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High-speed rolling bearing lubrication reliability analysis based on probability box model 基于概率盒模型的高速滚动轴承润滑可靠性分析
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-19 DOI: 10.1016/j.probengmech.2024.103612
Qishui Yao , Liang Dai , Jiachang Tang , Haotian Wu , Tao Liu

An efficient and high-precision method is proposed for the analysis and evaluation of high-speed rolling bearing lubrication reliability based on a probability box (p-box) model. This method expands the application of mixed aleatory and epistemic uncertainties analysis within the realm of bearing lubrication reliability. Initially, the method establishes a reliability model for high-speed rolling bearing lubrication, taking into account the shear thermal effect through the analytical solution of a Γубин-type entrance zone. Subsequently, the uncertainty surrounding lubrication parameters under high-speed conditions is examined, with its mixed aleatory and epistemic uncertainties accurately depicted by using the p-box model. Furthermore, an effective and precise method for analyzing the reliability of rolling bearing lubrication is introduced based on the p-box model, in which the optimization model involved is efficiently solved using a decoupling method. Finally, lubrication reliability analysis and sensitivity analysis of parameter uncertainty levels are conducted for high-speed rolling bearings in this study. The research results demonstrate that the proposed method achieves higher accuracy and efficiency.

基于概率盒(p-box)模型,提出了一种分析和评估高速滚动轴承润滑可靠性的高效、高精度方法。该方法在轴承润滑可靠性领域拓展了已知和认识混合不确定性分析的应用。首先,该方法建立了高速滚动轴承润滑可靠性模型,通过对Γубин型入口区的分析求解,将剪切热效应考虑在内。随后,研究了高速条件下润滑参数的不确定性,并利用 p-box 模型准确地描述了其混合的已知和未知不确定性。此外,还介绍了一种基于 p-box 模型的有效而精确的滚动轴承润滑可靠性分析方法,其中涉及的优化模型采用解耦方法进行了有效求解。最后,本研究对高速滚动轴承进行了润滑可靠性分析和参数不确定性水平的敏感性分析。研究结果表明,所提出的方法实现了更高的精度和效率。
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引用次数: 0
Probabilistic slope stability analysis: A novel distribution for soils exhibiting highly variable spatial properties 斜坡稳定性概率分析:针对空间特性变化极大的土壤的新型分布方法
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-15 DOI: 10.1016/j.probengmech.2024.103586
Vincent Renaud, Marwan Al Heib

Slope stability calculation depends on the soil properties (cohesion and the friction angle) of the soil. Heterogeneous terrains are frequently observed in civil and mining projects where the properties are highly spatially variable. Based on a real data from case studies, this paper presents a probabilistic analysis of the slope stability of highly heterogeneous terrains with a very high coefficient of variation (COV) of the cohesion distribution. The existing deterministic and probabilistic approaches for calculating slope stability lack the capability to effectively consider the significant heterogeneity present in the terrain The objective of the paper is to develop a new bounded interval distribution having a COV that is as high (>150%) as the COV of the cohesion distribution The results obtained with this new distribution are compared to 4 other semi-infinite distributions. To consider the correlation between cohesion and the friction angle, a specific formulation was developed to generate friction angles varying between fixed minimum and maximum limits and having the desired correlation coefficient, mean, and standard deviation. The new cohesion and friction angle distributions were incorporated and tested in a probabilistic numerical model. The new distribution can presently be applied to geotechnical studies for terrains and heterogenous materials with properties exhibiting high spatial variability.

边坡稳定性计算取决于土壤的特性(内聚力和摩擦角)。在土木工程和采矿工程中经常可以看到异质地形,这些地形的特性在空间上变化很大。本文基于案例研究的真实数据,对内聚力分布变异系数(COV)非常高的高度异质地形的边坡稳定性进行了概率分析。本文的目的是开发一种新的有界区间分布,其 COV 与内聚力分布的 COV 一样高(150%)。为了考虑内聚力和摩擦角之间的相关性,我们开发了一种特定的公式,用于生成在固定的最小和最大限制之间变化的摩擦角,并具有所需的相关系数、平均值和标准偏差。新的内聚力和摩擦角分布已纳入概率数值模型并进行了测试。目前,新的分布可用于地形和异质材料的岩土工程研究,这些材料的特性表现出很高的空间变异性。
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引用次数: 0
Effects of limit state data on constructing accurate surrogate models for structural reliability analyses 极限状态数据对构建结构可靠性分析精确替代模型的影响
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-12 DOI: 10.1016/j.probengmech.2024.103595
Nhu Son Doan , Huu-Ba Dinh

Engineering problems are mainly defined in implicit processes; hence, the fully probabilistic analyses, e.g., Monte Carlo simulations (MCS), are expensive to implement. In practice, two approaches to overcome the issues are either reducing the size of simulations or developing surrogate models for actual problems. The latter does not sacrifice the size of MCS and requires less insight into probabilistic calculation; hence, it is preferable to most engineers. This study proposes an efficient framework to develop reliable and accurate surrogate models by considering data at the limit state margins (LS data). Effects of involving LS data in the training process and performances of the proposed metamodels are investigated for most issues relating to reliability analyses, including nonlinear performance functions, multiple failure modes, and implicitly defined problems. Two machine learning algorithms, including artificial neural networks and the Gaussian process, are employed to prove the ability of the proposed method. Investigations reveal that the limit state data plays a vital role in developing accurate surrogate models for reliability analyses, and accumulating them into the training dataset helps quickly construct accurate metamodels. This work contributes a practical framework for reliability analyses because the LS data can be detected easily without insight into probabilistic calculations.

工程问题主要是在隐含过程中定义的;因此,完全概率分析,如蒙特卡罗模拟(MCS),实施起来非常昂贵。在实践中,有两种方法可以解决这个问题,一是缩小模拟规模,二是开发实际问题的替代模型。后者不会牺牲 MCS 的大小,而且对概率计算的深入了解要求较低;因此,大多数工程师更倾向于后者。本研究提出了一个有效的框架,通过考虑极限状态边缘数据(LS 数据)来开发可靠、准确的代用模型。针对与可靠性分析有关的大多数问题,包括非线性性能函数、多重失效模式和隐式定义问题,研究了在训练过程中考虑 LS 数据的效果以及所建议的元模型的性能。为了证明所提方法的能力,采用了两种机器学习算法,包括人工神经网络和高斯过程。研究表明,极限状态数据在建立准确的可靠性分析代用模型方面发挥着至关重要的作用,将这些数据积累到训练数据集中有助于快速构建准确的元模型。这项工作为可靠性分析提供了一个实用框架,因为无需深入了解概率计算,就能轻松检测 LS 数据。
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引用次数: 0
Efficient metamodel-based importance sampling coupled with single-loop estimation method for parameter global reliability sensitivity analysis 基于元模型的高效重要度抽样与单回路估算方法相结合,用于参数全局可靠性灵敏度分析
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-12 DOI: 10.1016/j.probengmech.2024.103597
Wanying Yun , Fengyuan Li , Xiangming Chen , Zhe Wang

To efficiently estimate the main effects and total effects of uncertain distribution parameters on the uncertainty of failure probability, we construct single-loop estimation formulas by introducing auxiliary variables through the equal probability transformation. This approach circumvents the original nested triple-loop process. For generating samples used in the derived single-loop estimation formulas, direct Monte Carlo simulation can be employed. To reduce the number of samples in Monte Carlo simulation, the important sampling technique can be integrated into the proposed single-loop estimation formulas. Additionally, to enhance the efficiency of identifying the states (failure or safety) of all used samples, an adaptive Kriging model can be introduced. Subsequently, the adaptive Kriging model coupled with Monte Carlo simulation, and the adaptive Kriging model coupled with the importance sampling technique, are integrated into the derived single-loop formulas to concurrently and efficiently estimate the main effects and total effects of uncertain distribution parameters. The results of three case studies validate the accuracy and efficiency of the proposed method.

为了有效估计不确定分布参数对故障概率不确定性的主效应和总效应,我们通过等概率变换引入辅助变量,构建了单环估计公式。这种方法规避了原有的嵌套三环过程。为了生成推导出的单环估计公式中使用的样本,可以直接采用蒙特卡罗模拟。为减少蒙特卡罗模拟中的样本数量,可将重要的抽样技术集成到所提出的单环估计公式中。此外,为了提高识别所有使用样本的状态(故障或安全)的效率,可以引入自适应克里金模型。随后,将自适应克里金模型与蒙特卡罗模拟相结合,以及将自适应克里金模型与重要性抽样技术相结合,整合到推导出的单环公式中,从而同时有效地估计不确定分布参数的主效应和总效应。三个案例研究的结果验证了所提方法的准确性和高效性。
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引用次数: 0
Time-dependent kinematic reliability of motion mechanisms with dynamic factors 具有动态因素的运动机构的运动可靠性与时间有关
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-12 DOI: 10.1016/j.probengmech.2024.103598
Xinchen Zhuang, Xin Li, Chang Liu, Tianxiang Yu, Bifeng Song

Time-dependent kinematic reliability of a motion mechanism is critical for optimizing its operational performance. Dynamic factors, including material deterioration and wear in the joints, are disregarded in the prior study. As such, the envelope method is employed to undertake time-dependent kinematic reliability analysis of motion mechanisms, accounting for dynamic factors. Firstly, a decoupling strategy is proposed for decoupling the time-dependent motion error stemming from motion input and the dynamic factors. Thus, the kinematic reliability is delineated into two distinct temporal parameter-dependent issues. Subsequently, the envelope function is extended to solve the kinematic reliability. The expansion temporal points determination function (ETPDF) in the envelope function is approximated using a first-order method coupled with an active learning Kriging mode. After the expansion temporal points are found, the time-dependent reliability can be efficiently calculated via a multivariate Gaussian integral. Finally, the effectiveness and accuracy of the proposed method is verified by means of a 4-bar function generating mechanism.

运动机构随时间变化的运动可靠性对于优化其运行性能至关重要。之前的研究忽略了动态因素,包括接头的材料劣化和磨损。因此,我们采用包络法对运动机构进行随时间变化的运动可靠性分析,同时考虑动态因素。首先,提出了一种解耦策略,以解耦运动输入和动态因素产生的随时间变化的运动误差。因此,运动可靠性被划分为两个不同的时间参数问题。随后,包络函数被扩展用于解决运动可靠性问题。包络函数中的扩展时间点确定函数(ETPDF)采用一阶方法和主动学习克里金模式进行近似。在找到扩展时点后,可通过多元高斯积分有效地计算随时间变化的可靠性。最后,通过 4 条函数生成机制验证了所提方法的有效性和准确性。
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引用次数: 0
Separable Gaussian neural networks for high-dimensional nonlinear stochastic systems 用于高维非线性随机系统的可分离高斯神经网络
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-11 DOI: 10.1016/j.probengmech.2024.103594
Xi Wang , Siyuan Xing , Jun Jiang , Ling Hong , Jian-Qiao Sun

This paper extends the recently developed method of separable Gaussian neural networks (SGNN) to obtain solutions of the Fokker–Planck–Kolmogorov (FPK) equation in high-dimensional state space. Several challenges when extending SGNN to high-dimensional state space are addressed including proper definition of domain for placing Gaussian neurons and region for data sampling, and numerical integration issue of evaluating marginal probability density functions. Three benchmark nonlinear dynamic systems with increasing complexity and dimension are examined with the SGNN method. In particular, the steady-state probability density of the response is obtained with the SGNN method and compared with the results of extensive Monte Carlo simulations. It should be pointed out that some solutions of high-dimensional FPK equations for nonlinear dynamic systems would be very difficult to obtain without SGNN.

本文扩展了最近开发的可分离高斯神经网络(SGNN)方法,以获得高维状态空间中福克-普朗克-科尔莫戈罗夫(FPK)方程的解。本文探讨了将 SGNN 扩展到高维状态空间时面临的几个挑战,包括高斯神经元放置域和数据采样区域的正确定义,以及评估边际概率密度函数的数值积分问题。利用 SGNN 方法研究了复杂度和维度不断增加的三个基准非线性动态系统。特别是,利用 SGNN 方法获得了响应的稳态概率密度,并与大量蒙特卡罗模拟的结果进行了比较。需要指出的是,如果没有 SGNN,某些非线性动态系统的高维 FPK 方程解将很难获得。
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引用次数: 0
A method to reduce the sampling variability of time-domain fatigue life by optimizing parameters in Monte Carlo simulations 通过优化蒙特卡洛模拟参数减少时域疲劳寿命采样变异性的方法
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-01-01 DOI: 10.1016/j.probengmech.2024.103591
Hong Sun , Yuanying Qiu , Jing Li , Jin Bai , Ming Peng

Monte Carlo numerical simulations for generating stationary Gaussian random time-domain signal samples fulfil an important role in random fatigue life prediction. Control parameters such as the random seed, the sampling frequency and the number of sampling points in the numerical simulations have significant effects on the time-domain random fatigue life. In this paper, the effects are investigated systematically by utilizing commonly used power spectrum samples and engineering materials, and so a new method for optimizing the control parameter values is proposed. The proposed method solves the critical problem found in many papers that the relative error between the frequency-domain fatigue life and the time-domain fatigue life increases with the slope K of the S–N curve. Furthermore, it observably reduces the sampling variability of time-domain fatigue life for the large slope K, which will help the related researchers to establish better frequency-domain models for fatigue life prediction by using the time-domain fatigue life values as standard data.

用于生成静态高斯随机时域信号样本的蒙特卡罗数值模拟在随机疲劳寿命预测中发挥着重要作用。数值模拟中的随机种子、采样频率和采样点数等控制参数对时域随机疲劳寿命有显著影响。本文利用常用的功率谱样本和工程材料系统地研究了这些影响,并提出了优化控制参数值的新方法。本文提出的方法解决了许多论文中发现的关键问题,即频域疲劳寿命和时域疲劳寿命之间的相对误差会随着曲线斜率的增加而增大。此外,它还明显降低了大斜率时域疲劳寿命的采样变异性,这将有助于相关研究人员利用时域疲劳寿命值作为标准数据,建立更好的频域疲劳寿命预测模型。
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引用次数: 0
A DPIM-based probability analysis framework to obtain railway vehicle vibration characteristics considering the randomness of OOR wheel 基于 DPIM 的概率分析框架,用于获取考虑到 OOR 车轮随机性的铁路车辆振动特性
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-01-01 DOI: 10.1016/j.probengmech.2024.103587
Tengfei Wang , Jinsong Zhou , Wenjing Sun , Dao Gong , Kai Zhou , Zhanfei Zhang , Zhixin Liu , Guoshun Li

The OOR (out-of-roundness) wheel is one of the main excitation sources causing vehicle vibration. However, the OOR wheel occurs randomly, indicating that the vibration behavior of a vehicle cannot be comprehensively evaluated using a deterministic approach. Thus, a probability analysis framework is proposed to obtain vehicle vibration characteristics while considering the randomness of the OOR wheel. The probability model of the random OOR wheel is derived by reducing the high-dimensional variables into a few independent variables of the radius, amplitude, and phase. Then, the vertical vehicle-track coupled system with OOR wheels is modelled. A DPIM (direct probability integral method) is further developed to analyze the evolution of excitation to response probabilities. Finally, the statistics of the random vibration of the vehicle are calculated. The proposed framework is verified using a numerical case. Results show that the PDF (probability density function) shape of the vehicle random vibration, induced by the Gaussian-distributed OOR wheel, deviates from the Gaussian distribution due to the nonlinear wheel/rail contact force. Instead, it exhibits a right-skewed shape, significantly impacting the dynamic performance. As the mean or coefficient of variation of the OOR wheel amplitude increases linearly, the reliability of the vehicle Sperling index experiences a quadratic or double-sloping decrease. Consequently, a maintenance threshold for OOR wheel amplitudes is given based on reliability considerations. Compared to Monte Carlo simulation, the proposed framework offers a computational efficiency improvement of at least one order of magnitude.

OOR(失圆)车轮是引起车辆振动的主要激励源之一。然而,OOR 车轮是随机出现的,这表明无法使用确定性方法对车辆的振动行为进行全面评估。因此,本文提出了一种概率分析框架,在考虑 OOR 车轮随机性的同时获取车辆振动特性。通过将高维变量简化为半径、振幅和相位等几个独立变量,得出了随机 OOR 车轮的概率模型。然后,对带有 OOR 轮的垂直车辆-轨道耦合系统进行建模。进一步开发了 DPIM(直接概率积分法)来分析激励到响应概率的演变。最后,计算车辆随机振动的统计数据。利用数值案例对所提出的框架进行了验证。结果表明,由高斯分布的 OOR 车轮诱发的车辆随机振动的 PDF(概率密度函数)形状偏离了高斯分布,这是由于车轮/轨道接触力的非线性造成的。相反,它呈现出右偏的形状,对动态性能产生了重大影响。当 OOR 轮振幅的平均值或变异系数线性增加时,车辆 Sperling 指数的可靠性会出现二次或双斜率下降。因此,基于可靠性考虑,给出了 OOR 车轮振幅的维护阈值。与蒙特卡罗模拟相比,所提出的框架至少提高了一个数量级的计算效率。
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引用次数: 0
Structural reliability analysis based on probability density evolution method and stepwise truncated variance reduction 基于概率密度演化法和逐步截断方差缩小法的结构可靠性分析
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-01-01 DOI: 10.1016/j.probengmech.2024.103580
Tong Zhou , Tong Guo , You Dong , Yongbo Peng

To address the substantial computational burden associated with probability density evolution method (PDEM) in structural reliability analysis, this study proposes a novel look-ahead learning function named stepwise truncated variance reduction (STVR), integrating polynomial chaos Kriging (PCK) and PDEM. Three key features of STVR are highlighted. First, it enables quantifying the maximum reduction in predictive errors of PCK within the regions of interest (ROI) when adding a new point. Second, closed-form expression for STVR is derived through Kriging update formulas, eliminating the need for computationally intensive Gauss–Hermite quadrature or extensive conditional simulations of PCK. Third, a dynamic adjustment procedure is proposed for the probability level-related parameter in STVR, with the aim of achieving a good balance between the exploitation and exploration of ROI during the sequential experimental design process. The performance of STVR is demonstrated through two benchmark analytical functions and three numerical examples of varying complexity. Results indicate that the dynamic adjustment procedure for the probability level-related parameter in STVR outperforms the empirical setting of a minor value. Then, STVR proves more advantageous than existing pointwise and look-ahead learning functions, particularly in addressing complex dynamic reliability problems.

为了解决结构可靠性分析中与概率密度演化法(PDEM)相关的大量计算负担,本研究提出了一种名为逐步截断方差缩小(STVR)的新型前瞻学习函数,将多项式混沌克里金(PCK)和 PDEM 整合在一起。STVR 有三大特点。首先,当增加一个新点时,它能量化 PCK 在感兴趣区域(ROI)内预测误差的最大减小。其次,通过克里金更新公式推导出了 STVR 的闭式表达式,从而省去了计算密集型的高斯-赫米特二次方程或 PCK 的大量条件模拟。第三,针对 STVR 中与概率水平相关的参数提出了一种动态调整程序,目的是在顺序实验设计过程中实现 ROI 利用与探索之间的良好平衡。通过两个基准分析函数和三个不同复杂度的数值示例证明了 STVR 的性能。结果表明,STVR 中概率水平相关参数的动态调整程序优于根据经验设定的次要值。因此,STVR 比现有的定点学习函数和前瞻学习函数更具优势,尤其是在解决复杂的动态可靠性问题时。
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引用次数: 0
Topology optimization of bridges under random traffic loading using stochastic reduced-order models 利用随机降序模型优化随机交通荷载下的桥梁拓扑结构
IF 2.6 3区 工程技术 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-01-01 DOI: 10.1016/j.probengmech.2024.103583
Kaiming Luo , Xuhui He , Haiquan Jing

This paper presents a framework for robust topology optimization of bridges under random traffic loading. Traffic loading is simulated using a stream of random moving loads parameterized by their masses, speeds, directions, and arrival times. The stochastic reduced-order model approach is combined with the equivalent static load method to achieve uncertainty-informed dynamic response topology optimization. The stochastic reduced-order model approach propagates uncertainty and reduces problem dimension, whereas the equivalent static load method is employed for dynamic response topology optimization. The effectiveness of the proposed optimization framework is demonstrated using several numerical examples. The proposed framework is found to be effective in optimizing structures under traffic loading, making it a promising solution for the topological design of bridges.

本文提出了一种在随机交通荷载条件下对桥梁进行稳健拓扑优化的框架。交通荷载是通过以质量、速度、方向和到达时间为参数的随机移动荷载流来模拟的。随机减阶模型方法与等效静荷载方法相结合,实现了不确定性信息动态响应拓扑优化。随机减阶模型方法传播了不确定性并降低了问题维度,而等效静态载荷方法则用于动态响应拓扑优化。通过几个数值示例证明了所提出的优化框架的有效性。结果表明,所提出的框架能有效优化交通荷载下的结构,是桥梁拓扑设计的一个很有前途的解决方案。
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引用次数: 0
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Probabilistic Engineering Mechanics
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