Enhanced goal-oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems

This work focuses on providing accurate low-cost approximations of stochastic ¿nite elements simulations in the framework of linear elasticity. In a previous work, an adaptive strategy was introduced as an improved Monte-Carlo method for multi-dimensional large stochastic problems. We provide here a complete analysis of the method including a new enhanced goal-oriented error estimator and estimates of CPU (computational processing unit) cost gain. Technical insights of these two topics are presented in details, and numerical examples show the interest of these new developments.Postprint (author's final draft

A level II reliability approach to tunnel support design

A reliability approach to tunnel support design is presented in this paper. The aim of the work is the incorporation of classical Level II techniques to the current design method based on the study of the ground-support interaction diagram

Uncertainties in dynamic response of buildings with non-linear base-isolators

Dynamic response of base-isolated buildings under uni-directional sinusoidal base excitation is numerically investigated considering uncertainties in the isolation and excitation parameters. The buildings are idealized as single degree of freedom (SDOF) system and multi-degrees of freedom (MDOF) system with one lateral degree of freedom at each floor level. The isolation system is modeled using two different mathematical models such as: (i) code-recommended equivalent linear elastic-viscous damping model and (ii) bi-linear hysteretic model. The uncertain parameters of the isolator considered are time period, damping ratio, and yield displacement. Moreover, the amplitude and frequency of the sinusoidal base excitation function are considered uncertain. The uncertainty propagation is investigated using generalized polynomial chaos (gPC) expansion technique. The unknown gPC expansion coefficients are obtained by non-intrusive sparse grid collocation scheme. Efficiency of the technique is compared with the sampling method of Monte Carlo (MC) simulation. The stochastic response quantities of interest considered are bearing displacement and top floor acceleration of the building. Effects of individual uncertain parameters on the building response are quantified using sensitivity analyses. Effect of various uncertainty levels of the input parameters on the dynamic response of the building is also investigated. The peak bearing displacement and top floor acceleration are more influenced by the amplitude and frequency of the sinusoidal base excitation function. The effective time period of the isolation system also produces a considerable influence. However, in the presence of similar uncertainty level in the time period, amplitude and frequency of the sinusoidal forcing function, the effect of uncertainties in the other parameters of the isolator (e.g., damping ratio and yield displacement) is comparatively less. Interestingly, the mean values of the response quantities are found to be higher than the deterministic values in several instances, indicating the need of conducting stochastic analysis. The gPC expansion technique presented here is found to be a computationally efficient yet accurate alternative to the MC simulation for numerically modeling the uncertainty propagation in the dynamic response analyses of the base-isolated buildings

Stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty

The problem of representing random fields describing the material and boundary properties of the physical system at discrete points of the spatial domain is studied in the context of linear stochastic finite element method. A randomly parameterized diffusion system with a set of independent identically distributed stochastic variables is considered. The discretized parametric fields are interpolated within each element with multidimensional Lagrange polynomials and integrated into the weak formulation. The proposed discretized random-field representation has been utilized to express the random fluctuations of the domain boundary with nodal position coordinates and a set of random variables. The description of the boundary perturbation has been incorporated into the weak stochastic finite element formulation using a stochastic isoparametric mapping of the random domain to a deterministic master domain. A method for obtaining the linear system of equations under the proposed mapping using generic finite element weak formulation and the stochastic spectral Galerkin framework is studied in detail. The treatment presents a unified way of handling the parametric uncertainty and random boundary fluctuations for dynamic systems. The convergence behavior of the proposed methodologies has been demonstrated with numerical examples to establish the validity of the numerical scheme

Gaussian process assisted stochastic dynamic analysis with applications to near-periodic structures

This paper characterizes the stochastic dynamic response of periodic structures by accounting for manufacturing variabilities. Manufacturing variabilities are simulated through a probabilistic description of the structural material and geometric properties. The underlying uncertainty propagation problem has been efficiently carried out by functional decomposition in the stochastic space with the help of Gaussian Process (GP) meta-modelling. The decomposition is performed by projected the response onto the eigenspace and involves a nominal number of actual physics-based function evaluations (the eigenvalue analysis). This allows the stochastic dynamic response evaluation to be solved with low computational cost. Two numerical examples, namely an analytical model of a damped mechanical chain and a finite-element model of multiple beam-mass systems, are undertaken. Two key findings from the results are that the proposed GP based approximation scheme is capable of (i) capturing the stochastic dynamic response in systems with well-separated modes in the presence of high levels of uncertainties (up to 20), and (ii) adequately capturing the stochastic dynamic response in systems with multiple sets of identical modes in the presence of 5–10 uncertainty. The results are validated by Monte Carlo simulations