Seismic reliability analysis of energy-dissipation structures by combining probability density evolution method and explicit time-domain method

Xian, Jianhua; Su, Cheng; Guo, Houzuo

doi:10.1016/j.strusafe.2020.102010

Cited by 14 publications

(9 citation statements)

References 37 publications

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“…Figure 2 shows a domain decomposition up to a level of expansion 2. When 𝑚 = 0, that is, a single domain is considered, 𝛀 0,1 Θ = 𝛀 Θ (Figure 2A), then residual is the same as for PCE, in Equation (31). For multi-level of expansion, Equation ( 30) is re-written as…”

Section: Stochastic Spectral Embeddingmentioning

confidence: 99%

“…The reliability analysis of the shell structure coupled with a viscoelastic damper was studied by Xu et al [30] where the probabilistic response of the structure was estimated using PDEM. Xian et al [31] showed the seismic reliability analysis of the structure coupled with buckling restrained braces using a hybrid method of PDEM and an explicit time-domain method. Feng et al [32] investigated the robustness of the reinforced concrete structure subjected to progressive collapse using PDEM.…”

Section: Introductionmentioning

confidence: 99%

“…Xian et al. [ 31 ] showed the seismic reliability analysis of the structure coupled with buckling restrained braces using a hybrid method of PDEM and an explicit time‐domain method. Feng et al.…”

Section: Introductionmentioning

confidence: 99%

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Reliability analysis of structures using probability density evolution method and stochastic spectral embedding surrogate model

Das

Tesfamariam

2023

Earthq Engng Struct Dyn

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This study presents an efficient reliability analysis method using probability density evolution method (PDEM) and stochastic spectral embedding (SSE) based surrogate model. The PDEM is used to estimate the structural response's probability density function (PDF). The PDEM is derived based on the principle of probability conservation where generalized density evolution equations (GDEEs) are decoupled from the physical system. The GDEEs are solved using finite difference method coupled with total variation diminishing, in which a set of representative points of random parameters are generated using the generalized F-discrepancy scheme. To obtain satisfactory accuracy of the numerical solution, representative points are needed, which becomes computationally expensive for complex structures. To reduce the computation burden, the SSE is used, which approximates the original response surface. The SSE is a class of supervised machine learning algorithm where it is trained by few observations and enables output prediction as spectral representation. This is achieved by minimizing the residual using domain decomposition technique. To illustrate the proposed SSE-based PDEM, three numerical examples are investigated, including the reliability analysis of four-branch problem and shear building frame subjected to ground acceleration, and the reliability-based design optimization of a moment-resisting frame coupled with the nonlinear energy sink with negative stiffness and sliding friction. Numerical results show that the proposed SSE-based PDEM can estimate failure probability using a very small number of representative points without compromising accuracy compared with Monte Carlo simulation, which leads to a reduction in computational costs.

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Section: Stochastic Spectral Embeddingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reliability analysis of structures using probability density evolution method and stochastic spectral embedding surrogate model

Das

Tesfamariam

2023

Earthq Engng Struct Dyn

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“…The above system limit-state function corresponds to the reliability problem of series systems. For parallel systems or series-parallel-coupled systems, the system limit-state function can be found in reference [40].…”

Section: System Limit-state Functionmentioning

confidence: 99%

An Efficient Monte-Carlo Simulation for the Dynamic Reliability Analysis of Jacket Platforms Subjected to Random Wave Loads

Wang

2021

JMSE

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The growing demand for the application of jacket platforms in deep water requires more attention on the assessment of structural reliability. This paper is devoted to the dynamic reliability analysis of jacket platforms subjected to random wave loads with Monte-Carlo simulation (MCS), in which a sample size of the order of magnitude of 104 to 105 for repeated time–history analyses is required for small failure probability problems, and a duration time up to three hours needs to be considered in the time–history analyses for a specific sea condition. To tackle the difficulty involved in MCS, the explicit time-domain method (ETDM) is used for the required time–history analyses of jacket platforms, in which truncated explicit expressions of critical responses with regards to the contributing loading terms are first established and then used for numerous repeated sample analyses. The use of ETDM greatly enhances the computational efficiency of MCS, making it feasible for the dynamic reliability analysis of jacket platforms under random wave loads. A jacket platform with 11,688 degrees of freedom was analyzed for the evaluation of dynamic reliability under a given sea condition, indicating the accuracy and efficiency of the present approach and its feasibility to practical structures.

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“…The computational challenges of reliability analysis are featured by expensive computational models, highdimensional uncertainties, and low failure probabilities. An increasing amount of reliability methods are developed to address these challenges, e.g., the first-and second-order reliability methods [1,2], momentbased methods [3][4][5][6], surrogate modeling-based methods [7][8][9][10][11][12], and probability density evolution-based methods [13][14][15][16]. These reliability methods more or less suffer from the curse of dimensionality, restriction to specialized problems, and inaccuracy for low-probability events.…”

Section: Introductionmentioning

confidence: 99%

Relaxation-based importance sampling for structural reliability analysis

Xian¹,

Wang²

2023

Preprint

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This study presents an importance sampling formulation based on adaptively relaxing parameters from the indicator function and/or the probability density function. The formulation embodies the prevalent mathematical concept of relaxing a complex problem into a sequence of progressively easier sub-problems. Due to the flexibility in constructing relaxation parameters, relaxation-based importance sampling provides a unified framework to formulate various existing variance reduction techniques, such as subset simulation, sequential importance sampling, and annealed importance sampling. More crucially, the framework lays the foundation for creating new importance sampling strategies, tailoring to specific applications. To demonstrate this potential, two importance sampling strategies are proposed. The first strategy couples annealed importance sampling with subset simulation, focusing on low-dimensional problems. The second strategy aims to solve high-dimensional problems by leveraging spherical sampling and scaling techniques. Both methods are desirable for fragility analysis in performance-based engineering, as they can produce the entire fragility surface in a single run of the sampling algorithm. Three numerical examples, including a 1000-dimensional stochastic dynamic problem, are studied to demonstrate the proposed methods.

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Seismic reliability analysis of energy-dissipation structures by combining probability density evolution method and explicit time-domain method

Cited by 14 publications

References 37 publications

Reliability analysis of structures using probability density evolution method and stochastic spectral embedding surrogate model

Reliability analysis of structures using probability density evolution method and stochastic spectral embedding surrogate model

An Efficient Monte-Carlo Simulation for the Dynamic Reliability Analysis of Jacket Platforms Subjected to Random Wave Loads

Relaxation-based importance sampling for structural reliability analysis

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