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There is a rising attention of using numerical models for effcient structural monitoring and ensuring the structure's safety. Setting up virtual models as twin for real structures requires a model identification process calculating the unknown model parameters, which mostly are only indirectly measurable. This is a computationally very costly inverse optimization process, which often makes it unfeasible for real applications. Effcient surrogate models such as reduced order models can be used, to overcome this limitation. But the influence of the model accuracy on the identification process has then to be considered. The aim is to automatically control the influence of the model's accuracy on the identification. Here, a variational Bayesian inference approach[3] is coupled with a reduced forward model using the Proper Generalized Decomposition (PGD) method. The influence of the model accuracy on the inference result is studied and measured. Therefore, besides the commonly used Bayes factor the Kullback-Leibler divergences between the predicted posterior pdfs are proposed. In an adaptive inference procedure, the surrogate's accuracy is iteratively increased, and the convergence of the posterior pdf is analysed. The proposed adaptive identification process is applied to the identification of spatially distributed damage modeled by a random eld for a simple example with synthetic data as well as a small, reinforced bridge with real measurement data. It is shown that the proposed criteria can mirror the influence of the model accuracy and can be used to automatically select a suffciently accurate surrogate model.
The main challenge in using numerical models as digital twins in real applications for prognosis purposes, such as reliability analysis, is the calibration and validation of the models based on uncertain measurement data. Uncertainties are not limited to the measurement data, but the numerical model itself will not be perfect due to the modelling assumptions.
In this contribution, a probabilistic inference method for model calibration, based on the Bayes’ Theorem, is used to face that issue. Such inference approaches include uncertainties on the data as well as on the model parameters, allowing to compute an a posteriori distribution for the model parameters as well as a noise term reflecting the measured data. However, such probabilistic inference methods require a lot of evaluations of the numerical forward model for different model parameters. An improvement of the efficiency is obtained by replacing the forward model with a reduced model. Model reduction, e.g. the proper generalized decomposition (PGD) method, is a popular concept to decrease the computational effort, where each evaluation of the reduced forward model is a pure less costly function evaluation.
The heterogeneous spatial distribution of material parameters in the forward model is described by a lognormal random field. This allows identifying a variable stiffness over the spatial directions by identifying the random field variables with given measurement data. These changes can e.g. be caused by damage. The lognormal field is approximated as series expansion for the PGD problem.
The derived efficient model identification procedure is shown using a real reinforced prestress demonstrator bridge and stereophotogrammetry measurement data. A digital twin for that demonstrator bridge is build up using a set of measurement data and verified by testing additional measurement data. PGD model error against the FEM model is discussed based on an importance sampling analysis computing the Bayes Factor.
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.
With increasing focus on industrialized processing, investigating, understanding, and modelling the structural build-up of cementitious materials becomes more important. The structural build-up governs the key property of fresh printable materials -- buildability -- and it influences the mechanical properties after the deposition. The structural build-up rate can be adjusted by optimization of the mixture composition and the use of concrete admixtures. Additionally, it is known, that the environmental conditions, i.e. humidity and temperature have a significant impact on the kinetic of cement hydration and the resulting hardened properties, such as shrinkage, cracking resistance etc. In this study, small amplitude oscillatory shear (SAOS) tests are applied to examine the structural build-up rate of cement paste subject to different temperatures under controlled humidity. The results indicate significant influences of the ambient temperature on the intensity of the re-flocculation (Rthix) rate, while the structuration rate (Athix) is almost not affected. A bi-linear thixotropy model extended by temperature dependent parameters coupled with a linear viscoelastic material model is proposed to simulate the mechanical behaviour considering the structural build-up during the SAOS test
With increasing focus on industrialized processing, investigating, understanding, and modelling the structural build-up of cementitious materials becomes more important. The structural build-up governs the key property of fresh printable materials -- buildability -- and it influences the mechanical properties after the deposition. The structural build-up rate can be adjusted by optimization of the mixture composition and the use of concrete admixtures. Additionally, it is known, that the environmental conditions, i.e. humidity and temperature have a significant impact on the kinetic of cement hydration and the resulting hardened properties, such as shrinkage, cracking resistance etc. In this study, small amplitude oscillatory shear (SAOS) tests are applied to examine the structural build-up rate of cement paste subject to different temperatures under controlled humidity. The results indicate significant influences of the ambient temperature on the intensity of the re-flocculation (Rthix) rate, while the structuration rate (Athix) is almost not affected. A bi-linear thixotropy model extended by temperature dependent parameters coupled with a linear viscoelastic material model is proposed to simulate the mechanical behaviour considering the structural build-up during the SAOS test.
The High-Fidelity Generalized Method of Cells (HFGMC) is one technique, distinct from traditional finite-element approaches, for accurately simulating nonlinear composite material behavior. In this work, the HFGMC global system of equations for doubly periodic repeating unit cells with nonlinear constituents has been reduced in size through the novel application of a Petrov-Galerkin Proper Orthogonal Decomposition order-reduction scheme in order to improve its computational efficiency. Order-reduced models of an E-glass/Nylon 12 composite led to a 4.8–6.3x speedup in the equation assembly/solution runtime while maintaining model accuracy. This corresponded to a 21–38% reduction in total runtime.Thesignificant difference in assembly/solution and total runtimes was attributed to the evaluation of integration point inelastic field quantities; this step was identical between the unreduced and order-reduced models. Nonetheless, order-reduced techniques offer the potential to significantly improve the computational efficiency of multiscale calculations.
The efficiency of structural model updating and the subsequent reliability analysis is increased by using the advantages of reduced order models. Coupling a reduced model of the structure of interest with a Bayesian model updating approach or an reliability analysis to estimate the failure probability reduce the computational cost of such complex analyses drastically.
One of the most important goals in civil engineering is to guarantee the safety of the construction. Standards prescribe a required failure probability in the order of 10−4 to 10−6. Generally, it is not possible to compute the failure probability analytically.
Therefore, many approximation methods have been developed to estimate the failure probability. Nevertheless, these methods still require a large number of evaluations of the investigated structure, usually finite element (FE) simulations, making full probabilistic design studies not feasible for relevant applications. The aim of this paper is to increase the efficiency of structural reliability analysis by means of reduced order models. The developed method paves the way for using full probabilistic approaches in industrial applications. In the proposed PGD reliability analysis, the solution of the structural computation is directly obtained from evaluating the PGD solution for a specific parameter set without computing a full FE simulation. Additionally, an adaptive importance sampling scheme is used to minimize the total number of required samples. The accuracy of the failure probability depends on the accuracy of the PGD model (mainly influenced on mesh discretization and mode truncation) as well as the number of samples in the sampling algorithm. Therefore, a general iterative PGD reliability procedure is developed to automatically verify the accuracy of the computed failure probability. It is based on a goal-oriented refinement of the PGD model around the adaptively approximated design point. The methodology is applied and evaluated for 1D and 2D examples. The computational savings compared to the method based on a FE model is shown and the influence of the accuracy of the PGD model on the failure probability is studied.
The key point of structural reliability analysis is the estimation of the failure probability (Pf), typically a rare event. This probability is defined as the integral over the failure domain which is given by a limit state function. Usually, this function is only implicit given by an underlying finite element simulation of the structure. It is generally not possible to solve the integral for Pf analytically. For that reason, simulation-based methods as well as methods based on surrogate modeling (or Response surface methods) has been developed. Nevertheless, these variance reducing methods still require a few thousand calculations of the underlying finite element model, making reliability Analysis computationally expensive for real applications.
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.”