Mathematical and statistical literacy: an analysis based on PISA results

In this paper we discuss the distinction between statistical literacy and mathematical literacy. The starting point of this discussion is the fact that within the Programme for International Student Assessment (PISA) statistical survey items are elaborated only from the mathematical literacy point of view. We first present theoretical elements on the differences between mathematics and statistics, between mathematical and statistical literacy and we elaborate on the growing interest in statistical literacy as a specific competence. Second we present results of an empirical analysis based on the PISA 2003 data. The analysis showed an extremely high correlation between mathematical and statistical literacy. In the conclusion we emphasise the necessity to reveal the notion of statistical literacy within the PISA results

A tangential force-displacement model for elastic frictional contact between particles in triaxial test simulations

A tangential contact model for three-dimensional discrete element simulations is proposed and used in the micro-mechanical simulation of a drained triaxial test. In this model, the dependence of the tangential contact force on the contact loading history is accounted for. A representative volume element with spherical discrete elements and periodic boundary conditions is used in the simulations to reduce the computation costs. Numerical results of a triaxial test obtained with a linear and the proposed tangential contact model are compared. The results for both contact models are qualitatively in agreement with theory. The linear contact model needs calibration as the used parameters lack physical meaning, while the proposed contact model only uses physical properties of the particles

Multi-temporal decomposition for elastoplastic ratcheting solids

This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation. In contrast with the standard incremental approach, which solves the (non-linear and computationally intensive) mechanical balance equations at every time step, the proposed PGD approach allows the mechanical balance equations to be solved exclusively for the small-time intra-cyclic response, while the large-time inter-cyclic response is described by simple scalar algebraic equations. Numerical simulations exhibiting complex cyclic responses, including a 2D problem and an application to a monopile foundation, demonstrate that PGD solutions with a limited number of space-time degrees of freedom may be obtained numerically, only requiring a few modes to accurately capture the reference response.Comment: Version accepted for publication in Computer Methods in Applied Mechanics and Engineerin

An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem

[EN] Problems in civil engineering are often characterized by significant uncertainty in their material parameters. Sampling methods are a straightforward manner to account for this uncertainty, which is typically modeled as a random field. A popular sampling method consists of the classic Multilevel Monte Carlo method (h-MLMC). Its most distinctive feature consists of a hierarchy of h-refined meshes, where most of the samples are taken on coarse and computationally inexpensive meshes, and few are taken on finer but computationally expensive meshes. We present an improvement upon the classic Multilevel Monte Carlo, called the prefined Multilevel quasi-Monte Carlo method (p-MLQMC). Its key features consist of a mesh hierarchy constructed from a p-refinement scheme combined with a deterministic set of samples points (quasi-Monte Carlo points). In this work we show how the uncertainty needs to be accounted for and present results comparing the total computational cost of the h-ML(Q)MC and p-MLQMC method. Specifically, we present two novel approaches in order to account for the uncertainty in case of p-MLQMC. We benchmarking the different multilevel methods on a slope stability problem, and find that p-MLQMC outperforms h-MLMC up to several orders of magnitude.The authors gratefully acknowledge the support from the Research Council of KU Leuven through project C16/17/008 “Efficient methods for large-scale PDE-constrained optimization in the presence of uncertainty and complex technological constraints”. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government – department EWI.Blondeel, P.; Robbe, P.; François, S.; Lombaert, G.; Vandewalle, S. (2022). An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 25-35. https://doi.org/10.4995/YIC2021.2021.12236OCS253

Estimation methods for computing a branch’s total value added from incomplete annual accounting data. National Bank of Belgium, Working Paper No. 371

Timely monitoring of the economic performance of a particular sector is generally hindered by the fact that not all companies have deposited their annual accounts by the time that an evaluation is made. In view of this, we develop several imputation strategies that each enable predicting a company’s value added based on available information from past and current years for those companies where the value added was not timely reported. For each proposed strategy we discuss the assumptions which must be fulfilled for unbiased estimation and calculate the estimation uncertainty. In particular, the proposed imputation procedures all rely on an assumption of missing at random, namely that the values added in companies that did not yet deposit their annual accounts are similar (in some way) to those in companies with the same characteristics (e.g. the same historical data) that did deposit their accounts by the evaluation date. We show how to retrospectively assess the validity of this assumption, and how to adjust the imputation procedure in case the assumption fails. The importance of the availability of the uncertainty margins should not be underestimated because they will result in faster and higher quality publications. Finally we retrospectively apply each strategy to data from the Belgian Port sector and compare their performance at several evaluation dates. All the proposed methods show good results on these data. The method using (ordinary least squares) regression is preferred because it is very flexible in the use of auxiliary variables, requires weaker assumptions, has smaller estimation uncertainty and is easily automatable

Non-linear static analysis of masonry structures

A meso-scale model is used to model a masonry structure where bricks are modelled using finite volume elements and mortar joints are modelled using finite interface elements. A plasticity based cohesive zone model is used for the interfaces as cracks mainly propagate at the mortar joints. To avoid numerical problems associated with snapbacks observed in experiments on masonry walls, a dissipation based arc-length method is used to trace the static equilibrium path. Finally, a numerical simulation of a shear test on a 2 × 1.5 brick wall is performed