Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

Extremum response surface method of reliability analysis on two-link flexible robot manipulator

In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.

Study on slope reliability method Response Surface Method based on Morgenstern-Price Method

The combination of Morgenstern-Price Method （MPM） with Response Surface Method （RSM） improves the eonventional RSM by replacing Finite-Element Method （FEM） with MPM, which is a type of reliability analysis method-RSM based on MPM, and makes the computing process simpler. The stability of the slope was re-evaluated by use of Monte Carlo method （MCM） and the result contrasted with the fore is the conclusion. The reliability analysis of the artificial slope in Donggang Power Station was carried on, and obtained the reliable charaeteristics, which provided basis for the project.

Comparative Study on Response Surfaces for Reliability Analysis of Spatially Variable Soil Slope

This paper focuses on the performance of the second-order polynomial-based response surfaces on the reliability of spatially variable soil slope. A single response surface constructed to approximate the slope system failure performance function G（X） （called single RS） and multiple response surfaces constructed on finite number of slip surfaces （called multiple RS） are developed, respectively. Single RS and multiple RS are applied to evaluate the system failure probability pf for a cohesive soil slope together with Monte Carlo simulation （MCS）. It is found thatpe calculated by single RS deviates significantly from that obtained by searching a large number of potential slip surfaces, and this deviation becomes insignificant with the decrease of the number of random variables or the increase of the scale of fluctuation. In other words, single RS cannot approximate G（X） with reasonable accuracy. The value of pc from multiple response surfaces fits well with that obtained by searching a large number of potential slip surfaces. That is, multiple RS can estimate G（X） with reasonable accuracy.

NON-LINEAR STOCHASTIC RESPONSE AND ITS EXTREME VALUE OF JACK UP PLATFORMS

The non-linear stochastic response of a jack-up platform subjected to wave load has been analyzed dynamically in this paper, and the analysis method in time domain is considered. Monte Carlo simulation is used to generate random sea. An emphasis is placed on the nonlinear hydrodynamic force. Several distributions for the statistical estimation of extreme responses are compared. For Gumble distribution, the parameters of its asymptotic distribution expression have been checked. The results show that the Gumble distribution agrees well with the simulated values of the responses.

Frequency response range of terahertz pulse coherent detection based on THz-induced time-resolved luminescence quenching

It has been proposed previously that the coherent detection of a terahertz（THz） pulse can be achieved based on the time-resolved luminescence quenching. In this paper, we investigate the frequency response range of this novel detection technology by simulating the motion of carriers in gallium arsenide（GaAs） by the ensemble Monte Carlo method. At room temperature, for a direct-current（DC） voltage of 20 kV/cm applied to the semiconductor（GaAs） and sampling time o140 fs, the luminescence quenching phenomena induced by terahertz pulses with different center frequencies are studied The results show that the quenching efficiency is independent of the THz frequency when the frequency is in a range o0.1 THz–4 THz. However, when the frequency exceeds 4 THz, the efficiency decreases with the increase of frequency Therefore, the frequency response range is 0.1 THz–4 THz. Moreover, when the sampling time is changed to 100 fs the frequency response range is extended to be approximately 0.1 THz–5.6 THz. This study of the frequency-dependen characteristics of the luminescence response to the THz pulse can provide a theoretical basis for the exploration of THz detection technology.

基于响应面-蒙特卡罗法的超高性能混凝土性价比研究

目前,学者对于UHPC的研究大多集中在其力学性能方面。本文以UHPC材料的性价比为研究目标,采用响应面-蒙特卡罗法构建响应面函数,并进行随机取样,研究钢纤维掺量对UHPC材料性价比的影响规律。分析了响应面-蒙特卡罗法参数的取值,发现随着钢纤维掺量的增加,UHPC材料的抗拉性价比和抗压性价比均减小。同时,得到了UHPC抗拉性价比和抗压性价比的最佳配比。

γ射线泥浆密度测试系统响应特性与灵敏度的Monte Carlo计算

γ射线密度测量系统是基于γ射线透射原理的非接触在线实时泥浆密度计,系统的响应特性与灵敏度是影响测量准确性的主要因数。利用Monte Carlo方法模拟计算了系统的响应特性和灵敏度,研究结果为类似利用γ射线透射原理系统的优化设计提供理论上的指导。

Monte Carlo模拟法与基坑变形的可靠度分析

将ＭｏｎｔｅＣａｒｌｏ模拟法与有限元技术结合，对基坑变形的稳定性进行可靠度分析，并通过重构响应面来提高ＭｏｎｔｅＣａｒｌｏ模拟法的计算效率。研究表明该方法可行，计算结果较符合实际。

热中子屏蔽性能测试平台设计优化及影响因素分析

材料热中子屏蔽性能测试是评价新型中子屏蔽材料屏蔽性能的重要手段,并为材料的改进和应用提供重要指导,在中子辐射屏蔽领域具有重要的研究意义。目前,基于同位素中子源的纯热中子场不易获得,而常用的热中子探测器能量响应范围较宽,导致材料的热中子屏蔽性能测试结果的准确性较差。针对此问题,提出一种基于“镉差法”的热中子屏蔽性能方法并建立相应的测试平台。该平台基于252Cf同位素中子源与3He正比计数器,以误差最小化为设计原则,利用蒙特卡罗模拟方法对该平台的辐射屏蔽体、中子慢化体、准直体及探测器屏蔽体的材料及尺寸进行优化。对常用辐射防护材料的热中子屏蔽性能进行测试以验证测试方法可行性与准确性,并对探测系统类型、中子源强度、探测系统远近距离、探测系统偏移及中子源类型5种影响因素进行了实验分析。研究表明,该平台的材料热中子屏蔽性能测试结果重复性高、再现性强,可实现对材料热中子屏蔽性能的准确测试。

套管井中补偿密度测井响应特性的Monte Carlo数值模拟

为了研究常规密度测井在套管井中的测井响应特性,应用Monte Carlo方法,从光子与物质相互作用的机理出发,利用Schlumberger公司的TLD仪器,计算得到了不同套管条件下光子通量的能量谱、光子通量与源距和地层电子密度的关系、长源距计数与短源距计数的交会图以及套管或水泥环厚度对长、短源距计数的影响等。计算结果表明,当套管和水泥环厚度小于4.4cm时,常规的TLD密度测井仪器在套管井中对地层密度的变化反应仍然灵敏。也就是说,在套管井中,密度测井仪器能够测量地层的密度;可以用双源距裸眼井密度测井的补偿原理来处理套管井密度测井的数据。但在套管井密度测井中,当套管厚度大于一定值后,仪器将难以正确识别地层的岩性。

基于Monte Carlo法的结构动力学模型确认

提出一种蒙特卡洛模拟(MCS)与多元回归分析相结合的有限元模型确认方法。采用基于动态响应面法生成的代理模型改进直接MCS,用一种逐步迭代的方式改进代理模型保证模型确认的精度。传统欧氏距离/马氏距离从不同方面描述了两点间距离,然而如果在距离准则中能够同时考虑两者则会更全面。在相关性分析过程中,综合欧氏/马氏距离的特点,采用了一种欧氏/马氏距离相结合的不确定量化方法(距离判别方法),并给出了基于此指标的迭代收敛判断准则。算例仿真结果表明:所提出的有限元模型确认方法和此距离判别方法的使用,能比较大地降低MCS的计算量并能得到满意的模型确认结果,迭代收敛的稳定性和精度都有了提高。

基于隆起变形分析的基坑坑底抗隆起稳定可靠度分析

采用土体硬化(Hardening Soil)模型,在PLAXIS 2D中建立基坑开挖数值模型,在获取坑底特征点隆起变形数据的基础上构建坑底隆起变形超限失效模式对应的极限状态函数,为提高计算效率,应用响应面法代替有限元计算快速获取坑底特征点隆起变形值,结合蒙特卡罗模拟方法进行坑底抗隆起稳定性可靠度分析,分析结果表明:第三层土的卸载再加载模量E_(3)^(ur)以及有效内摩擦角φ’_(3)的变异性对坑底抗隆起稳定性影响显著;第一层土的有效黏聚力c’_(1)、有效内摩擦角φ’_(1)、割线模量E_(1)^(50)、切线模量E_(1)^(oed)以及第二层土的有效黏聚力c’_(2)的变异性对坑底抗隆起稳定性影响较小,但相对而言,第二层土的有效黏聚力c’_(2)对坑底抗隆起稳定性的影响较大;对于坑底土体为粉砂的深基坑来说,对坑内土体进行加固可以有效约束坑底隆起变形。

倒边盖挖逆作法基坑支护结构可靠性分析

为了解决采用标准Monte Carlo法计算复杂基坑工程上常见小概率失效,导致计算效率低的问题,以南京市湖南路地下商业街工程为工程背景,首先,将随机响应面法与基坑工程三维模型相结合,求解极限功能函数的响应面方程,并用标准Monte Carlo法计算失效概率和可靠指标,探讨采用倒边盖挖逆作法作为基坑支护结构施工方法的可行性;其次,基于该响应面方程,以土体的弹性模量为随机变量参数,采用马尔可夫链蒙特卡罗子集模拟法(MCMC子集模拟法)计算基坑支护结构的失效概率,并与标准Monte Carlo法结果进行对比分析。结果表明:当支护结构最大侧移控制指标为25 mm时,计算得到的可靠指标均大于4.6,即采用倒边盖挖逆作法施工过程中基坑是安全的;10万次和50万次标准Monte Carlo法计算得到的失效概率均为零,说明对于标准Monte Carlo法,在计算小概率失效问题时10万与50万的样本量是不足的;而MCMC子集模拟法用2.98万个样本计算出的结果与标准Monte Carlo法采用100万个样本计算的结果相对误差仅为1.7%,表明MCMC子集模拟法对于小概率失效问题求解的优势。所提算法在一定程度上提高了计算结构系统小概率失效问题的效率,对结构系统可靠性的相关研究具有一定参考价值。

基于截尾分布的永久路面结构可靠度分析

为建立基于实测参数变异范围的永久路面结构可靠度分析方法,首先基于概率等效原则和逆变换法建立参数“有界”性的双侧截尾分布随机数抽样方法;然后选取现行沥青路面设计规范中面层、基层和路基结构的验算指标建立极限状态方程并开发多指标可靠度计算程序,将分析结果与理论分布随机变量可靠度程序对比;最后结合实测参数变异性水平,使用建立的可靠度分析方法评估京德高速永久路面结构的工后可靠度。结果表明:截尾分布更符合工程参数的真实分布,计算的可靠度更准确;中等交通荷载等级下,京德高速的路面结构可靠度为95.2%~98.7%;在累计当量轴次失效点后,永久路面结构面层、基层和路基的可靠度值均随轴次的增大而减小,且荷载越大,可靠度值下降速率越快,可靠度也越低。

独塔混合梁斜拉桥参数灵敏度分析

为提高桥梁监控单位复核仿真模型的效率,同时研究施工过程中独塔混合梁斜拉桥不同参数对成桥状态的影响,该文以跨径(200+68+46)m的佛山同济路斜拉桥为工程背景,采用单一控制变量法和响应面‒蒙特卡罗法对斜拉桥进行灵敏分析,以主梁线形、主塔线形、主梁应力及斜拉索成桥索力变化作为控制目标,研究主梁自重、初张索力等参数变化对成桥状态的影响。结果表明:主梁自重和初张索力属于灵敏参数,施工临时荷载属于较灵敏参数,主梁刚度和索弹性模量属于非灵敏参数。

基于响应面法的汽轮机转子等效应力分析

为分析汽轮机转子材料制备、加工、安装和运行过程中结构尺寸、材料物性参数、温度等随机变量对其等效应力的影响,以某300MW级汽轮机高压转子为例,采用有限元方法计算得到了冷态启动过程中最大等效应力出现的时刻和部位,并且结合变量随机性,分别采用多项式响应面法和支持向量回归(SVR)响应面法拟合转子最大等效应力与随机变量之间的关系,比较分析了其拟合效果.同时,采用蒙特卡洛模拟法探究了在冷态启动过程中转子强度的可靠性和各随机变量的敏感性,得到了转子半径等6个随机变量的敏感性指数排列顺序.结果表明:SVR响应面法拟合效果比多项式响应面法拟合效果更好,2种响应面法得出冷态启动曲线的强度可靠性分别为96.99%和94.16%;在6个随机变量中,对汽轮机转子等效应力影响最大的是转子材料的弹性模量.

基于Monte Carlo的喷淋响应时间特性研究

自动喷水灭火系统可以有效控制和扑灭初期火灾,因此整个系统的响应时间成了灭火的关键。利用Monte Carlo方法进行随机取样模拟实验,建立了包含喷头响应时间指数、火灾增长因子、火源与喷头径向间距、火源与顶棚垂直间距等影响因素的喷头响应时间模型,并通过大量数据分析得到了响应时间的分布特性。结果表明,响应时间基本符合对数正态分布。响应时间与喷头响应时间指数线性相关,随火灾增长因子的增大而缩短,随径向间距的增大而增长,随着垂直间距的增大先是略为下降而后上升。

Monte-Carlo抽样法在边坡可靠性分析中的应用研究

针对复杂边坡可靠性分析时,功能函数具有高度非线性和隐式表达的特性,为克服传统边坡可靠性分析解决此类问题的不足,将Monte-Carlo重要抽样与响应面法相结合,利用响应面法实现边坡极限状态函数的显式表达,并确定设计验算点,以该点为新的抽样中心应用Monte-Carlo重要抽样计算边坡的失效概率。通过两个算例进行了分析,结果表明:该方法在保证精度的同时提高计算效率,适于解决含有大量随机变量的复杂边坡工程可靠性分析。

基于Monte Carlo抽样的响应面法零件结构可靠性分析

通过综合分析Monte Carlo法和响应面法的特点,运用ANSYS建立零部件的结构参数化可靠性模型,选择了经过简单Monte Carlo抽样的样本点作为响应面的拟合样本点,拟合出零件结构可靠性的响应面。最后以此响应面替代有限元模型进行大量Monte Carlo抽样得到零件可靠度,达到了更方便高效的对零件进行可靠性分析的目的。文中最后以汽车转向直拉杆作为分析实例,为现代机械零件可靠性分析提供了一种高效途径。