Abstract By adopting a Multilevel Monte Carlo (MLMC) framework, this paper shows that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of a composite structure, as opposed to the many thousands typically needed in classical Monte Carlo analyses. The paper introduces the MLMC method and provides an extension called MLMC with selective refinement to efficiently calculated structural failure probabilities. Simple-to-implement, self-adaptive algorithms are given, and the results demonstrate huge computational gains for two novel, real world example problems in composites performance analysis: (i) the effects of fibre waviness on the compressive strength of a composite material and (ii) the uncertain buckling performance of a composite panel with random ply orientations. For the most challenging test case of estimating a 1 ∕ 150 probability of buckling failure of a composite panel the results demonstrate a speed-up factor of > 1000 over classical Monte Carlo. In absolute terms, the computational time was reduced from 218 CPU days to just 4.4 CPU hours, making stochastic simulations that would otherwise be unthinkable now possible.
Abstract It is important to account for inherent variability in the material properties in the design and analysis of engineering structures. These properties are typically not homogeneous, but vary across the spatial coordinates within a structure, as well as from specimen to specimen. This form of uncertainty is commonly modelled using random fields within the Stochastic Finite Element Method. Simulation within this framework can be complicated by the dependence of a random field’s correlation...
In this paper, we present a generalization of the multilevel Monte Carlo (MLMC) method to a setting where the level parameter is a continuous variable. This continuous level Monte Carlo (CLMC) estimator provides a natural framework in PDE applications to adapt the model hierarchy to each sample. In addition, it can be made unbiased with respect to the expected value of the true quantity of interest provided the quantity of interest converges sufficiently fast. The practical implementation of the...
Abstract This paper presents a novel stochastic framework to quantify the knock down in strength from out-of-plane wrinkles at the coupon level. The key innovation is a Markov Chain Monte Carlo algorithm which rigorously derives the stochastic distribution of wrinkle defects directly informed from image data of defects. The approach significantly reduces uncertainty in the parameterization of stochastic numerical studies on the effects of defects. To demonstrate our methodology, we present an or...
Last. Axel Målqvist(Chalmers University of Technology)H-Index: 17
view all 3 authors...
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or above) some critical value. By combining recent results on quantile estimation and the multilevel Monte Carlo method, we develop a method that reduces computational cost without loss of accuracy. We show how the computational cost of the method relates to error ...
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large-scale applications with high-dimensional parameter spaces, e.g., in uncertainty quantification in porous media flow. We propose a new multilevel Metropolis--Hastings algorithm and give an abstract, problem-dependent theorem on the cost of the new multilevel estimator based on a set of simple, verifiable assumptions. For a typical model problem in subsurface fl...
Assuming independence between failure modes makes system reliability calculation simple but it adds approximation error. Interestingly, error due to ignoring dependence can be negligible for a highly reliable system. This paper investigates the reasons and the factors affecting the error. Error in system probability of failure (PF) is small for high reliability when tail-dependence is not very strong or the ratio between individual PFs is large. We created various conditions using copulas and ob...
#2Abdul-Lateef Haji-Ali(KAUST: King Abdullah University of Science and Technology)H-Index: 8
Last. Raul Tempone(KAUST: King Abdullah University of Science and Technology)H-Index: 36
view all 5 authors...
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average...
The author’s presentation of multilevel Monte Carlo path simulation at the MCQMC 2006 conference stimulated a lot of research into multilevel Monte Carlo methods. This paper reviews the progress since then, emphasising the simplicity, flexibility and generality of the multilevel Monte Carlo approach. It also offers a few original ideas and suggests areas for future research.
#2Alfonso Pagani(Polytechnic University of Turin)H-Index: 25
Last. Chao Zhang(NPU: Northwestern Polytechnical University)H-Index: 123
view all 4 authors...
It is well known that fabrication processes inevitably lead to defects in the manufactured components. However, thanks to the new capabilities of the manufacturing procedures that have emerged during the last decades, the number of imperfections has diminished while numerical models can describe the ground truth designs. Even so, a variety of defects has not been studied yet, let alone the coupling among them. This paper aims to characterise the buckling response of Variable Stiffness Composite ...
