TY - JOUR A1 - Coelho Lima, Isabela A1 - Robens-Radermacher, Annika A1 - Titscher, Thomas A1 - Kadoke, Daniel A1 - Koutsourelakis, P.-S. A1 - Unger, Jörg F. T1 - Bayesian inference for random field parameters with a goal-oriented quality control of the PGD forwardmodel's accuracy N2 - Numerical models built as virtual-twins of a real structure (digital-twins) are considered the future ofmonitoring systems. Their setup requires the estimation of unknown parameters, which are not directly measurable. Stochastic model identification is then essential, which can be computationally costly and even unfeasible when it comes to real applications. Efficient surrogate models, such as reduced-order method, can be used to overcome this limitation and provide real time model identification. Since their numerical accuracy influences the identification process, the optimal surrogate not only has to be computationally efficient, but also accurate with respect to the identified parameters. This work aims at automatically controlling the Proper Generalized Decomposition (PGD) surrogate’s numerical accuracy for parameter identification. For this purpose, a sequence of Bayesian model identification problems, in which the surrogate’s accuracy is iteratively increased, is solved with a variational Bayesian inference procedure. The effect of the numerical accuracy on the resulting posteriors probability density functions is analyzed through two metrics, the Bayes Factor (BF) and a criterion based on the Kullback-Leibler (KL) divergence. The approach is demonstrated by a simple test example and by two structural problems. The latter aims to identify spatially distributed damage, modeled with a PGD surrogate extended for log-normal random fields, in two different structures: a truss with synthetic data and a small, reinforced bridge with real measurement data. For all examples, the evolution of the KL-based and BF criteria for increased accuracy is shown and their convergence indicates when model refinement no longer affects the identification results. KW - Variational inference KW - Proper generalized decomposition KW - Goal-oriented KW - Digital twin KW - Random field PY - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-555755 SN - 1432-0924 SP - 1 EP - 22 PB - Springer CY - Berlin AN - OPUS4-55575 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Jafari, Abbas A1 - Titscher, Thomas A1 - Chatzi, E. A1 - Unger, Jörg F. T1 - Variational Bayesian inference of damage in concrete material using spatially-dense data N2 - Numerical simulators, such as finite element models, have become increasingly capable of predicting the behaviour of structures and components owing to more sophisticated underlying mathematical models and advanced computing power. A common challenge lies, however, in calibrating these models in terms of their unknown/uncertain parameters. When measurements exist, this can be achieved by comparing the model response against measured data. Besides uncertain model parameters, phenomena like damage can give rise to further uncertainties; in particular, quasi-brittle materials, like concrete, experience damage in a heterogeneous manner due to various imperfections, e.g. in geometry and boundary conditions. This hardens an accurate prediction of the damaged behaviour of real structures that comprise such materials. In this study, which draws from a data-driven approach, we use the force-version of the finite element model updating method (FEMU-F) to incorporate measured displacements into the identification of the damage parameters, in order to cope with heterogeneity. In this method, instead of conducting a forward evaluation of the model and comparing the model response (displacements) against the data, we impose displacements to the model and compare the resulting force residuals with measured reaction forces. To account for uncertainties in the measurement of displacements, we endow this approach with a penalty term, which reflects the discrepancy between measured and imposed displacements, where the latter is assumed as unknown random variables to be identified as well. A Variational Bayesian approach is used as an approximating tool for computing posterior parameters. The underlying damage model considered in this work is a gradient-enhanced damage model. We first establish the identification procedure through two virtual examples, where synthetic data (displacements) are generated over a certain spatially-dense set of points over the domain. The procedure is then validated on an experimental case-study; namely a 3-point bending experiment with displacement measurements resulting from a digital image correlation (DIC) analysis. T2 - MSE 2022 CY - Online meeting DA - 27.09.2022 KW - Heterogeneity KW - Gradient damage KW - Model updating KW - Variational Bayesian KW - Concrete PY - 2022 AN - OPUS4-56625 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Kindrachuk, Vitaliy A1 - Titscher, Thomas A1 - Hirthammer, Volker A1 - Unger, Jörg F. ED - Meschke, G. ED - Pichler, B. ED - Rots, J.G. T1 - A continuum damage model for the simulation of concrete under cyclic loading N2 - Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states. Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales. However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time. The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods. First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses [1]. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach [2]. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed. Finally, the developed methods will be validated and compared to experimental data. [1] Vitaliy Kindrachuk, Marc Thiele, Jörg F. Unger. Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression, International Journal of Fatigue, 78:81-94, 2015 [2] Vitaliy Kindrachuk, Jörg F. Unger. A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration, International Journal of Fatigue, 100:215-228, 2017 T2 - Conference on Computational Modelling of concrete and concrete structures (EURO_C 2018') CY - Bad Hofgastein, Austria DA - 26.02.2018 KW - Fatigue KW - Concrete KW - Damage PY - 2018 SN - 978-1-138-74117-1 U6 - https://doi.org/10.1201/9781315182964-19 SP - 155 EP - 164 PB - CRC Press, Taylor & Francis Group CY - Boca Raton, Lodon, New York, Leiden AN - OPUS4-47999 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Kindrachuk, Vitaliy A1 - Titscher, Thomas A1 - Unger, Jörg F. T1 - A Fourier transformation-based method for gradient-enhanced modeling of fatigue N2 - A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations. The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs. KW - Accelerated temporal integration KW - Fourier series KW - Gradient-enhanced fatigue model PY - 2018 U6 - https://doi.org/10.1002/nme.5740 SN - 1097-0207 SN - 0029-5981 VL - 114 IS - 2 SP - 196 EP - 214 PB - Wiley AN - OPUS4-44008 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Robens-Radermacher, Annika A1 - Held, Felix A1 - Coelho Lima, Isabela A1 - Titscher, Thomas A1 - Unger, Jörg F. T1 - Efficient identification of random fields coupling Bayesian inference and PGD reduced order model for damage localization N2 - One of the main challenges regarding our civil infrastructure is the efficient operation over their complete design lifetime while complying with standards and safety regulations. Thus, costs for maintenance or replacements must be optimized while still ensuring specified safety levels. This requires an accurate estimate of the current state as well as a prognosis for the remaining useful life. Currently, this is often done by regular manual or visual inspections within constant intervals. However, the critical sections are often not directly accessible or impossible to be instrumented at all. Model‐based approaches can be used where a digital twin of the structure is set up. For these approaches, a key challenge is the calibration and validation of the numerical model based on uncertain measurement data. The aim of this contribution is to increase the efficiency of model updating by using the advantage of model reduction (Proper Generalized Decomposition, PGD) and applying the derived method for efficient model identification of a random stiffness field of a real bridge.” KW - Model reduction KW - Model updating KW - Proper generalized decomposition KW - Random field KW - Variational Bayesian Inference PY - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-521275 VL - 20 IS - 1 SP - e202000063 PB - Wiley Online Libary AN - OPUS4-52127 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Titscher, Thomas A1 - Robens-Radermacher, Annika A1 - Unger, Jörg F. T1 - Model calibration and damage detection for a digital twin N2 - Numerical models are an essential tool in predicting and monitoring the behavior of civil structures. Inferring the model parameters is a challenging tasks as they are often measured indirectly and are affected by uncertainties. Digital twins couple those models with real-world data and can introduce additional, systematic sensor uncertainties related to the sensor calibration, i.e. uncertain offsets and calibration factors. In this work, the challenges of data processing, parameter identification, model selection and damage detection are explored using a lab-scale cable stayed bridge demonstrator. By combining force measurements in the cables with displacement measurements from both laser and stereo-photogrammetry systems, the elastic parameters of a three-dimensional finite element beam model are inferred. Depending on the number of sensors and the number of datasets used, parametrizing the sensor offsets and factors, leads to model with over 100 parameters. With a real-time solution of the problem in mind, a highly efficient analytical variational Bayesian approach is used to solve it within seconds. An analysis of the required assumptions and limitations of the approach, especially w.r.t. to the computed evidence, is provided by a comparison with dynamic nested sampling in a simplified problem. Finally, by inferring the value of additional damage parameters along the bridge, the method is successfully used to detect the location of an artificially introduced weak spot in the demonstrator bridge. T2 - ECCOMAS 2022 CY - Oslo, Norway DA - 05.06.2022 KW - Bayesian identification KW - Digital twin KW - Variational Bayesian KW - Damage detection PY - 2022 AN - OPUS4-55083 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Titscher, Thomas A1 - Unger, Jörg F. T1 - Concrete mesostructure geometry modelling with growing and colliding hard spheres T2 - 11th World Congress on Computational Mechanics (WCCM XI); 5th European Conference on Computational Mechanics (ECCM V); 6th European Conference on Computational Fluid Dynamics (ECFD VI) CY - Barcelona, Spanien DA - 2014-07-20 PY - 2014 AN - OPUS4-32897 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Titscher, Thomas A1 - Unger, Jörg F. A1 - Oliver, J. T1 - Implicit/explicit (IMPL-EX) integration of the gradient enhanced damage model N2 - Isotropic damage models are widely used for the finite element simulation of softening materials, e.g. in mesoscale simulations of concrete. Regularization techniques must be employed to obtain a physically meaningful fracture energy upon mesh refinement. In regularized local damage models the strains localize in single elements allowing them to represent weak or strong discontinuities. In implicit integration schemes, these models can exhibit convergence Problems caused by an ill-conditioned tangent stiffness. This corresponds to the loss of ellipticity of the local rate equilibrium equations. Oliver et al. developed the implicit/explicit (IMPL-EX) integration scheme which overcomes These problems in local damage models. The internal damage driving variable is extrapolated based on previous implicitly determined values. This provides two main benefits: First, it always results in a symmetric positive semi-definite algorithmic stiffness matrix which precludes ill-posedness. Second, the system becomes incrementally linear and converges in one Newton-Raphson iteration. Even though the IMPL-EX algorithm, like explicit algorithms in general, requires smaller time steps than implicit schemes to obtain the same accuracy, it leads to a computational speedup. The gradient enhanced damage model by Peerlings is a nonlocal damage model that provides the regularization by limiting the curvature of the damage-driving strains. These models do not lose their ellipticity. However, structural instabilities often require tiny time steps and many iterations to obtain convergence. Here, the second aspect of the IMPL-EX scheme reduces the computational costs. This is shown in simulations of the complex geometry of concrete mesostructures, where only the gradient enhanced matrix material and linear elastic aggregates are considered. With regard to future mesoscale simulations, the remaining component of the mesoscopic structure, the interfacial transition zone and its degradation, has to be included. This adds a local damage model to the nonlocal problem. Thus, an IMPL-EX implementation has to be provided for both models to benefit from the increase of robustness and performance. T2 - ECCOMAS Congress 2016 CY - Crete, Greece DA - 05.06.2016 KW - Concrete KW - Mesoscale KW - IMPL-EX PY - 2016 AN - OPUS4-38671 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Titscher, Thomas A1 - Unger, Jörg F. A1 - Oliver, Javier T1 - Cycle-by-cycle fatigue damage model for concrete N2 - Damage caused by stress concentrations in the complex mesoscopic geometry of concrete leads to continuous stress redistribution over the material's life time. The presented fatigue damage model captures this by resolving each load cycle in a cycle-by-cycle time integration. The model extends a static damage model to failure caused by the (time dependent) strain amplitudes and, thus, allows calibrating the majority of the material's parameters in static experiments. T2 - 7th GACM Colloquium on Computational Mechanics CY - Stuttgart, Germany DA - 11.10.2017 KW - Fatigue KW - Damage model KW - Cycle-by-cycle integration PY - 2017 AN - OPUS4-43612 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Titscher, Thomas A1 - Unger, Jörg F. A1 - Oliver, J. T1 - High-order cycle jump integration of a fatigue damage model N2 - Accurate models for the long term behavior of concrete structures are important to ensure a durable and reliable design. A variety of interacting phenomena, such as the loss of prestress, the degradation due to chemical reactions or creep and shrinkage, influence the fatigue resistance. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required. The presented fatigue model is an extension of a static damage model to allow easy coupling in a multiphysics context. The evolution equation of the damage driving variable is enhanced to allow damage growth below the static limit. The model is defined in the time domain and does not include the number of cycles as a parameter. Thus, it can capture both static and cyclic failure. Additionally, this allows calibrating the majority of the model parameters static experiments. The model is integrated by resolving each loading cycle, requiring about ten time steps per cycle. The high computational costs are handled via a time scale separation. The short time scale describes one cycle with marginal changes in the internal variables. These changes are integrated along the large time scale of material deterioration. Various high-order time integration schemes are compared. Wöhler curves relate loading amplitudes to the number of cycles that the material endures. They are used to validate the model against experimental data. T2 - 6th European Conference on Computational Mechanics (ECCM 6) CY - Glasgow, UK DA - 11.06.2018 KW - Fatigue damage KW - Time scale separation KW - Cycle jump PY - 2018 AN - OPUS4-45706 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -