@article{Bos2020,
title = {Bayesian model calibration with interpolating polynomials based on adaptively weighted Leja nodes},
author = {Laurent M. M. van den Bos and Benjamin Sanderse and Wim A. A. M. Bierbooms and Gerard J. W. van Bussel},
url = {https://arxiv.org/abs/1802.02035},
doi = {10.4208/cicp.oa-2018-0218},
year = {2020},
date = {2020-01-00},
journal = {Communications in Computational Physics},
volume = {27},
number = {1},
pages = {33--69},
publisher = {Global Science Press},
abstract = {An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics: using a prior distribution and a likelihood, the posterior distribution is obtained through application of Bayes’ law. Our novel algorithm to accurately determine this posterior requires significantly fewer discrete model evaluations than traditional Monte Carlo methods. The key idea is to replace the expensive model by an interpolating surrogate model and to construct the interpolating nodal set maximizing the accuracy of the posterior. To determine such a nodal set an extension to weighted Leja nodes is introduced, based on a new weighting function. We prove that the convergence of the posterior has the same rate as the convergence of the model. If the convergence of the posterior is measured in the Kullback–Leibler divergence, the rate doubles. The algorithm and its theoretical properties are verified in three different test cases: analytical cases that confirm the correctness of the theoretical findings, Burgers’ equation to show its applicability in implicit problems, and finally the calibration of the closure parameters of a turbulence model to show the effectiveness for computationally expensive problems.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{Bos2018a,
title = {Efficient ultimate load estimation for offshore wind turbines using interpolating surrogate models},
author = {Laurent M. M. van den Bos and Benjamin Sanderse and Lindert Blonk and Wim A. A. M. Bierbooms and Gerard J. W. van Bussel},
doi = {10.1088/1742-6596/1037/6/062017},
year = {2018},
date = {2018-00-00},
journal = {Journal of Physics: Conference Series},
volume = {1037},
number = {6},
pages = {062017},
publisher = {IOP Publishing},
abstract = {During the design phase of an offshore wind turbine, it is required to assess the impact of loads on the turbine life time. Due to the varying environmental conditions, the effect of various uncertain parameters has to be studied to provide meaningful conclusions. Incorporating such uncertain parameters in this regard is often done by applying binning, where the probability density function under consideration is binned and in each bin random simulations are run to estimate the loads. A different methodology for quantifying uncertainties proposed in this work is polynomial interpolation, a more efficient technique that allows to more accurately predict the loads on the turbine for specific load cases. This efficiency is demonstrated by applying the technique to a power production test problem and to IEC Design Load Case 1.1, where the ultimate loads are determined using BLADED. The results show that the interpolating polynomial is capable of representing the load model. Our proposed surrogate modeling approach therefore has the potential to significantly speed up the design and analysis of offshore wind turbines by reducing the time required for load case assessment.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{vandenBos2017,
title = {Non-intrusive uncertainty quantification using reduced cubature rules},
author = {Laurent M. M. van den Bos and Barry Koren and Richard P. Dwight},
url = {https://ir.cwi.nl/pub/25311},
doi = {10.1016/j.jcp.2016.12.011},
year = {2017},
date = {2017-03-00},
journal = {Journal of Computational Physics},
volume = {332},
pages = {418--445},
abstract = {For the purpose of uncertainty quantification with collocation, a method is proposed for generating families of one-dimensional nested quadrature rules with positive weights and symmetric nodes. This is achieved through a reduction procedure: we start with a high-degree quadrature rule with positive weights and remove nodes while preserving symmetry and positivity. This is shown to be always possible, by a lemma depending primarily on Carathéodory's theorem. The resulting one-dimensional rules can be used within a Smolyak procedure to produce sparse multi-dimensional rules, but weight positivity is lost then. As a remedy, the reduction procedure is directly applied to multi-dimensional tensor-product cubature rules. This allows to produce a family of sparse cubature rules with positive weights, competitive with Smolyak rules. Finally the positivity constraint is relaxed to allow more flexibility in the removal of nodes. This gives a second family of sparse cubature rules, in which iteratively as many nodes as possible are removed. The new quadrature and cubature rules are applied to test problems from mathematics and fluid dynamics. Their performance is compared with that of the tensor-product and standard Clenshaw–Curtis Smolyak cubature rule.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}