7.7 Modellierung und Simulation
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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.
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.
In materials and component research, artificial intelligence methodologies will lead to massive upheavals in the coming years. The processes of material development, material processing, lifetime prediction and material characterization will change significantly. By combining AI methods and new forms of knowledge representation, the data-based management of product life cycles will take on new qualities. To address this emerging field of research Fraunhofer IWM set up the online workshop »AI Methods for Fatigue Behavior Assessment and Component Lifetime Prediction«
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.
The quality of a model - and thus its predictive capabilities - is influenced by numerous uncertainties. They include possibly unknown boundary and initial conditions, noise in the data used for its calibration and uncertainties in the model itself. Here, the latter part is not only restricted to uncertain model parameters, but also refers to the choice of the model itself. Inferring these uncertainties in an automatic way allows for an adaption of the model to new data sets and for a reliable, reproducible model assessment. Note that similar concepts apply at the structural level, where a continuously updated digital twin allows virtual measurements at inaccessible positions of the structure and a simulation based lifetime prediction.
This work presents an inference workflow that describes the difference of measured data and simulated model responses with a generic interface that is independent from the specific model or even the geometry and can easily incorporate multiple data sources. A variational Bayesian inference algorithm is then used to a) calibrate a set of models to given data and to b) identify the best fitting one. The developed concepts are applied to a bridge Demonstrator equipped with displacement sensors, force sensors and a stereophotogrammetry system to perform a system identification of the material parameters as well as a real-time identification of a moving load.