the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Probabilistic surrogate modeling of damage equivalent loads on onshore and offshore wind turbines using mixture density networks
Abstract. The use of load surrogates in offshore wind turbine site assessment has gained attention as a way to speed up the lengthy and costly siting process. We propose a novel probabilistic approach using mixture density networks to map 10-minute average site conditions to the corresponding load statistics. The probabilistic framework allows for the modeling of the uncertainty in the loads as a response to the stochastic inflow conditions. We train the data-driven model on the OpenFAST simulations of the IEA-10MW-RWT and compare the predictions to the widely used Gaussian process regression. We show that mixture density networks can recover the accurate mean response in all load channels with values for the coefficient of determination (R2) greater than 0.95 on the test dataset. Mixture density networks completely outperform Gaussian process regression in predicting the quantiles, showing an excellent agreement with the reference. We compare onshore and offshore sites for training to conclude the need for a more extensive training dataset in offshore cases due to the larger feature space and more noise in the data.
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RC1: 'Comment on wes-2024-20', Anonymous Referee #1, 03 Apr 2024
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General Comments
The paper presents a probabilistic surrogate which models the aleatory uncertainty in the model output. The epistemic uncertainty is not considered in the presented method. The overall quality of the paper is in general good with significant contribution. However, the authors should provide more explanations in some parts of the manuscript (see in the specific comments) in order to improve the reader’s comprehension and to ensure the reproducibility of their work.
Specific Comments
Comment 1:
In Section 3.3, it is mentioned that “The 10-minute fatigue is calculated using short-term damage equivalent loads (DELST)”
But, Section 4.1 says “The network is trained on the tower base fore-aft moment standard deviation (TwrBsMyt [kN-m] stddev)”.
It is not clear what are the inputs and outputs of the surrogate. Please formulate the surrogate model formally and mathematically.
Comment 2:
Section 3.5 Accuracy metric should be better explained with more detailed information.
Equation 18: It is not clear if the summation is over the whole test dataset or over the seed repetitions of each test sample. How many samples are drawn from the MDN output distribution to compute the statistics (mean, std, and the quantiles)?
Equation 19: How are the quantile functions computed, by combining closed-form formulations for each Gaussian or through sampling directly from the output mixed distribution?
Comment 3:
The seed repetitions with the same input variables are not necessary since the prediction is inferred from neighboring inputs, however, it also means that many neighborhood points are still required to have a good estimate of aleatory uncertainty. In addition, when modelling in high dimensional input space, the actual distance between the test point and the input points might be far. What is the robustness of the model in such case?
Comment 4:
Line 215 “It pushes the coefficients of uninformative features towards zero, effectively pruning the feature space. “
Additional explanations or references would improve the reader’s comprehension.
Comment 5:
Table 1. What is the sensitivity of mixture component numbers in terms of accuracy and computational resources?
Comment 6:
Please describe what is the specific purpose of having two different test datasets TEST1 and TEST2.
Comment 7:
Figure 3: Why is the marginal distribution of alpha a deterministic value only? Isn’t it a uniform distribution for the ‘train’ and ‘test 1’ according to Table 2?
Comment 8:
Figure 6: Please define the spread of the boxes and whiskers (within which quantiles?).
Technical Corrections
Comment 9:
Line 174 “L-BFGS-B algorithm” Limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm for simple bound constraints is not defined.
Citation: https://doi.org/10.5194/wes-2024-20-RC1
Data sets
Training and validation datasets for training probabilistic machine learning models on NREL's 10-MW reference wind turbine Deepali Singh https://doi.org/10.4121/21939995
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