Value,Weibull,and Gaussian Mixture Model(GMM)distributions,shows that the GMM distribution is better than the others for characterizing the statistical distributions of the hull motion,and mooring line tension responses.Furthermore,the GMM distribution has the best accuracy of response prediction.

基于高斯混合模型的采煤工作面冲击危险性评价

【目的】深入了解声发射或微震能量分布所蕴含的概率学信息,对于工作面回采过程中的冲击危险性评价具有重要意义。【方法】以陕西大佛寺煤矿4号煤层40111工作面作为工程背景,运用物理相似模拟实验、理论分析、现场监测等相关方法进行分析,研究了声发射监测数据在回采过程中的演化规律,阐明了声发射能量概率分布呈现波动性的物理意义,提出了基于高斯混合模型(Gaussianminture model,GMM)及置信区间的冲击危险性评价指标模型,并由现场微震数据进行验证。【结果和结论】结果表明:回采过程中上覆岩层周期性垮落并伴随声发射能量的集中释放。总能量的概率密度函数呈现多自由度的非对称分布,通过对比残差平方和等多项拟合效果指标,确定高斯混合模型为最佳拟合模型。基于EM(expectation maximization)算法的GMM聚类分析,将声发射事件总能量分布划分为两类:高频低能型和低频高能型,其中低频高能型与冲击事件的突发性和高能量破坏特征一致。依据概率-能量梯度变化特征,对工作面开采过程中冲击危险性进行了评估。研究成果为采煤工作面冲击危险性评价提供了概率学上的创新思路,具有在冲击地压监测预警及后续防治中的潜在应用价值。

铁道车辆轴箱振动非高斯特征与分布研究

以对铁道车辆轴箱振动非高斯特征与分布为对象开展研究。基于列车线路轴箱实测加速度信号,提取由轨道冲击引起的轴箱振动特征非高斯信号。使用多个概率密度函数(Probability Density Function,PDF)模型对实测信号进行拟合,并与实测特征信号的经验分布进行对比,评估各模型对轴箱特征非高斯信号的拟合精度。基于W-H非线性变换模型,建立一种非高斯信号模拟方法。利用模拟信号分析非高斯特征对各模型拟合精度的影响。结果表明:列车在行驶过程中具有非高斯特征,当列车经过轨道焊接接头、道岔与波磨路段时,由于轮轨冲击,非高斯特征明显增大,车轮多边形对信号非高斯特征几乎没有影响;基于W-H模型的非线性变换法,可以在保证模拟信号功率谱与指定功率谱基本一致的情况下,进行不同非高斯特征的信号模拟;高斯混合模型能够对铁道车辆非高斯信号较为准确地拟合;随着模拟非高斯信号峭度与偏度的增大,各模型与经验分布的相对误差也会增大,其中高斯混合模型拟合精度相对较高。

两相自适应训练策略与高效可靠度分析方法研究

概率密度演化方法对于复杂工程结构的系统可靠度分析有良好的适用性,但对于高维随机系统依然存在效率不高的问题.近年来通过少量训练样本训练目标代理模型,来替代目标随机系统提升可靠度分析效率的做法受到众多研究者的青睐.为提升构建自适应代理模型的精度和效率,文章提出了一种两相自适应训练策略,通过对概率空间分层次剖分,逐层次获得训练样本集.在两相训练策略的基础上分两步训练Kriging模型,不仅提升了Kriging模型对概率空间内失效边界的近似精度,更进一步降低了训练过程对计算机物理内存的消耗需求.随后通过结合概率密度演化理论,提出了一种基于等价极值理论的高效可靠度分析方法.为验证建议方法的有效性,分析了不同类型功能函数为目标的代理模型构建效率,并进行了一幢钢筋混凝土框架结构的抗震可靠度分析.结果表明:两相自适应训练策略极大提升了目标代理模型的导出速率并保有较高的分析精度,弥补了概率密度演化理论在处理罕遇失效事件时精度不足的缺陷.值得说明的是,两相训练策略不仅适用于基于Kriging模型的代理模型训练,同时对其他类型的自适应代理模型的训练也有指导意义,并不受代理模型基本类型限制.

基于行为轨迹的中庭式酒店COVID-19感染概率研究

中庭式酒店建筑因中庭空间人员密集、气流波动大,属呼吸道传染疾病高感染概率区域,建筑高大公共空间的传染概率有待研究.以某中庭式酒店为研究对象,基于该酒店人流状况、行为轨迹的实测,通过回归分析,得到该酒店人流密度的分布规律;运用Anylogic软件,结合Wells-Riley感染概率计算模型,对不同类型人员感染后的酒店人群感染概率进行模拟.通过模拟可知,住宿人群、就餐人群、商务会议三类人群中单一人群感染时,感染概率分别为29.3%,17.9%,36.4%;当三类人员及后勤人员共同耦合感染时,感染概率增加至42.6%.通过对污染物颗粒的时空分布规律的分析发现三层、标准层污染物颗粒较多;人员交叉与感染概率呈正相关;流线交叉较多的就餐空间、滞留时间较长休闲空间、竖向交通空间等应重点考虑设计措施以降低其感染概率;该研究为人员行为轨迹下的酒店空间的布局优化提供研究思路,为疫情背景下寒冷地区中庭式酒店平疫结合酒店空间布局设计研究提供理论依据.

基于用户群体体验研究的人体工学椅优化设计

目的为提升人体工学椅的群体用户体验水平,从用户需求出发,研究产品的群体用户体验设计策略。方法首先,从白领人群对产品的行为特征、操作习惯和情感变化出发,结合唐·诺曼(Don Norman)提出的三层次理论,从欲望层次、行为层次和反应层次确定群体用户体验的关键评价指标,其次,应用提出的“概率密度有序加权”(Probability Density Ordered Weighting,PDOW)方法构建产品用户群体体验综合评价模型,克服用户体验测试的不确定性,并探寻用户群体评价结果与评价指标的联系。最后,设计白领人群人体工学椅产品用户体验实验,确定人体工学椅最佳方案。结果建模结果表明,应用综合评价模型,能够很好地反映出白领人群对人体工学椅外观、交互和情感的偏好,设计出用户体验更好的产品。结论“概率密度有序加权”方法可有效消除测试的不确定性,准确得出用户群体对产品的综合评价结果,其低成本、便捷高效的特性有助于产品设计过程中更好地了解用户群体的偏好,给产品设计中用户群体体验优化提供了新的解决思路。

基于椭圆随机超曲面模型CPHD滤波器的多扩展目标跟踪算法

复杂场景下多扩展目标跟踪在自动驾驶、目标识别等领域具有很高的应用价值。文中提出了一种基于椭圆随机超曲面模型(ERHM)的势概率假设密度(CPHD)滤波器。首先,基于有限集统计理论,利用CPHD滤波器建立多扩展目标的贝叶斯滤波框架;然后,采用ERHM描述扩展目标的量测源分布,并利用无迹变换嵌入CPHD滤波流程;最后,仿真实验结果表明,ERHM-CPHD滤波器对椭圆扩展目标的跟踪性能优于传统的伽马高斯逆威沙特CPHD滤波器,在杂波密度较高、目标新生的位置比较确定的场景或者扩展目标数目较多时,对扩展目标的参数估计更为准确。所提方法在高分辨率雷达多目标跟踪方面具备很好的运用前景。

生物氧化预处理过程pH值随机分布控制方法研究

生物氧化预处理过程中氧化槽pH值是影响细菌活性的关键因素之一,而pH值输出形态分布不符合高斯分布,使传统的均值和方差难以描述输出pH值分布,本文提出一种对矿浆输出pH的概率密度函数(PDF)统计信息控制方法。首先,采用B样条逼近矿浆输出pH值的PDF统计信息;其次,针对权值向量之间的关系,利用动态神经网络(DNN)建立控制输入和权值向量之间的非线性动态模型,基于建立pH的PDF统计信息权值模型,设计滑模变结构控制器,通过构造Lyapunov函数进行稳定性分析;最后,实现输出PDF统计信息对目标PDF统计信息的跟踪。仿真结果验证了所提方法的有效性,为生物氧化预处理过程提供了新方法。

基于PDEM的台风作用下柱式隔离开关随机可靠性及失效风险分析

为评估柱式隔离开关在台风过程中的结构失效风险,考虑了风场和材料抗力的随机性,建立了隔离开关结构随机可靠性高效求解模型。首先,基于功率谱密度模型,考虑了地面粗糙度、平均风速和分界波数的随机性,给出了台风的随机场模型;其次,利用Abaqus有限元分析软件,建立了隔离开关结构的三维结构力学分析模型。同时,基于概率密度演化(Probability Density Evolution Model,PDEM)理论,给出了结构目标变量的概率密度函数计算方法;最后,采用Matlab-Abaqus进行联合模拟分析计算,实现了隔离开关结构可靠性的高效求解。结果表明,隔离开关绝缘支柱底部的极限应力为结构控制参数,风场和材料抗力的随机性对结构易损性曲线影响显著,设计过程中应控制材料抗力层次的随机性。

中国GDP增长率概率分布的预测分析——基于分位数因子模型

研究GDP增长率的概率分布,可以掌握经济增长的可能范围和经济发展趋势的不确定性,有助于决策者评估经济增长的风险和挑战,制定有效的经济政策。本文基于分位数因子模型(Quantile Factor Models,QFM),从高维宏观经济变量中提取分位数因子,拟合以分位数因子为条件的GDP增长率概率分布。实证结果表明:第一,分位数因子可为经济预测提供额外解释信息,提高模型的预测精度;第二,样本期间条件概率密度拟合结果表明QFM对GDP增长率的短期预测效果较好;第三,对比以分位数因子为条件和以实际GDP增长率为条件的两种概率分布,分位数因子为条件的分布在经济受到冲击时不确定性增大。本文对GDP增长率分布预测的研究与传统的均值预测相比,能提供比较全面和精确的经济预测信息,为经济不确定性和下行风险研究提供新思路,为经济波动机制的深入理解提供支持。

一类具有Ornstein-Uhlenbeck过程的随机捕食者-食饵模型的指数绝灭、平稳分布和概率密度函数

该文建立了一类具有Ornstein-Uhlenbeck过程、恐惧效应、Crowley-Martin型和修正的Leslie-Gower型功能反应函数的捕食者-食饵模型.首先通过构造合适的Lyapunov函数证明了全局解的存在唯一性,随后获得了两物种指数绝灭和平稳分布存在的充分条件.进一步通过求解相应的Fokker-Planck方程得到了概率密度函数的具体表达式.最后通过三个数值例子验证了理论结果的可行性,其研究表明随机干扰的波动强度和回复速率均会影响种群的生存.

基于高斯混合模型的物流非高斯随机振动损伤分析

针对公路运输环境中的振动信号具有明显的非高斯性,提出一种非高斯随机振动疲劳损伤分析方法。为了描述振动信号的幅值概率密度分布,采用移动加速度均方根来代表该段信号的振动强度,并引入高斯混合模型对加速度均方根值进行描述。在此基础上结合Tovo-Benasciutti方法和Dirlik方法推导出非高斯宽带频域疲劳损伤计算方法。最后,以雨流计数法作为参考,对不同峭度的实测振动信号进行疲劳损伤分析,结果表明,与传统频域疲劳损伤计算方法相比较,提出的非高斯疲劳损伤方法具有更高的计算精度。该研究对于运输包装件的随机振动加速试验设计有实际意义。

考虑多重不确定性的光伏支撑体系动力可靠性分析

提出了考虑多重不确定性的光伏支撑体系(Photovoltaic Support System,PSS)随机动力可靠性分析方法。首先,构建了基于概率密度演化理论(Probability Density Evolution Method,PDEM)的光伏支撑体系可靠性分析模型,包括概率守恒方程、基本控制方程和密度演化方程;然后,建立了光伏支撑体系的有限元分析模型,包括结构受力模型、荷载组合形式、网格划分算法等。仿真模型中考虑了结构所受荷载与结构本身的随机性,共计6个随机变量和44个代表点。为提升算法分析效率,提出了Abaqus⁃PDEM的联合仿真算法,仿真分析表明,光伏支撑体系的失效模式主要为应力控制和位移控制两种,后者影响更为明显,基本荷载组合工况下的可靠度为0.928。随着风力等级的提高,结构可靠性逐渐降低,在高风速区间(大于40 m/s),结构本身的不确定性会高估结构的可靠性水平,在设计中应予以关注。