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A Bayesian framework to identify random parameter fields based on the copula theorem and Gaussian fields: Application to polycrystalline materials Rappel, Hussein ; ; et al in Journal of Applied Mechanics (in press) For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application ... [more ▼] For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application approaches the length scale of the micro-structure however, spatially fluctuating parameter fi elds (which vary from one realization of the fi eld to another) can be incorporated to make the model capture the stochasticity of the underlying micro-structure. Randomly fluctuating parameter fields are often described as Gaussian fields. Gaussian fi elds however assume that the probability density function of a material parameter at a given location is a univariate Gaussian distribution. This entails for instance that negative parameter values can be realized, whereas most material parameters have physical bounds (e.g. the Young's modulus cannot be negative). In this contribution, randomly fluctuating parameter fi elds are therefore described using the copula theorem and Gaussian fi elds, which allow di fferent types of univariate marginal distributions to be incorporated, but with the same correlation structure as Gaussian fields. It is convenient to keep the Gaussian correlation structure, as it allows us to draw samples from Gaussian fi elds and transform them into the new random fields. The bene fit of this approach is that any type of univariate marginal distribution can be incorporated. If the selected univariate marginal distribution has bounds, unphysical material parameter values will never be realized. We then use Bayesian inference to identify the distribution parameters (which govern the random fi eld). Bayesian inference regards the parameters that are to be identi fied as random variables and requires a user-defi ned prior distribution of the parameters to which the observations are inferred. For the homogenized Young's modulus of a columnar polycrystalline material of interest in this study, the results show that with a relatively wide prior (i.e. a prior distribution without strong assumptions), a single specimen is su ciffient to accurately recover the distribution parameter values. [less ▲] Detailed reference viewed: 162 (10 UL)Estimating fibres' material parameter distributions from limited data with the help of Bayesian inference Rappel, Hussein ; Beex, Lars in European Journal of Mechanics. A, Solids (2019), 75 Numerous materials are essentially structures of discrete fibres, yarns or struts. Considering these materials at their discrete scale, one may distinguish two types of intrinsic randomness that affect ... [more ▼] Numerous materials are essentially structures of discrete fibres, yarns or struts. Considering these materials at their discrete scale, one may distinguish two types of intrinsic randomness that affect the structural behaviours of these discrete structures: geometrical randomness and material randomness. Identifying the material randomness is an experimentally demanding task, because many small fibres, yarns or struts need to be tested, which are not easy to handle. To avoid the testing of hundreds of constituents, this contribution proposes an identification approach that only requires a few dozen of constituents to be tested (we use twenty to be exact). The identification approach is applied to articially generated measurements, so that the identified values can be compared to the true values. Another question this contribution aims to answer is how precise the material randomness needs to be identified, if the geometrical randomness will also influence the macroscale behaviour of these discrete networks. We therefore also study the effect of the identified material randomness to that of the actual material randomness for three types of structures; each with an increasing level of geometrical randomness. [less ▲] Detailed reference viewed: 235 (33 UL)Probabilistic modeling natural way to treat data Rappel, Hussein Presentation (2019, February 12) Detailed reference viewed: 85 (7 UL)A Tutorial on Bayesian Inference to Identify Material Parameters in Solid Mechanics Rappel, Hussein ; Beex, Lars ; Hale, Jack et al in Archives of Computational Methods in Engineering (2019) The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already ... [more ▼] The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already been used for this purpose, but most of the literature is not necessarily easy to understand for those new to the field. The reason for this is that most literature focuses either on complex statistical and machine learning concepts and/or on relatively complex mechanical models. In order to introduce the approach as gently as possible, we only focus on stress–strain measurements coming from uniaxial tensile tests and we only treat elastic and elastoplastic material models. Furthermore, the stress–strain measurements are created artificially in order to allow a one-to-one comparison between the true parameter values and the identified parameter distributions. [less ▲] Detailed reference viewed: 749 (112 UL)Identifying elastoplastic parameters with Bayes' theorem considering double error sources and model uncertainty Rappel, Hussein ; Beex, Lars ; et al in Probabilistic Engineering Mechanics (2019), 55 We discuss Bayesian inference for the identi cation of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in ... [more ▼] We discuss Bayesian inference for the identi cation of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in the strain measurements. Since a difference between the model and the experimental data may still be present if the data is not contaminated by noise, we also incorporate the possible error of the model itself. The three formulations to describe model uncertainty in this contribution are: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from a normal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. Our results show that incorporating model uncertainty often, but not always, improves the results. If the error in the strain is considered as well, the results improve even more. [less ▲] Detailed reference viewed: 403 (67 UL)Geometrical and material uncertainties for the mechanics of composites ; Bordas, Stéphane ; et al Scientific Conference (2019) Detailed reference viewed: 144 (15 UL)Model and parameter identification through Bayesian inference in solid mechanics Rappel, Hussein Doctoral thesis (2018) Predicting the behaviour of various engineering systems is commonly performed using mathematical models. These mathematical models include application-specific parameters that must be identified from ... [more ▼] Predicting the behaviour of various engineering systems is commonly performed using mathematical models. These mathematical models include application-specific parameters that must be identified from measured data. The identification of model parameters usually comes with uncertainties due to model simplifications and errors in the experimental measurements. Quantifying these uncertainties can effectively improve the predictions as well as the performance of the engineering systems. Bayesian inference provides a probabilistic framework for quantifying these uncertainties in parameter identification problems. In a Bayesian framework, the user's initial knowledge, which is represented by a probability distribution, is updated by measurement data through Bayes' theorem. In the first two chapters of this thesis, Bayesian inference is developed for the identification of material parameters in elastoplasticity and viscoelasticity. The effect of the user's prior knowledge is systematically studied with respect to the number of measurements available. In addition, the influence of different types of experiments on the uncertainty is studied. Since all mathematical models are simplifications of reality, uncertainties of the model itself may also be incorporated. The third chapter of this thesis presents a Bayesian framework for parameter identification in elastoplasticity in which not only the uncertainty of the experimental output is included (i.e. stress measurements), but also the uncertainty of the model and the uncertainty of the experimental input (i.e. strain). Three different formulations for describing the model uncertainty are considered: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from a normal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. In the fourth chapter of this thesis, a Bayesian scheme is proposed to identify material parameter distributions, instead of material parameters. The application in this chapter are random fibre networks, in which the set of material parameters of each fibre is assumed to be a realisation from a material parameter distribution. The fibres behave either elastoplastically or in a perfectly brittle manner. The goal of the identification scheme is to avoid the experimentally demanding task of testing hundreds of constituents. Instead, only 20 fibres are considered. In addition to their material randomness, the macroscale behaviours of these fibre networks are also governed by their geometrical randomness. Another question aimed to be answered in this chapter is therefore is `how precise the material randomness needs to be identified, if the geometrical randomness will also influence the macroscale behaviour of these discrete networks'. [less ▲] Detailed reference viewed: 287 (41 UL)Identifying fibre material parameter distributions with little experimental efforts Rappel, Hussein ; Beex, Lars ; Bordas, Stéphane Scientific Conference (2018, July 23) Detailed reference viewed: 113 (15 UL)Identifying material parameter distributions of fibers with extremely limited experimental efforts Rappel, Hussein ; Beex, Lars ; Bordas, Stéphane Scientific Conference (2018, July 22) Detailed reference viewed: 89 (6 UL)Bayesian inference to identify parameters in viscoelasticity Rappel, Hussein ; Beex, Lars ; Bordas, Stéphane in Mechanics of Time-Dependent Materials (2017) This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, (ii ... [more ▼] This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, (ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned issues, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity. [less ▲] Detailed reference viewed: 547 (177 UL)Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety
: primer on Bayesian Inference Bordas, Stéphane ; Hale, Jack ; Beex, Lars et al Speeches/Talks (2015) Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre break- age, cell-wall buckling, are examples of nano ... [more ▼] Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre break- age, cell-wall buckling, are examples of nano/micro or meso-scale mechanisms which can lead to global failure of the material and structure. Such mech- anisms cannot, for computational and practical reasons, be accounted at structural scale, so that acceleration methods are necessary. We review in this presentation recently proposed approaches to reduce the computational expense associated with multi-scale modelling of frac- ture. In light of two particular examples, we show connections between algebraic reduction (model order reduction and quasi-continuum methods) and homogenisation-based reduction. We open the discussion towards suitable approaches for machine-learning and Bayesian statistical based multi-scale model selection. Such approaches could fuel a digital-twin concept enabling models to learn from real-time data acquired during the life of the structure, accounting for “real” environmental conditions during predictions, and, eventually, moving beyond the era of factors of safety. [less ▲] Detailed reference viewed: 211 (5 UL)Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety Bordas, Stéphane ; Beex, Lars ; et al Scientific Conference (2015, November 18) Authors: S. P. A. Bordas, L. A. A. Beex, P. Kerfriden, D. A. Paladim, O. Goury, A. Akbari, H. Rappel Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety ... [more ▼] Authors: S. P. A. Bordas, L. A. A. Beex, P. Kerfriden, D. A. Paladim, O. Goury, A. Akbari, H. Rappel Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre breakage, cell-wall buckling, are examples of nano/micro or meso-scale mechanisms which can lead to global failure of the material and structure. Such mechanisms cannot, for computational and practical reasons, be accounted at structural scale, so that acceleration methods are necessary. We review in this presentation recently proposed approaches to reduce the computational expense associated with multi-scale modelling of fracture. In light of two particular examples, we show connections between algebraic reduction (model order reduction and quasi-continuum methods) and homogenisation-based reduction. We open the discussion towards suitable approaches for machine-learning and Bayesian statistical based multi-scale model selection. Such approaches could fuel a digital-twin concept enabling models to learn from real-time data acquired during the life of the structure, accounting for “real” environmental conditions during predictions, and, eventually, moving beyond the “factors of safety” era. [less ▲] Detailed reference viewed: 425 (19 UL)Discrete Multiscale Modelling and Future Research Plans concerning Metals (presentation) Beex, Lars ; Bordas, Stéphane ; Rappel, Hussein et al Presentation (2014, October 14) Detailed reference viewed: 159 (10 UL)Discrete Multiscale Modelling and Future Research Plans concerning Metals Beex, Lars ; Bordas, Stéphane ; Rappel, Hussein et al Presentation (2014, October 14) Detailed reference viewed: 157 (11 UL)Bayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights Rappel, Hussein ; Beex, Lars ; Hale, Jack et al E-print/Working paper (n.d.) We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼] We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲] Detailed reference viewed: 378 (106 UL) |
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