A geometrical interpretation of the addition of nodes to an interpolatory quadrature rule while preserving positive weights

A novel mathematical framework is derived for the addition of nodes to univariate and interpolatory quadrature rules. The framework is based on the geometrical interpretation of the Vandermonde matrix describing the relation between the nodes and the weights and can be used to determine all nodes that can be added to an interpolatory...

Fatigue design load calculations of the offshore NREL 5 MW benchmark turbine using quadrature rule techniques

A novel approach is proposed to reduce, compared with the conventional binning approach, the large number of aeroelastic code evaluations that are necessary to obtain equivalent loads acting on wind turbines. These loads describe the effect of long-term environmental variability on the fatigue loads of a horizontal-axis wind turbine. In...

Quadrature Methods for Wind Turbine Load Calculations

Two sources of uncertainty can be distinguished in models for wind turbine calculations. Firstly, the environment the wind turbine has to withstand is uncertain and has a direct impact on the life time of the turbine. Secondly, the models used to predict the forces acting on the turbine contain an unknown error, which can also be modeled as a...

Adaptive sampling-based quadrature rules for efficient Bayesian prediction

A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian prediction. The novel idea is to construct a sequence of nested quadrature rules with positive weights...

Generating nested quadrature rules with positive weights based on arbitrary sample sets

For the purpose of uncertainty propagation a new quadrature rule technique is proposed that has positive weights, has high degree, and is constructed using only samples that describe the probability distribution of the uncertain parameters. Moreover, nodes can be added to the quadrature rule, resulting in a sequence of nested rules. The rule...

Bayesian model calibration with interpolating polynomials based on adaptively weighted leja nodes

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...

Efficient ultimate load estimation for offshore wind turbines using interpolating surrogate models

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...

Improved Non-Intrusive Uncertainty Propagation in Complex Fluid Flow Problems

The problem of non-intrusive uncertainty quantification is studied, with a focus on two computational fluid dynamics cases. A collocation method using quadrature or cubature rules is applied, where the simulations are selected deterministically. A one-dimensional quadrature rule is proposed which is nested, symmetric, and has positive weights....