The study is based on operational data collected from an offshore wind farm comprising 44 monopile-supported turbines that are broadly similar in terms of structural dynamics. As noted by , such a fleet can be treated as a homogeneous population, though minor variability in resonance frequencies arises from differences in seabed depth, fabrication, and installation tolerances. The layout and sensing configuration are shown in Fig. . All turbines are equipped with nacelle-mounted dedicated accelerometers that provide the high-frequency vibration data used in this study. Each nacelle unit contains C=3 channels (fore–aft, side–side, and vertical directions) sampled at 31.25 Hz. SCADA signals, by contrast, are recorded by the turbine control system at a low frequency of 1/600 Hz (1 min averages) and are used solely for evaluation and interpretation. Strain gauges installed near the tower–transition piece interface on five “fleet leader” turbines are used to provide fatigue reference data but are costly; consequently, only a limited subset is instrumented, as is common in offshore monitoring . Farm-wide fatigue is typically extrapolated from these leaders using SCADA-based models . In this study, the strain-gauge measurements will be utilized only in Sect.  as the source of ground truth for 10 min damage-equivalent moments (DEMs).

Wind turbine operation is traditionally classified from SCADA data using rule-based thresholds applied to variables such as rotor speed, blade pitch, power output, wind speed, and occasionally yaw. Typical operational states include the following:

parked and rotor lock – rotor stopped (locked), no power production;

Such SCADA-based classification requires expert-defined thresholds; for example, distinguishing parked from idling often involves checking both rotor speed and wind speed against predefined limits. Such schemes assume stationarity, i.e., that conditions remain constant over the 10 min window. While often reasonable, this assumption hides short-term dynamics such as rotor stops and restarts. Figure  illustrates this point. The spectrogram of nacelle acceleration, obtained with 65 s windows, with 30 s overlap, reveals clear differences between idling and stops, as well as short-lived transitions that would not be visible in SCADA records. Restricting the spectrum to the 0–3 Hz band focuses on the dominant rotor dynamics. These patterns indicate that the 10 min stationarity assumption does not always hold.

The acceleration-based approach developed here addresses these shortcomings. By operating directly on high-frequency vibration signals, it enables inference of operational states and transient events at sub-10 min resolution without the need for threshold specification. This enables finer temporal resolution of state estimation and allows for event counting, complementing rather than replacing SCADA. In this study, SCADA signals are used solely for interpretation and validation of the acceleration-derived representations and not for training or direct state inference.

The objective of this work is to derive compact, expressive, and turbine-invariant descriptors of the acceleration signals that capture operational variability across the fleet. Such descriptors are generally referred to as representations, and, when expressed as numerical vectors produced by a neural network, they are referred to as embeddings. An embedding can be understood as a vectorized representation of a signal – a compressed summary of an input window that preserves the essential dynamical information while discarding redundancies. Conceptually, embeddings play a similar role to manually engineered statistical features (e.g., minimum, maximum, variance) but are learned automatically by the network in a data-driven manner.

In the resulting embedding space, signals recorded under similar operational and environmental conditions are expected to map close together, while signals reflecting different dynamics should be located further apart. The structure of this space should yield well-separated clusters, whereas subtler variations (e.g., between adjacent load levels) should appear to be closer. To ensure that the embeddings remain physically meaningful, they are expected to exhibit strong mutual information with key supervisory variables such as rotor speed, wind speed, and blade pitch angle, the latter being particularly important as it directly defines the turbine’s control state.

The dataset is composed of accelerometer measurements recorded in multiple directions (e.g., fore–aft, side–side, vertical). These signals can be ingested by the model in several ways: (i) a separate model may be trained for each direction, (ii) a shared architecture may be used while fitting independent model instances per direction, or (iii) a multi-channel architecture may be adopted in which all directions are processed jointly.

In this work, the third strategy is adopted, with each direction being treated as an input channel, analogously to the color channels in image processing. The detailed multi-channel architecture is provided in Sect. . For clarity, the preprocessing pipeline is first described in the uni-variate (single-channel) case, and its extension to the three-channel setting is trivial.

After training, each embedding is associated with a set of soft-assignment probabilities qij reflecting its similarity to the learned centroids μj (Eq. ). The most probable centroid is interpreted as the current operational regime.

As a result of the combined objective, the latent space remains compact, turbine-invariant, and discretized into regimes that are directly interpretable in terms of turbine operation (e.g., idling, sub-rated, rated, or curtailed states).

Although the encoder and clustering components operate on short, quasi-stationary spectral segments, fatigue-related quantities such as the 10 min damage-equivalent moment (DEM) depend on how operating conditions evolve over time. To capture these temporal dependencies, the sequence of latent embeddings produced by the encoder {zt} is processed by a recurrent model that integrates information across successive windows. In practice, a two-layer long short-term memory (LSTM) network aggregates the embeddings within each 10 min interval and outputs a compact hidden representation summarizing the latent trajectory of the turbine’s dynamic state. A linear regression head then maps this representation to the corresponding DEM value, trained under a mean-squared-error objective using reference strain gauge measurements from the fleet leader turbines. During this stage, the encoder parameters are frozen so that the recurrent model learns to interpret the latent dynamics rather than to modify their structure.

Here, the linear regression head refers to a single fully connected layer that takes as input the LSTM output representation (context vector). The LSTM and this linear layer are trained end-to-end for DEM prediction, while the encoder remains fixed.

This design introduces a clear hierarchy: the auto-encoder acts as a spatial compressor that distills high-dimensional vibration spectra into a compact, turbine-invariant representation; the recurrent module integrates these representations temporally; and the regression head translates the aggregated latent dynamics into a physically meaningful fatigue indicator. Conceptually, this mirrors the structure of world models proposed by , in which a variational auto-encoder encodes raw observations, a recurrent model captures temporal evolution in latent space, and a lightweight head operates upon that representation. In a similar spirit, the present framework constructs a latent “world view” of turbine dynamics: one that encapsulates both the instantaneous and evolving behavior of the structure – thereby enabling fatigue estimation directly from vibration-derived embeddings without recourse to SCADA data.

Acceleration data are stored in 1 h files, each containing three directional components, hereafter referred to as channels. Corresponding SCADA and fatigue-related data are maintained in a database with a temporal resolution of 10 min. For model training, the acceleration signals are segmented and transformed into spectrograms. Each 1 min spectrogram window is represented as a tensor x∈RB×C×F×T, with batch size B, channels C=3 (fore–aft, side–side, vertical), frequency bins F≈200 covering 0–3 Hz, and T time frames within the minute. The network comprises per-channel encoders, a latent fusion block, and per-channel decoders, with an LSTM head used only for DEM estimation.

Per-channel encoders. For each channel c∈{1,…,C}, the slice x(c)∈RB×F×T is reshaped to (BT,F) and passed through a small multi-layer perceptron (MLP) ϕc:RF→Rdc (three 128-unit layers with normalization and ReLU). Each timestamp is treated as an independent sample. We set dc=16. The resulting per-frame latents {zt(c)}t=1T are concatenated: ztcat=[zt(1);…;zt(C)]∈RCdc.

All network parameters were optimized using the Adam optimizer , with an initial learning rate of 5×10-3. The learning rate was adapted using a ReduceLROnPlateau scheduler (reduction factor of 0.2, patience of 5, minimum learning rate of 10-5), monitored on the basis of the validation reconstruction loss. A batch size of 1024 was used throughout. To ensure stable optimization, gradient clipping with a maximum ℓ2 norm of 1.0 and early stopping with a patience of 50 epochs were applied.

For the final model, the gradient reversal scale was set to γ=0.4, and DEC centroids were initialized using k-means with nclusters=5.

All models were trained for up to 1000 epochs, although convergence was typically achieved earlier due to early stopping. The resulting loss evolution is discussed in Sect. .

For training, a random subset of 1000 h per turbine was selected from the year 2023, corresponding to approximately 6 weeks of data per turbine. Each turbine was assigned an anonymized identifier, and only 11 out of the 44 turbines were used for model training, corresponding to one-quarter of the fleet. This split was adopted to limit overfitting and to explicitly assess generalization to unseen turbines. Model testing for operational-state inference was conducted on data from the first 2 weeks of 2024, which constitute a temporally disjointed hold-out dataset used exclusively for evaluation and visualization. For the fatigue-related task, data from June to September 2024 were used for testing as this period contains a high number of start–stop events and a wide range of operational conditions. Since high-frequency SCADA labels are unavailable, and low-frequency SCADA signals (mean power, rotor speed, pitch, wind speed), assumed to be constant within each 10 min interval, are used as a reference for evaluation. Under this assumption, a lower-bound estimate of how well the embeddings capture operational information is obtained.

After training, two key aspects are examined: (i) whether the learned embeddings eliminated turbine-specific fingerprints and achieve invariance across turbines and (ii) whether the embeddings remain informative about the underlying operational state.

Figure  summarizes the evolution of the loss components during training under the staged optimization strategy described in Sect. . During the warm-up phase (epochs 0–30), only the reconstruction loss Lrec is optimized. The rapid decrease and subsequent stabilization of this loss indicate that the auto-encoder learns a consistent reconstruction manifold before additional objectives are introduced.

At tstart,dann=30, the domain-adversarial objective is activated. Its weighting coefficient λ is increased linearly over tduration,dann=100 epochs until it reaches λmax⁡=0.8. Immediately after introduction, the domain classification loss Ldomain drops sharply. This transient behavior reflects the ability of the newly trained domain classifier fdom to exploit turbine-specific information still present in the latent representation. As training progresses and the gradient reversal mechanism becomes effective, the encoder increasingly suppresses turbine identity, causing the domain classification loss to rise.

With 11 training turbines, random guessing corresponds to a cross-entropy of log⁡(11)≈2.4. As shown in Fig. , the domain classification loss stabilizes at 2.1 The observed plateau therefore indicates that turbine identity becomes increasingly difficult to infer from the latent space, although weak residual turbine-specific structure remains. This behavior is consistent with the objective of domain-adversarial training.

The clustering objective is introduced at tstart,dec=60. Its weighting coefficient β is increased linearly over tduration,dec=100 epochs until it reaches βmax⁡=10. Upon activation, the clustering loss LDEC initially takes on high values, reflecting the absence of well-formed clusters. As the latent space is reshaped to promote compact and separable regimes, a transient increase in reconstruction error is observed, caused by a temporary mismatch between the decoder and the reorganized latent geometry. As optimization continues, the decoder adapts, and the reconstruction loss decreases again.

The values of λmax⁡ and βmax⁡ were selected heuristically. Moderate variations around these values did not qualitatively affect the results. The guiding principle was to scale the different loss terms at their max to comparable magnitudes once the reconstruction loss had stabilized. Excessively large values were found to be detrimental. In particular, setting βmax⁡=50 led to a significant degradation of reconstruction quality, indicating excessive distortion of the latent space.

This part focuses on the first two dimensions of evaluation. Turbine invariance is quantified by means of pairwise mutual information (MI) between turbine identity and the latent embeddings, while operational informativeness is evaluated through normalized mutual information (NMI) between embeddings and key SCADA variables – namely power, rotor speed, pitch angle, and wind speed.

Turbine invariance was assessed by comparing two models: a plain auto-encoder without adversarial training (γ=0) and the same auto-encoder with a domain-adversarial component applied to the latent space (γ=0.4). The corresponding pairwise MI matrices, D(0) and D(0.4), are presented in Figs.  and .

In the absence of DANN, elevated MI values were observed for many turbine pairs (Fig. ), indicating that turbine-specific fingerprints were retained in the embeddings alongside operational content. Subgroups of turbines were seen to be more similar to each other than to the remainder of the fleet, consistently with residual structural or site variability encoded in the latent space.

With DANN, pairwise MI values were reduced across the matrix D(0.4) (Fig. ), showing that turbine identity was suppressed while operational features were preserved. Two turbines (ID nos. 28 and 39) remained more separable than the rest, which is interpreted as a genuinely distinct dynamic rather than a training artifact. No checkerboard pattern indicative of leakage from the odd–even train–test split was observed. A small increase in reconstruction error was induced by the adversarial term, but downstream use was not compromised.

The GRL scale γ was selected by scanning {0.01,0.2,0.4,0.6} and monitoring the mean of the pairwise MI matrix D. The mean MI was reduced from 0.65 to 0.36 and then to 0.15 and 0.12, with an elbow around γ=0.4. Larger values did not yield meaningful gains and were found to risk latent collapse, and so γ=0.4 was adopted in the final model.

Starting from the precomputed pairwise MI matrix D (Fig. ), which was interpreted as a symmetric dissimilarity measure in bits (larger values corresponding to lower similarity), agglomerative hierarchical clustering was performed, resulting in the identification of five clusters (Appendix ). A detailed explanation of hierarchical clustering can be found in .

In Fig. , the geographic layout of the wind farm is shown, with colors indicating the clusters obtained; numbers correspond to anonymized turbine identifiers. The map was examined to verify that the clustering was not a by-product of wake geometry or simple row positioning (front versus back turbines). No systematic alignment or consistent relation with water depth was observed. The clusters nevertheless appeared to be structured rather than random yet could not be explained by straightforward spatial factors. It is therefore inferred that the grouping most likely reflects a combination of site-specific conditions, control strategies, or structural variability not captured in the available metadata.

Two turbines (anonymized ID nos. 28 and 39) were assigned to single-member clusters and also remained the most separable after adversarial training, which suggests that their distinct behavior arises from genuine dynamic differences rather than artifacts of the clustering procedure.

A central objective of this study is to determine whether operational information typically derived from SCADA can instead be recovered directly from high-frequency acceleration. To evaluate this, normalized mutual information (NMI) values between embeddings and SCADA variables were computed on unseen turbines and are reported in Table . NMI was used because it captures both linear and nonlinear dependencies and provides a normalized measure that is comparable across variables, making it well suited for assessing how much operational content is retained in the embeddings.

Across all variables, higher mean NMI values were obtained after adversarial training, with improvements ranging from +0.016 for power to +0.027 for wind speed. Values in the range of 0.75–0.92 indicate that a substantial fraction of the variability in SCADA signals can be captured by the learned embeddings despite the fact that SCADA data were not used during training. This demonstrates that high-frequency acceleration contains operationally relevant information that can be effectively extracted through the proposed representation-learning framework.

As an external validation, random forest regressors (nest=100) were trained to predict SCADA variables from the learned embeddings using a 50 % train–test split. The models achieved mean R2 scores of 0.923 for power, 0.882 for pitch, 0.937 for wind speed, and 0.925 for rotor speed across the 44 turbines, indicating that the embeddings retain strong operationally relevant information.

Because SCADA variables are available only as 10 min averages, any intra-interval variability captured by the vibration-based embeddings cannot be directly validated. The reported correspondence metrics therefore quantify alignment with a temporally aggregated proxy of the operational state and should be interpreted as conservative lower bounds with respect to the unobserved instantaneous dynamics rather than as an upper limit on achievable predictive performance.

The objective in this section is to determine whether the learned latent space can be used to identify distinct operational states of the turbine. As shown previously, the embeddings capture SCADA-like information with high accuracy; here, the focus is on whether these representations can be organized into discrete and interpretable regimes.

When no clustering constraint is applied (i.e., DEC is disabled and β=0), the latent space is shaped only by reconstruction and domain-adversarial objectives. In this setting, there is no explicit geometric incentive for the encoder to form multiple compact, well-separated operational regimes. The embedding therefore organizes primarily according to the largest, most separable dynamical differences in the data. Empirically, this yields three dominant groups, as illustrated in Fig. : two small clusters corresponding to non-producing conditions (standstill and parked) and one large cluster that aggregates the full continuum of producing operation. The separation between the two non-producing clusters is consistent with a control-driven distinction (mainly pitch angle differences under low or zero rotor speed), which produces distinct low-frequency spectral signatures. In contrast, within the producing regime, sub-rated, rated, and curtailed behavior form a smooth progression in spectral space (driven by gradual changes in rotor speed, aerodynamic loading, and control action) and therefore remain embedded as a single connected manifold rather than splitting into discrete clusters. This behavior is visible in Fig. , where producing states form a single connected manifold; the splitting is mainly driven by the pitch angle.

By introducing DEC, the latent structure is explicitly encouraged to become clusterable. DEC adds a set of learnable centroids {μj}j=1K and optimizes the encoder such that embeddings are pulled toward these centroids via a KL divergence objective between soft assignments and a sharpened target distribution. This explicitly trades a purely continuous representation for one that partitions the operating manifold into K compact regions. With DEC enabled and K=5 (a user-defined choice), the previously broad operating manifold is refined into multiple regimes that distinguish different levels of power production and control action. This five-cluster configuration aligns with the canonical division of turbine behavior used in SCADA-based classification while being inferred directly from vibrations and at a higher temporal resolution.

Additionally, DEC integrates clustering into the training objective: centroids are part of the model and are refined jointly with the encoder during optimization. In that sense, regime discovery is learned end-to-end rather than imposed only as a purely post hoc clustering step on the final embeddings (although, as is standard in DEC, centroids are initialized from a preliminary clustering such as k-means before being refined during training).

Figure  shows the resulting latent-space partition for the first five turbines during the initial 2 weeks of 2024, serving as the calibration dataset (Sect. ). The identified clusters align clearly with rotor speed thresholds, as shown in Fig. .

Overall, the discovered clusters correspond to well-known operating behaviors: parked or idling, standstill, sub-rated, and rated generation. Collapsing the latent geometry into discrete states provides an interpretable layer on top of the embeddings, enabling event monitoring tasks such as start–stop counting at sub-10 min resolution. In scenarios without SCADA, clusters can be interpreted by visually inspecting representative samples; once identified, they can be relabeled with meaningful operational states.

To further validate the clustering, the regimes are projected onto SCADA references. In the power curve (Fig. ), the regimes separate into five operating zones. Clusters 3 and 4 overlap at low power, but their distinction becomes clear on the pitch versus wind speed plot (Fig. ), where cluster 4 corresponds to high pitch (curtailed or stopped) and cluster 3 corresponds to lower pitch (idling). A small overlap is also observed between the rated and ramp-up regions, reflecting their similarity in terms of RPM (rotations per minute) and the resulting spectra. These comparisons should be regarded as a lower-bound validation since SCADA signals are available only as 10 min averages, whereas embeddings are computed at a 30 s hop length. The assumption of constant SCADA over 10 min introduces unavoidable mismatches.

Finally, the method enables monitoring of high-frequency operational events. By applying the model continuously, it is possible to identify and count start–stop transitions within each hour, capturing short events that are lost in coarse 10 min SCADA averages. Figure  illustrates such a case: six stop–start events are detected, with transitions from low-rate production to standstill. These rapid fluctuations have direct implications for fatigue life, underlining the value of high-resolution, acceleration-based regime inference.

Operational-state information is fundamental for wind turbine fatigue assessment. Damage-equivalent moment (DEM) estimation is traditionally performed using SCADA-based models trained on 10 min averages and calibrated on a limited number of strain-instrumented reference turbines. In this work, DEM estimation is used as an auxiliary validation task to assess whether the learned acceleration-derived embeddings preserve load-relevant information.