Related papers: A sample-based stochastic finite element method fo…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the past two decades, a growing interest has been devoted to stochastic finite element method (SFEM) for the propagation of…
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true system response. We provide a probabilistic error analysis…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
A new method for estimating structural equation models (SEM) is proposed and evaluated. In contrast to most other methods, it is based directly on the data, not on the covariance matrix of the data. The new approach is flexible enough to…
The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
Factor-based Structural Equation Modeling (SEM) relies on likelihood-based estimation assuming a nonsingular sample covariance matrix, which breaks down in small-sample settings with $p>n$. To address this, we propose a novel estimation…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…
This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…
Handling latent variables in Structural Equation Models (SEMs) in a case where both the latent variables and their corresponding indicators in the measurement error part of the model are random curves presents significant challenges,…
The Statistical Finite Element Method (statFEM) offers a Bayesian framework for integrating computational models with observational data, thus providing improved predictions for structural health monitoring and digital twinning. This paper…
Efficient structural damage localization remains a challenge in structural health monitoring (SHM), particularly when the problem is coupled with uncertainty of conditions and complexity of structures. Traditional methods simply based on…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…
Numerical modeling of slope failures seeks to predict two key phenomena: the initiation of failure and the post-failure runout. Currently, most modeling methods for slope failure analysis excel at one of these two but are deficient in the…