Related papers: A sample-based stochastic finite element method fo…
This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…
The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesise finite element models with observed data. Through embedding uncertainty inside of the governing equations, finite element…
This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM…
Within the performance-based earthquake engineering (PBEE) framework, the fragility model plays a pivotal role. Such a model represents the probability that the engineering demand parameter (EDP) exceeds a certain safety threshold given a…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the…
We present an interval-based approach for parameter identification in structural static inverse problems. The proposed inverse formulation exploits the Interval Finite Element Method (IFEM) combined with adjoint-based optimization. The…
This tutorial teaches parts of the finite element method (FEM), and solves a stochastic partial differential equation (SPDE). The contents herein are considered "known" in the numerics literature, but for statisticians it is very difficult…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Structural equation modeling (SEM) is a prevalent approach for studying constructs.Traditionally, these constructs are modeled as reflectively measured latent variables - common factors that account for the variance-covariance structure of…
Existing variance reduction techniques used in stochastic simulations for rare event analysis still require a substantial number of model evaluations to estimate small failure probabilities. In the context of complex, nonlinear finite…
Finite-sample bias is a pervasive challenge in the estimation of structural equation models (SEMs), especially when sample sizes are small or measurement reliability is low. A range of methods have been proposed to improve finite-sample…
This work presents a novel surface decomposition method for the sensitivity analysis of first-passage dynamic reliability of linear systems subjected to Gaussian random excitations. The method decomposes the sensitivity of first-passage…
Extreme response assessment is important in the design and operation of engineering structures, and is a crucial part of structural risk and reliability analyses. Structures should be designed in a way that enables them to withstand the…
Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation…
In this work, we propose a new estimation method of a Structural Equation Model. Our method is based on the EM likelihood-maximization algorithm. We show that this method provides estimators, not only of the coefficients of the model, but…
A radial basis function (RBF) based sequential surrogate reliability method (SSRM) is proposed, in which a special optimization problem is solved to update the surrogate model of the limit state function (LSF) iteratively. The objective of…
The performance evaluation of a potentially unstable slope involves two key components: the initiation of the slope failure and the post-failure runout. The Finite Element Method (FEM) excels at modeling the initiation of instability but…
Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…
The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…