Learning of model discrepancy for structural dynamics applications using Bayesian history matching

P Gardner,C Lord,R J Barthorpe,T J Rogers

doi:10.1088/1742-6596/1264/1/012052

P Gardner, C Lord + Show 2 more

Open Access

https://doi.org/10.1088/1742-6596/1264/1/012052

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Abstract

Calibration of computer models for structural dynamics is often an important task in creating valid predictions that match observational data. However, calibration alone will lead to biased estimates of system parameters when a mechanism for model discrepancy is not included. The definition of model discrepancy is the mismatch between observational data and the model when the ‘true’ parameters are known. This will occur due to the absence and/or simplification of certain physics in the computer model. Bayesian History Matching (BHM) is a ‘likelihood-free’ method for obtaining calibrated outputs whilst accounting for model discrepancies, typically via an additional variance term. The approach assesses the input space, using an emulator of the complex computer model, and identifies parameter sets that could have plausibly generated the target outputs. In this paper a more informative methodology is outlined where the functional form of the model discrepancy is inferred, improving predictive performance. The algorithm is applied to a case study for a representative five storey building structure with the objective of calibrating outputs of a finite element (FE) model. The results are discussed with appropriate validation metrics that consider the complete distribution.

Highlights

Bayesian History Matching (BHM) is a ‘likelihood-free’ method for calibrating computer models under the assumption of model discrepancy, i.e. given the simulator was evaluated with the ‘true’ parameter set there would still be a difference between these predictions and observed data
It is noted that other importance sampling based approaches to marginalising the hyperparameters from a Gaussian Processes (GP) are adaptive importance sampling [16], where the proposal is iterative amended in order to improve convergence, and Sequential Monte Carlo (SMC) [17]
The mean predictions of the GP emulators for the 1000 Monte Carlo realisations are presented in Fig. 4 against the observational data used within BHM z(xz) with ±cσ(Vo,j + Vm,j) bounds, where cσ is the standard deviation associated with 99% probability mass of a standard normal

Summary

Introduction

Bayesian History Matching (BHM) is a ‘likelihood-free’ method for calibrating computer models (here defined as simulators) under the assumption of model discrepancy, i.e. given the simulator was evaluated with the ‘true’ parameter set there would still be a difference between these predictions and observed data. For multivariate implausibilities the threshold T is set as a high percentile (i.e. α > 95%) from a chi-squared distribution with either j or the input size x degrees of freedom, i.e. T = Fχ−21 (α) — the output from a chi-squared quantile function This can be thought of as performing a frequentist hypothesis test on the parameter combination, using a chi-squared (χ2) test. The examples shows that during each wave new simulator evaluations are added, decreasing the code uncertainty of the emulator This in turn leads to increased parts of the parameter space begin discarded, until the implausibility metric identifies two non-implausibility regions for this example, i.e. the areas where the simulator crosses the observational uncertainty bounds.

Model Discrepancy Inference via Importance Sampling

Representative Five Storey Building Structure

Findings

Conclusions