Efficient statistical parameter calibration for complex structural dynamics systems under consideration of model uncertainty
Engineering Design, Machine Elements, Product Development
Final Report Abstract
The research project addressed the question of how to quantify the data uncertainty of a complex technical system while taking into account the model uncertainty, in order to increase the prediction accuracy of mathematical models. Using the SFB 805 demonstrator as an example, a method for statistical model calibration was developed and tested. The demonstrator was designed on the basis of an airplane landing gear and modelled as a flexible multi-body system. The method to efficiently calibrate this computationally intensive but accurate high-fidelity model is to combine it with a fast but less accurate low-fidelity model. This multi-fidelity approach, known from the literature, was combined in this project with the consideration of model uncertainty with the aim of increasing prediction accuracy. The model uncertainty was considered following the framework of Kennedy and O'Hagan with a Gaussian process (GP)-based discrepancy function. The GP is based on a quadratic exponential covariance function. Some of its hyperparameters were not identifiable and were determined in advance by optimisation. The remaining hyperparameters, i.e. the signal variances, were calibrated together with the dominant model parameters determined as part of a sensitivity analysis. Polynomial chaos kriging was used as the basis for the low-fidelity model. This offered the advantage that, compared to a pure GP with a linear or without mean function, a better approximation of the highfidelity model could be achieved with less training data and thus less computational effort. At the same time, the low-fidelity model was combined with two adaptation schemes that selectively improved the low-fidelity model during calibration for improved filtering of the two-stage approach. The calibration was also accelerated by parallelizing the Markov chains on the Lichtenberg high performance cluster at the TU Darmstadt, which simultaneously allows the sampling of multimodal a-posteriori distributions. During the project, it turned out that in the case of uniformly distributed a priori distributions of the signal variances, the calibration tends to explain the measurement data primarily by the discrepancy function and less by the model. The use of an exponential distribution as the a priori distribution of the signal variances remedied this and led to a successful calibration. In addition to the calibration of the model, the incorporation of a discrepancy function greatly improved the predictive accuracy of the SFB 805 demonstrator model.
Publications
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A Methodology for the Efficient Quantification of Parameter and Model Uncertainty. Journal of Verification, Validation and Uncertainty Quantification, 7(3).
Feldmann, R.; Gehb, C. M.; Schaeffner, M. & Melz, T.
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Ein Beitrag zur effizienten Quantifizierung von Parameter- und Modellunsicherheit strukturdynamischer Systeme. Dissertation. TU Darmstadt
Feldmann, R.
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Beam Truss Code for MATLAB (Version 1.0) [Computer software]
Feldmann, R.
