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Identifying elastoplastic parameters with Bayes' theorem considering double error sources and model uncertainty Rappel, Hussein ; Beex, Lars ; et al in Probabilistic Engineering Mechanics (in press) 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: 61 (13 UL)Classification of states and model order reduction of large scale Chemical Vapor Deposition processes with solution multiplicity ; ; Beex, Lars et al in Computers and Chemical Engineering (2018), 121 This paper presents an equation-free, data-driven approach for reduced order modeling of a Chemical Vapor Deposition (CVD) process. The proposed approach is based on process information provided by ... [more ▼] This paper presents an equation-free, data-driven approach for reduced order modeling of a Chemical Vapor Deposition (CVD) process. The proposed approach is based on process information provided by detailed, high-fidelity models, but can also use spatio-temporal measurements. The Reduced Order Model (ROM) is built using the method-of-snapshots variant of the Proper Orthogonal Decomposition (POD) method and Artificial Neural Networks (ANN) for the identification of the time-dependent coefficients. The derivation of the model is completely equation-free as it circumvents the projection of the actual equations onto the POD basis. Prior to building the model, the Support Vector Machine (SVM) supervised classification algorithm is used in order to identify clusters of data corresponding to (physically) different states that may develop at the same operating conditions due to the inherent nonlinearity of the process. The different clusters are then used for ANN training and subsequent development of the ROM. The results indicate that the ROM is successful at predicting the dynamic behavior of the system in windows of operating parameters where steady states are not unique. [less ▲] Detailed reference viewed: 11 (1 UL)An equation-free, nested, concurrent multiscale approach without scale-separation Beex, Lars ; Scientific Conference (2018, September) Detailed reference viewed: 33 (0 UL)Identifying fibre material parameter distributions with little experimental efforts Rappel, Hussein ; Beex, Lars ; Bordas, Stéphane Scientific Conference (2018, July 23) Detailed reference viewed: 35 (8 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: 20 (2 UL)A hyper-reduction method using adaptivity to cut the assembly costs of reduced order models Hale, Jack ; ; Baroli, Davide et al E-print/Working paper (2018) At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The ... [more ▼] At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The projected small linear systems are cheap to solve, but assembly and projection are now the dominant computational cost. In this paper we introduce a new hyper-reduction strategy called reduced assembly (RA) that drastically cuts these costs. RA consists of a triangulation adaptation algorithm that uses a local error indicator to con- struct a reduced assembly triangulation specially suited to the reduced order basis. Crucially, this reduced assembly triangulation has fewer cells than the original one, resulting in lower assembly and projection costs. We demonstrate the efficacy of RA on a Galerkin-POD type reduced order model (RAPOD). We show performance increases of up to five times over the baseline Galerkin-POD method on a non-linear reaction-diffusion problem solved with a semi-implicit time-stepping scheme and up to seven times for a 3D hyperelasticity problem solved with a continuation Newton-Raphson algorithm. The examples are implemented in the DOLFIN finite element solver using PETSc and SLEPc for linear algebra. Full code and data files to produce the results in this paper are provided as supplementary material. [less ▲] Detailed reference viewed: 56 (7 UL)ECCOMAS Newsletter - Computational and Data Sciences in Luxembourg Beex, Lars ; Bordas, Stéphane ; Hale, Jack et al Report (2018) Detailed reference viewed: 190 (25 UL)Multiscale Modelling of Damage and Fracture in Discrete Materials Using a Variational Quasicontinuum Method ; ; Beex, Lars et al Scientific Conference (2017, September 05) Detailed reference viewed: 32 (1 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: 362 (152 UL)eXtended Variational Quasicontinuum Methodology for Modelling of Crack Propagation in Discrete Lattice Systems ; ; et al Scientific Conference (2017, July 17) Detailed reference viewed: 23 (0 UL)An equation-free multiscale method: a result of extending the quasicontinuum method to irregular structures Beex, Lars ; Scientific Conference (2017, July 16) Detailed reference viewed: 32 (1 UL)An Enriched Quasi-Continuum Approach to Crack Propagation in Discrete Lattices ; ; et al Scientific Conference (2017, June 14) Detailed reference viewed: 31 (0 UL)An equation-free multiscale method applied to discrete networks Beex, Lars ; Scientific Conference (2017, June 06) Detailed reference viewed: 31 (1 UL)Reduced basis Nitsche-based domain decomposition: a biomedical application Baroli, Davide ; Beex, Lars ; Hale, Jack et al Scientific Conference (2017, March 10) Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity ... [more ▼] Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity of solving different substructure, e.g. tissues or organs, with different numbers of the degrees of freedom and of coupling the reduced order spaces for each substructure poses a challenge in the on-fly simulation. In this talk, this challenge is taken into account employing the Nitsche-based domain decomposition technique inside the reduced order model [1]. This technique with respect to other domain decomposition approach allows obtaining a solution with the same accuracy of underlying finite element formulation and to flexibly treat interface with non-matching mesh. The robustness of the coupling is determined by the penalty coefficients that is chosen using ghost penalty technique [2]. Furthermore, to reduce the computational complexity of the on-fly assembling it is employed the empirical interpolation approach proposed in [3]. The numerical tests, performed using FEniCS[4], petsc4py and slepc4py [5], shows the good performance of the method and the reduction of computation cost. [1] Baroli, D., Beex L. and Bordas, S. Reduced basis Nitsche-based domain decomposition. In preparation. [2] Burman, E., Claus, S., Hansbo, P., Larson, M. G., & Massing, A. (2015). CutFEM: Discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7), 472-501. [3] E. Schenone, E., Beex,L., Hale, J.S., Bordas S. Proper Orthogonal Decomposition with reduced integration method. Application to nonlinear problems. In preparation. [4] A. Logg, K.-A. Mardal, G. N. Wells et al. Automated Solution of Differential Equations by the Finite Element Method, Springer 2012. [5] L. Dalcin, P. Kler, R. Paz, and A. Cosimo, Parallel Distributed Computing using Python, Advances in Water Resources, 34(9):1124-1139, 2011. http://dx.doi.org/10.1016/j.advwatres.2011.04.013 [less ▲] Detailed reference viewed: 206 (10 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 (2017) 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: 297 (94 UL)A variational formulation of dissipative quasicontinuum methods ; Beex, Lars ; et al in International Journal of Solids and Structures (2016), 102-103 Lattice systems and discrete networks with dissipative interactions are successfully employed as meso-scale models of heterogeneous solids. As the application scale generally is much larger than that of ... [more ▼] Lattice systems and discrete networks with dissipative interactions are successfully employed as meso-scale models of heterogeneous solids. As the application scale generally is much larger than that of the discrete links, physically relevant simulations are computationally expensive. The QuasiContinuum (QC) method is a multiscale approach that reduces the computational cost of direct numerical simulations by fully resolving complex phenomena only in regions of interest while coarsening elsewhere. In previous work (Beex et al., J. Mech. Phys. Solids 64, 154-169, 2014), the originally conservative QC methodology was generalized to a virtual-power-based QC approach that includes local dissipative mechanisms. In this contribution, the virtual-power-based QC method is reformulated from a variational point of view, by employing the energy-based variational framework for rate-independent processes (Mielke and Roub cek, Rate-Independent Systems: Theory and Application, Springer-Verlag, 2015). By construction it is shown that the QC method with dissipative interactions can be expressed as a minimization problem of a properly built energy potential, providing solutions equivalent to those of the virtual-power-based QC formulation. The theoretical considerations are demonstrated on three simple examples. For them we verify energy consistency, quantify relative errors in energies, and discuss errors in internal variables obtained for different meshes and two summation rules. [less ▲] Detailed reference viewed: 68 (8 UL)Bayesian inference for parameter identification in computational mechanics Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Poster (2016, December 12) Detailed reference viewed: 128 (8 UL)Bayesian inference for material parameter identification in elastoplasticity Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Scientific Conference (2016, September 07) Detailed reference viewed: 196 (29 UL)POD-based reduction methods, the Quasicontinuum Method and their Resemblance Beex, Lars ; ; Hale, Jack Scientific Conference (2016, June 27) Detailed reference viewed: 95 (8 UL)A Bayesian approach for parameter identification in elastoplasticity Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Scientific Conference (2016, June 09) Detailed reference viewed: 114 (14 UL) |
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