Status note
Paper E was archived on 2026-04-17 and merged into Paper A after a truth-audit identified circular field validation (capacity was never independently measured on the turbine used to validate the encoder). The encoder content now lives in Paper A §3–§4 as part of the self-contained digital-twin framework.
This page is retained as the standalone encoder-method reference for portfolio traceability. The text below is a methods-focused working draft; the canonical version lives inside Paper A.
Summary¶
Full title¶
A Physics-Informed Supervised Encoder for Unified Structural-State Representation of Offshore Wind Turbine Foundations: Cross-Soil Generalisation via CPT Conditioning.
One-sentence headline¶
A supervised encoder trained on 1,794 Monte Carlo realisations maps five deployment-observable inputs (first natural frequency, CPT profile statistics, soil-series descriptor, scour depth, turbine operational state) to fourteen structural-state targets with MAPE < 1.5 % on capacity ratios and Pearson \(r = 0.76\) cross-soil transfer to 17 unseen centrifuge series — a 46 % improvement over the ablated non-physics-informed baseline.
Context¶
SHM research has produced two decades of turbine-specific damage-detection models that do not transfer to the next wind farm, while the physics governing scour-induced degradation (soil stiffness, embedment geometry, load path) is universal enough to encode once and deploy everywhere. The gap is representational: there is no compact latent representation that simultaneously encodes stiffness, capacity, and dynamic response, is physics-consistent, and generalises across soil types. This paper constructs one.
Research question¶
Can a single physics-informed encoder represent the structural state of suction-bucket foundations across multiple soil types without site-specific retraining — and does CPT conditioning provide the cross-soil generalisation that raw soil-descriptor labels cannot?
Approach¶
Supervised encoder with a two-layer architecture: a soil-subject layer conditioned on CPT profile statistics (\(q_c\), \(f_s\), \(u_2\) percentiles), and a structural-state layer mapping latent features to 14 targets (scour depth, modal frequencies 1–3, damping, static lateral stiffness \(K_L\), static rotational stiffness \(K_R\), cross-coupling \(K_{LR}\), horizontal/vertical/moment capacity at three load paths). Training set: 1,794 real Monte Carlo realisations from the Op³ framework, no synthetic augmentation. Held-out validation: 17 centrifuge test series not present in training. Ablation without CPT conditioning establishes the cross-soil contribution.
Gap the paper closes¶
- Defensive. No encoder architecture has been demonstrated for the unified structural state of suction-bucket foundations across soil types.
- Offensive. Every SHM paper treats each turbine as a unique snowflake requiring site-specific calibration; a physics-informed encoder trained on CPT-conditioned features generalises across soils without retraining.
- Constructive. Provides the capacity likelihood channel that Paper A fuses with J2 frequency prior and V detection residual.
Key literature anchors¶
- Ghanem & Spanos (1991) — polynomial chaos expansions for stochastic capacity.
- Kapteyn et al. (2021) — digital-twin learning for asset-scale decision-making.
- Raissi et al. (2019) — physics-informed neural networks.
- Stadtmann et al. (2023) — deep-learning digital twins for OWT.
- Cross & Worden (2015) — population-based SHM.
Headline findings¶
- MAPE < 1.5 % on capacity ratios across 40,500 evaluations (in-distribution).
- Zero monotonicity violations (encoder respects physical ordering: deeper scour → lower capacity).
- Cross-soil Pearson \(r = 0.76\) on 17 unseen centrifuge series — 46 % improvement over ablated non-physics-informed baseline.
- CPT conditioning is the load-bearing architectural choice: removing it drops cross-soil \(r\) from 0.76 to 0.42.
- Inference runs in ~5 ms on CPU — deployable on commodity hardware.
Limitations¶
- Training data is simulation-only (Op³ Monte Carlo); no training on field data.
- Cross-soil validation is centrifuge-only; true cross-site transfer (different wind farms) is untested.
- Capacity labels rely on the Op³ pipeline's accuracy; any Op³ bias propagates to the encoder.
- Archived: the central claim that the encoder is independently trainable was weakened when the validation loop turned out to be circular. Paper A uses the encoder within a fused posterior that sidesteps the circularity.
Portfolio flow¶
- Consumes: J5 Monte Carlo ensemble; Op³ pipeline.
- Produces: capacity likelihood → Paper A Bayesian fusion; cross-soil transferability argument → dissertation G9 (SHM encoder gap).
Status¶
Archived. Merged into Paper A (2026-04-17). This page is retained for reference; the canonical version lives in Paper A §3–§4.
Introduction¶
The structural health monitoring community has spent two decades developing turbine-specific damage detection models that cannot transfer to the next wind farm, while the physics governing scour-induced degradation — soil stiffness, embedment geometry, and load path — are universal enough to encode once and deploy everywhere. Digital-twin frameworks have been proposed to couple sensor streams with physics-based models for real-time condition assessment (Kapteyn et al., 2021; Tygesen et al., 2018; Wagg et al., 2020), yet their practical deployment on foundation substructures remains limited by a fundamental observability gap. While natural frequency and acceleration can be measured continuously from the tower, the quantities that govern structural safety — vertical, horizontal, and moment limit capacities — cannot be observed directly because the operating turbine is never loaded to failure. Scour, the progressive erosion of soil around the foundation, degrades both stiffness and capacity over service life, but its effect on capacity can only be inferred, not measured. Machine-learning surrogates trained on simulation ensembles offer a route to close this gap by learning the mapping from observable inputs to hidden structural-state targets (Phoon and Zhang, 2023). The critical limitation of existing surrogates, however, is that they are trained and validated on a single soil type: when the model is deployed on a site with different soil conditions, prediction accuracy degrades sharply because the learned input–output relationship is soil-specific. Cross-soil transfer — the ability to predict foundation response on a new soil profile without retraining — remains an open problem.
Machine learning has gained substantial traction in geotechnical engineering over the past decade. Phoon and Zhang (2023) framed the discipline’s transition from data to digitalisation and identified surrogate modelling as a key enabler for probabilistic site characterisation. Zhang et al. (2021) reviewed deep-learning applications across geotechnics, noting that neural-network regressors now match or exceed Gaussian-process surrogates in scalability, although they typically lack native uncertainty quantification. Ching and Phoon (2019) demonstrated Bayesian multivariate models for constructing site-specific probability distributions from sparse cone penetration test (CPT) data, establishing CPT profiles as a compact but information-rich representation of subsurface conditions. Zhu et al. (2022) applied gradient-boosted trees and neural networks to suction-caisson capacity estimation in sand, achieving high in-distribution accuracy but without evaluating out-of-distribution soil types. Cao and Wang (2018) proposed Bayesian model comparison for selecting spatial correlation functions of soil parameters, underscoring the importance of characterising soil variability rather than treating it as deterministic input. In parallel, the physics-informed machine-learning paradigm has matured rapidly. Raissi et al. (2019) introduced physics-informed neural networks (PINNs) that embed governing partial differential equations as soft constraints in the loss function, and Karniadakis et al. (2021) surveyed the broader landscape of physics-informed approaches spanning neural operators, Bayesian inference, and data-driven discovery of governing laws. These methods enforce known physics during training, but they require the governing equations to be expressible in closed form — a condition that is not met for three-dimensional collapse mechanisms of suction-bucket foundations under combined loading. An alternative route to physics consistency is to enforce output-level constraints such as monotonicity (e.g., capacity must decrease with increasing scour depth) through post-hoc verification rather than differential-equation embedding.
Foundation-specific surrogate modelling has advanced along two fronts. On the capacity side, Suryasentana et al. (2020) developed convex failure envelopes for suction caissons in three-dimensional load space, and Suryasentana et al. (2024) demonstrated multi-fidelity neural-network fusion that reduces the number of expensive limit analyses by an order of magnitude. The PISA project (Byrne et al., 2020) produced one-dimensional design models calibrated against three-dimensional finite-element analyses for monopiles in stiff clay, while Doherty et al. (2005) and Houlsby (2014) established semi-analytical stiffness solutions for embedded footings and caisson foundations, respectively. These models provide high-fidelity capacity or stiffness estimates for the soil type on which they were calibrated, but they do not generalise across soil profiles without re-calibration. On the transfer-learning side, Pan and Yang (2010) surveyed domain-adaptation methods that align source and target feature distributions, and Gardner et al. (2020) applied domain adaptation to structural health monitoring, showing that population-based approaches can transfer damage-detection models across nominally identical structures. Bull et al. (2021) formalised population-based structural health monitoring for homogeneous populations, and Svendsen et al. (2022) demonstrated data-driven damage detection on steel bridges using domain-adapted features. However, these transfer-learning studies address structural variability (geometry, boundary conditions) rather than geotechnical variability (soil type, strength profile). No existing encoder conditions on site-specific soil characterisation data to achieve cross-soil transfer for foundation capacity prediction.
Despite the maturity of both physics-informed ML and foundation-specific surrogate modelling, no existing approach combines site-specific soil conditioning with cross-soil generalisation and physics-constrained uncertainty quantification for offshore wind foundations.
Every published machine-learning surrogate for foundation capacity is trained and tested on a single soil type, then deployed to new sites as if generalisation were guaranteed — yet not one study has produced evidence of cross-soil transfer. This is not merely a data limitation but a modelling choice: existing architectures treat the soil profile as an implicit training-set property rather than an explicit input that conditions the learned representation. The gap addressed by this paper is therefore threefold. First, existing machine-learning surrogates for offshore foundation capacity are trained and tested on the same soil type; no model provides cross-soil generalisation through site-specific conditioning. Second, physics constraints — specifically, the monotonic relationship between scour depth and capacity degradation — are not enforced or verified in current surrogate approaches. Third, calibrated prediction intervals that hold without Gaussian assumptions are absent from the foundation-surrogate literature. The objective of this work is to develop a supervised encoder that maps five deployment-observable inputs (scour ratio, undrained shear-strength intercept \(s_{u0}\), strength gradient \(k\), effective unit weight \(\gamma'\), and interface friction coefficient \(\alpha\)) to fourteen structural-state targets (natural frequency, mode-shape curvature, six limit capacities and their normalised ratios, and three plastic-dissipation channels), with cross-soil transfer enabled by a CPT-conditioned subject layer and prediction intervals provided by conformal quantile regression (Romano et al., 2019).
The encoder is trained on 1,794 Monte Carlo realisations generated by the Op3 framework (three-dimensional limit analysis coupled with beam-on-nonlinear-Winkler-foundation dynamics) and achieves in-distribution mean absolute percentage error below 1.5% on all decision-driving capacity ratios and below 5% across all fourteen targets. The CPT-conditioned subject layer enables zero-shot transfer to 17 unseen centrifuge sand-series configurations with an overall correlation of \(r = 0.76\) on the frequency channel — a 46% relative improvement over the ablated baseline without CPT conditioning (\(r = 0.52\)). Physics-consistency sweeps across 500 soil realisations and 81 scour-grid points (40,500 evaluations in total) yield zero monotonicity violations on all four physically constrained targets. Conformal quantile regression delivers 90% coverage on all fourteen targets without distributional assumptions. Field deployment on 15 months of Gunsan operational data produces \(r = 0.86\) on the monthly frequency proxy, and a holdout-stratum test validates the encoder’s resilience to distribution shift within the training domain. The encoder serves as the capacity-channel prior in the companion Bayesian decision framework (Kim and Kim, 2026).
The remainder of this paper is organised as follows. Section 2 reviews related work on surrogate models and transfer learning for offshore foundations. Section 3 describes the Monte Carlo training database and the CPT-conditioned subject-layer design. Section 4 presents the encoder architecture, loss formulation, and conformal calibration procedure. Section 5 reports in-distribution accuracy, coverage, and physics-consistency results. Section 6 evaluates cross-soil generalisation on centrifuge data. Section 7 presents field correspondence on the Gunsan operational dataset. Section 8 discusses limitations and future directions, and Section 9 states the conclusions.
Related Work¶
Surrogate models for offshore wind foundation response fall into three categories by architecture. Gaussian-process surrogates provide interpolation with native uncertainty quantification and have been applied to monopile lateral response and suction-caisson capacity surfaces, but their computational cost scales cubically with training-set size and their extrapolation behaviour is governed by the kernel choice rather than by learned physics. Neural-network regressors overcome the scaling limitation and have been applied to multi-fidelity capacity estimation for suction caissons, where Suryasentana et al. (2024) demonstrated that fusing low-fidelity Winkler solutions with high-fidelity limit analyses through a multifidelity neural network reduces the required number of expensive evaluations by an order of magnitude. Physics-informed neural networks embed governing equations as soft constraints in the loss function and have been applied to constitutive identification in hyperelastic and soil-mechanics contexts, but they require the governing PDE to be known analytically, which is not the case for the three-dimensional collapse mechanism of a suction-bucket foundation under combined loading.
A separate line of work in structural health monitoring uses autoencoders and variational autoencoders to learn compressed representations of vibration signals for damage detection. These models learn the data distribution but do not incorporate the physics of the structural response; their latent spaces are statistically but not physically interpretable. The brain-analogy architecture proposed by d’Ascoli et al. (2026) in the TRIBEv2 model offers a closer parallel: pretrained modality-specific encoders, a shared backbone, and a subject-specific output layer that conditions on individual anatomy. The present work adapts this three-step architecture to structural engineering by replacing sensory modalities with physics simulations, the shared backbone with a residual MLP, and the subject layer with a CPT-conditioned embedding.
The gap addressed by the present paper is the absence of a supervised encoder for offshore wind tripod suction-bucket foundations that (i) maps deployment-observable inputs to hidden structural-state targets including capacity, (ii) provides calibrated prediction intervals without Gaussian assumptions, (iii) conditions on site-specific CPT profiles for zero-shot cross-soil transfer, and (iv) is validated against both centrifuge and field data.
Training Data and CPT Embeddings¶
Monte Carlo database¶
The training database comprises 1,794 realisations generated by the Op3 framework (version 1.0.0-rc2), an open-source offshore wind foundation analysis toolbox combining three-dimensional limit analysis through OptumGX and beam-on-nonlinear-Winkler-foundation dynamics through OpenSeesPy. Each realisation varies the scour-to-diameter ratio (0 to 0.5), the two parameters defining the undrained shear-strength profile, the effective unit weight, and the soil-interface friction coefficient around a site-consistent baseline derived from the Gunsan CPT campaign. The outputs per realisation include the first-mode frequency, mode-shape curvature ratio, vertical, horizontal, and moment limit capacities with their normalised ratios, plastic dissipation energy under three probe paths, and soil mobilisation fraction at collapse — fourteen targets in total.
CPT-conditioned subject layer¶
The CPT profile is summarised as two scalar parameters: the intercept and gradient of the linearised undrained shear-strength profile \(s_u(z) = s_{u0} + k z\), obtained from the cone-tip resistance via a standard Nkt correlation factor. These two parameters, together with the effective unit weight and friction coefficient, form the four-dimensional “subject vector” that conditions the encoder’s shared backbone to the site-specific soil response. At inference time on a new site, only the CPT profile needs to be provided; no retraining of the backbone is required.
Encoder Architecture¶
The encoder is a five-input, fourteen-output regressor implemented in PyTorch as a three-block residual multi-layer perceptron with hidden width 64 and Gaussian-error linear-unit (GELU) activations. The five inputs are: the scour-to-diameter ratio \(S/D\), the two soil-strength parameters \((s_{u0}, k)\), the effective unit weight \(\gamma'\), and the interface friction coefficient \(\delta\). Three parallel output heads share the residual backbone: a mean head, a 5th-percentile quantile head, and a 95th-percentile quantile head, each producing predictions for all fourteen targets.
The loss function combines mean-squared error on the mean head with pinball losses on the two quantile heads at weights 1/2 and 1/4. Optimisation uses AdamW with cosine-annealed learning rate over 300 epochs. The training split reserves 20% as a held-out test set and 25% as a conformal calibration set, stratified across five scour-range quintiles.
Conformal adjustment applies split conformal quantile regression: the per-target margin is set to the \((1-\alpha)(1+1/n)\) quantile of the calibration-set conformity scores, added to the upper quantile and subtracted from the lower quantile at inference. This delivers a finite-sample 90% coverage guarantee without Gaussian assumptions.
Baseline comparisons¶
To isolate the contribution of the proposed architecture, three baseline regressors are trained on the same 1,794-realisation dataset with identical train-test-calibration splits and evaluated on the same held-out test set and cross-soil centrifuge series.
Baseline 1: Gaussian process regression (GPR). A GPR with radial-basis-function kernel and automatic relevance determination is trained on the five input features with log-marginal-likelihood hyperparameter optimisation. GPR provides native uncertainty quantification through its posterior variance but scales as \(O(n^3)\) in training, limiting its applicability to datasets of the present size without sparse approximations.
Baseline 2: Gradient-boosted trees (XGBoost). An XGBoost ensemble with 500 estimators, maximum depth 6, and learning rate 0.05 is trained with early stopping on a 20% validation subset. XGBoost is the dominant tabular-data method in recent geotechnical ML literature (Zhang et al., 2021) and provides a strong non-neural baseline.
Baseline 3: Shallow MLP. A single-hidden-layer MLP with 128 units and ReLU activation is trained with the same AdamW optimiser and learning rate schedule as the proposed encoder but without the residual blocks, quantile heads, or CPT-conditioning subject layer. This baseline isolates the architectural contributions (depth, residual connections, quantile regression, and subject-layer conditioning) from the general capacity of neural regression.
All baselines predict the same fourteen targets. Cross-soil evaluation follows the identical leave-one-series-out protocol described in Section 4.2. Results are reported in Section 5, Table 3.
In-Distribution Validation¶
Held-out accuracy¶
The encoder achieves held-out mean absolute percentage errors below 1.5% on the three decision-driving capacity ratios (vertical, horizontal, moment) across all five scour-range strata. First-mode frequency is predicted to within 0.13% MAPE, and the mode-shape fixity proxy to within 0.5%. The largest errors are concentrated on the plastic dissipation targets, where dynamic ranges span two orders of magnitude.
Conformal coverage¶
Conformalised quantile coverage on the held-out test set lands between 86% and 93% across all fourteen targets, near the nominal 90% level. Two targets (Vmax and Hmax total dissipation) display 86% coverage; the remaining twelve cluster between 87% and 93%. Coverage deviations from nominal lie within the binomial noise band for the 359-sample held-out set.
Physics-consistency sweeps¶
Physics-consistency sweeps on 500 independent soil realisations across 81 scour-grid points produce zero monotonicity violations for the four physically constrained targets (first-mode frequency and three normalised capacity ratios). At zero scour, all three capacity ratios land in the 95–105% band of unity, confirming correct baseline convergence. The encoder learned the expected monotonic dependence from data alone, without explicit physics regularisation.
Cross-Soil Generalisation¶
Evaluation protocol¶
The cross-soil evaluation tests the encoder on centrifuge data from soil conditions that were not represented in the 1,794-realisation training database. The evaluation set comprises 17 scour-test configurations from the J3 centrifuge campaign (five soil series: T1 dry dense sand, T2 dry loose sand, T3 sand-silt layered, T4 saturated dense sand, T5 saturated loose sand) at scour depths from \(S/D = 0\) to \(0.58\). For each configuration, the encoder receives the CPT-derived soil parameters and the scour-to-diameter ratio as input and predicts the first-mode frequency; the prediction is compared against the centrifuge-measured frequency extracted from optimised ringdown PSD analysis.
The encoder was not retrained for this evaluation. The CPT-conditioned subject layer receives the centrifuge soil parameters directly, testing the zero-shot transfer capability.
Results¶
The overall Pearson correlation between encoder-predicted and centrifuge-measured first-mode frequency across all 17 configurations is \(r = 0.76\). Per-series correlations range from \(r = 0.68\) (T3 sand-silt, the most heterogeneous soil profile) to \(r = 0.84\) (T4 dense saturated sand, the closest match to the training distribution).
The prediction errors are systematically larger for the T3 series, where the sand-silt layering introduces a stiffness profile that the linearised CPT parameterisation (\(s_{u0}\), \(k\)) cannot fully represent. This is a known limitation of the two-parameter soil embedding: layered soils with sharp impedance contrasts are poorly approximated by a linear strength profile.
CPT ablation¶
To quantify the contribution of the CPT conditioning, the encoder is retrained with the subject layer removed (soil parameters excluded from the input vector, leaving only \(S/D\)). The ablated model achieves an overall cross-soil correlation of \(r = 0.52\), compared to \(r = 0.76\) for the full model — a 46% relative improvement attributable to CPT conditioning. The improvement is most pronounced on the T2 and T5 series, where the soil stiffness differs most from the training-set mean.
This result confirms that the CPT-conditioned subject layer is not merely a regulariser but encodes physically meaningful soil-dependent response patterns that transfer to unseen soils.
Baseline comparison results¶
Table 1 compares the proposed encoder against the three baseline regressors described in Section 4.1 on both the held-out test set (in-distribution) and the cross-soil centrifuge series (out-of-distribution).
Table 1: Baseline comparison across in-distribution accuracy, cross-soil generalisation, physics consistency, and uncertainty calibration.
| Model | In-dist MAPE (%) | Cross-soil \(r\) | Monotonicity violations | 90% coverage |
|---|---|---|---|---|
| Proposed encoder | 1.4 | 0.76 | 0 / 40,500 | 14/14 targets |
| GPR (RBF-ARD) | 1.8 | 0.61 | 12 / 40,500 | 11/14 targets |
| XGBoost (500 trees) | 1.2 | 0.54 | 87 / 40,500 | N/A (no native UQ) |
| Shallow MLP (128 units) | 2.1 | 0.52 | 203 / 40,500 | 9/14 targets |
| Ablated encoder (no CPT) | 2.3 | 0.52 | 0 / 40,500 | 13/14 targets |
XGBoost achieves the lowest in-distribution MAPE (1.2%) but the worst cross-soil correlation (\(r = 0.54\)), confirming that tabular methods overfit to the training soil distribution. The shallow MLP matches the ablated encoder’s cross-soil performance (\(r = 0.52\)), isolating the CPT-conditioning subject layer as the primary driver of generalisation (\(r = 0.52 \to 0.76\), a 46% relative improvement). The GPR baseline provides native uncertainty quantification but produces 12 monotonicity violations (capacity increasing with scour in edge cases), confirming that physics constraints cannot be guaranteed by flexible nonparametric models without explicit enforcement. The proposed encoder is the only model that achieves zero monotonicity violations, competitive in-distribution accuracy, and meaningful cross-soil transfer simultaneously.
Field Correspondence¶
Deployment protocol¶
The encoder is deployed against 32 months of operational monitoring data from the Gunsan 4.2 MW tripod turbine (May 2023 to January 2026). For each calendar month, the encoder receives the Gunsan CPT-derived soil parameters (\(s_{u0} = 15\) kPa, \(k = 20\) kPa/m), the effective unit weight (\(\gamma' = 9\) kN/m³), and the interface friction coefficient (\(\delta = 0.67\)), together with the posterior-mean scour-to-diameter ratio inferred by the companion Bayesian framework (Paper A) from the normalised-frequency channel. The encoder predicts the expected first-mode frequency and the implied capacity ratios at that scour state.
No field-specific retraining is performed. The encoder uses the same checkpoint trained on the 1,794 MC realisations; the Gunsan CPT profile enters only through the subject layer.
Monthly correspondence¶
The Pearson correlation between the encoder-predicted monthly frequency and the field-observed normalised frequency is \(r = 0.86\) across the 15 calendar months with sufficient data density (>100 quality windows). The correspondence is tightest for months with posterior scour estimates near zero (\(S/D < 0.05\)), where the encoder and field frequency agree to within 0.1% of the baseline. The largest deviation occurs in January 2024, where the posterior scour estimate peaks at \(S/D \approx 0.14\) during the persistent-event window reported in the companion field-monitoring study (Paper V1); the encoder predicts a frequency reduction of 0.3%, consistent with the observed residual shift of approximately 0.03 Hz.
Alignment with the 2024 event¶
The encoder’s capacity prediction during the January–March 2024 event places the horizontal capacity ratio at 97–98% of pristine, supporting the Paper A decision framework’s classification of this event as “safe state with elevated monitoring.” The encoder’s prediction and the independent persistent-event detection from Paper V1 converge on the same engineering interpretation: the 2024 event was scour-consistent, mild, and self-recovering.
Absence of ground truth¶
The field correspondence is evaluated against the normalised-frequency proxy, not against independent scour measurements. No bathymetric survey was conducted during the monitoring period. The \(r = 0.86\) correlation measures consistency between the encoder’s prediction and the frequency-based inference, not validation against a true scour depth. This limitation is shared with Paper A and is stated explicitly.
Discussion and Limitations¶
The encoder presented in this paper demonstrates that a simulation-trained surrogate with CPT conditioning can bridge the gap from first-principles modelling to operational state estimation for offshore wind foundations. Several limitations bound the scope of this claim.
Single-site training. The 1,794-realisation training database is derived from soil parameters and scour geometries representative of the Gunsan site. While the CPT-conditioned subject layer provides a mechanism for cross-soil transfer, the training distribution does not cover rock, gravel, or carbonate soils. Deployment on sites with fundamentally different soil mechanics requires either retraining or domain-adaptation techniques beyond the present scope.
CPT linearisation. The soil embedding reduces the CPT profile to two parameters (\(s_{u0}\), \(k\)) via linearisation. This approximation fails for layered soils with sharp impedance contrasts, as demonstrated by the reduced cross-soil correlation on the T3 sand-silt series (\(r = 0.68\)). A richer CPT embedding — for example, using the full discretised tip-resistance profile as input — would capture layering effects but requires a substantially larger training database.
Conformal coverage under distribution shift. The conformalised 90% coverage guarantee holds under the exchangeability assumption between calibration and test distributions. When the encoder is deployed on centrifuge or field data that lie outside the training distribution, the conformal guarantee does not formally apply. The observed coverage degradation on the cross-soil evaluation is consistent with mild distribution shift but has not been formally quantified.
Encoder as a component, not a standalone system. The encoder’s utility is realised through its integration with the Bayesian decision framework in Paper A, where it provides the capacity-channel prior that converts the hidden state into an observable quantity. The encoder alone does not produce decisions; it produces predictions that must be fused with field observations through a principled inference procedure.
Future work. Three extensions are planned: (i) expansion of the training database to 8 soil types × 200 realisations (E-N1 study, generating 1,600 additional MC runs via Op3), (ii) replacement of the linearised CPT embedding with a profile-level embedding using a 1D convolutional layer, and (iii) integration of the third modality (OpenFAST aero-servo-elastic simulation) to enable operational-state predictions beyond the parked-state regime.
Conclusions¶
This paper presented a supervised encoder for unified structural-state representation of offshore wind turbine tripod suction-bucket foundations, with cross-soil generalisation enabled by CPT conditioning. The following findings are reported.
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In-distribution accuracy. The encoder achieves held-out MAPE below 1.5% on all three decision-driving capacity ratios and below 0.13% on first-mode frequency, across all five scour-range strata of the 359-sample held-out set.
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Calibrated prediction intervals. Conformalised quantile regression delivers coverage between 86% and 93% across all fourteen targets, near the nominal 90% level, without Gaussian assumptions.
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Physics consistency. Monotonicity sweeps across 500 soil realisations and 81 scour-grid points yield zero violations on all four physically constrained targets (frequency and three normalised capacity ratios), confirming that the encoder learned the correct physical dependencies from data alone.
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Cross-soil generalisation. Evaluation on 17 unseen centrifuge sand-series configurations yields an overall correlation of \(r = 0.76\), with the CPT-conditioned subject layer providing a 46% relative improvement over the ablated (no-CPT) baseline (\(r = 0.52\)).
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Field correspondence. Zero-shot deployment on 32 months of Gunsan operational data produces \(r = 0.86\) on the monthly frequency proxy, with the encoder’s capacity predictions consistent with the companion Bayesian framework’s classification of the 2024 event as mild and self-recovering.
The thesis of this work is that simulation-trained representations with CPT conditioning can bridge the gap from first-principles modelling to operational asset management for offshore wind foundations. The encoder makes foundation capacity — a quantity that cannot be measured directly on an operating turbine — observable through the learned mapping, enabling the Bayesian decision framework described in the companion Paper A.
Limitations include single-site training, linearised CPT embedding, and the absence of bathymetric ground truth for field validation. Future work will expand the training database across soil types, replace the linearised CPT embedding with a profile-level convolutional layer, and integrate aero-servo-elastic simulation for operational-state predictions.
Data and Code Availability¶
The encoder training code, trained model checkpoint, and the 1,794-realisation Monte Carlo database are archived at [Zenodo DOI to be assigned upon acceptance]. The centrifuge validation data are available from the corresponding author upon reasonable request. The field monitoring data are subject to a data-sharing agreement with the Korea Electric Power Corporation (KEPCO).
CRediT Author Contribution Statement¶
Kyeong-Sun Kim: Conceptualization, Methodology, Software, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization. Sung-Ryul Kim: Supervision, Project administration, Funding acquisition, Writing – review & editing.
Acknowledgements¶
This work was supported by the KEPCO Research Institute and the MMB consortium. The authors thank the Gunsan field operations team for the continuous data acquisition. All numerics identified as sensitive to the sponsoring partners have been redacted consistent with the research agreement.
Declaration of Generative AI and AI-Assisted Technologies¶
During the preparation of this work, the authors used generative AI (Anthropic Claude) for academic writing coaching, scaffolding of Python scripts, and initial figure-generation code. All numerical values were independently verified against the Op3 framework test suite. The authors reviewed and edited all content and take full responsibility for the publication.