Stochastic period-doubling bifurcation analysis of a Rssler system with a bounded random parameter

This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic RSssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rossler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rossler system.

Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter

Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.

Shrinkage Estimation in the Random Parameters Logit Model

In this paper, we explore the properties of a positive-part Stein-like estimator which is a stochastically weighted convex combination of a fully correlated parameter model estimator and uncorrelated parameter model estimator in the Random Parameters Logit (RPL) model. The results of our Monte Carlo experiments show that the positive-part Stein-like estimator provides smaller MSE than the pretest estimator in the fully correlated RPL model. Both of them outperform the fully correlated RPL model estimator and provide more accurate information on the share of population putting a positive or negative value on the alternative attributes than the fully correlated RPL model estimates. The Monte Carlo mean estimates of direct elasticity with pretest and positive-part Stein-like estimators are closer to the true value and have smaller standard errors than those with fully correlated RPL model estimator.

Modelling lane-changing execution behaviour in a connected environment:A grouped random parameters with heterogeneity-in-means approach

Lane-changing is performed either to follow the route to a planned destination(i.e.,mandatory lane-changing)or to achieve better driving conditions(i.e.,discretionary lane-changing).A connected environment is expected to assist during lane-changing manoeuvres,but it is not known well how driving aids in a connected environment assist lane-changing execution.As such,this study investigates the impact of a connected environment on lanechanging execution time during mandatory and discretionary lane-changing manoeuvres.To this end,this study designed an advanced driving simulator experiment where 78 drivers performed these manoeuvres on a simulated motorway in three randomised driving conditions.The conditions were baseline(without driving aids),a fully functioning connected environment with a perfect supply of driving aids,and an impaired connected environment with delayed driving aids.The lane-changing execution time has been modelled by a random parameters hazard-based duration modelling approach,which accounts for the panel nature of data and captures the unobserved heterogeneity.Results suggest that,compared to the baseline condition(i.e.,a non-connected environment),most of the drivers in the connected environment take more time to complete their lane-changing manoeuvres,indicating drivers’safer lane-changing execution behaviour in the connected environment.The communication delay driving condition has been found to have more deteriorating effects on mandatory lanechanging manoeuvres than discretionary lane-changing manoeuvres.This study concludes that(i)the connected environment increases safety margin during both lane-changing manoeuvres,and(ii)a higher magnitude of safety margin is observed during mandatory lane-changing manoeuvres whereby drivers have a higher need for assistance.

Investigating safety and liability of autonomous vehicles:Bayesian random parameter ordered probit model analysis

Purpose–This study aims to investigate the safety and liability of autonomous vehicles(AVs),and identify the contributing factors quantitatively so as to provide potential insights on safety and liability of AVs.Design/methodology/approach–The actual crash data were obtained from California DMV and Sohu websites involved in collisions of AVs from 2015 to 2021 with 210 observations.The Bayesian random parameter ordered probit model was proposed to reflect the safety and liability of AVs,respectively,as well as accommodating the heterogeneity issue simultaneously.Findings–The findings show that day,location and crash type were significant factors of injury severity while location and crash reason were significant influencing the liability.Originality/value–The results provide meaningful countermeasures to support the policymakers or practitioners making strategies or regulations about AV safety and liability.

Modeling severities of motorcycle crashes using random parameters

One of the critical areas of road safety is motorcycle safety. Motorcyclists are more vulnerable to injuries than occupants of other motor vehicles when involved in crashes.Researchers have studied the relationships between motorcycle crash severity and crash contributing factors. They are crash characteristics, roadway geometric design features,traffic characteristics, socio-demographics and environmental conditions. However, few researchers considered unobserved heterogeneity effects when modeling motorcycle crash injury severities, let alone interaction effects. In this research, motorcycle crashes in Wyoming that occurred from 2008 to 2017 were analyzed. Specifically, the injury severities of single motorcycle crashes and multiple vehicle crashes involving motorcycles were modeled. The response was whether the motorcycle crash incurred an incapacitating injury or fatality or not. The binary logistic regression and mixed binary logistic regression modeling structures were implemented. The mixed models revealed effects that otherwise would have been undisclosed in the binary logistic regression models’ results. According to the results of single motorcycle crashes, the majority of motorcycle-animal crashes and of motorcycle-barrier crashes were likely to be severe relative to other single motorcycle crashes. It was also found that horizontal curves increased the risk of severe injuries.Young riders were found to be less at risk of being gravely injured in single motorcycle crashes than older riders as well. Furthermore, riding under the influence and high posted speed limits increased the odds of severe crashes regardless of whether the crashes were single motorcycle crashes or multiple vehicle crashes involving motorcycles. Additionally,the mixed models uncovered interaction effects and unobserved effects pertaining to speed limits.

Evaluating the impact of traffic violations on crash injury severity on Wyoming interstates:An investigation with a random parameters model with heterogeneity in means approach

This study investigated the impact of traffic violations on crash injury severity on Wyoming’s interstate highways.A random parameters multinomial logit(MNL)model with heterogeneity in means was estimated as an alternative to the mixed logit model.This was done to better account for unobserved heterogeneity in the crash data.As per the results,the random parameters model with heterogeneity in means not only exhibited a better fit but also uncovered more insights regarding the factors influencing crash injury severity.The advanced model showed that traffic violations,crash characteristics and environmental characteristics among other factors impact crash injury severity on Wyoming’s interstate highways.With regards to traffic violations,driving too fast for prevailing conditions and driving under the influence of alcohol and drugs were identified as the main violations that significantly influenced crash severity.Among other useful insights,the heterogeneity in mean specification indicated that the likelihood of severe injury crashes is increased by the interactive effect between non-trucks(vehicles not classified as trucks)and driving too fast for conditions.This is a significant implication that high speed behavior by non-truck drivers in adverse weather conditions is ranked as one of the hazardous traffic violations on Wyoming’s interstates.This study provided for the first time important information on the impact of traffic violations on crash severity of crashes that occurred on challenging roadways that characterized by mountainous terrain and severe weather conditions.Results from the study will help enforcement agencies in the state to better identify appropriate countermeasures to mitigate the impact of violations on crash severity.

Exploring traffic safety climate with driving condition and driving behaviour:a random parameter structural equation model approach

This study aimed to explore traffic safety climate by quantifying driving conditions and driving behaviour.To achieve the objective,the random parameter structural equation model was proposed so that driver action and driving condition can address the safety climate by integrating crash features,vehicle profiles,roadway conditions and environment conditions.The geo-localized crash open data of Las Vegas metropolitan area were collected from 2014 to 2016,including 27 arterials with 16827 injury samples.By quantifying the driving conditions and driving actions,the random parameter structural equation model was built up with measurement variables and latent variables.Results revealed that the random parameter structural equation model can address traffic safety climate quantitatively,while driving conditions and driving actions were quantified and reflected by vehicles,road environment and crash features correspondingly.The findings provide potential insights for practitioners and policy makers to improve the driving environment and traffic safety culture.

Dynamic simulation of beam-like structure with a crack subjected to a random moving mass oscillator

In this paper, dynamic simulation of a beam-like structure with a transverse open crack subjected to a random moving mass oscillator is investigated. The simultaneous effect of a crack and a random oscillator has not been addressed up to now. The crack in the beam at different locations and with different depths is considered as one group of damage, each as an individual imperfection. In addition, bearing immobility is considered as another type of problem in the beam. Mass, stiffness, damping and velocity of the oscillator are assumed to be random parameters. An improved perturbation technique is applied to reduce the simulation time. It was found that there is a maximum value of the variance of each uncertain parameter, in which the maximum reliability of the perturbation method can be achieved, and that this maximum value can be obtained by the Alpha-Hilber Monte-Carlo simulation method. The simulation results reveal that the mass and the velocity uncertainty cause high uncertainty in the deflection of the beam. Also, the pattern of the deflection is not affected by different random oscillator parameters, and as a result, the type of damage can be identified even with high uncertainty. Moreover, the deflection in the nodes around the mid-span of the beam provides the best information regarding the imperfections, and consequently leads to the best sensor locations in an actual experiment.

Hopf bifurcation of nonlinear system with multisource stochastic factors

The article mainly explores the Hopf bifurcation of a kind of nonlinear system with Gaussian white noise excitation and bounded random parameter.Firstly,the nonlinear system with multisource stochastic fac-tors is reduced to an equivalent deterministic nonlinear system by the sequential orthogonal decomposi-tion method and the Karhunen-Loeve(K-L)decomposition theory.Secondly,the critical conditions about the Hopf bifurcation of the equivalent deterministic system are obtained.At the same time the influence of multisource stochastic factors on the Hopf bifurcation for the proposed system is explored.Finally,the theorical results are verified by the numerical simulations.

参数化设计方法在非线性形体建筑设计中的应用研究

对参数化设计方法进行简要分析并探究其在建筑设计中的应用策略,主要阐述参数化的概念及其性质,介绍非线性建筑设计的概念及其特点,对参数化在建筑设计过程中的关键环节进行详细论述,并对建筑参数化思维的常用设计方法进行分析。

Alpha稳定分布的参数表征及仿真

仿真服从标准参数系下任意参数的Alpha稳定分布(αS)随机变量是开展相关信号处理研究的基础。服从对称Alpha稳定分布(SαS)的随机变量较易生成,而产生服从αS分布随机变量较为困难,一个重要的因素是存在易于混淆的不同参数表征。本文在讨论Alpha稳定分布概念、性质的基础上,讨论了三种主要参数系,提出并证明了正确的产生服从αS分布随机变量的变换公式及仿真方法,并通过Monte-carlo仿真比较了三种参数系表征的αS分布的概率密度函数的差异。对Pearson海杂波的仿真表明了该方法的有效性,而Chambers方法存在分布位置的偏差。

Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer-van der Pol system

In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.

GRAPES区域集合预报系统模式不确定性的随机扰动技术研究

为进一步描述GRAPES(Global/Regional Assimilation and Prediction System)区域集合预报系统(GRAPES Me—soscale Ensemble Prediction System,GRAPES—MEPS)中GRAPES—Meso模式的不确定性特征,本研究在GRAPES—MEPS系统中引人了模式物理参数化倾向随机扰动方案(Stochastically Perturbed Parameterization Tendencies,SPPT),随机扰动型的产生是基于-阶马尔科夫链,其具有时间相关性特征,并服从正态分布,另外经过谱展开随机场具有空间结构特征,在水平结构上较平滑和连续。本文开展了基于SPPT方案的GRAPES—MEPS集合预报试验,针对SPPT方案中随机场的扰动幅度和时间相关尺度参数开展了一系列敏感性试验,并对试验结果进行了较全面的集合预报客观检验,此外,针对一次强降水过程,分析了SPPT方案对降水预报的影响。试验结果表明,引入SPPT方案能在一定程度上提高GRAPES—MEPS系统的预报技巧,降低系统的漏报率;且能显著改进预报后期大雨量级降水的预报技巧。通过敏感性试验发现,对于GRAPES—MEPS系统,SPPT方案的效果与随机扰动场幅度的范围,及扰动场的时间相关尺度选择相关,需经过敏感性试验确定出较适合的参数。

混凝土随机参数化骨料模型及加载的数值模拟

在细观层次上,混凝土被认为是一种由粗骨料、水泥砂浆以及二者间的黏结界面所组成的三相非均质复合材料。为此,在二维情形下,基于参数曲线的自由变形技术,将混凝土骨料及黏结界面的轮廓线用确定的、形式统一的参数方程予以表示,建立了混凝土随机参数化骨料数学模型。对骨料为卵石和碎石的混凝土,分别给出了级配、含量、配合比等可控制的随机混凝土数值试样。该数学模型描述了骨料、砂浆与黏结界面组成的二维三相复合结构形式。最后,使用MATLAB、AutoCAD和ANSYS软件建立了有限元网格模型,并进行了数值加载试验。结果表明,该方法可较好地满足混凝土动静力学性能细观数值分析的要求。

对流边界层顶部夹卷层厚度特征及其参数化分析

运用大涡模拟结果分析并讨论了对流边界层顶部夹卷层厚度特征及其参数化.常见的参数化方案是建立归一化夹卷层厚度与对流理查森数(Ri*)之间的指数对应关系,但不同研究结果得到的幂指数有很大差异.分析表明:"Ri*方案"本身是造成这种不确定性的原因;另一种理查森数(RiN),即浮力理查森数,可以较好地表征夹卷层厚度.大涡模拟结果表明:"RiN方案"能够有效地减小夹卷层厚度参数化的不确定性.为消除湍流随机性对参数化的影响,我们对大涡模拟结果进行了时间平均处理,并用所得数据讨论了夹卷层厚度与浮力理查森数之间的关系.结果表明:两者之间有很好的指数对应关系,平均幂指数为-2/5;计算结果同时显示,幂指数仍然存在一定的变化范围(-1/3^-1/2).夹卷层厚度的这种特性反映出夹卷过程的复杂性,即兼有热泡和界面振荡的特征.

基于WRF模式的风电场短期风速集成预报方法研究

风能始源于大气的运动,具有很大的随机性和间歇性。风速预测是风电场风功率预测的基础,其准确性具有重要的意义。对于复杂地形条件下,风速的预报一直是各国研究的难点和重点。为了提高风电场短期风速预报的准确性,本研究采用多种边界层参数化方案来集成预报风速,将各单一边界层参数化方案预报的风速及相应的实测风速数据,应用随机森林算法建立集成预报模型,对风电场的短期风速进行集成预报研究。试验结果表明,采用集成预报风速方法,预报的风速误差相比于单一边界层参数化方案预报的风速误差明显减小,对研究区域的风速、风向等气象要素有着较好的模拟效果,能够有效提高风速预报的准确率。

纯方位距离参数化概率假设密度和势概率假设密度滤波器

考虑多目标跟踪中量测源的不确定性,本文提出两个基于随机有限集(RFS)的多距离假设纯方位跟踪(BOT)滤波器.首先,详细推导距离参数化高斯混合概率假设密度(PHD)滤波器的递推公式.然后,详细推导距离参数化高斯混合势概率假设密度(CPHD)滤波器的势分布和强度的递推公式.此外,为跟踪随机出现的目标,提出一种自适应BOT新生目标强度的建立方法.仿真验证了算法的有效性.

单向编组站配流与调机运用综合问题

单向编组站配流与调机运用综合问题研究的是确定出发列车的编组内容,指派并调度解体和编组调机的任务,使得出发列车满足列车编组要求,调机任务没有冲突,且车辆在站总停留时间最小。基于并行机调度和资源分配理论,建立该问题的混合整数线性规划模型。设计有偏随机键遗传算法求解该优化模型,基于平均分配和随机分配规则生成初始种群,并采用参数均匀交叉算子以使子代能有效继承父代的优化特征。最后,以1个实际算例对所提出方法的有效性进行测试,并与现场采用的贪婪算法、直接求解模型的优化求解器CPLEX进行比较。算例结果显示所提算法在计算质量和计算效率上的优越性。

随机图点覆盖1度顶点核化算法分析

将随机图引入参数计算领域,利用随机图统计和概率分布等特性,从全局和整体上研究参数化点覆盖问题1度点核化过程中问题的核及度分布演变的内在机制和变化规律,并得出关于随机图1度点核化强度与顶点平均度关系及随机图点覆盖问题的决策与度分布关系的两个重要推论.最后分别从MIPS和BIND提取数据进行1度核化实验和分析.初步结果表明,对随机图点覆盖问题的分析方法不仅具有理论上的意义,而且随着问题随机度的大小而对问题有不同程度的把握能力.