Filtern
Dokumenttyp
- Zeitschriftenartikel (3)
- Vortrag (2)
Sprache
- Englisch (5) (entfernen)
Schlagworte
- Proper generalized decomposition (5) (entfernen)
Organisationseinheit der BAM
Paper des Monats
- ja (1)
Eingeladener Vortrag
- nein (2)
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.”
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.
Despite the advances in hardware and software techniques, standard numerical methods fail in providing real-time simulations, especially for complex processes such as additive manufacturing applications. A real-time simulation enables process control through the combination of process monitoring and automated feedback, which increases the flexibility and quality of a process. Typically, before producing a whole additive manufacturing structure, a simplified experiment in the form of a beadon-plate experiment is performed to get a first insight into the process and to set parameters suitably. In this work, a reduced order model for the transient thermal problem of the bead-on-plate weld simulation is developed, allowing an efficient model calibration and control of the process. The proposed approach applies the proper generalized decomposition (PGD) method, a popular model order reduction technique, to decrease the computational effort of each model evaluation required multiple times in parameter estimation, control, and optimization. The welding torch is modeled by a moving heat source, which leads to difficulties separating space and time, a key ingredient in PGD simulations. A novel approach for separating space and time is applied and extended to 3D problems allowing the derivation of an efficient separated representation of the temperature.
The results are verified against a standard finite element model showing excellent agreement. The reduced order model is also leveraged in a Bayesian model parameter estimation setup, speeding up calibrations and ultimately leading to an optimized real-time simulation approach for welding experiment using synthetic as well as real measurement data.
The main challenge using numerical models as digital twins in real applications is the calibration and validation of the model based on uncertain measurement data. Therefore, model updating approaches which are inverse optimization processes are applied. This requires a huge number of computations of the same numerical model with slightly different model parameters. For that reason, model updating becomes computationally very expensive for real applications.
Model reduction, e.g. the proper generalized decomposition method, is a popular concept to decrease the computational effort of complex numerical simulations. Therefore, a reduced model of the structure of interest is derived and will be used as surrogate model in a Variational Bayesian procedure to create a very efficient digital twin of the structure.
An efficient model updating approach by means of a PGD reduced model with random field material stiffness parameters is shown. The random field allows, to calibrate the model considering parameter changes over the spatial direction. These changes can be caused by local damages as well as by production. As an exemplary application a demonstrator bridge is used. Digital twins can reduce the costs for maintenance and inspections especially for the costly civil infrastructure with high requirements at their performance over the whole lifetime. Currently, the current state of the structure is determined by regular manual and visual inspections within constant intervals. However, the critical sections are often not directly accessible or impossible to be instrumented at all. In this case, model-based approaches where a digital twin is set up can improve the process. Based on this digital twin, a prognosis of the future performance of the structure, e.g. the failure probability, can be computed.
The influences of the reduction degree, the mesh discretization as well as the correlation length in the PGD Bayesian approach are studied by means of the digital twin of a simple pre-stressed concrete two field bridge.
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.