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arxiv: 2211.00642 · v2 · submitted 2022-10-31 · 💻 cs.LG · cs.AI· cs.SY· eess.SY· stat.CO

Farm-wide virtual load monitoring for offshore wind structures via Bayesian neural networks

N. Hlaing , Pablo G. Morato , F. d. N. Santos , W. Weijtjens , C. Devriendt , P. Rigo This is my paper

Pith reviewed 2026-05-24 10:49 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.SYeess.SYstat.CO
keywords virtual load monitoringBayesian neural networksoffshore wind farmfleet leaderstructural loadsuncertainty quantificationvirtual sensing
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The pith

Bayesian neural networks trained on one offshore wind turbine can predict loads on the rest of the farm with uncertainty estimates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a virtual load monitoring system for offshore wind farms using Bayesian neural networks. A model is trained on data from a single fully-instrumented fleet-leader turbine and then used to estimate structural loads on other turbines that only provide standard operational data. This avoids the high cost of instrumenting every turbine while the Bayesian approach supplies uncertainty measures to identify when predictions may be unreliable. The method was validated through testing in an operational offshore wind farm.

Core claim

A virtual load monitoring framework formulated via Bayesian neural networks enables load predictions for non-fully monitored wind turbines based on data from a fleet-leader turbine, with the networks intrinsically announcing uncertainties to detect inaccurate estimations.

What carries the argument

Bayesian neural networks that learn mappings from standard operational data to structural loads from the fleet-leader and produce predictions accompanied by uncertainty estimates for deployment on other turbines.

If this is right

  • Structural load monitoring becomes feasible for entire wind farms without full instrumentation on each turbine.
  • Uncertainty estimates allow operators to flag and potentially discard inaccurate load predictions.
  • Reduced uncertainties in load data support more optimal lifecycle management decisions for wind structures.
  • Monitoring systems remain functional even if some physical sensors fail after marine exposure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar BNN virtual monitoring could apply to other distributed infrastructure like bridges or solar farms where full instrumentation is costly.
  • Integration with physics-based deterioration models might further reduce uncertainties by combining data-driven predictions with mechanistic knowledge.
  • The fleet-leader concept could be extended by selecting multiple leaders or rotating the role to improve generalization across varying conditions.

Load-bearing premise

The mapping from standard data to loads learned on the fleet-leader turbine applies equally well to the other turbines in the farm, and the uncertainty estimates reliably indicate when a prediction is inaccurate.

What would settle it

Measure actual loads on a non-leader turbine over a period and check whether the BNN predictions consistently fall within the reported uncertainty intervals; systematic deviations outside those intervals would falsify the generalization claim.

Figures

Figures reproduced from arXiv: 2211.00642 by C. Devriendt, F. d. N. Santos, N. Hlaing, Pablo G. Morato, P. Rigo, W. Weijtjens.

Figure 1
Figure 1. Figure 1: Schematic diagrams comparing the topology and constituents of a standard deterministic neural network (DNN) and a Bayesian neural network (BNN), both mapping standard input monitoring data x to a load indicator y. high epistemic uncertainty in regions where only a few (or none) training points are available. When modeling BNNs, and similarly to ANNs, the selection of the network architecture plays a key ro… view at source ↗
Figure 2
Figure 2. Figure 2: Graphical representation of the reparametrization trick, where by reformulating stochastic network parameters θ as a function of statistical distribution parameters and additional stochastic inputs, the back-propagation of the loss with respect to variational parameters can be effectively computed. a natural solution for the implementation of a farm-wide monitoring strategy, i.e., one or a set of represent… view at source ↗
Figure 3
Figure 3. Figure 3: Rationale of the proposed farm-wide virtual load monitoring framework featuring Bayesian neural networks as data-based virtual sensors. (Top left) A fleet leader BNN is trained based on available load measurement labels. (Top right) At the deployment stage (measurement labels are no longer available), the pre-trained BNN indicates whether the generated predictions might be inaccurate by reporting a high mo… view at source ↗
Figure 4
Figure 4. Figure 4: Flowchart diagram illustrating the steps needed for the implementation of the proposed farm-wide virtual load monitoring framework. where the network parameters, θ are randomly drawn from the posterior weights and biases associated distributions, and f symbolizes the Bayesian network model itself. Note that, in this case, the retrieved predictive uncertainty estimate V(ˆy | x) encompasses both aleatory and… view at source ↗
Figure 5
Figure 5. Figure 5: Illustration depicting the monitoring setup installed on an operational offshore wind turbine, from which data was continuously collected during the course of the experimental campaign. The monitoring setup includes a standard SCADA system, accelerometers at three different levels, and strain gauges installed at the lowest level. speed, yaw and pitch attitude, and instantaneous power. The sensor setup does… view at source ↗
Figure 6
Figure 6. Figure 6: Illustration showcasing the performance of load prediction data-based models. Each bar corresponds to a model specified with a specific set of input monitoring signals, i.e., SCADA, wave, and/or acceleration data. The red box indicates the selected reduced set of input monitoring signals. predictions of damage equivalent moments in the side-to￾side (DEMtl) and fore-aft (DEMtn) directions. Note that all net… view at source ↗
Figure 7
Figure 7. Figure 7: Graphical representation and comparison between the usual training behavior of [top] standard deterministic neural networks (DNNs) and [bottom] Bayesian neural networks (BNNs). Training and testing losses are plotted for both models over epochs. The automatic overfitting control featured by BNNs can be observed in the illustration. samples in each batch share the stochastic weights ε, there is potential co… view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of a specific bias from the neural network over training epochs. The reduction of model uncertainty can be appreciated by observing the plunge of the bias’ coefficient of variation (CoV) over the course of the training task. The prior weights’ distributions of the Bayesian neural networks are assigned to follow a multivariate standard normal distribution. Since the BNN needs to minimize the negat… view at source ↗
Figure 9
Figure 9. Figure 9: Illustration of the virtual monitoring model performance over specific data collection periods. It can be noticed that the amount of data collected differs for each period, e.g., the information retrieved over the course of the second trimester is scarce. Note that the plots indicate the mean of the model’s performance over the test dataset. of the variance, V(.). Even if the model uncertainty, i.e., CoV(µ… view at source ↗
Figure 10
Figure 10. Figure 10: Load predictions generated by the Bayesian neural networks at the deployment stage for all analyzed offshore wind turbines. The retrieved expected damage equivalent moments, E[µDEM], are classified into discrete bins colored according to their associated model uncertainty CoV(µDEM). The height of each bar represents its probability and the color intensity indicates its associated model uncertainty. metric… view at source ↗
Figure 11
Figure 11. Figure 11: Representation of BNN’s model performance for farm-wide load prediction. In particular, the model uncertainty is reported for the fleet-leader (both train and test datasets), MP01, and MP02 offshore wind turbines. In the figure, the orange line and the red￾dotted line represent, respectively, the median and mean values of CoV(µDEM) over the corresponding dataset, and the boxes span between 25th and 75th p… view at source ↗
Figure 12
Figure 12. Figure 12: Representation of the minimum Euclidean distance from each wind turbine’s input test dataset to the fleet-leader’s input training dataset. The minimum Euclidean distances are plotted for the fleet-leader (test dataset), MP01, and MP02 offshore wind turbines. In the figure, the orange line and the red￾dotted line represent, respectively, the median and mean values of rmin(xtest, X) distances over their cor… view at source ↗
Figure 13
Figure 13. Figure 13: Prediction error associated with DNN and epistemic BNN predictions. The mean absolute error (MAE) corresponding to DNNs and epistemic BNNs is represented with light and dark grey bars, respectively. Additionally, model uncertainty metrics, CoV(µDEM), reported by the epistemic BNN (without the need for ground truth labels) are represented with blue bars. yields slightly more accurate point load estimates t… view at source ↗
Figure 14
Figure 14. Figure 14: Model uncertainty associated with the load predictions generated by the investigated Bayesian neural networks. BNNs capturing only epistemic uncertainties are colored in light blue. Spreading over each wind turbine dataset, box plots represent the corresponding model uncertainty, CoV(µDEM), within the interquartile range, with whiskers that span from 2.5th to 97.5th percentiles. Additionally, the median a… view at source ↗
read the original abstract

Offshore wind structures are subject to deterioration mechanisms throughout their operational lifetime. Even if the deterioration evolution of structural elements can be estimated through physics-based deterioration models, the uncertainties involved in the process hurdle the selection of lifecycle management decisions. In this scenario, the collection of relevant information through an efficient monitoring system enables the reduction of uncertainties, ultimately driving more optimal lifecycle decisions. However, a full monitoring instrumentation implemented on all wind turbines in a farm might become unfeasible due to practical and economical constraints. Besides, certain load monitoring systems often become defective after a few years of marine environment exposure. Addressing the aforementioned concerns, a farm-wide virtual load monitoring scheme directed by a fleet-leader wind turbine offers an attractive solution. Fetched with data retrieved from a fully-instrumented wind turbine, a model can be trained and then deployed, thus yielding load predictions of non-fully monitored wind turbines, from which only standard data remains available. In this paper, we propose a virtual load monitoring framework formulated via Bayesian neural networks (BNNs) and we provide relevant implementation details needed for the construction, training, and deployment of BNN data-based virtual monitoring models. As opposed to their deterministic counterparts, BNNs intrinsically announce the uncertainties associated with generated load predictions and allow to detect inaccurate load estimations generated for non-fully monitored wind turbines. The proposed virtual load monitoring is thoroughly tested through an experimental campaign in an operational offshore wind farm and the results demonstrate the effectiveness of BNN models for fleet-leader-based farm-wide virtual monitoring.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper proposes a farm-wide virtual load monitoring scheme for offshore wind structures that trains Bayesian neural networks (BNNs) on data from a single fully instrumented 'fleet-leader' turbine and deploys them to predict loads on other turbines using only standard operational data. BNNs are presented as advantageous over deterministic models because their predictive uncertainties can flag inaccurate estimations. The framework is tested through an experimental campaign in an operational offshore wind farm, with the abstract stating that the results demonstrate effectiveness for fleet-leader-based monitoring.

Significance. If the generalization and uncertainty calibration claims hold under quantitative scrutiny, the approach could enable scalable, lower-cost structural monitoring across entire wind farms, reducing reliance on full instrumentation and supporting better-informed lifecycle decisions amid deterioration uncertainties. The real-world experimental testing in an operational farm is a clear strength, as is the explicit focus on uncertainty quantification via BNNs rather than point estimates alone.

major comments (1)
  1. [Experimental campaign / results] The central effectiveness claim (abstract and introduction) rests on two unverified assumptions: (1) that the input-output mapping learned on the fleet-leader transfers to other turbines despite possible differences in structural response or sensor placement, and (2) that BNN predictive uncertainty reliably identifies high-error cases. No cross-turbine error distributions, uncertainty calibration plots, or accuracy comparisons between flagged and unflagged predictions are reported, leaving the farm-wide generalization and the claimed advantage of BNNs over deterministic models without direct quantitative support.
minor comments (1)
  1. [Abstract] The abstract states that the method was 'thoroughly tested' yet supplies no numerical performance metrics, farm size, number of turbines monitored, or data volume; adding these would improve clarity without altering the technical content.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment below and agree that additional quantitative analyses will strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Experimental campaign / results] The central effectiveness claim (abstract and introduction) rests on two unverified assumptions: (1) that the input-output mapping learned on the fleet-leader transfers to other turbines despite possible differences in structural response or sensor placement, and (2) that BNN predictive uncertainty reliably identifies high-error cases. No cross-turbine error distributions, uncertainty calibration plots, or accuracy comparisons between flagged and unflagged predictions are reported, leaving the farm-wide generalization and the claimed advantage of BNNs over deterministic models without direct quantitative support.

    Authors: We agree that the manuscript does not currently include the specific quantitative elements mentioned (cross-turbine error distributions, uncertainty calibration plots, or direct accuracy comparisons between high- and low-uncertainty predictions). To address the two assumptions and provide direct support for the advantage of BNNs, the revised manuscript will add: (1) error distributions across all turbines to demonstrate transfer of the learned mapping, (2) uncertainty calibration plots (e.g., reliability diagrams) to evaluate whether predictive uncertainty correlates with actual error, and (3) comparative metrics (such as MAE or RMSE) for predictions flagged by high uncertainty versus those with low uncertainty. These additions will be placed in the experimental results section. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical validation on operational data

full rationale

The paper trains BNNs on fully-instrumented fleet-leader data and deploys them for load prediction on other turbines, with uncertainty used to flag errors. This is a standard supervised modeling pipeline whose effectiveness claim rests on experimental testing in an operational farm rather than any equation reducing a prediction to its own fitted inputs by construction. No self-definitional mappings, fitted-input-as-prediction steps, or load-bearing self-citation chains appear in the provided text. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach depends on standard machine learning assumptions plus the domain assumption that one turbine's data represents the farm; no new physical entities are introduced.

free parameters (1)
  • BNN architecture, priors, and variational parameters
    Network depth, width, prior distributions over weights, and inference hyperparameters are selected or optimized during model construction and training.
axioms (1)
  • domain assumption Data from the fleet-leader turbine is representative of load behavior across the farm
    The transfer learning step assumes structural and environmental similarity sufficient for generalization.

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