scholarly journals Efficient Bayesian calibration of aerodynamic wind turbine models using surrogate modeling

2021 ◽  
Author(s):  
Benjamin Sanderse ◽  
Vinit V. Dighe ◽  
Koen Boorsma ◽  
Gerard Schepers
Keyword(s):  
New Mexico ◽  
Wind Turbine ◽  
Polynomial Chaos ◽  
Global Sensitivity Analysis ◽  
Measurement Data ◽  
Model Parameters ◽  
Test Cases ◽  
Parameter Calibration ◽  
Bayesian Calibration ◽  
Polynomial Chaos Expansions

Abstract. This paper presents an efficient strategy for the Bayesian calibration of parameters of aerodynamic wind turbine models. The strategy relies on constructing a surrogate model (based on adaptive polynomial chaos expansions), which is used to perform both parameter selection using global sensitivity analysis and parameter calibration with Bayesian inference. The effectiveness of this approach is shown in two test cases: calibration of airfoil polars based on the measurements from the DanAero MW experiments, and calibration of five yaw model parameters based on measurements on the New MEXICO turbine in yawed conditions. In both cases, the calibrated models yield results much closer to the measurement data, and in addition they are equipped with an estimate of the uncertainty in the predictions.

scholarly journals Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Gustavo Tapia ◽  
Wayne King ◽  
Luke Johnson ◽  
Raymundo Arroyave ◽  
Ibrahim Karaman ◽  
...  
Keyword(s):  
Additive Manufacturing ◽  
Computational Models ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Model Parameters ◽  
Powder Bed Fusion ◽  
Multiple Sources ◽  
Powder Bed ◽  
Model Code ◽  
Polynomial Chaos Expansions

Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are essential for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study presents one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.

scholarly journals Efficient Uncertainty Assessment in EM Problems via Dimensionality Reduction of Polynomial-Chaos Expansions

Technologies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 37
Author(s):  
Christos Salis ◽  
Nikolaos Kantartzis ◽  
Theodoros Zygiridis
Keyword(s):  
Dimensionality Reduction ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Uncertainty Assessment ◽  
Test Cases ◽  
Stochastic Inputs ◽  
Dimensionality Reduction Technique ◽  
Sensitivity Analysis Method ◽  
Polynomial Chaos Expansions ◽  
Involved Field

The uncertainties in various Electromagnetic (EM) problems may present a significant effect on the properties of the involved field components, and thus, they must be taken into consideration. However, there are cases when a number of stochastic inputs may feature a low influence on the variability of the outputs of interest. Having this in mind, a dimensionality reduction of the Polynomial Chaos (PC) technique is performed, by firstly applying a sensitivity analysis method to the stochastic inputs of multi-dimensional random problems. Therefore, the computational cost of the PC method is reduced, making it more efficient, as only a trivial accuracy loss is observed. We demonstrate numerical results about EM wave propagation in two test cases and a patch antenna problem. Comparisons with the Monte Carlo and the standard PC techniques prove that satisfying outcomes can be extracted with the proposed dimensionality-reduction technique.

Polynomial Chaos Based Design of Robust Input Shapers

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Tarunraj Singh ◽  
Puneet Singla ◽  
Umamaheswara Konda
Keyword(s):  
Polynomial Chaos ◽  
Probabilistic Approach ◽  
Uncertain System ◽  
Residual Energy ◽  
Model Parameters ◽  
Minimax Optimization ◽  
Stochastic Space ◽  
System States ◽  
Polynomial Chaos Expansions ◽  
The Cost

A probabilistic approach, which exploits the domain and distribution of the uncertain model parameters, has been developed for the design of robust input shapers. Polynomial chaos expansions are used to approximate uncertain system states and cost functions in the stochastic space. Residual energy of the system is used as the cost function to design robust input shapers for precise rest-to-rest maneuvers. An optimization problem, which minimizes any moment or combination of moments of the distribution function of the residual energy is formulated. Numerical examples are used to illustrate the benefit of using the polynomial chaos based probabilistic approach for the determination of robust input shapers for uncertain linear systems. The solution of polynomial chaos based approach is compared with the minimax optimization based robust input shaper design approach, which emulates a Monte Carlo process.

scholarly journals Sensitivity-Based Parameter Calibration and Model Validation Under Model Error

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Na Qiu ◽  
Chanyoung Park ◽  
Yunkai Gao ◽  
Jianguang Fang ◽  
Guangyong Sun ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Calibration Method ◽  
Model Error ◽  
Model Parameters ◽  
Observation Data ◽  
Parameter Calibration ◽  
Bayesian Calibration ◽  
Modeling Errors ◽  
Model Discrepancy ◽  
Better Than

In calibrating model parameters, it is important to include the model discrepancy term in order to capture missing physics in simulation, which can result from numerical, measurement, and modeling errors. Ignoring the discrepancy may lead to biased calibration parameters and predictions, even with an increasing number of observations. In this paper, a simple yet efficient calibration method is proposed based on sensitivity information when the simulation model has a model error and/or numerical error but only a small number of observations are available. The sensitivity-based calibration method captures the trend of observation data by matching the slope of simulation predictions and observations at different designs and then utilizing a constant value to compensate for the model discrepancy. The sensitivity-based calibration is compared with the conventional least squares calibration method and Bayesian calibration method in terms of parameter estimation and model prediction accuracies. A cantilever beam example, as well as a honeycomb tube crush example, is used to illustrate the calibration process of these three methods. It turned out that the sensitivity-based method has a similar performance with the Bayesian calibration method and performs much better than the conventional method in parameter estimation and prediction accuracy.

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