Meng-Ze Lyu

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• Doctor of Philosophy
• PostDoc Position at Hong Kong University of Science and Technology

Performance of engineering structures exhibit large degree of uncertainties, due to the factors like geometric variations, material variability, and stochastic loads. Therefore, reliability is essential for rational assessment of structural performance and safety. To explicitly consider uncertainties in structural design, reliability-based design o...

The evaluation of engineering structures under various disastrous dynamic actions involves significant uncertainties inherent in both external excitations and structural parameters. Assessing the safety of these structures subjected to multiple hazards and developing appropriate response analysis methods are of paramount importance. In recent years...

Predicting the performance of complex dynamical systems is essential in many fields of science and engineering. The response of dynamical systems is uncertain, due to stochastic external excitations and random system parameters. To obtain accurate and effective predictions of dynamical systems, these uncertainties must be accounted for. To this end...

Understanding the intricate dynamics of complex nonlinear stochastic systems is pivotal in both scientific inquiry and engineering practice. These systems are fraught with uncertainties originating from diverse sources such as material properties, external excitations, and inherent nonlinear behaviors. Due to the coupling between nonlinearity and s...

In the fields of mechanics and engineering, addressing uncertainties is crucial for ensuring the safety, performance, and resilience of structures and systems. Uncertainties may arise from a variety of sources, including material properties, loading conditions, environmental factors, and system parameters. When large-scale systems are exposed to na...

The significance of understanding and effectively addressing uncertainties associated with natural disasters cannot be overstated. Events such as strong winds, earthquakes, floods, and other disasters pose significant threats to the safety and resilience of urban buildings and bridges. Uncertainties inherent in these disasters, ranging from variabi...

Surrogate modeling can drastically reduce the computational efforts when evaluating complex nonlinear dynamical systems subjected to stochastic excitation. However, existing surrogate modeling techniques suffer from the "curse of dimensionality" when emulating complex nonlinear systems due to the discretization of the stochastic excitation. In this...

The response analysis of high-dimensional, nonlinear engineering systems under various excitations is inevitably associated with significant randomness and uncertainty. To assess engineering reliability accurately, a detailed stochastic model for the system must be developed first. However, some system parameters, such as those in modeling the nonl...

The inherent randomness of engineering structures significantly influences the analysis of structural stochastic responses and safety assessments. It is critical to quantify the three aspects of random fields, including the randomness of individual variables, the probabilistic interdependence among multiple variables, and the spatiotemporal correla...

This study examines how coupled particle-scale uncertainties in the inter-particle friction coefficient (μs) and particle shear modulus (Gp) influence macro-scale soil behaviors using the discrete element method (DEM). To achieve a comprehensive probabilistic quantification, we employed copula theory to model the joint dependence between these part...

Computational models are of utmost importance in various aspects of structural design and optimization, uncertainty quantification, risk assessment, and other engineering fields. Among numerous critical issues for model-based uncertainty quantification, the issue of joint probabilistic modelling of dependent model parameters under the condition of...

高维非线性系统在随机动力作用下的响应与可靠性分析长久以来是科学和工程领域的重要挑战性难题。在经典随机动力学框架下，高维非线性系统响应的概率密度满足的控制方程往往是一个高维偏微分方程（如Liouvile方程、Fokker-Planck方程等），难以解析或数值求解。然而，若仅关心系统中某一个或几个感兴趣响应，则有望建立该响应瞬时概率密度满足的低维控制方程。研究证明，对于系统中任一维路径连续的随机过程（即满足Dynkin-Kinney条件），其瞬时概率密度将精确满足一个一维或二维偏微分方程，而不受系统维数与Markov性限制。本研究将该控制方程称为降维概率密度演化方程，该方程是精确成立的，但方程中的本征漂移与扩散函数需要根据系统特性进行解析或数值构造。这一理论可进一步将扩展至一类路径非连续随机过程...

The seismic engineering demand parameters (EDPs) of building clusters exhibit significant spatial correlations and need full consideration in regional risk and reliability assessments. This study presents an efficient scheme to determine the joint distribution of multi-structure EDPs, which captures all EDP correlations and enables direct calculati...

Dynamic-reliability-based design optimization (DRBDO) is a promising methodology to address the significant challenge posed by the new generation of structural design theories centered around reliability considerations. Solving DRBDO problems typically requires iterations ranging from a dozen to several hundreds, with each iteration dedicated to up...

For over half a century, the analysis, control, and optimization design of high-dimensional nonlinear stochastic dynamical systems have posed long-standing challenges in the fields of science and engineering. Emerging scientific ideas and powerful technologies, such as big data and artificial intelligence (AI), offer new opportunity for addressing...

Performance-based earthquake engineering (PBEE) is critical for ensuring the safety and resilience of structures subjected to seismic events. Conducting seismic fragility analysis within this framework is essential for understanding and mitigating seismic risks. Traditional methods for seismic fragility analysis often rely heavily on double-loop re...

The probabilistic response determination of high-dimensional nonlinear dynamical systems has long been a challenging issue in science and engineering fields. The stochastic excitation experienced by these systems can often be modeled as Gaussian or Poisson (white/colored) noise. However, the transient probability density function (PDF) of system re...

高维非线性系统在随机动力作用下的响应与可靠性分析是长期困扰科学和工程界的难题。在经典随机动力学框架下，系统响应的概率密度通常由高维偏微分方程描述，难以解析或数值求解。然而，在实际工程中，通常只关心少数几个响应变量。在这种情况下，可以建立响应概率密度满足的低维控制方程。研究表明，任意路径连续的随机过程，其瞬时概率密度可精确满足一维或二维偏微分方程，不受动力系统维数或随机过程Markov性的限制。本文将该方程称为降维概率密度演化方程。尽管该方程精确成立，其本征漂移与扩散函数需根据系统特性解析或数值构造。研究探讨了几类高维系统中本征漂移函数的解析表达，并提出了一般系统下基于有限分析数据的数值求解方法。为解决首次超越准则下的可靠性问题，构造了吸收边界过程并建立了相应的降维概率密度演化方程，实现了时变...

Probabilistic response and reliability analysis of complex high-dimensional nonlinear stochastic dynamical systems often need to be estimated based on numerous stochastic simulations or representative analysis data. Most stochastic dynamic approaches typically yield estimates with accuracy in the order of to against representative analysis data. Ac...

The randomness in engineering structures, which greatly affects structural stochastic response analysis and safety assessment, stems from the inherent variability and imperfections present in materials. Therefore, establishing appropriate models quantifying the random sources is essential. Three aspects characterize the uncertainty in random source...

We invite researchers to submit their work to MS24 at ISRERM 2024. The conference will be held in Hefei, China, from 18 to 21 October 2024. Abstract Submission Deadline: 29 February 2024. Submission Link: http://isrerm2024.aconf.org/ We look forward to receiving your contributions and welcoming you at ISRERM 2024!

The study of complex nonlinear stochastic dynamical systems is of paramount importance in both science and engineering. These systems exhibit a myriad of uncertainties, stemming from various sources such as material properties, external excitations, and inherent nonlinearities. These uncertainties introduce significant ambiguity into the response o...

复杂非线性随机动力系统中的不确定性传播和可靠性分析是科学和工程领域的重大挑战。系统参数和外部激励的随机性对复杂非线性系统的动力特性具有显著影响。对于复杂系统中任意路径连续的感兴趣响应，可建立其瞬时概率密度函数的控制方程，称为降维概率密度演化方程。当考虑单一响应时，降维概率密度演化方程是一个一维或二维偏微分方程，其中本征漂移函数是导致不确定性传播的关键物理驱动因素。该方程可进一步扩展至Poisson噪声激励下的路径非连续系统，建立系统响应瞬时概率密度函数的偏微分-积分型控制方程。为求解多响应量的联合概率密度函数，还提出了一类解耦多变量概率密度演化方法，该方法避免了高维偏微分方程求解，可给出多响应联合概率密度函数的数值解。此外，为求解高维系统的首次穿越可靠性，建立了吸收边界过程的降维概率密度演化...

多变量非Gauss随机场的建模与模拟是科学与工程领域的重要问题。然而，目前的多变量随机场建模往往仅考虑变量间的线性相依性，即采用相关函数表征；无法在考虑各变量非Gauss分布与空间变异性的同时把握变量间的非线性相依性。本文提出了一类新的非线性相依多变量非Gauss随机场模型，可以同时刻画各随机场边缘分布的非Gauss性、不同相关长度的空间变异性、以及各变量场之间的非线性概率相依性。随机场间的非线性相依性采用蔓式连接函数刻划。为解决同时准确表征随机场变量间非线性相依性与各变量空间变异性的难题，建立了不同连接函数形式下表征各随机场空间相关函数间映射关系的桥函数模型，并通过桥函数模拟多变量随机场使之同时满足变量间的连接函数模型以及各自的空间相关性，由此证明了本模型的变量间-空间相关的相容性。在此基...

The inherent variability and imperfections in materials lead to randomness in engineering structures, greatly affecting structural stochastic response analysis and safety assessment. Therefore, it is essential to establish the rational modeling and precise simulation of random sources. The uncertainty in random sources is characterized by three asp...

The modeling of engineering materials and the mechanism of randomness propagation are two fundamental research foundations of the advanced structural design theory. Due to the stochastic and heterogeneous meso-structures, concrete-like quasi-brittle materials exhibit complex cracking processes that can result in stochastic failure modes in structur...

工程结构的抗灾可靠性分析和设计是保障工程安全的基石。一百余年来，结构设 计理论已经过两代发展，当前正在向第三代结构设计理论迈进。如何科学地给出工程 结构抗灾整体可靠性的定量描述，业已成为工程领域亟待解决的关键问题。

This research pioneers a stochastic discrete element method (DEM) by integrating the probability density evolution method (PDEM), offering a novel approach to connect particle-scale property uncertainties, specifically inter-particle friction coefficient (μ) and particle shear modulus (G_p), with macroscale soil behavior. Through 1,100 DEM simulati...

Engineering structures are inherently susceptible to a multitude of uncertainties, ranging from geometric variations to external stochastic loads. These uncertainties wield significant influence over structural performance and, in severe cases, can lead to structural failure. Thus, structural uncertainty quantification, which encompasses uncertaint...

The probabilistic response determination of high-dimensional non-linear stochastic dynamical systems has long been a challenge in sciences and engineering fields. Both the randomness from system parameters, such as the material properties and geometric sizes, and external excitations, such as the earthquake ground motion or wind load, have signific...

Complex engineering structures are subject to various sources of uncertainty, including geometric and material variations, and randomness in external loads/excitations. In addition, the coupling of nonlinearity and randomness in high-dimensional or large-degree-of-freedom stochastic systems leads to a formidable challenge. To ensure the safety and...

High-dimensional stochastic dynamical systems enforced by Poisson white noise (PWN) are encountered widely in physics, chemistry, biology, and engineering fields, but it is hard to capture the probability density function (PDF) of the quantity of interest of these systems. Recently, the dimension-reduced probability density evolution equation (DR-P...

The probabilistic response determination of complex nonlinear stochastic dynamical systems is a key concern in the fields of science and engineering. In many cases, of interest in complex systems are not only the transient probability density functions (PDFs) of individual response process but also the transient joint PDF of multiple response proce...

Engineering structures are subject to multiple uncertainties, encompassing factors such as geometric variations, material inconsistencies, and stochastic external loads. These uncertainties have the potential to substantially impact structural performance, and in more severe instances, precipitate to structural failure. The goal of reliability anal...

In the ever-evolving field of engineering, ensuring the reliability of structural systems is of paramount importance. Addressing the complex buildings and structures subjected to stochastic excitations, this mini-symposium highlights the importance of accounting for uncertainties, the design and modelling of input loads, and the utilization of adva...

This work addresses the critical task of accurately estimating failure probabilities in dynamic systems by utilizing a probabilistic load model based on a set of data with similar characteristics, namely the relaxed power spectral density (PSD) function. A major drawback of the relaxed PSD function is the lack of dependency between frequencies, whi...

This paper presents a copula-based cloud analysis method for seismic fragility assessment with practical applications for nuclear power plant structures. Copula theory enables the flexible and efficient modeling of joint probability density function (PDF) for critical parameters, specifically the intensity measures (IM) and the engineering demand p...

Performance-based earthquake engineering (PBEE) is essential for ensuring engineering safety. Conducting seismic fragility analysis within this framework is imperative. Existing methods for seismic fragility analysis often rely heavily on double loop reanalysis and empirical data fitting, leading to challenges in obtaining high-precision results wi...

Coated granular materials, whether naturally occurring or synthetically produced in laboratories, offers substantial potential for various engineering applications. This study focuses on the use of dimethyldichlorosilane as a coating solution, inducing water repellency for granular materials, a property of interest in the development of advanced ma...

实际工程结构遭受的灾害性动力作用（如强风、地震等）往往具有显著的随机性和非平稳性。考虑这些复杂随机激励因素下高维非线性系统的动力可靠度精细化分析，对于实际工程结构的抗灾设计和优化具有重要意义。基于一般连续随机过程的广义概率密度全局演化方程，给出了一类非平稳随机激励下的高维非线性系统动力可靠度分析方法。具体地，若仅关心系统某一感兴趣量在给定安全域下的首次超越问题，则可以构造该感兴趣量在安全域内的吸收边界过程，并建立其瞬时概率密度函数满足的二维偏微分方程，即广义密度全局演化方程。方程中的本征漂移系数是驱动概率密度演化的全局性物理驱动力，可以通过原系统有限次代表性确定性动力分析获取的数据进行数值构造。采用数值方法求解广义密度全局演化方程，即可获得系统的动力可靠度解答。文中通过两个算例，验证了该方法...

The joint probability density function (PDF) of multiple response processes of a system is a crucial topic in the fields of science and engineering. It is adopted to describe the dependent uncertainty propagation in complex stochastic dynamical systems, including the displacement and velocity of one degree of freedom (DOF), and the nonlinear probab...

高维随机动力系统在物理学、化学、生物学和工程学等领域有广泛的应用。最近，降维概率密度演化方程在随机响应分析方面体现出显著优势，特别是对于高维和强非线性的路径连续过程，但在路径非连续过程方面仍然存在挑战，例如Poisson白噪声激励下的系统，其响应会出现随机跳跃。本研究针对多个乘性Poisson白噪声激励下高维非线性系统，建立了其感兴趣响应量的瞬时概率密度函数所满足的降维概率密度演化方程。不管系统的维度如何，该方程始终是一个一维的Kolmogorov-Feller型偏微分积分方程。降维概率密度演化方程中的本征漂移函数和本征发生率函数（后者用于乘性激励）可以通过几百次代表性确定性动力分析的数据进行数值识别。然后通过数值求解降维概率密度演化方程，可以得到感兴趣响应量的瞬时概率密度函数的数值解。最后...

The related code can be found at https://github.com/JCERSM/DR-PDEE-MATLAB, https://github.com/JCERSM/DR-PDEE-Julia or https://jcersm.tongji.edu.cn/ef/84/c14795a323460/page.htm.

Coated soils have recently been spotlighted for their prospective applications in geotechnical engineering. Prior studies have shown that Polydimethylsiloxane (PDMS) coatings can substantially mitigate surface roughness and have suggested that such coatings may experience abrasion under stress conditions. However, comprehensive studies exploring th...

High-dimensional stochastic dynamical systems enforced by Poisson white noise have a wide range of applications in physics, chemistry, biology, and engineering fields. Recently, the globally-evolving-based generalized density evolution equation (GE-GDEE) has shown significant advantages in probabilistic response determination of path-continuous pro...

The first-passage problem of high-dimensional nonlinear stochastic dynamical systems has long been a challenge in mechanics and engineering fields. Both the randomness from system parameters, such as the material properties and component sizes, and external excitations, such as the earthquake ground motion or wind load, have significant effects on...

Dynamic reliability evaluation of large-scale reinforced concrete (RC) structures is one of the most challenging problems in engineering practices. Although extensive endeavors have been devoted to mechanical analysis of concrete structures in the past decades, it was recognized that the randomness from both structural parameters and excitations ha...

Stochastic seismic response and dynamic reliability analyses of large-scale high-rise building structures under earthquake actions is one of the most challenging problems in engineering field. Both the randomness from structural parameters and external excitations have significant effects on the stochastic dynamic behaviors of structures with compl...

Stochastic seismic response and dynamic reliability analyses of large-scale high-rise building structures under earthquake actions is one of the most challenging problems in engineering field. Both the randomness from structural parameters and external excitations has significant effects on the stochastic dynamic behaviors of structures with comple...

Significant uncertainty exists in granular materials, as demonstrated by experimental and simulation studies. Quantifying this uncertainty by integrating refined discrete element analysis with direct stochastic simulation is challenging due to computational cost constraints. To this end, the probability density evolution method (PDEM) is introduced...

本书是中国科学院院士李杰教授和国家杰出青年科学基金获得者陈建兵教授在随机动力学领域的重要著作。本书主要内容包括随机过程和随机场的基本概念、工程中常用的随机动力激励模型、随机结构分析和随机振动分析的经典方法、概率密度演化方法的理论基础和数值实现，以及结构动力可靠度和随机最优控制的一般理论与方法。本书最大特色是将随机结构和随机振动问题纳入了统一的物理随机系统框架之下，并在此基础上建立了刻划随机性在物理机制驱动下传播规律的概率密度演化理论，在这一理论框架下可以实现复杂非线性随机动力系统的响应分析、可靠度计算以及控制优化。 本书主要面向土木工程、机械工程、航空航天和海洋工程以及力学领域的研究生和专业人士。

The recently developed globally-evolving-based generalized density evolution equation (GE-GDEE) provides a promising tool to obtain the instantaneous probability density of any quantity of interest of stochastically excited high-dimensional systems. By introducing an absorbing boundary process (ABP) determined by failure criteria, a corresponding G...

The response analysis of high-dimensional nonlinear stochastic dynamical systems has long been one of the main challenges in science and engineering. Both the randomness from system parameters, such as the material properties and component sizes, and external excitations, such as the ground motion or wind load, have significant effects on the dynam...

高维非线性系统在随机动力作用下的可靠性分析对实际工程结构的抗灾设计和优化具有重要意义，但长久以来是力学和工程领域的重要挑战性难题。实际工程结构遭受的灾害性动力作用（如强风、地震等）往往具有显著的随机性、非平稳性和非白噪声特性，考虑这些复杂随机激励因素下的动力可靠度精细化分析尤为关键。本文基于广义概率密度全局演化方程，给出了一类高维非线性系统在非平稳非白噪声激励下动力可靠度计算的数值方法。具体地，对于非平稳非白噪声激励下的高维非线性系统，若仅关心某一感兴趣响应量在给定安全域下的首次超越可靠度，则可以构造该感兴趣量和某一辅助过程在安全域内的吸收边界过程，并建立吸收边界过程的广义密度全局演化方程。一般地，广义密度全局演化方程是一个二维偏微分方程，其中的本征漂移系数是驱动概率密度演化的全局性物理驱动...

Stochastic fractional differential systems are important and useful in the mathematics, physics, and engineering fields. However, the determination of their probabilistic responses is difficult due to their non-Markovian property. The recently developed globally-evolving-based generalized density evolution equation (GE-GDEE), which is a unified par...

The risk of damage of glass curtain walls in residential areas caused by impact of wind-borne debris has been given increasing importance. In this paper, by incorporating the numerical analysis of three-dimensional (3D) flight trajectories of wind-borne debris and computational fluid dynamics (CFD) simulation of the local wind environment in the co...

Increasing attention has been attached to the risk assessment and fragility analysis of envelopes of high-rise buildings subjected to the impact of wind-borne debris in hurricanes or typhoons. A probabilistic model of wind-borne debris is proposed in the present paper for risk assessment and fragility analysis of high-building curtain walls based o...

极值分布是随机过程与随机力学领域研究的重要课题之一。研究Markov过程的时变极值过程的概率分布特征对于很多随机动力学问题有着重要的意义，例如分析随机动力系统的首次超越可靠度。然而，长期以来仅有少数极特殊过程的极值分布具有已知的解析表达；对于更一般的情形则需要根据经验假设或借助数值方法，例如蒙特卡罗模拟方法、等价极值事件方法、极值—状态量联合Markov向量过程方法等。本文从Lindeberg条件以及首次超越时间与时变极值过程的关系入手，对于一般的连续Markov过程，在给定初始条件下，导出了其时变极值过程的概率密度所满足的Volterra积分方程。在该方程中，核函数完全由Markov过程的转移概率密度函数决定。根据这一概率演化积分方程，若已知原过程在任意两个时刻的转移概率分布信息，则可以解...

Reliability evaluation of large-scale high-rise building structures under disastrous dynamic actions is one of the most challenging problems in engineering field. Both the randomness from structural parameters, e.g., the material properties, and external excitations, such as the ground motion or wind load, have significant effects on the stochastic...

In practice, the randomness might be involved in both structural parameters and external dynamical actions, which leads to coupling effects on the stochastic response statistics of structures. In the paper, based on the globally-evolving-based generalized density evolution equation (GV-GDEE), a novel method to capture the response statistics of hig...

The reliability analysis of high-dimensional nonlinear stochastic dynamical systems has long been one of the major challenges in sciences and engineering fields, and no satisfactory method with high efficiency and accuracy has been developed as yet. In the paper, a new globally-evolving-based generalized density evolution equation (GV-GDEE) is adop...

In practice, the randomness might be involved in both structural parameters and external dynamical actions, which leads to coupling effects on the stochastic response statistics of structures. In the paper, based on the globally-evolving-based generalized density evolution equation (GV-GDEE), a novel method to capture the response statistics of hig...

The reliability analysis of high-dimensional nonlinear stochastic dynamical systems has long been one of the major challenges in sciences and engineering fields, and no satisfactory method with high efficiency and accuracy has been developed as yet. In the paper, a new globally-evolving-based generalized density evolution equation (GV-GDEE) is adop...

Reliability analysis for engineering structures subjected to disastrous stochastic dynamical actions is of paramount importance for the performance-based decision-making of design, and has long been one of the major challenges in civil and various engineering fields. In the present paper, a novel method based on the globally-evolving-based generali...

Reliability analysis for engineering structures subjected to disastrous stochastic dynamical actions is of paramount importance for the performance-based decision-making of design, and has long been one of the major challenges in civil and various engineering fields. In the present paper, a novel method based on the globally-evolving-based generali...

The stochastic response analysis and first-passage reliability evaluation of multi-dimensional nonlinear systems subjected to non-white-noise engineering dynamic excitations have long been challenging problems. The recently developed globally-evolving-based generalized density evolution equation (GE-GDEE) provides a promising tool and is extended i...

First-passage reliability assessment of engineering structures under disastrous stochastic dynamic excitations is of paramount importance for the performance-based decision-making of structural design. However, it is still of great challenge due to the coupling of nonlinearity and randomness in the high-dimensional systems. In the present paper, a...

It has long been one of the main challenges in science and engineering to capture the probabilistic response of high-dimensional nonlinear stochastic dynamic systems involving double randomness, i.e. randomness in both system parameters and excitations. For this purpose, a globally-evolving-based generalized density evolution equation (GE-GDEE) is...

高维非线性随机动力系统的响应和可靠度分析长期以来是科学和工程领域的重要挑战性难题。近年来国内外研究者们发展了许多针对实际复杂结构系统的可靠度评估方法，然而大多方法对于罕遇灾害性动力作用下结构的小失效概率仍难以精确估计。随着向第三代结构设计理论的迈进，这一问题愈显重要而迫切。 概率密度演化理论及其群演化路径的提出为这一问题的精细化高效实现提供了新的视角。遵循这一路径，本文建立并发展了广义概率密度全局演化方程，为一般连续随机过程的概率密度演化分析建立了统一的理论框架。在此框架下，各类经典的概率密度演化方程（如Liouville方程、Fokker-Planck-Kolmogorov（FPK）方程等）均可以视为广义密度全局演化方程针对某些具体物理系统的特殊形式。值得指出的是，这一方程不需要随机过程的...

Time-variant reliability assessment of engineering systems subjected to stochastic excitations, especially for rare events, is of paramount importance for the performance-based decision-making of design, but is still of great challenge due to the nonlinear and random coupling in high-dimensional systems. For this purpose, a globally-evolving-based...

The response analysis of multi-degree-of-freedom (MDOF) structures subjected to stochastic dynamic actions, e.g., earthquake ground motions, is one of the major challenges in the field of earthquake engineering. Actually, except the crude or various improved Monte Carlo simulation (MCS) methods, the accurate and efficient numerical methods for the...

The response analysis of multi-degree-of-freedom (MDOF) structures subjected to stochastic dynamic actions, e.g., earthquake ground motions, is one of the major challenges in the field of earthquake engineering. Actually, except the crude or various improved Monte Carlo simulation (MCS) methods, the accurate and efficient numerical methods for the...

The probabilistic response analysis of high-dimensional nonlinear systems with random structural parameters enforced by stochastic dynamical actions is one of the significant challenges in sciences and engineering fields. Actually, the accurate and efficient numerical methods for the probabilistic information of nonlinear structural responses are s...

The probabilistic response analysis of high-dimensional nonlinear systems with random structural parameters enforced by stochastic dynamical actions is one of the significant challenges in sciences and engineering fields. Actually, the accurate and efficient numerical methods for the probabilistic information of nonlinear structural responses are s...

The response analysis of high-dimensional nonlinear stochastic dynamical systems has long been one of the major challenges in various engineering fields. In engineering practice, the randomness in both structural parameters and external excitations leads to coupling effects on the stochastic response statistics of structures, which is of even great...

Stochastic dynamic response analysis and reliability assessment of engineering structures subjected to earthquakes are of paramount importance for the performance-based decision-making of design. Intensive efforts have been devoted to these issues in the past decades and great progresses have been made, yielding, e.g., among others the various meth...

The time-variant maximal value process (MVP) of a Markov process has significant applications in various science and engineering fields. In the present paper, the closed-form solutions for the probability distribution of the time-variant MVP for some classes of Markov process are studied. For general continuous Markov processes, a unified Volterra...

The reliability analysis of high-dimensional stochastic dynamical systems subjected to random excitations has long been one of the major challenges in civil and various engineering fields. Despite great efforts, no satisfactory method with high efficiency and accuracy has been available as yet for high-dimensional systems even when they are linear...

研究Markov过程的时变极值过程在科学与工程领域有着重要的意义. 例如, 对于随机动力系统的首次超越问题的求解即可转化为上述问题. 然而, 长期以来仅有极少数特殊过程的极值分布解析表达已知, 一般情况下则需要采用数值方法求解, 例如构造极值-状态量联合Markov向量过程的方法. 本文从首次超越时间的角度出发, 对于一般的连续Markov过程 , 推导了在给定初值下, 其时变极值过程的概率演化积分方程. 根据这一方程, 若已知原过程的概率分布信息, 则可以解析或数值地获得其时变极值过程的概率分布信息, 进而应用于首次超越破坏问题的求解. 最后, 本文通过算例与蒙特卡罗模拟 (MCS) 的对比, 验证了概率演化积分方程求解结果的正确性.

The reliability evaluation of multi-degree-of-freedom (MDOF) structures subjected to stochastic excitations has long been one of the major challenges in civil engineering, and no satisfactory method with high efficiency and accuracy has been published as yet. In this paper, a new ensemble evolving-based generalized density evolution equation (EV-GD...

The reliability evaluation of multi-degree-of-freedom (MDOF) structures subjected to stochastic excitations has long been one of the major challenges in civil engineering, and no satisfactory method with high efficiency and accuracy has been published as yet. In this paper, a new ensemble evolving-based generalized density evolution equation (EV-GD...

高维非线性随机动力系统的可靠度分析是科学与工程领域的重要挑战性问题之一。基于近年来在概率密度演化理论的基础上发展起来的概率密度群演化方程（EV-GDEE），本文提出了一种计算高维非线性随机动力系统时变可靠度的新方法，该方法可适用于Gauss白噪声激励下高维非线性系统的首次超越可靠度分析，且具有较高的数值精度与计算效率。对于高维非线性随机动力系统，若仅关心系统中某一响应量在给定安全域下的首次超越破坏问题，则可通过采用群演化思想降维，获得基于物理驱动的概率密度群演化方程。其中，等价漂移系数是一个条件期望函数，可以通过确定性物理-力学分析给出的数据构造。进而，在给定首次超越问题的安全域边界处，对群演化方程施加吸收边界条件，可以通过数值求解获得感兴趣响应量的剩余概率密度，从而积分获得时变可靠度的数值...

长期以来，复杂高层建筑结构在随机动力作用下的可靠性评估一直是土木工程领域的富有挑战性的难题之一，迄今尚无精确高效的解析或数值方法。本文基于广义密度群演化方程（EV-GDEE），提出了一类高维随机动力系统首次超越可靠度计算的新方法。对于加性激励下的高维随机动力系统，若仅关心系统中特定响应量的分析及相应的首次超越破坏问题，则可通过对Fokker-Planck-Kolmogorov方程的群演化降维，获得该响应量概率密度所满足的群演化方程。这是一个一维或二维偏微分方程，可以采用数值方法获得其概率密度解。其中，等价漂移系数是一个条件期望函数，可以通过有限次确定性分析给出的数据构造得到其数值表达。进而，在给定首次超越问题的安全域边界处，对群演化方程施加吸收边界条件，可以通过数值求解获得感兴趣响应量的剩余...

The extreme value distribution (EVD) of stochastic processes is an important but still challenging problem for the determination of reliability function and distribution of first excursion time in various science and engineering fields. In the present paper, a new method to evaluate the time-variant probability density function (PDF) of the maximal...

在科学与工程领域中，随机过程或随机系统响应的时变极值过程概率分布是人们关注的重要挑战性问题之一。本文对Markov过程的时变极值过程及其概率分布进行了研究。尽管时变极值过程本身不具有Markov性，但可以构造极值—状态量联合向量过程，并严格证明其Markov性。进而，通过极值与状态量之间的关系，建立了联合向量过程的转移概率密度函数的解析表达。在此基础上，结合Chapman—Kolmogorov方程及其路径积分求解，提出了时变极值概率密度求解的数值方法。由此，可以得到Markov过程极值过程的时变概率密度。该方法可进一步用于结构动力可靠度分析等问题。通过数值算例，验证了本文所提方法对于不同噪声激励及不同非线性系统的有效性。结合概率密度演化群演化方法，该方法有望进一步推广到高维随机系统的极值分布...

随机过程或随机系统响应的最大绝对值概率分布往往是科学与工程中关心的重要挑战性问题。本文从理论与数值上进行了Markov过程的时变最大绝对值过程及其概率分布研究。文中，通过引入扩展状态向量，构造了最大绝对值-状态量联合向量过程，由此将不具有Markov性的最大值过程转化为具有Markov性的向量随机过程。在此基础上，通过最大绝对值-状态量之间的关系，建立了联合向量过程的转移概率密度函数。进而，结合Chapman-Kolmogorov方程和路径积分方法，提出了最大绝对值概率密度函数求解的数值方法。由此，可以得到Markov过程最大绝对值过程的时变概率密度函数，可进一步用于结构动力可靠度分析等。通过数值算例，验证了本文所提方法的有效性。该方法有望推广到更一般随机系统的极值分布估计之中。

The probability density function (PDF) of the time-variant extreme value process for structural responses is of great importance. Poisson white noise excitation occurs widely in practical engineering problems. The extreme value distribution of the response of systems excited by Poisson white noise processes is still not yet readily available. For t...

In the present paper a method to determine the probability distribution of the maximum value process (MVP) of a Markov process is proposed. In this method, an augmented vector process of a physical process and its MVP is constructed. The joint probability density function is then calculated by the path integral solution (PIS), and further the proba...

In the present paper a method to determine the probability distribution of the maximum value process (MVP) of a Markov process is proposed. In this method, an augmented vector process of a physical process and its MVP is constructed. The joint probability density function is then calculated by the path integral solution (PIS), and further the proba...

非线性随机动力系统的响应统计与可靠度研究是工程领域所面临的重大挑战之一。求解系统响应时变极值过程的概率密度信息为非线性随机动力系统的可靠度分析提供了新的解决方案。另一方面，Poisson白噪声激励在路桥交通荷载、飞机翼尾振动等许多实际工程问题中有着重要的应用。在本文中，针对Poisson白噪声激励下的非线性随机动力系统，从理论与数值上开展有关其响应时变极值过程概率信息的定量研究。为此，将构造极值—状态量联合向量过程，并根据其Markov性采用路径积分法求解其联合概率密度，进而获得时变极值过程的概率密度函数数值结果。在此基础上，即可进一步求解获取结构体系的动力可靠度。通过典型的数值算例，验证了提出的方法。对于维数不高的非线性随机动力系统，该方法具有很高的精度与较高的效率。本文的思想方法可以进一...

工程随机动力系统的可靠度研究是结构工程领域所面临的重大挑战之一。获取动力响应过程的时变极值分布，将为结构动力可靠度求解提供可行途径。作为初步探索，本文从理论与数值上开展了Markov过程最大值过程的研究。考察了最大值过程的Markov性，提出了通过构造最大值—状态量联合向量过程并对其进行路径积分求解，从而最终获得最大值过程时变概率密度函数的方法。典型数值算例的研究表明，本文提出的方法具有很高的精度。

The security risks of glass curtain wall of high-rise building have become increasingly important. Taking into account the local wind environment, the wind damage caused by debris impacting on glass curtain walls is studied in this paper. The factors influencing the flight characteristics of spherical debris are analyzed. The three-dimensional flig...

中国是世界上遭受台风灾害最为严重的国家之一，每年因台风灾害造成的经济损失十分严重。研究表明，在我国东南沿海地区，高层建筑幕墙玻璃在历次风灾中多次因遭受碎片撞击而发生严重破坏，对城市安全造成严重影响。开展高层建筑玻璃幕墙由于碎片撞击导致的灾害危险性分析，对城市防灾减灾工作至关重要。本文针对典型碎片的飞行特性进行了分析，并考虑城市区域局部风环境的影响对建筑幕墙遭受碎片撞击的破坏开展研究，进一步提出了基于碎片危险性分析的高层建筑玻璃幕墙风灾评估概率模型。研究成果将为进一步开展城市区域风灾评估与工程防御提供基础。本文主要内容包括以下几个方面： 1. 针对球状与板状两种典型碎片类型，通过求解三维运动方程，对两类碎片的飞行轨迹进行数值模拟，并开展影响碎片飞行特性的初始参数分析。特别针对板状碎片，基于运动...