Probabilistic Engineering Mechanics最新文献_第3页

The Enhanced Analytical Spectral Moments method for probabilistic characterization of large DOF systems under seismic actions 地震作用下大自由度系统概率表征的增强解析谱矩法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103870

Giacomo Navarra, Francesco Lo Iacono, Maria Oliva

Building codes typically define earthquake load design values using Response Spectra, which depend on site seismicity, soil conditions, structure importance, assumed ductility and limit states. Despite its popularity among engineers for predicting peak displacements and internal forces without directly integrating motion, this method is strictly valid only for single Degrees Of Freedom (DOF) systems. For multi-degrees of freedom structures, approximations in the determination of the modal response correlation coefficients must be used. An alternative approach is to model earthquakes as Gaussian processes using a Power Spectral Density (PSD) function. This probabilistic approach defines seismic input for linear multi-degree of freedom systems based on random vibration theory. When dealing with systems that exhibit weak nonlinearities, statistical linearization technique is applied to refine the solution, enabling the generation of artificial ground motions that match the response spectra for use in Monte Carlo Simulations. However, the computational burden of the PSD approach, especially for large DOF or heavy problems, makes it less convenient than the traditional Response Spectrum method. This paper presents an efficient analytical method with validated closed-form expressions of spectral moments for large-DOF systems. This approach facilitates the analysis of structural response statistics under seismic loads and enables the efficient assessment of the probabilistic distribution of response maxima for large-DOF systems, minimizing the need for computationally intensive numerical evaluations. In order to assess the effectiveness of the proposed method, a practical application on a base-isolated building structure has been carried out by comparing it with the Response Spectrum Method (RSM) and the analytical approach proposed in a previous work, demonstrating that it yields the smallest error compared to Monte Carlo simulations.

建筑规范通常使用响应谱来定义地震荷载设计值，这取决于现场地震活动性、土壤条件、结构重要性、假设延性和极限状态。尽管这种方法在工程师中很流行，因为它可以在不直接积分运动的情况下预测峰值位移和内力，但这种方法仅对单自由度系统严格有效。对于多自由度结构，在确定模态响应相关系数时必须采用近似方法。另一种方法是使用功率谱密度（PSD）函数将地震建模为高斯过程。这种基于随机振动理论的概率方法定义了线性多自由度系统的地震输入。在处理表现出弱非线性的系统时，应用统计线性化技术来改进解决方案，从而能够生成与蒙特卡罗模拟中使用的响应谱相匹配的人工地面运动。然而，PSD方法的计算量很大，特别是对于大自由度或重问题，使得它不如传统的响应谱方法方便。本文提出了一种有效的大自由度系统谱矩封闭表达式的解析方法。这种方法有助于分析地震荷载下的结构响应统计数据，并能够有效地评估大自由度系统的响应最大值的概率分布，从而最大限度地减少对计算密集型数值评估的需求。为了评估所提出的方法的有效性，通过将其与响应谱法（RSM）和先前工作中提出的分析方法进行比较，在基础隔震建筑结构上进行了实际应用，表明与蒙特卡罗模拟相比，该方法产生的误差最小。

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引用次数: 0

Uncertainty quantification of neural network models of evolving processes via Langevin sampling 演化过程神经网络模型的朗格万抽样不确定性量化

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103854

Cosmin Safta , Reese E. Jones , Ravi G. Patel , Raelynn Wonnacot , Dan S. Bolintineanu , Craig M. Hamel , Sharlotte L.B. Kramer

We propose an inference hypernetwork as a general model of history-dependent processes. The framework is a hybrid between purely sampling- and optimization-based uncertainty quantification methods. The flexible data model is based on a neural ordinary differential equation (NODE) representing the evolution of internal states together with a trainable observation model subcomponent. The posterior distribution corresponding to the data model parameters (weights and biases) follows a stochastic differential equation with a drift term related to the score of the posterior that is learned jointly with the data model parameters. This Langevin sampling approach offers flexibility in balancing the computational budget between the evaluation cost of the data model and the approximation of the posterior density of its parameters. We demonstrate performance of the ensemble sampling hypernetwork on chemical reaction and material physics data and compare it to standard variational inference.

我们提出了一个推理超网络作为历史依赖过程的一般模型。该框架是纯采样和基于优化的不确定性量化方法的混合。灵活的数据模型是基于表示内部状态演化的神经常微分方程（NODE）和可训练的观测模型子组件。数据模型参数（权重和偏差）对应的后验分布遵循一个随机微分方程，该方程具有与数据模型参数共同学习的后验分数相关的漂移项。这种朗格万抽样方法在平衡数据模型的评估成本和参数的后验密度近似值之间的计算预算方面提供了灵活性。我们证明了集合抽样超网络在化学反应和材料物理数据上的性能，并将其与标准变分推理进行了比较。

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引用次数: 0

A novel Bayesian method for simultaneous identification of structural mass and stiffness parameters 一种同时识别结构质量和刚度参数的贝叶斯方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103868

Menghao Ping, Wenhua Zhang, Liang Tang

Using modal properties to identify mass and stiffness parameters leads to an underdetermined inverse problem, resulting in non-unique solutions, and consequently to unidentifiable Bayesian inference. Therefore, conventional Bayesian methods typically assume mass parameters to be known and focus only on stiffness parameter identification. However, inaccurate mass assumption may introduce significant errors in stiffness estimation. To circumvent mass assumptions, this study proposes a novel Bayesian method integrating a mass addition strategy for mass and stiffness parameter identification. We obtain two sets of modal properties: one from the original structure and the other from the structure with an added known mass. These datasets are then employed to construct a Bayesian modeling framework to infer the joint distribution of mass and stiffness parameters. Specifically, we modify the Metropolis–Hastings (MH) algorithm into a two-stage sampling scheme where each stage establishes the target distribution based on the likelihood function derived from one dataset independently, which ensures that the resulting samples satisfy both independent likelihood functions. We can consider the samples generated by the modified MH algorithm as approximate samples of the joint posterior distribution of mass and stiffness parameters by leveraging the equivalence between the joint likelihood and the combination of the two independent likelihoods. To further apply the proposed method to high-dimensional problems, we modify the Transitional Markov Chain Monte Carlo (TMCMC) to make it compatible with the two likelihood functions and then integrate it with the modified MH algorithm. The proposed Bayesian method with modified sampling algorithms is validated on dynamic models, demonstrating its effectiveness in mass and stiffness parameter identification. It is then applied to damage identification, where improved accuracy is realized in damage localization and damage extent estimation.

使用模态特性来识别质量和刚度参数会导致欠定逆问题，导致非唯一解，从而导致无法识别的贝叶斯推理。因此，传统的贝叶斯方法通常假设质量参数是已知的，只关注刚度参数的识别。然而，不准确的质量假设可能会在刚度估计中引入重大误差。为了规避质量假设，本研究提出了一种集成质量附加策略的贝叶斯方法，用于质量和刚度参数的识别。我们得到了两组模态属性：一组来自原始结构，另一组来自已知质量增加的结构。然后利用这些数据集构建贝叶斯建模框架来推断质量和刚度参数的联合分布。具体而言，我们将Metropolis-Hastings （MH）算法修改为两阶段抽样方案，其中每阶段基于从一个数据集独立导出的似然函数建立目标分布，从而确保结果样本同时满足两个独立的似然函数。我们可以利用关节似然和两个独立似然的组合之间的等价性，将改进MH算法生成的样本视为质量和刚度参数的关节后验分布的近似样本。为了进一步将该方法应用于高维问题，我们对过渡马尔可夫链蒙特卡罗（TMCMC）进行了改进，使其与两种似然函数兼容，然后将其与改进的MH算法相结合。在动力学模型上对改进采样算法的贝叶斯方法进行了验证，证明了该方法在质量和刚度参数识别方面的有效性。将该方法应用于损伤识别，提高了损伤定位和损伤程度估计的精度。

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引用次数: 0

Vibration control performance of linear and nonlinear mass damping systems under stochastic excitation 随机激励下线性和非线性质量阻尼系统的振动控制性能

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103863

Dimitra A. Karatzia , George C. Tsiatas , Panos Tsopelas

This paper investigates the vibration control performance of both linear and nonlinear mass damping system devices under stochastic excitation. These devices are installed atop a primary structure, modeled as a typical linearly elastic single-degree-of-freedom (SDOF) system, and subjected to Gaussian White Noise (GWN) ground acceleration. To estimate the stochastic response of the nonlinear system, the Statistical Linearization (SL) method is employed. This approach approximates the original nonlinear system with an equivalent linear one by minimizing the mean-square error between their respective statistical properties. As a result, it facilitates the application of linear stochastic system theory to analyze the complex dynamics of nonlinear systems under random excitation. The SL method proves particularly effective in estimating the mean and variance of system responses in nonlinear dynamic systems. Several case studies are presented to illustrate the method's application and to demonstrate its computational efficiency and accuracy in comparison with Monte Carlo (MC) simulations. Furthermore, the results provide valuable insights into the stochastic response characteristics of both linear and nonlinear mass damping systems. Notably, a key finding challenges the prevailing belief: stiffness nonlinearity does not improve the passive device's capacity to absorb and dissipate energy from the primary structure.

本文研究了随机激励下线性和非线性质量阻尼系统装置的振动控制性能。这些装置安装在一个主结构的顶部，模拟成一个典型的线性弹性单自由度（SDOF）系统，并承受高斯白噪声（GWN）地面加速度。为了估计非线性系统的随机响应，采用了统计线性化（SL）方法。该方法通过最小化各自统计性质之间的均方误差，将原始非线性系统近似为等效线性系统。因此，它便于应用线性随机系统理论来分析随机激励下非线性系统的复杂动力学。该方法在估计非线性动态系统响应的均值和方差方面特别有效。本文给出了几个实例来说明该方法的应用，并与蒙特卡罗（MC）模拟比较了其计算效率和准确性。此外，结果为线性和非线性质量阻尼系统的随机响应特性提供了有价值的见解。值得注意的是，一个关键的发现挑战了普遍的观点：刚度非线性并不能提高被动器件从主结构吸收和耗散能量的能力。

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引用次数: 0

First-passage analysis of nonlinear oscillators by leveraging information in the Wiener path integral most probable path 利用维纳路径积分最可能路径中的信息对非线性振子进行第一遍分析

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103860

Ilias G. Mavromatis , Yuanjin Zhang , Ioannis A. Kougioumtzoglou

A technique is developed, based on an extrapolation approach within the Wiener path integral (WPI) methodology, for addressing the first-passage problem and for determining the time-dependent survival probability of stochastically excited nonlinear oscillators. The novelty and contributions of this paper are twofold. First, the nonlinear oscillator response transition probability density function (PDF) is determined in a computationally efficient manner. This is done, within the WPI framework, by solving numerically only a relatively small number of standard optimization problems, each yielding a corresponding most probable path. Next, the information embedded in the time histories of these most probable paths is exploited for extrapolating and for determining, at no additional cost, new paths to be used for evaluating the response transition PDF for any combination of initial and final states. Second, relying on the efficiently determined response transition PDF, an appropriate time-domain discretization is employed for evaluating the nonlinear oscillator survival probability in relatively short time steps. Two representative numerical examples are considered for demonstrating the high degree of accuracy exhibited by the developed technique. These pertain to a Duffing nonlinear oscillator and to a vibro-impact nonlinear oscillator with fractional derivative elements. Juxtapositions with pertinent Monte Carlo simulation data are included as well.

基于维纳路径积分（WPI）方法中的外推方法，开发了一种技术，用于解决第一通道问题并确定随机激发非线性振荡器的随时间生存概率。本文的新颖性和贡献是双重的。首先，以计算效率高的方式确定非线性振子响应跃迁概率密度函数（PDF）。在WPI框架内，这是通过在数值上只解决相对少量的标准优化问题来完成的，每个问题产生一个相应的最可能路径。接下来，利用嵌入在这些最可能路径的时间历史中的信息进行外推，并在没有额外成本的情况下确定用于评估任何初始状态和最终状态组合的响应转换PDF的新路径。其次，基于有效确定的响应转移PDF，采用适当的时域离散化方法在相对较短的时间步长内评估非线性振荡器的生存概率。通过两个有代表性的数值算例，说明了所开发的技术具有很高的精度。这两个问题分别属于Duffing非线性振子和具有分数阶导数的振动冲击非线性振子。并置与相关的蒙特卡罗模拟数据也包括在内。

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引用次数: 0

The memory-dependent FPK equation for fractional Gaussian noise 分数阶高斯噪声的记忆相关FPK方程

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103856

Lifang Feng , Bin Pei , Yong Xu

This paper aims to explore non-Markovian dynamics of nonlinear dynamical systems subjected to fractional Gaussian noise (FGN) and Gaussian white noise (GWN). A novel memory-dependent Fokker–Planck–Kolmogorov (memFPK) equation is developed to characterize the probability structure in such non-Markovian systems. The main challenge in this research comes from the long-memory characteristics of FGN. These features make it impossible to model the FGN-excited nonlinear dynamical systems as finite dimensional GWN-driven Markovian augmented filtering systems, so the classical FPK equation is no longer applicable. To solve this problem, based on fractional Wick–Itô–Skorohod integral theory, this study first derives the fractional Itô formula. Then, a memory kernel function is constructed to reflect the long-memory characteristics from FGN. By using fractional Itô formula and integration by parts, the memFPK equation is established. Importantly, the proposed memFPK equation is not limited to specific forms of drift and diffusion terms, making it broadly applicable to a wide class of nonlinear dynamical systems subjected to FGN and GWN. Due to the historical dependence of the memory kernel function, a Volterra adjustable decoupling approximation is used to reconstruct the memory kernel dependence term. This approximation method can effectively solve the memFPK equation, thereby obtaining probabilistic responses of nonlinear dynamical systems subjected to FGN and GWN excitations. Finally, some numerical examples verify the accuracy and effectiveness of the proposed method.

本文旨在研究分数阶高斯噪声（FGN）和高斯白噪声（GWN）下非线性动力系统的非马尔可夫动力学。建立了一个新的记忆相关的Fokker-Planck-Kolmogorov （memFPK）方程来表征这种非马尔可夫系统的概率结构。本研究的主要挑战来自于FGN的长记忆特性。这些特征使得fgnn激励的非线性动力系统不可能建模为有限维gwn驱动的马尔可夫增广滤波系统，因此经典的FPK方程不再适用。为了解决这一问题，本研究首先基于分数阶Wick-Itô-Skorohod积分理论，推导出分数阶Itô公式。然后，构造一个记忆核函数来反映FGN的长记忆特性。利用分数阶Itô公式和分部积分法，建立了memFPK方程。重要的是，所提出的memFPK方程不局限于漂移和扩散项的特定形式，使其广泛适用于受FGN和GWN影响的各种非线性动力系统。由于记忆核函数的历史依赖性，采用Volterra可调解耦近似来重建记忆核依赖项。该近似方法可以有效地求解memFPK方程，从而得到非线性动力系统在FGN和GWN激励下的概率响应。最后，通过数值算例验证了该方法的准确性和有效性。

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引用次数: 0

Neural network-based probabilistic tracking control for levitation systems under stochastic track irregularities 随机轨迹不规则条件下基于神经网络的悬浮系统概率跟踪控制

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103866

Wantao Jia , Zhengrong Jin , Fei Ni , Weiqiu Zhu

In electromagnetic suspension (EMS) maglev trains, maintaining the suspension gap within a set range is crucial for levitation control. Research often addresses deterministic systems or those disturbed by Gaussian white noise, overlooking stochastic jump noise from factors like railway track joint offset. This study introduces a probabilistic tracking control approach in which a single-point electromagnet levitation system subject to Gaussian and Poisson white noise is modeled using Physics-Informed Neural Networks (PINNs). By constructing two deep neural networks to respectively approximate the system response probability density function (PDF) and control input, the forward Kolmogorov equation constraints and target PDF tracking task are unified into an optimization problem. The Monte Carlo integration manages Poisson white noise integrals, and an adaptive sampling strategy based on the target PDF improves training efficiency. The control problems involving two pre-specified PDFs in practical scenarios are addressed using the proposed approach. The results indicate that this method is capable of designing feedback control forces for both linearized and nonlinear systems. Validity is also tested on linearized and nonlinear levitation systems subjected to Gaussian white noise under exact control conditions. The close match between the proposed control and the exact solution confirms the effectiveness of the method.

在电磁悬浮（EMS）磁悬浮列车中，保持悬浮间隙在一定范围内是悬浮控制的关键。研究通常针对确定性系统或受高斯白噪声干扰的系统，而忽略了由铁路轨道接头偏移等因素引起的随机跳跃噪声。本文介绍了一种概率跟踪控制方法，利用物理信息神经网络（pinn）对高斯白噪声和泊松白噪声影响下的单点电磁铁悬浮系统进行建模。通过构建两个深度神经网络分别逼近系统响应概率密度函数（PDF）和控制输入，将前向Kolmogorov方程约束和目标概率密度跟踪任务统一为一个优化问题。蒙特卡罗积分管理泊松白噪声积分，基于目标PDF的自适应采样策略提高了训练效率。使用所提出的方法解决了实际场景中涉及两个预先指定pdf的控制问题。结果表明，该方法能够设计线性化和非线性系统的反馈控制力。在精确控制条件下，对高斯白噪声作用下的线性化和非线性悬浮系统进行了有效性测试。所提控制与精确解之间的紧密匹配证实了该方法的有效性。

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引用次数: 0

A sequential stratified importance sampling method for extremely small time-dependent failure probability with high-dimensional input vector 一种具有高维输入向量的极小时变失效概率的序贯分层重要性抽样方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103861

Yixin Lu , Zhenzhou Lu , Yuhua Yan , Hengchao Li

To address the challenge of estimating extremely small time-dependent failure probability (TDFP) high-dimensional input vector, we propose a sequential stratified importance sampling method (SSIS) with an ensemble stochastic configuration network (eSCN) embedded within SSIS (eSCN-SSIS) to improve efficiency. Initially, stratified cluster analysis is employed, enabling SSIS to construct a series of explicit importance sampling densities to explore the time-dependent failure domain layer by layer, thereby mitigating exploration of rare time-dependent failure domains and reducing variance in estimating extremely small TDFP. Subsequently, owing to the robust predictive capability of eSCN for high-dimensional input vector, eSCN is adaptively embedded into SSIS to replace the time-dependent performance function model; consequently, the required model evaluations are substantially reduced. Notably, even when applied to an explicit model, eSCN-SSIS is superior to Monte Carlo simulation (MCS), requiring considerably fewer model evaluations and shorter computational time. In contrast, although importance sampling based on the Kriging model surpassed MCS in term of model evaluations, it remained inferior in computational time. Owing to its hierarchical construction of explicit importance sampling densities and adaptive embedding of the eSCN, the proposed eSCN-SSIS applies to engineering problems characterized by extremely small TDFP and high-dimensional input vector, as verified by the presented examples.

为了解决估计极小的时间相关失效概率（TDFP）高维输入向量的挑战，我们提出了一种顺序分层重要性抽样方法（SSIS），该方法在SSIS中嵌入了一个集成随机配置网络（eSCN-SSIS）以提高效率。首先，采用分层聚类分析，使SSIS能够构建一系列显式重要采样密度来逐层探索时变失效域，从而减少对罕见时变失效域的探索，并减少估计极小TDFP时的方差。随后，利用eSCN对高维输入向量的鲁棒预测能力，将eSCN自适应嵌入到SSIS中，取代时变性能函数模型；因此，所需的模型评估大大减少。值得注意的是，即使应用于显式模型，eSCN-SSIS也优于蒙特卡罗模拟（MCS），需要更少的模型评估和更短的计算时间。相比之下，基于Kriging模型的重要性抽样虽然在模型评价上优于MCS，但在计算时间上仍有劣势。本文提出的eSCN- ssis基于显式重要采样密度的分层结构和eSCN的自适应嵌入，适用于TDFP极小、输入向量高维的工程问题。

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引用次数: 0

Multi-objective design optimization of structural systems based on probabilistic life-cycle criteria through a sequential decision process 基于概率生命周期准则的结构系统多目标设计优化

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103855

Aditya Sharma, Gordon P. Warn

A challenge with incorporating life-cycle criteria into design optimization is the need to quantify time-varying reliability of structural systems deteriorating in uncertain and non-stationary environments. This paper presents a computational methodology that addresses this challenge by combining set-based design with multi-fidelity modeling to broadly and efficiently explore a diverse set of design alternatives while systematically converging to the set of Pareto optimal designs. The result is a framework for multi-objective design optimization of structural systems based on probabilistic life-cycle criteria through a sequential decision process (SDP). At each decision state, design alternatives are evaluated and compared using bounds on decision criteria, and dominated (less-promising) designs are eliminated from further evaluation. Computational efficiency is achieved by sequencing models of increasingly higher fidelity. The SDP accommodates multiple objectives, discrete design variables, varying structural concepts, accounts for redundancy and system reliability, and the risk attitude of decision maker(s). The efficacy of the methodology is demonstrated through numerical examples involving multi-objective design optimization of steel trusses, where the goal is to identify optimal design variables that simultaneously minimize the expected value of the life-cycle cost and the corresponding risk of deviation from the expected value. By sequencing models of increasing fidelity, SDP is shown to efficiently converge to the set of Pareto optimal designs using 0.125–0.151 times the number of model evaluations in comparison to full evaluation by the highest fidelity model. Furthermore, the influence of structural configuration, material grade, and cross-sectional areas on tradeoffs among life-cycle costs is shown for Pareto optimal designs.

将生命周期准则纳入设计优化的一个挑战是需要量化结构系统在不确定和非平稳环境中恶化的时变可靠性。本文提出了一种计算方法，通过将基于集的设计与多保真度建模相结合来解决这一挑战，从而在系统地收敛到帕累托最优设计集的同时，广泛有效地探索各种设计方案集。通过序列决策过程（SDP），建立了基于概率生命周期准则的结构系统多目标设计优化框架。在每个决策状态下，使用决策标准的界限来评估和比较设计方案，并从进一步的评估中消除主导（不太有希望的）设计。计算效率是通过越来越高的保真度排序模型来实现的。SDP包含多个目标、离散的设计变量、不同的结构概念、冗余和系统可靠性以及决策者的风险态度。通过涉及钢桁架多目标设计优化的数值实例证明了该方法的有效性，其目标是确定同时最小化寿命周期成本期望值和相应偏离期望值风险的最优设计变量。通过增加保真度的排序模型，与最高保真度模型的完全评估相比，SDP可以有效地收敛到Pareto最优设计集，模型评估次数为0.125-0.151倍。此外，结构配置、材料等级和横截面积对帕累托最优设计生命周期成本权衡的影响。

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引用次数: 0

Multidisciplinary uncertainty propagation method considering correlated field variables for rocket systems 考虑相关场变量的火箭系统多学科不确定性传播方法

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics

Pub Date : 2025-10-01 DOI: 10.1016/j.probengmech.2025.103857

Siyi Du , Chunna Li , Yang Liu , Chunlin Gong , Weikai Gao

Throughout a rocket's lifecycle, numerous random uncertainties can significantly influence performance. However, existing uncertainty propagation (UP) methods for multidisciplinary systems often neglect correlations among field variables, leading to reduced accuracy. To overcome this limitation, we propose a multidisciplinary UP method that explicitly incorporates these correlations. For variables propagated from upper-level disciplines, the Nataf transformation is applied to generate correlated input samples for the current discipline, which then serve as the basis for uncertainty analysis. To accelerate the calculation of the probability density function of field variables within the Nataf transformation, we further introduce a warm-start strategy integrated with the maximum entropy method. In the case study of UP across multiple disciplines of a solid rocket system, using Monte Carlo simulation (MCS) as the benchmark, incorporating variable correlations yields notable improvements: the standard deviation accuracy of velocity and total energy at the first-stage separation point increased by 22.75 % and 32.57 %, respectively, while the accuracy of their lower bounds improved by 5.20 % and 4.20 %. These results demonstrate that the proposed method effectively addresses UP problems involving both numerical and field correlated variables, significantly enhancing the accuracy of UP.

在火箭的整个生命周期中，许多随机的不确定性会对性能产生重大影响。然而，现有的多学科系统不确定性传播（UP）方法往往忽略了场变量之间的相关性，导致精度降低。为了克服这一限制，我们提出了一种明确结合这些相关性的多学科UP方法。对于从上层学科传播的变量，应用Nataf变换为当前学科生成相关的输入样本，然后作为不确定性分析的基础。为了加快Nataf变换中场变量概率密度函数的计算，我们进一步引入了与最大熵法相结合的热启动策略。在固体火箭系统多学科的UP实例研究中，以蒙特卡罗模拟（MCS）为基准，结合变量相关性得到了显著的改进：第一级分离点速度和总能量的标准差精度分别提高了22.75%和32.57%，下界精度分别提高了5.20%和4.20%。结果表明，该方法有效地解决了包括数值变量和场相关变量在内的UP问题，显著提高了UP的精度。

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引用次数: 0