Physics-Informed Virtual Sensing for Wind Turbine Blade Degradation Detection Using Flapwise–Edgewise Load Coupling

Abstract

Early detection of blade structural degradation is critical for wind turbine reliability, as unplanned failures contribute to approximately 25% of operational downtime. Traditional blade condition monitoring methods based on distributed vibration, strain, or acoustic emission sensing often suffer from high hardware complexity and substantial data-processing requirements. Consequently, blade load measurements at the blade root have emerged as a promising and more practical alternative for structural health monitoring. This study introduces a physics-informed virtual sensing framework that combines high-fidelity aeroelastic simulation with machine learning trained exclusively on healthy operational data for blade degradation detection. The proposed method is based on the premise that, under healthy conditions, the relationship between flapwise and edgewise bending moments remains consistent across operating conditions, whereas structural degradation disrupts this coupling and induces measurable deviations from the learned correlation. To implement this concept, OpenFAST simulations of the NREL 5MW reference turbine are conducted under multiple operating conditions with progressively introduced stiffness degradation, forming a comprehensive dataset. A Random Forest model is trained to predict edgewise bending moments from flapwise loads and structural parameters using only healthy-condition data, achieving high predictive accuracy under healthy operating conditions (R² = 0.98; MAPE = 3.67%). Fault detection is performed by analysing residuals between predicted and simulated edgewise bending moments, which increase systematically when degradation is present. The proposed framework achieved an overall classification accuracy of 88.9%, sensitivity of 88.9%, precision of 96.0%, F1-score of 0.923, and an AUC of 0.951 across all degradation levels and operating conditions, while achieving 100% detection of severe (20%) torsional stiffness degradation cases. Notably, degradation reduces absolute blade loads due to aeroelastic twist-to-feather coupling, yet introduces distinctive load asymmetry patterns that enable effective discrimination. The method demonstrates strong generalisation across the investigated wind speed conditions without retraining. By reconstructing unmeasured edgewise loads from readily available flapwise measurements, the proposed approach enables scalable structural health monitoring of existing wind turbine fleets without hardware retrofitting, offering a practical pathway toward physics-guided digital twin development.

1. Introduction

Wind turbine blades remain one of the most demanding structural components to monitor on a utility-scale wind turbine. They operate under turbulent aerodynamic loading, cyclic gravitational loading, rotor rotation, pitch activity and long-term environmental exposure. As turbine ratings and rotor diameters increase, the structural demand on the blade also increases, making early detection of degradation important for reliability, fatigue management and maintenance planning [1]. Blade-related intervention is particularly difficult offshore, where vessel access, weather windows and repair logistics can turn a local structural defect into a costly outage [2]. For this reason, blade condition monitoring is not only a diagnostic problem; it is also an availability and operating-cost problem.

Most established wind turbine condition monitoring systems have historically been built around drivetrain faults, including gearbox, bearing and generator defects, because these components are easier to instrument and often produce clearer vibration or temperature signatures [3]. Blade faults are more difficult to detect at an early stage. Traditional blade condition monitoring methods based on distributed vibration, strain, or acoustic emission sensing often suffer from high hardware complexity and substantial data-processing requirements. Consequently, blade load measurements at the blade root have emerged as a promising and more practical alternative for blade health monitoring. However, the blade is a rotating composite structure, and its measured response varies with wind speed, turbulence, yaw condition, controller action and azimuth position. These normal operating variations can mask the early effect of stiffness loss or load redistribution. This is a known limitation in practical turbine monitoring, where the difficulty is often not only the collection of data, but also the separation of genuine fault behaviour from normal operational variability [3,4]. This is usually very challenging in practice.

To provide a reliable solution for wind turbine blade health monitoring, this study proposes the use of the relationship between flapwise and edgewise bending moments as an indicator of blade structural condition. Flapwise bending moments are mainly associated with aerodynamic thrust and out-of-plane loading, while edgewise bending moments carry information related to gravity loading, rotor-plane dynamics and bending–torsion coupling. Under healthy conditions, the relationship between flapwise and edgewise bending moments is consistent across operating conditions, whereas structural degradation will disrupt this coupling. The proposed framework estimates the blade rotating-frame edgewise root bending moment from physically related structural features. The input representation is built around Blade 1’s flapwise bending moment, blade pitch, rotor rotational speed, temporal load-history features, rolling statistical descriptors and rotor azimuth encoding. The approach follows the principle of normal behaviour modelling, in which a model is trained under healthy operation and abnormal behaviour is detected later through prediction residuals. This sort of idea has been well established in wind turbine condition monitoring, where expected values of operational variables are learned from healthy data and deviations are treated as possible fault indicators [5,6].

The residual is central to the method used here. A model trained only on healthy structural behaviour should reproduce the nominal relationship between the selected input features and the target edgewise bending moment. If the blade is degraded, the aeroelastic relationship changes. The predicted edgewise moment then begins to depart from the measured response, and residual amplification becomes the health indicator. This formulation is more appropriate than direct thresholding of raw loads because blade structural degradation does not always create a simple increase or decrease in absolute load magnitude.

1.1. Torsional Stiffness Degradation as the Fault Case

In this study, torsional stiffness degradation is used as the main structural fault because it directly affects the twist response of the blade. Blade torsion changes the local aerodynamic angle of attack and modifies the coupling between flapwise, edgewise and torsional deformation. Jeong et al. highlighted the role of torsional stiffness in shaping the dynamic stability and aeroelastic behaviour of horizontal-axis wind turbine blades [7]. It is therefore not sufficient to treat torsional degradation as a simple static stiffness reduction. It changes the way the blade carries and redistributes aerodynamic loading.

The fault case in this study is introduced through controlled reductions in Blade 1’s torsional stiffness, while Blades 2 and 3 remain structurally healthy. For the simulation, structural deterioration was introduced at three levels, 5%, 10% and 20%, corresponding to mild, moderate and severe degradation. These levels are not intended to reproduce a specific field failure mechanism. They provide controlled structural perturbations so that the sensitivity of the virtual sensing model and residual-based health indicators can be tested across severity. This is important because torsional degradation can be counter-intuitive: a softened blade may twist in a way that reduces the effective aerodynamic loading in some regions, yet still creates detectable blade-wise asymmetry and residual growth.

1.2. Simulation-Driven Virtual Sensing Framework

The framework is developed using high-fidelity aero-servo-elastic simulation. OpenFAST is used because it couples aerodynamic, structural, drivetrain, control and inflow modules in a time-domain wind turbine simulation environment [8]. The NREL 5 MW reference turbine is adopted as the baseline model because it is a well-documented benchmark turbine widely used in aeroelastic, structural and control research [9]. BeamDyn is activated for the blade structural model because the present study requires a representation that can capture flexible blade behaviour and bending–torsion coupling under varying torsional stiffness [10].

For the turbulent inflow simulations, mean hub-height wind speeds of 6 m/s, 8 m/s and 12 m/s were used. The simulations include healthy cases used for model training, validation, testing and threshold estimation, as well as independent faulty cases used only for degradation evaluation. This distinction is important. The Random Forest virtual sensor is trained exclusively on healthy data, so it learns the healthy structural mapping without being exposed to the fault cases. Faulty data are then used to test whether the healthy-trained model fails to generalise when torsional stiffness degradation changes the underlying aeroelastic response.

A Random Forest regressor is selected for the virtual sensing model because it can learn nonlinear relationships, handle mixed structural and operational features, and remain robust under stochastic turbulent loading [11]. Random Forest and related tree-based methods have also been used in data-driven wind turbine fault detection studies, which supports their suitability for turbine monitoring problems with nonlinear feature interactions [12]. In this work, however, the model is used as a regression-based virtual sensor rather than as a supervised fault classifier. The fault decision is made based on residual energy and the proposed residual exceedance decision framework, not from a model trained directly on labelled fault classes.

1.3. Contribution of This Work

The main contribution of this work is the introduction of a physics-informed blade health indicator based on the aeroelastic coupling between flapwise and edgewise blade-root bending moments. Unlike conventional approaches that rely on direct measurement of multiple sensing channels or changes in absolute load magnitude, the proposed method exploits the observation that healthy blades exhibit a stable flapwise–edgewise load relationship across operating conditions, whereas structural degradation alters this coupling. Building on this principle, a virtual sensing framework is developed to predict edgewise bending moments from healthy-condition flapwise bending moment data and to detect degradation by examining residuals. The resulting approach enables reliable blade condition monitoring using limited instrumentation and offers a practical pathway for deployment on existing wind turbine fleets without hardware retrofitting.

2. Materials and Methods

2.1. Overview

The proposed framework integrates physics-based aeroelastic simulation with machine-learning-driven structural virtual sensing to detect torsional blade degradation. The methodology consists of four sequential stages: (i) high-fidelity aeroelastic simulation under healthy and degraded conditions using OpenFAST (v3.5.0, National Renewable Energy Laboratory, Golden, CO, USA), (ii) extraction and construction of structural moment-based features, (iii) healthy-only training of a regression-based virtual sensing model to predict edgewise bending moments, and (iv) evaluation of model generalisation under unseen torsional stiffness degradation.

The use of the NREL 5 MW Reference Wind Turbine, National Renewable Energy Laboratory, Golden, CO, USA reference wind turbine, together with the OpenFAST–BeamDyn aeroelastic simulation framework, also enhances the reproducibility of the proposed methodology. Both the reference turbine model and the simulation environment are widely adopted within the wind energy research community, enabling future studies to reproduce the present simulation scenarios, compare alternative virtual sensing algorithms under identical operating conditions, and evaluate new degradation-detection strategies using a common benchmark platform. Consequently, the proposed framework provides a reproducible baseline for future investigations into blade structural health monitoring and virtual sensing.

Figure 1 illustrates the overall framework adopted in this study. Healthy and degraded structural responses are generated through controlled torsional stiffness modification within the BeamDyn structural model. Structural-response features derived from blade-root bending moments and temporally enriched load representations are used to train the virtual sensing model. Fault detection is achieved through analysis of prediction residual amplification and residual exceedance statistics derived from healthy-condition baseline behaviour when the trained model is exposed to degraded conditions.

The key principle underpinning this framework is that a model trained exclusively on healthy structural behaviour will exhibit bounded prediction residuals under nominal conditions, while systematic degradation introduces deviation patterns that violate the learned healthy mapping. This enables generalisation-based detection without requiring faulty data during training.

Unlike conventional normal behaviour models (NBMs), which are predominantly applied to SCADA-derived temperature, vibration and power signals, the proposed framework migrates the NBM paradigm to aeroelastic blade load monitoring. The novelty lies in combining high-fidelity OpenFAST simulations with structural-load-based virtual sensing to reconstruct healthy blade behaviour and identify degradation through residual analysis. To the authors’ knowledge, limited studies have applied healthy-data-driven NBM principles specifically to blade-root load reconstruction for rotor condition monitoring, with most existing NBM applications concentrated on SCADA-based drivetrain, power-curve and temperature monitoring.

2.2. Aeroelastic Simulation Framework

Aeroelastic simulations were conducted using the OpenFAST framework developed by NREL [8]. The NREL 5 MW reference wind turbine [9] was adopted as the baseline configuration due to its widespread use in wind turbine structural and control research. Blade structural dynamics were represented using BeamDyn [10], which enables geometrically exact beam modelling capable of capturing torsion–bending coupling and large deflection effects. Aerodynamic loads were computed using AeroDyn [13] under blade element momentum (BEM) theory. Tower and drivetrain flexibility were incorporated through ElastoDyn to ensure full aeroelastic coupling among aerodynamic forces, structural response, and rotor rotation. Turbulent wind fields were generated using TurbSim [14] under normal turbulence intensity conditions. Three mean wind speeds were considered: 6 m/s, 8 m/s, and 12 m/s. Detailed healthy and faulty dataset generation procedures, including simulation duration, seed selection, and transient removal, are described in Section 2.2.3 and Section 2.2.4.

2.2.1. Wind Turbine Model

The turbine was modelled as a three-bladed horizontal-axis wind turbine with a hub height of 90 m and a rotor diameter of 126 m. The structural, aerodynamic, and control responses were coupled through the OpenFAST modular framework. Aerodynamic loading was computed using AeroDyn, while tower, nacelle, drivetrain, and overall turbine rigid–flexible dynamics were represented through ElastoDyn. Blade structural dynamics were represented using BeamDyn because the present study focuses on blade-root moment reconstruction and torsional stiffness degradation. BeamDyn is a high-fidelity blade structural solver based on geometrically exact beam theory and is suitable for slender, initially curved and twisted composite blades undergoing large displacement and rotation [10,15].

In this study, BeamDyn was activated for all three blades. This is an important modelling choice because torsional degradation cannot be adequately represented using only simplified blade-root global moment channels. BeamDyn allows blade structural response to be resolved in the local blade coordinate system, which is more appropriate for analysing bending–torsion coupling and blade-specific degradation effects. The general coupled structural dynamic response of the blade can be expressed in simplified matrix form as

$$M\ddot{q}+C\dot{q}+Kq=F_{aero}+F_{grav}+F_{inertial}$$

(1)

where $M\ddot{q}$, $C\dot{q}$, and $Kq$ represent the blade structural mass, damping, and stiffness matrices, respectively; $q$ is the blade deformation state vector; and $F_{aero}$, $F_{grav}$, and $F_{inertial}$ represent aerodynamic, gravitational, and inertial loading contributions. In the present fault cases, torsional degradation was introduced by modifying the torsional stiffness component of the BeamDyn blade structural representation.

Blade-root response channels were extracted from the BeamDyn/OpenFAST outputs for all three blades. The primary local rotating-frame blade-root moment channels considered were flapwise and edgewise bending moments.

Figure 2 illustrates the local BeamDyn blade-root coordinate system [16]. In this study, the local BeamDyn blade-root channels were selected instead of the global ElastoDyn channels because the BeamDyn rotating-frame blade-root channels provided valid structural-response values for all three blades. Therefore, the BeamDyn rotating-frame blade-root channels were used to obtain the structural responses required for this study. Specifically, B1RootMxr was used as the primary structural input feature, while B1RootMyr served as the target variable for virtual sensing. Additional engineered features, including rotor speed, Blade 1 pitch angle, lagged flapwise bending moments, rolling statistical features, and rotor azimuth encoding, were subsequently constructed from these measurements.

The target variable for the virtual sensing model was the Blade 1 rotating-frame edgewise root bending moment, B1RootMyr. The selection of blade-root bending moments is consistent with recent wind turbine virtual sensing studies, where blade-root loads are commonly treated as critical structural-response quantities for fatigue monitoring, load reconstruction, and digital-twin-based condition monitoring [17,18]. The use of local BeamDyn blade-root channels also provides blade-specific structural-response measurements required for the proposed residual-based degradation assessment, as the torsional stiffness reduction was applied only to Blade 1, while Blades 2 and 3 remained structurally healthy.

2.2.2. Wind Field Generation

Turbulent inflow wind fields were generated using TurbSim [14], which is a stochastic full-field wind simulator developed by NREL for aeroelastic wind turbine analysis. TurbSim generates three-dimensional turbulent wind velocity fields that are spatially coherent across the rotor plane and compatible with OpenFAST aeroelastic simulations.

In this study, turbulent wind fields were generated under normal turbulence model (NTM) conditions using the IEC 61400-1 turbulence framework. Three mean hub-height wind speeds were considered, 6 m/s, 8 m/s, and 12 m/s, representing below-rated, transitional, and near-rated operating conditions for the NREL 5 MW reference turbine. These operating regions were selected to ensure that the proposed virtual sensing framework was evaluated under varying aerodynamic loading regimes and rotor dynamic conditions.

The generated turbulent wind fields were exported as binary turbulent wind files (.bts) and coupled directly with OpenFAST through the InflowWind module. Each wind field consisted of a spatially varying turbulent velocity distribution across the rotor-swept area, enabling a realistic representation of turbulence-induced aeroelastic loading. The generated wind grids covered the complete rotor domain to ensure that all blade elements experienced temporally and spatially varying inflow conditions during rotor rotation.

To improve dataset diversity and machine learning generalisation capability, multiple stochastic turbulent seeds were generated for each wind speed condition. Different turbulent seeds produce statistically similar mean wind conditions while introducing unique turbulence realisations and transient aerodynamic fluctuations. This approach increases variability in the structural-response dataset and reduces the risk of overfitting the virtual sensing model to a limited turbulence pattern.

The turbulent inflow generation process also enabled realistic excitation of blade flapwise, edgewise, and torsional dynamics. Under turbulent operation, the aerodynamic loading acting on the rotating blades continuously varies with blade azimuth position, turbulence intensity, and local inflow velocity fluctuations. Consequently, the generated structural-response datasets contain both deterministic rotor-periodic loading behaviour and stochastic, turbulence-induced structural variations, which are essential for robust machine-learning-based structural virtual sensing.

The turbulent wind fields generated by TurbSim were internally discretised into high-resolution spatial and temporal grids prior to OpenFAST coupling. The OpenFAST solver time step was set to DT = 0.00125 s, corresponding to an internal numerical integration frequency of 800 Hz. The tabular output interval was set to DTOut = 0.00625 s, corresponding to an exported output sampling frequency of 160 Hz used for subsequent feature engineering and machine learning analysis. This output sampling rate provided sufficient temporal resolution to capture rapidly varying aeroelastic interactions and transient blade-root structural responses while maintaining computational efficiency for data processing.

2.2.3. Healthy Dataset Generation

Healthy-condition datasets were generated using the OpenFAST–BeamDyn aeroelastic simulation framework under stochastically turbulent inflow conditions. The primary objective of the healthy dataset generation stage was to construct a sufficiently large and physically representative structural-response database for healthy-condition machine learning training and baseline residual-threshold estimation.

Three mean wind speed operating conditions were considered: 6 m/s, 8 m/s, and 12 m/s. These operating regions were selected to represent the below-rated and near-rated aerodynamic operating conditions of the NREL 5 MW reference wind turbine defined by Jonkman et al. [9]. Turbulent inflow fields corresponding to each wind speed condition were generated using TurbSim [14] under normal turbulence model conditions.

To improve statistical diversity and reduce dependence on a single turbulent realisation, multiple stochastic turbulent inflow seeds were generated for each operating condition. Healthy-condition simulations were generated using the following:

• 10 turbulent seeds at 6 m/s;
• 50 turbulent seeds at 8 m/s;
• 100 turbulent seeds at 12 m/s.

The larger number of simulations at higher wind speeds was intentionally selected because aerodynamic loading variability and turbulence-induced structural-response amplitudes increase significantly with wind speed. Consequently, additional stochastic realisations were required to improve the representation of the healthy operational manifold under increased aeroelastic loading conditions and to improve the robustness of the machine learning training dataset.

Each healthy-condition simulation was executed for a total simulation duration of

$$T_{max}=600 \mathrm{s}$$

(2)

where $T_{max}$ denotes the total OpenFAST simulation time.

The extended simulation duration was selected specifically for machine learning dataset generation and statistical threshold estimation. Long-duration turbulent simulations improve the representation of stochastic structural loading behaviour and reduce sensitivity to local turbulence realisations during model training.

The initial 30 s of each simulation was discarded to eliminate startup transients associated with rotor acceleration, controller stabilisation, and initial aeroelastic settling effects. Consequently, the effective structural-response duration used for feature extraction was

$$T_{eff}=T_{max}-30$$

(3)

OpenFAST internally solves the coupled aeroelastic equations at high temporal resolution. The simulations produced approximately 162 computational structural-response samples per second of physical simulation time, corresponding to an effective computational time increment of approximately

$$\Delta t\approx {\displaystyle \frac{1}{162}} \mathrm{s}$$

(4)

This high temporal resolution enabled a detailed representation of transient turbulent inflow interactions, blade structural vibrations, and aeroelastic load fluctuations.

The approximate total number of structural-response samples extracted from each simulation can therefore be estimated as follows:

$$N_{samples}=f_s\times T_{eff}$$

(5)

where $f_s$ denotes the effective computational sampling frequency and $T_{eff}$ represents the transient-free simulation duration.

Blade-root structural-response channels were extracted directly from the BeamDyn rotating-frame outputs for all three blades. The primary healthy-condition structural-response variables considered in this study are flapwise blade-root bending moments and edgewise blade-root bending moments.

The extracted BeamDyn blade-root channels were ($\mathrm{B}1\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{M}\mathrm{x}\mathrm{r},\mathrm{B}1\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{M}\mathrm{y}\mathrm{r}$), ($\mathrm{B}2\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{M}\mathrm{x}\mathrm{r},\mathrm{B}2\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{M}\mathrm{y}\mathrm{r}$), and ($\mathrm{B}3\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{M}\mathrm{x}\mathrm{r},\mathrm{B}3\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{M}\mathrm{y}\mathrm{r}$). These blade-root moments represent physically meaningful aeroelastic structural loading quantities associated with blade flapwise deformation and edgewise rotor-plane loading, respectively. Blade-root loads are widely recognised as critical structural indicators for wind turbine fatigue analysis, load monitoring, virtual sensing, and digital-twin-based condition monitoring applications [19]. Blade-root load reconstruction has also been extensively employed in modern wind turbine structural health monitoring frameworks due to the strong coupling between aerodynamic excitation and blade structural response [20].

The healthy dataset was generated exclusively from structurally undamaged turbine conditions without any torsional stiffness degradation. Consequently, the healthy dataset represents the nominal aeroelastic operating behaviour of the turbine under stochastic turbulence excitation and forms the reference healthy operating manifold learned by the virtual sensing framework. Validation of the generated healthy dataset confirmed that different TurbSim seeds produced statistically distinct turbulent inflow fields and corresponding structural responses, ensuring that the generated datasets as per (

Table 1. Summary of OpenFAST healthy and faulty simulation datasets.

Dataset	Wind Speeds	TurbSim Seed IDs	Cases	Simulation Time	Effective Time After 30 s Removal	Purpose
Healthy	6, 8, 12 m/s	10, 50, 100	9	600 s	570 s	RFR training, validation, testing, threshold baseline
Faulty	6, 8, 12 m/s	10, 50, 100	27	200 s	170 s	Independent fault evaluation
Fault severities	5%, 10%, 20% GJ reduction	—	27	200 s	170 s	Blade 1 torsional degradation testing

), represented independent stochastic realisations rather than duplicated simulations. Figure 3 illustrates the low cross-correlation observed between representative turbulent seed cases for the inflow velocity, rotor-speed response, and blade-root structural loading signals.

2.2.4. Faulty Dataset Generation

Torsional blade degradation was simulated by introducing controlled reductions in the torsional stiffness parameter within the BeamDyn structural blade model. In composite wind turbine blades, the torsional rigidity governs resistance to twisting deformation under aerodynamic loading. Progressive degradation of composite laminate integrity, adhesive interfaces, or internal structural components can reduce the effective torsional stiffness and alter the coupled aeroelastic response of the blade [21].

The present study considered three degradation severities corresponding to 5%, 10%, and 20% reductions in blade torsional stiffness. These degradation levels were selected to represent mild, moderate, and severe structural deterioration, respectively, while maintaining stable aeroelastic simulation behaviour. Similar stiffness-reduction approaches have been widely adopted in numerical wind turbine structural health monitoring studies because they provide controlled and physically interpretable fault progression scenarios without requiring destructive experimental testing [22].

Torsional degradation was introduced only in Blade 1, while Blades 2 and 3 retained their original structural properties. This configuration enables the investigation of the structural-response changes introduced by localised torsional stiffness degradation while preserving healthy reference behaviour in the remaining blades. Under healthy operation, the three blades exhibit statistically similar structural responses after accounting for rotational phase differences. However, localised stiffness degradation alters the aeroelastic coupling behaviour of the affected blade, resulting in measurable asymmetry within the blade-root structural moment responses.

The modified torsional stiffness matrix is expressed as follows:

$$G{J}_{fault}=\left(1−\delta \right)G{J}_{healthy}$$

(6)

where $G{J}_{healthy}$ denotes the original blade’s torsional stiffness, $G{J}_{fault}$ represents the degraded stiffness, and $\delta$ is the fractional degradation level corresponding to 0.05, 0.10, or 0.20.

To verify that the imposed torsional stiffness reductions produced measurable structural asymmetry, several statistical and frequency-domain health indicators were evaluated across the healthy, 5%, 10%, and 20% fault cases. As shown in Figure 4, the RMS-based health indicator in Figure 4a demonstrates a gradual increase in vibration energy with increasing fault severity. The blade asymmetry index in Figure 4b has been used as one of several indicators to demonstrate that the simulated stiffness reductions produce physically meaningful structural changes. The proposed detection methodology, which is presented later in the paper, relies on the residual-based virtual sensing framework rather than the blade asymmetry index. Figure 4c presents the statistical kurtosis variation associated with changing load distributions under degraded stiffness conditions. The frequency-domain indicator in Figure 4d illustrates the increase in 3P harmonic energy caused by rotational imbalance and periodic structural asymmetry. The crest factor trend in Figure 4e reflects variations in transient load peaks and dynamic response characteristics. Finally, the combined health index shown in Figure 4f integrates multiple indicators into a unified degradation metric, demonstrating a clear progression from healthy to severely faulty operating conditions. Overall, the results confirm that the imposed stiffness reductions generated physically distinguishable aeroelastic responses suitable for virtual sensing and threshold-based fault classification studies.

All faulty-condition simulations were performed under turbulent inflow conditions generated using TurbSim at mean wind speeds of 6 m/s, 8 m/s, and 12 m/s, consistent with the healthy-condition simulations. Each faulty simulation was executed for 200 s. Compared with the healthy-condition datasets, shorter simulation durations were adopted because the faulty datasets were used exclusively for independent fault evaluation rather than machine learning model training. This reduced computational cost while preserving sufficient transient structural behaviour for degradation assessment.

The first 30 s of each faulty simulation was discarded to eliminate startup transients and ensure steady-state aeroelastic operation prior to structural feature extraction. Blade-root structural-response channels were subsequently extracted from the BeamDyn rotating-frame outputs for fault analysis and virtual sensing evaluation.

2.3. Data Preprocessing

The structural-response datasets generated from the OpenFAST- BeamDyn simulations were post-processed prior to machine learning training and fault evaluation analysis. The preprocessing stage was designed to ensure numerical consistency, remove transient behaviour, and construct physically meaningful input–output datasets suitable for structural virtual sensing.

For both healthy and faulty simulations, the initial 30 s of simulation data was discarded to eliminate startup transients associated with rotor acceleration, controller stabilisation, and aerodynamic initialisation effects. Only steady-state aeroelastic responses were retained for subsequent analysis. Similar transient-removal procedures are commonly adopted in wind turbine aeroelastic and condition-monitoring studies to avoid non-representative operating behaviour during feature generation [9].

The BeamDyn blade-root structural moment outputs were extracted directly from the OpenFAST output channels for all three blades. OpenFAST simulations were internally operated using a high-temporal-resolution aeroelastic solver. Approximately 162 computational time steps were generated within each second of simulation time, enabling detailed representation of transient turbulent loading behaviour and blade structural dynamics. This high-frequency sampling is beneficial for capturing short-duration aeroelastic fluctuations and transient load coupling associated with structural degradation.

Following extraction, the structural-response channels were converted into comma-separated value (CSV) datasets for machine learning processing using Python (v3.11, Python Software Foundation, Wilmington, DE, USA)-based post-processing scripts. Missing or invalid numerical entries were checked during preprocessing to ensure dataset consistency across all simulation cases. The BeamDyn rotating-frame channels provided complete and physically consistent structural-response outputs for all simulations.

The healthy-condition datasets from all wind speed cases and turbulent seeds were subsequently concatenated to form the global healthy training database used for virtual-sensing model development. The combined healthy dataset, therefore, contained structural-response variability arising from multiple turbulent inflow realisations and operating conditions, improving the robustness and generalisation capability of the machine learning model.

To improve numerical stability during machine learning training, the input structural-response variables were standardised using z-score normalisation. For each feature variable $x$, the normalised value $x_{norm}$ was computed as follows:

$$x_{norm}={\displaystyle \frac{x-{\mu }_x}{{\sigma }_x}}$$

(7)

where ${\mu }_x$ and ${\sigma }_x$ denote the mean and standard deviation of the corresponding feature computed from the healthy training dataset. Feature normalisation is widely used in wind turbine machine learning and structural health monitoring applications because it prevents variables with large numerical magnitudes from dominating the learning process and improves model convergence behaviour [23].

The target variable for the virtual sensing framework was the Blade 1 rotating-frame edgewise root-bending moment $\mathrm{B}1\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{M}\mathrm{y}\mathrm{r}$. The remaining structural-response channels and derived temporal features were subsequently used for feature engineering and machine learning model construction.

2.4. Structural Feature Engineering

The objective of the structural feature engineering stage was to construct physically meaningful input representations capable of capturing the coupled aeroelastic behaviour associated with healthy and degraded blade operation. Since the proposed virtual sensing framework relies on healthy-only learning, the selected features were required to preserve the dominant structural relationships governing blade-root loading behaviour under turbulent operating conditions.

The primary structural-response variables used for feature construction were the rotating-frame blade-root bending moments extracted from the BeamDyn solver. Particular emphasis was placed on the flapwise blade-root bending moments because flapwise loading is strongly influenced by aerodynamic thrust and rotor-induced structural dynamics, while torsional degradation alters the coupling relationship between flapwise and edgewise responses through modified aeroelastic behaviour [20].

The principal input features considered in this study were as follows:

• B1RootMxr;
• BldPitch1;
• RotSpeed;
• B1RootMxr_lag1;
• B1RootMxr_lag2;
• B1RootMxr_lag3;
• B1RootMxr_rolling_mean5;
• B1RootMxr_rolling_std5;
• Azimuth_sin;
• Azimuth_cos.

B1RootMxr denotes Blade 1’s rotating-frame flapwise blade-root bending moment, BldPitch1 is Blade 1’s pitch angle, RotSpeed is the rotor’s rotational speed, B1RootMxr_lag1–lag3 are lagged flapwise bending-moment features, B1RootMxr_rolling_mean5 and B1RootMxr_rolling_std5 are five-sample rolling statistical descriptors, and Azimuth_sin and Azimuth_cos provide cyclic encodings of the instantaneous rotor azimuth angle.

The target variable for the virtual sensing model was Blade 1’s edgewise blade-root bending moment, B1RootMyr.

The structural virtual sensing problem can therefore be represented as a nonlinear regression mapping between the flapwise structural loading behaviour and the corresponding edgewise response:

$${\widehat{M}}_{yr}^{B1}(t)={\widehat{f}}_{rf}(X\left(t\right))$$

(8)

where ${\widehat{M}}_{yr}^{B1}(t)$ represents the predicted Blade 1 edgewise blade-root moment, ${\widehat{f}}_{rf}(\cdot )$ denotes the nonlinear regression function learned by the Random Forest model, and $X(t)$ is the final engineered input feature vector defined in Equation (12).

The engineered feature set enables the regression model to learn the nonlinear relationship between Blade 1 flapwise structural loading, blade pitch, rotor rotational speed, short-term temporal load history and rotor azimuth under healthy operating conditions. Under healthy operation, these structural and operational variables exhibit a consistent relationship with the corresponding Blade 1 edgewise blade-root bending moment. Torsional stiffness degradation disrupts this learned healthy relationship, leading to increased prediction residuals that provide the basis for the proposed fault detection framework.

To improve the representation of transient aeroelastic behaviour, temporal feature enrichment was additionally performed using lagged structural-response variables. For a given structural-response signal $x(t)$, the lagged feature representation can be expressed as follows:

$$x_{lag}(t)=\left[x(t-1),x(t-2),\dots ,x(t-k)\right]$$

(9)

where $k$ denotes the number of previous temporal steps considered. Lagged structural-response features allow the regression model to incorporate short-term dynamic memory effects associated with turbulent inflow excitation and rotating structural behaviour. Similar temporal feature engineering approaches have been shown to improve machine-learning-based wind turbine load estimation and structural health monitoring performance [23].

Equation (8) defines the instantaneous mapping between the structural-response inputs and the target edgewise bending moment at time t. Equation (9) extends this formulation by incorporating lagged structural-response terms, which are concatenated into the engineered feature vector used in Equation (12). The bold-faced notation X(t) in Equation (13) therefore denotes the same complete feature vector, comprising instantaneous measurements, lagged structural-response variables, rotor-speed information and azimuth-encoding terms. Consequently, the Random Forest model predicts B1RootMyr(t) using both current and short-term historical structural information.

Rolling statistical features were also constructed to represent local transient turbulence behaviour and short-duration structural fluctuations. The moving-average structural-response feature over a rolling window of length $N_w$ was computed as follows:

$$\bar{x}(t)={\displaystyle \frac{1}{N_w}}{\sum }_{i=0}^{N_w-1}x(t-i)$$

(10)

where $\bar{x}(t)$ denotes the rolling-average structural-response feature. Rolling statistical representations improve robustness against stochastic turbulence-induced fluctuations while preserving dominant structural loading trends relevant to degradation detection.

Rotor azimuth position information was also encoded using cyclic trigonometric representations to preserve the periodic nature of rotating blade dynamics. The cyclic encoding was computed as follows:

$$\varphi (t)=\left[sin(\theta (t)),cos(\theta (t))\right]$$

(11)

where $\theta (t)$ denotes the instantaneous rotor azimuth angle. Cyclic encoding avoids discontinuities associated with angular wraparound and improves the representation of periodic rotor behaviour within the machine learning framework [24].

The final structural feature vector used for machine learning training can therefore be represented as follows:

$$X(t)=\left[{\widehat{M}}_{xr}^{B1}\left(t\right),\beta \left(t\right),\Omega \left(t\right),{\widehat{M}}_{xr}^{B1}\left(t-1\right),{\widehat{M}}_{xr}^{B1}\left(t-2\right),{\widehat{M}}_{xr}^{B1}\left(t-3\right),{\widehat{M}}_{xr}^{B1,\left(5\right)}\left(t\right),{\sigma }_{Mxr}^{B1.\left(5\right)}\left(t\right),sin(\theta (t)),cos(\theta \left(t\right))\right]$$

(12)

where $X(t)$ represents the temporally enriched structural-response input vector used for Random Forest training. For clarity and reproducibility, the final Random Forest model was trained using ten engineered features: B1RootMxr, RotSpeed, BldPitch1, B1RootMxr_lag1, B1RootMxr_lag2, B1RootMxr_lag3, B1RootMxr_rolling_mean (5-sample window), B1RootMxr_rolling_std (5-sample window), sin(θ), and cos(θ). These same features were subsequently used for healthy-condition prediction, feature-importance analysis, and fault detection evaluation.

From an implementation perspective, the selected features are routinely available or can be estimated in modern utility-scale wind turbines. Rotor speed, blade pitch angle, and azimuth position are standard measurements available through the turbine controller and SCADA system. Blade-root bending moments can be obtained through strain-gauge instrumentation, load-estimation algorithms or virtual sensing frameworks that are increasingly adopted within digital-twin architectures. The lagged and rolling statistical features do not require additional sensors, as they are derived directly from previously measured structural-load signals. Consequently, the proposed feature set remains compatible with practical wind turbine condition-monitoring deployments. The final engineered structural features used for the virtual sensing framework are summarised in

Table 2. Engineered structural-response features used for Random Forest virtual sensing.

Feature	Category	Physical Interpretation
RotSpeed	Rotor kinematics	Inertia-driven edgewise loading component
BldPitch1	Aerodynamic ctrl	Blade pitch angle aerodynamic load control
B1RootMxr	Structural load	Blade 1 flapwise blade-root bending response
B1RootMxr_lag1	Temporal feature	One-step historical flapwise load memory
B1RootMxr_lag2	Temporal feature	Two-step historical flapwise load memory
B1RootMxr_lag3	Temporal feature	Three-step historical flapwise load memory
Azimuth_$sin\left(\theta \right)$	Cyclic feature	Rotor azimuth periodicity encoding(sin)
Azimuth_$\mathrm{c}\mathrm{o}\mathrm{s}(\theta )$	Cyclic feature	Rotor azimuth periodicity encoding(cos)
B1RootMxr_rolling_mean5	Rolling statistical feature	5-sample rolling mean-local trend
B1RootMxr_rolling_std5	Rolling statistical feature	5-sample rolling std-local trend

. The selected features combine instantaneous blade-root loading information, temporal memory representations, and rotor-periodic behaviour descriptors to improve the prediction of the blade-root edgewise bending response under turbulent aeroelastic operating conditions.

The Random Forest regression model estimates the target edgewise blade-root moment by averaging predictions across multiple decision trees:

$$\widehat{y}(t)={\displaystyle \frac{1}{N_T}}{\sum }_{i=1}^{N_T}{T}_i\left(X(t)\right)$$

(13)

where $N_T$ denotes the total number of trees within the forest and $T_i(X(t))$ represents the prediction of the $i^{th}$ decision tree for the corresponding structural-response feature vector.

It should be noted that the feature vector X(t) used in Equation (13) corresponds to the engineered feature set defined in Equations (8)–(12). While several features are measured at the current time step t, additional lagged variables (e.g., B1RootMxr(t−1) and B1RootMxr(t−2)) are included to capture short-term temporal dependencies in blade loading dynamics. Therefore, the model output B1RootMyr(t) is predicted using both instantaneous and historical information contained within the feature vector. Equation (13) provides a compact representation of the complete feature set described previously.

Following feature construction, all engineered structural features were standardised using healthy-condition statistics prior to machine learning training, as described in Section 2.3. Figure 5 illustrates the structural feature engineering workflow adopted in this study, including extraction of BeamDyn blade-root responses, temporal enrichment, statistical feature generation, and assembly of the final regression input matrix.

The final feature-engineering strategy was intentionally restricted to physically interpretable structural-response variables rather than large collections of operational SCADA parameters. This improves the interpretability of the virtual sensing framework and ensures that degradation detection remains directly linked to blade structural behaviour and aeroelastic coupling mechanisms.

2.5. Virtual Sensing Model

This section presents the development of the machine-learning-based virtual sensing framework used to estimate the blade-root edgewise bending moment $\left(B1RootMyr\right)$ from measurable structural-response parameters generated under healthy operating conditions. A Random Forest regressor (RFR) was selected due to its strong nonlinear regression capability, robustness against overfitting, and suitability for high-dimensional aeroelastic datasets with coupled structural dynamics [11]. Unlike conventional analytical estimation approaches, the proposed framework learns the nonlinear mapping between turbine structural responses and the target blade load directly from OpenFAST-generated simulation data.

The model was trained using the preprocessed healthy-condition datasets described in Section 2.2.3. The faulty datasets described in Section 2.2.4 were excluded from model training and used only for independent degradation evaluation. This healthy-only training strategy was intentionally adopted so that deviations between predicted and measured structural responses under faulty operating conditions could later be used for fault-sensitive residual generation [6,25]. Such an approach is consistent with modern data-driven structural health monitoring methodologies, where baseline healthy behaviour is first learned before anomaly sensitive residual analysis is performed [6,25,26,27].

The final input space consisted of ten engineered features comprising the Blade 1 flapwise bending moment, blade pitch angle, rotor rotational speed, temporal lag features, rolling statistical descriptors, and cyclic rotor azimuth representations. These features enable the Random Forest model to capture the nonlinear relationship between structural loading history and the corresponding edgewise blade-root response under healthy operating conditions.

The combined healthy dataset contained 864,009 samples obtained from nine OpenFAST simulations. The dataset was randomly partitioned into training (60%), validation (20%) and testing (20%) subsets, resulting in 518,405 training samples, 172,802 validation samples and 172,802 testing samples.

The partitioning was performed randomly while preserving representation from all wind speed conditions and turbulent-seed realisations within each subset. The complete training configuration, optimisation strategy, and computational settings adopted for the Random Forest virtual sensing framework are summarised in

Table 3. Random Forest virtual sensing model configuration.

Parameter	Final Configuration
Model Specification
Algorithm	Random Forest Regressor (scikit-learn v1.4.0 (INRIA, Paris, France))
Prediction target	B1RootMyr (edgewise blade-root moment, N·m)
Number of input features	10 (see Table 2)
Training data	Healthy-condition simulations only
Wind speed conditions	6 m/s, 8 m/s, 12 m/s
Data Partitioning
Split strategy	Stratified random split by wind speed
Train/validation/test	60%/20%/20%
Stratification variable	Wind speed bin (balanced coverage across regimes)
Hyperparameter Optimisation
Search algorithm	RandomizedSearchCV
Cross-validation	3-fold
Candidate evaluations	25
Scoring criterion	R2 (coefficient of determination)
Optimised Hyperparameters
n_estimators	500
max_depth	None (fully grown trees, no pruning)
min_samples_split	2
min_samples_leaf	1
max_features	0.4
Bootstrap	True (sampling with replacement)
oob_score	Enabled (out-of-bag generalisation estimate)
Reproducibility and Performance
Random seed	42
Feature importance method	Mean Decrease in Impurity (MDI) and permutation importance
Training time (CPU)	45.3 min
Inference speed	<1 ms per sample (real-time capable)

Note: Training was performed on concatenated healthy simulation data from all wind speed bins and TurbSim seeds. Faulty data were withheld entirely during training and used only for independent evaluation.

.

2.5.1. Random Forest Regressor

The Random Forest regressor is an ensemble-learning algorithm based on the aggregation of multiple decision trees trained using bootstrap sampling and random feature selection [11]. The final prediction is obtained by averaging the outputs of all individual regression trees, thereby improving generalisation capability and reducing model variance [11]. Random Forest methods have been widely adopted in structural health monitoring and wind turbine condition monitoring applications due to their robustness under noisy operational environments and nonlinear structural-response behaviour [6,25,26].

For a dataset containing $N_t$ decision trees, the predicted blade-root edgewise moment $\widehat{y}$ can be expressed as follows:

$$\widehat{y}(x)={\displaystyle \frac{1}{N_t}}{\sum }_{i=1}^{N_t}{T}_i(x)$$

(14)

where

• $T_i(x)$ represents the prediction from the $i^{th}$ regression tree;
• $N_t$ denotes the total number of trees in the ensemble;
• $x$ represents the engineered structural feature vector.

The structural feature vector used in the present study is defined as follows:

$$x=M_{xr}\left(t\right),\beta \left(t\right),\Omega \left(t\right),M_{xr}^{t-1},M_{xr}^{t-2},M_{xr}^{t-3}, {\bar{M}}_{xr}^{\left(5\right)}\left(t\right),{\sigma }_{M_{xr}}^{\left(5\right)}\left(t\right),sin(\theta ),cos(\theta )$$

(15)

where $M_{xr}(t)$ is Blade 1’s flapwise blade-root bending moment, $\beta (t)$ is Blade 1’s pitch angle, $M_{xr}(t-1)$, $M_{xr}(t-2)$, and $M_{xr}(t-3)$ are lagged flapwise bending-moment features, ${\bar{M}}_{xr}^{\left(5\right)}(t)$ is the five-sample rolling mean of the flapwise bending moment, ${\sigma }_{M_{xr}}^{\left(5\right)}(t)$ is the five-sample rolling standard deviation of the flapwise bending moment, $\Omega (t)$ is the rotational speed of the rotor, and $\theta (t)$ is the instantaneous rotor azimuth angle represented by sine and cosine components.

The Random Forest model minimises the mean squared regression error during training:

$$L={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N(y_i-{\widehat{y}}_i{)}^2$$

(16)

where

• $y_i$ represents the true blade-root edgewise moment obtained from OpenFAST;
• ${\widehat{y}}_i$ denotes the predicted virtual sensing output;
• $N$ is the total number of training samples.

Compared with single-tree regression approaches, ensemble averaging significantly improves stability under turbulent inflow conditions and reduces sensitivity to local fluctuations in aeroelastic response data [11].

2.5.2. Training Strategy (Healthy Only)

The model was trained exclusively using healthy-condition OpenFAST simulations to establish a baseline representation of normal turbine aeroelastic behaviour. This strategy allows the trained virtual sensor to act as a reference model during later fault detection stages, where abnormal deviations between measured and predicted responses can indicate structural degradation or torsional stiffness reduction [6,25,26].

The complete healthy dataset included simulations generated using multiple turbulence seeds at three representative operating wind speeds:

• 6 m/s (below-rated condition);
• 8 m/s (near-rated condition);
• 12 m/s (above-rated condition).

To improve model generalisation across varying aerodynamic operating regimes, a stratified random split was implemented separately within each wind speed group. This prevented wind speed segregation between training and testing datasets and ensured that all operating conditions were represented in the training, validation, and test subsets [11].

The dataset partitioning strategy is as follows:

$$D=D_{train}\cup D_{val}\cup D_{test}$$

(17)

This is subject to

$$D_{train}:D_{val}:D_{test}=60\%:20\%:20\%$$

(18)

where

• $D_{train}$ represents the training subset;
• $D_{val}$ represents the validation subset;
• $D_{test}$ represents the independent testing subset.

Hyperparameter optimisation was performed using RandomizedSearchCV combined with three-fold cross-validation to identify robust model configurations while maintaining computational efficiency [11]. The optimisation process evaluated multiple combinations of

• Ensemble size;
• Tree depth;
• Feature sampling strategy;
• Node-splitting constraints;
• Terminal leaf constraints.

The final Random Forest configuration adopted in this work is summarised in Table 3.

2.6. Generalisation-Based Fault Detection

Torsional degradation was modelled by reducing the blade GJ stiffness by 5%, 10%, and 20%, representing mild, moderate, and severe structural deterioration. Unlike supervised classification approaches that require comprehensive labelled fault datasets for training [5], the proposed methodology operates using only healthy data, exploiting the hypothesis that structural degradation disrupts the learned relationships between input features and edgewise response, manifesting as elevated residuals.

For each test case, prediction residuals are computed as the difference between the true and predicted edgewise moments:

$$\epsilon \left(t\right)=My\left(t\right)-\widehat{\mathrm{M}}y(t)$$

(19)

where $\mathrm{M}\mathrm{y}(\mathrm{t})$ is the measured edgewise moment at time t and $\widehat{\mathrm{M}}y(t)$ is the Random Forest prediction. The case-level residual energy is quantified through the root mean square error (RMSE):

$$RMSE\epsilon =\sqrt{{\displaystyle \frac{1}{N}}\sum {\left[\epsilon \left(t\right)\right]}^2}$$

(20)

where N is the number of time steps in the evaluation window. Under healthy operation, $RMSE\epsilon$ reflects an irreducible prediction error arising from model approximation, sensor noise, and stochastic turbulence effects. Torsional degradation amplifies $RMSE\epsilon$ through altered aeroelastic coupling that violates the healthy-condition assumptions embedded in the trained model.

2.6.1. Detection Threshold Computation

To account for the natural variation in structural response across operating conditions, wind-speed-specific detection thresholds were established rather than employing a single global boundary. Aerodynamic loads scale with wind speed, inducing corresponding variations in baseline structural moments even under healthy operation. Consequently, residual magnitudes exhibit systematic wind speed dependence: a fixed threshold would be suboptimal, either reducing detection sensitivity at low wind speeds or generating spurious alarms at high wind speeds.

For each wind speed bin (6, 8, 12 m/s), healthy baseline statistics were characterised using the empirical distribution of absolute prediction residuals across all healthy simulation cases at that wind speed. Detection thresholds were then established using a percentile-based criterion:

$$Threshold ws=P_q+(|e_{ws}|)$$

(21)

where $P_q$ denotes the selected percentile of the healthy residual distribution, $\mathrm{q}\in \{\mathrm{95,97},99\}$, and ${(e}_{ws})$ represents the prediction residuals corresponding to wind speed $ws$ For each wind speed bin (6, 8 and 12 m/s), residual thresholds were obtained directly from the empirical distribution of absolute prediction residuals under healthy operating conditions. Rather than assuming a Gaussian residual distribution, percentile-based thresholds were evaluated to better represent the non-Gaussian characteristics of turbulent aeroelastic loading. Candidate thresholds corresponding to the 95th, 97th and 99th percentiles were subsequently assessed using the residual exceedance framework described in Section 3.2, with the P97 threshold providing the best overall classification performance [6].

A fault is detected when the case-level residual RMSE exceeds the threshold corresponding to the operating wind speed.

A fault is detected if

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\mathsf{\epsilon }>\mathrm{T}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d} \mathrm{w}\mathrm{s}$$

(22)

where the wind speed $\mathrm{w}\mathrm{s}$ is determined from the mean wind speed during the evaluation window. This binary classification criterion enables real-time fault flagging without requiring domain expertise or manual interpretation of residual patterns.

The wind-speed-adaptive framework offers three key advantages for practical deployment. First, it maintains uniform detection sensitivity across the operational envelope by normalising for load magnitude variations with wind speed. Second, it preserves the zero-fault-data training paradigm: threshold establishment requires only healthy operation statistics, avoiding the need for labelled fault examples that are difficult or dangerous to acquire in operational turbines. The percentile-based thresholding strategy provides a robust, distribution-free approach that avoids assumptions regarding Gaussian residual behaviour while maintaining transparent and interpretable fault-decision criteria.

2.6.2. Detection Metrics

Detection performance is evaluated using standard binary classification metrics computed across all 36 test cases (9 healthy, 27 faulty). The confusion matrix quantifies true positives (faulty cases correctly detected), true negatives (healthy cases correctly identified), false positives (healthy cases incorrectly flagged), and false negatives (faulty cases missed). Overall detection accuracy is defined as follows:

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}={\displaystyle \frac{(\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N})}{(\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N})}}\times 100\%$$

(23)

where TP, TN, FP, and FN denote true positives, true negatives, false positives, and false negatives, respectively. Detection performance is further stratified by fault severity (5%, 10%, 20% GJ reduction) and wind speed to assess sensitivity across degradation magnitudes and operating conditions. Receiver Operating Characteristic (ROC) curves are generated by varying the threshold multiplier, with the Area Under Curve (AUC) quantifying overall discriminative capability independent of the specific threshold choice.

2.7. Blade Asymmetry Index

To provide a physically interpretable reference metric for blade-specific structural imbalance, a blade asymmetry index (BAI) is formulated as a complementary indicator that may be used alongside the proposed residual-based virtual sensing framework in future blade-localisation studies. The BAI was developed to quantify the deviation of the degraded blade’s response from that of the corresponding healthy blades. Since the imposed torsional stiffness degradation was applied only to Blade 1, while Blades 2 and 3 retained their original structural properties, the asymmetry index provides a physically meaningful measure of blade-wise structural imbalance under rotating operational conditions. Similar asymmetry-based indicators have previously been employed in wind turbine structural health monitoring because local blade faults often produce periodic loading imbalance and asymmetric aeroelastic response behaviour [22].

For a given blade-root structural-response signal, the instantaneous Blade 1 asymmetry signal is defined as follows:

$$A\left(t_i\right)=\left|M_{\left\{yr\right\}}^{\left\{B1\right\}\left(t_i\right)}-{\displaystyle \frac{M_{\left\{yr\right\}}^{\left\{B2\right\}\left(t_i\right)}+M_{\left\{yr\right\}}^{\left\{B3\right\}\left(t_i\right)}}{2}}\right|$$

(24)

where $M_{yr}^{B1}(t_i)$, $M_{yr}^{B2}(t_i)$, and $M_{yr}^{B3}(t_i)$ denote the Blade 1, Blade 2, and Blade 3 edgewise blade-root bending moments, respectively, at time $t_i$.

A case-level blade asymmetry index was then computed using the root mean square value of the instantaneous asymmetry signal:

$$BAI=\sqrt{\left\{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{A}^{2\left(t_i\right)}\right\}}$$

(25)

where $N$ denotes the number of transient-free structural-response samples used for evaluation. Larger values of the BAI indicate stronger blade-wise load imbalance and therefore greater deviation from healthy structural symmetry. Previous structural monitoring studies have shown that stiffness degradation can alter blade dynamic response and generate measurable asymmetry within rotating structural systems [10].

To enable comparison across different operating conditions and wind speeds, a normalised asymmetry index was also computed relative to the healthy baseline response:

$$BA{I}_{norm}={\displaystyle \frac{BA{I}_{fault}}{BA{I}_{healthy}}}$$

(26)

where $BA{I}_{fault}$ represents the asymmetry index under degraded operation and $BA{I}_{healthy}$ denotes the corresponding healthy-condition asymmetry index for the same wind speed condition.

Although the blade asymmetry index provides a physically interpretable measure of blade-wise structural imbalance, the present study focuses on validating the residual-based virtual sensing framework as the primary degradation-detection methodology. Consequently, quantitative evaluation of the BAI is beyond the scope of the current work and will be investigated in future studies as a complementary localisation indicator for identifying the affected blade following anomaly detection. Accordingly, the present study evaluates only the residual-based virtual sensing framework, while the BAI formulation is included to establish a foundation for future blade-localisation extensions of the proposed methodology.

2.8. Rationale for Simulation-Based Development

High-fidelity aeroelastic simulation was adopted in this study because controlled torsional blade degradation is difficult to reproduce experimentally without permanently damaging expensive wind turbine blade structures. Simulation-based development enables systematic variation in degradation severity, wind speed, and turbulence realisation while maintaining full control over the imposed fault conditions and operating environment [10,22].

The first advantage of the simulation-based approach is controlled fault injection. In operational turbines, progressive torsional stiffness degradation cannot be introduced in a repeatable and safe manner. By contrast, the OpenFAST–BeamDyn framework enables direct modification of the blade structural stiffness representation through the following relation:

$$G{J}_{fault}=\left.\left(1-\delta \right.\right)G{J}_{healthy}$$

(27)

where $\mathsf{\delta }$ represents the imposed degradation level. This provides a physically interpretable method for generating mild, moderate, and severe degradation scenarios while preserving all other turbine and inflow conditions [10].

The second advantage is the availability of a complete structural-response ground truth. Operational turbines rarely provide direct measurement of internal blade-root bending and torsional moments. In contrast, OpenFAST provides access to local blade-root structural-response channels for all blades, enabling a direct comparison between simulated measurements and virtual sensor predictions. For completeness, the prediction residual introduced previously in the methodology is restated here because it forms the basis of the subsequent residual-based fault detection and simulation-ground-truth comparison:

$$\epsilon \left(t\right)=M_{y\left(t\right)}-{\widehat{M}}_{y\left(t\right)}$$

(28)

where ${\mathrm{M}}_{\mathrm{y}}(\mathrm{t})$ denotes the OpenFAST blade-root edgewise moment and ${\widehat{\mathrm{M}}}_{\mathrm{y}}(\mathrm{t})$ represents the corresponding Random Forest virtual sensing prediction. The availability of this ground-truth information enables objective evaluation of residual amplification, model generalisation behaviour, and degradation sensitivity [5].

The third advantage is safety and computational scalability. Experimental testing of degraded blades under turbulent inflow conditions requires specialised facilities, expensive instrumentation, and strict safety control. Aeroelastic simulation provides a lower-risk and fully repeatable environment for the development of structural health monitoring methodologies [28]. Furthermore, once validated numerically, the same framework can later be transferred to operational turbines, SCADA-based monitoring systems, or digital-twin environments [27].

The fourth advantage is compatibility with healthy-only learning strategies. In practical wind farms, labelled fault datasets are scarce because severe structural degradation events occur infrequently and maintenance intervention often prevents complete fault progression from being recorded. Consequently, healthy-condition operational data are typically much easier to obtain than comprehensive labelled degradation datasets. The simulation-based framework therefore enables the development of a healthy-only virtual sensing methodology consistent with realistic industrial deployment scenarios [6].

The present study is based on high-fidelity OpenFAST simulations and therefore assumes idealised measurement conditions. Environmental and operational factors such as sensor noise, sensor drift, temperature-dependent measurement variations, ice accretion, blade contamination, and communication-related data losses were not explicitly modelled. These factors are particularly relevant to the proposed residual-threshold detection approach, as slowly varying structural-response changes caused by temperature drift or ice accretion could plausibly be misattributed as torsional degradation, while sensor noise could mask genuine mild degradation below the detection threshold. Consequently, the reported fault detection performance should be interpreted within the context of these idealised assumptions, and the conclusions are most directly applicable to scenarios where the measured structural responses accurately reflect the underlying aeroelastic behaviour of the turbine. Future work will incorporate measurement uncertainty, environmental disturbances, and field-operational datasets to further evaluate the robustness of the proposed framework under real-world operating conditions.

Although simulation-based development provides controlled fault injection and complete access to structural-response variables, future experimental validation using operational SCADA measurements, strain-gauge instrumentation, or full-scale blade-test data is still required to evaluate real-world transferability and robustness under practical operating conditions.

3. Results

This section presents the performance evaluation of the proposed physics-informed virtual sensing framework for wind turbine blade-root edgewise load reconstruction and torsional stiffness degradation detection. The analysis is structured into two sequential stages consistent with the methodology described in Section 2. First, a Random Forest virtual sensor trained exclusively on healthy OpenFAST–BeamDyn simulation data is evaluated for predictive accuracy, physical interpretability, and generalisation capability (Section 3.1, Section 3.2 and Section 3.3). Second, the healthy-trained model is deployed as a digital-twin baseline to generate sample-level residuals under healthy and degraded operating conditions; residual exceedance statistics are then used to classify fault states without requiring any labelled fault data during training (Section 3.4 and Section 3.5). All healthy simulation data comprised 864,009 time steps from nine 600 s simulations (three seeds × three wind speeds) with the first 30 s removed; all fault evaluation cases used a separate dataset of 27 simulations (three seeds × three wind speeds × three degradation levels: 5%, 10%, 20% GJ reduction) at 200 s each, again with the first 30 s discarded.

3.1. Virtual Sensor Performance Under Healthy Operating Conditions

3.1.1. Prediction Accuracy

The predictive performance of the virtual sensor was evaluated using unseen healthy data following a 60/20/20 train–validation–test partition. Hyperparameter optimisation was performed using RandomizedSearchCV, which identified the optimal Random Forest configuration as: n_estimators = 500, max_depth = None, min_samples_split = 2, min_samples_leaf = 1, and max_features = 0.4. The resulting model achieved an out-of-bag (OOB) generalisation score of R² = 0.9814, which closely matched the independent test performance, indicating excellent generalisation capability and negligible overfitting prior to test-set evaluation. The coefficient of determination was computed as follows:

$${\mathrm{R}}^2=1-[{\displaystyle \frac{\sum {\left(y_i-{\widehat{y}}_i\right)}^2}{\sum {\left(y_i-\overline{y}\right)}^2}}]$$

(29)

where $y_i$ denotes the measured blade-root edgewise moment and ${\widehat{y}}_i$ the corresponding Random Forest prediction. The prediction error was additionally quantified using the root mean square error and mean absolute error:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{[\left({\displaystyle \frac{1}{N}}\right)\sum {\left(y_i-{\widehat{y}}_i\right)}^2]}$$

(30)

$$\mathrm{M}\mathrm{A}\mathrm{E}=\left({\displaystyle \frac{1}{N}}\right)\sum |y_i-{\widehat{y}}_i|$$

(31)

Full performance metrics on the test partition are summarised in

Table 4. Prediction performance of the Random Forest virtual sensor on the healthy test dataset.

Metric	Value
R2	0.9820
RMSE (N·m)	318,810
MAE (N·m)	202,170
MAPE (%)	3.67
EVS	0.9820
NMSE	0.00261

and illustrated in Figure 6.

The test R² of 0.9820 confirms that the model accounts for 98.2% of the variance in the edgewise blade-root bending moment (B1RootMyr) from structural-response features alone, without any direct measurement of the target channel. The test MAPE of 3.67% indicates sub-4% relative accuracy across the full dynamic load range, spanning approximately 0.2 × 10⁷ to 1.4 × 10⁷ N·m under all three wind speed regimes. As expected, the training error is lower than the validation and test errors because the Random Forest model is optimised using the training subset, whereas the validation and test subsets contain previously unseen turbulent realisations. Although the final model employs fully grown decision trees (max_depth = None), the close agreement between the validation (R² = 0.9818), test (R² = 0.9820) and out-of-bag (R² = 0.9814) performances demonstrates consistent generalisation to unseen data and does not indicate substantial overfitting. The near-identical validation and test metrics (ΔR² < 0.001, ΔRMSE = 1979 N·m) further confirm that the stratified partitioning produced statistically equivalent evaluation sets without evidence of data leakage between splits.

The predicted-versus-measured scatter plot (Figure 6a) shows tight adherence to the identity line across the complete operating range at all three wind speeds, with symmetric, unbiased dispersion confirming the absence of systematic model error. The residual distribution (Figure 6b) is centred at μ = 1800 N·m, indicating negligible prediction bias relative to the load magnitude. The homoscedasticity plot (Figure 6c) reveals uniform residual scatter with no systematic heteroscedastic pattern, confirming that model accuracy is consistent across the full operational load envelope. The Q-Q plot (Figure 6d) demonstrates near-Gaussian residual behaviour in the central quantile range (R = 0.9456), with heavier-than-normal tails attributable to transient peak loads under intense turbulent excitation, a characteristic of aeroelastic structural response rather than model deficiency.

3.1.2. Physical Interpretation of the Virtual Sensor

Establishing physical interpretability of the learned mapping is essential for confidence in the model’s suitability for condition-monitoring applications. Feature importance was assessed using two complementary methods: Mean Decrease in Impurity (MDI), computed from the full Random Forest ensemble, and permutation importance (ΔR²), evaluated on the held-out test set as an unbiased estimator that is less sensitive to spurious correlations and feature-cardinality effects.

The MDI importance for feature $j$ quantifies the cumulative reduction in node impurity attributable to that feature across all decision trees in the ensemble, and can be expressed as follows:

$$I_j=\sum _{t\in T_j}p(t)\Delta i(t)$$

(32)

where $p(t)$ represents the proportion of samples reaching node $t$, $\Delta i(t)$ denotes the impurity reduction generated by the split, and $T_j$ represents the set of tree nodes using feature $j$. To verify the robustness of the ranking, permutation importance was additionally computed by randomly shuffling each feature in the held-out test set and measuring the resulting decrease in prediction performance. Results are presented in Figure 7 and

Table 5. Feature importance rankings by MDI and permutation importance on the test set.

Feature	MDI (%)	Perm. ΔR2	Perm. SD
RotSpeed	61.4	1.179	0.0036
BldPitch1	11.3	0.206	0.0009
B1RootMxr	5.2	0.072	0.0002
Azimuth_cos	5.2	0.152	0.0004
B1RootMxr_rolling_std5	3.5	0.035	0.0001
B1RootMxr_lag1	3.4	0.040	0.0001
Azimuth_sin	3.4	0.171	0.0004
B1RootMxr_rolling_mean5	3.1	0.057	0.0002
B1RootMxr_lag3	1.7	0.042	0.0002
B1RootMxr_lag2	1.6	0.024	0.0001

.

Rotor speed (RotSpeed) is the dominant predictor, contributing 61.4% MDI and a permutation importance of 1.179. This is physically meaningful: edgewise loading is primarily inertia-driven rather than aerodynamically driven, and rotor speed directly controls the centrifugal and gravitational contributions to the in-plane blade structural response across all three wind speed operating regimes. The collective blade pitch angle (BldPitch1) is the second-ranked predictor by both methods (11.3% MDI, 0.206 permutation importance), reflecting its role in setting the aerodynamic operating regime of the blade: pitch angle governs the angle of attack and therefore the aerodynamic moment contribution superimposed on the dominant inertial loading, providing the model with direct information on the turbine’s control state across below-rated and near-rated conditions.

B1RootMxr (flapwise moment) contributes 5.2% MDI and 0.072 permutation importance, confirming a secondary aerodynamic coupling between out-of-plane and in-plane structural response under turbulent inflow. The temporal lag and rolling-statistics features derived from B1RootMxr (B1RootMxr_lag1, B1RootMxr_lag2, B1RootMxr_lag3, B1RootMxr_rolling_mean5, B1RootMxr_rolling_std5) together account for 13.3% MDI, demonstrating that aeroelastic memory effects—where the current edgewise load is partially determined by the recent flapwise excitation history—carry meaningful predictive information beyond the instantaneous structural state. The azimuthal position encodings (Azimuth_cos, Azimuth_sin) jointly contribute 8.6% MDI and rank third and fourth by permutation importance (0.152 and 0.171, respectively), capturing the once-per-revolution gravitational loading cycle characteristic of edgewise bending. The MDI and permutation importance rankings agree on the top two features (RotSpeed, BldPitch1), with only a minor reordering among the remaining azimuthal and flapwise-derived features, indicating that the learned relationships are physically grounded rather than artefacts of MDI’s known bias toward high-cardinality features.

The revised feature-importance analysis should not be interpreted as indicating that rotor speed alone determines the predicted edgewise response. Rather, the Random Forest model exploits complementary information provided by rotor kinematics, blade pitch, flapwise structural loading, temporal memory and azimuth-dependent cyclic loading. While RotSpeed provides the strongest individual contribution, accurate prediction is achieved through the combined interaction of all engineered features. Importantly, the final model no longer includes the torsional bending moment (B1RootMzr), which was removed during model refinement to improve model transparency and reproducibility. Despite its removal, the virtual sensing framework maintained excellent predictive performance (R² = 0.9820), demonstrating that the proposed methodology does not depend on direct torsional-response measurements.

3.1.3. Generalisation Performance and Dynamic Time-Series Tracking

The ability of the virtual sensor to generalise across operating conditions was assessed using the full train–validation–test metric comparison and direct time-series tracking. Full results are shown in Figure 8 and

Table 6. Generalisation performance of the Random Forest virtual sensor across data partitions.

Dataset	R2	RMSE (N·m)	MAE (N·m)	MAPE (%)
Training	0.9974	119,988	75,535	1.37
Validation	0.9818	320,789	202,697	3.66
Test	0.9820	318,810	202,170	3.67

; time-series tracking performance is illustrated in Figure 9.

Only a modest reduction in performance is observed between training and unseen evaluation sets. The train–test R² gap of 0.0154 is within the expected range for ensemble regression on stochastic aeroelastic data and is consistent with the OOB score, confirming effective generalisation without overfitting. The RMSE amplification from training (119,988 N·m) to test (318,810 N·m), a 2.7-fold increase, reflects the contribution of temporal lag features, which achieve lower within-sequence training error but face increased uncertainty when the temporal context is interrupted at sequence boundaries in the stratified partition. The near-identical validation and test R² values (0.9818 vs. 0.9820) confirm that the validation set used for hyperparameter selection is representative of the final held-out test distribution.

Time-series tracking over the first 2000 test samples (Figure 9) confirms that the virtual sensor accurately reproduces high-frequency aeroelastic load fluctuations, including sub-second peak-to-peak excursions spanning approximately one order of magnitude of the load range. The predicted trace closely overlies the measured signal at all load levels, with deviations visible only at isolated transient peak loads driven by intense turbulence events. Peak loads approaching 1.4 × 10⁷ N·m are successfully captured without systematic attenuation or phase lag, demonstrating that the virtual sensor preserves the temporal dynamic characteristics required for subsequent residual-based fault detection.

3.2. Residual Generation and Statistical Threshold Derivation

Following virtual sensor validation, the trained model was deployed as a healthy digital-twin baseline to generate sample-level prediction residuals for both healthy and faulty operating conditions. For statistical thresholding, the signed prediction residual defined in Equation (28) is converted to its absolute magnitude:

$$r_i=|y_i-{\widehat{y}}_i|$$

(33)

where $y_i$ is the OpenFAST B1RootMyr measurement and ${\widehat{y}}_i$ is the corresponding virtual sensor prediction (consistent with the prediction residual defined by Equation (28) in Section 2.8). Thresholds were derived from the residual distributions obtained from the nine complete healthy simulation datasets (three wind speeds with three turbulent-seed realisations each), rather than from the 20% machine learning test partition. Following training of the Random Forest virtual sensor, the healthy simulations were processed independently to establish wind-speed-specific residual distributions for threshold calibration. Consequently, the threshold-calibration stage is separate from the regression model training and does not introduce information leakage into the machine learning optimisation process. Pooling all 273,600 residual samples per wind speed class, rather than operating on case-level RMSE statistics from only three seeds per wind speed, yields substantially more statistically robust threshold estimates that are insensitive to individual turbulent-seed outliers. For each wind speed class ws, the sample residual threshold is the 97th percentile of the pooled healthy residual distribution:

$${\mathsf{\tau }}_{\mathrm{w}\mathrm{s}}=P_{97}(r_i:i ϵ healthy cases at wind speed ws)$$

(34)

For a given test case, the fault score is the fraction of its residual samples exceeding the healthy threshold:

$$f_{ws}=\left({\displaystyle \frac{1}{N}}\right){\sum }_i\mathbb{1}[{\mathrm{r}}_{\mathrm{i}}>{\tau }_{ws}]$$

(35)

$$Fault=\left\{\begin{array}{c}1, f_{ws}>\delta \\ 0, f_{ws}\le \delta \end{array}\right.$$

where $\delta$ denotes the exceedance decision threshold. Following the grid-search optimisation procedure described in Section 3.3, the optimum value was found to be $\delta =0.04$. N is the number of samples in the test case and $\mathbb{1}$[·] is the indicator function. A case is declared faulty when $f_{ws}$ exceeds a decision threshold δ, selected via a grid search, as described in Section 3.3. The derived P97 thresholds are summarised in

Table 7. Wind-speed-specific P97 residual thresholds derived from pooled healthy test-case residuals (N = 273,600 samples per wind speed).

Wind Speed	N Samples	Mean |Residual| (N·m)	P97 Threshold τ (N·m)
6 m/s	273,600	88,579	407,981
8 m/s	273,600	130,897	552,881
12 m/s	273,600	151,330	734,264

.

Each wind speed category contained three healthy simulations of equal duration and sampling frequency, resulting in an identical number of residual samples (273,600) for threshold estimation at each wind speed. The P97 thresholds increase monotonically with wind speed, reflecting the scaling of absolute aeroelastic loads with increasing inflow velocity. The 6 m/s and 8 m/s thresholds are relatively close (407,981 N·m and 552,881 N·m), which is consistent with below-rated operation where rotor speed is the primary load driver. The substantially elevated threshold at 12 m/s (734,264 N·m) reflects the larger absolute edgewise loads at near-rated conditions, where aerodynamic forcing contributes more strongly to in-plane structural response. Importantly, all three wind speed classes share identical sample counts (N = 273,600), confirming that the threshold estimates are based on statistically equivalent sample pools.

3.3. Threshold Optimisation via Grid Search

The optimal (percentile, δ) combination was identified by a grid search over percentile values {P95, P97, P99} and exceedance decision thresholds δ ∈ {1%, 2%, 3%, 4%, 5%}, evaluated across all 36 test cases (nine healthy + 27 faulty). The selection criterion was a maximum F1-score among all settings achieving precision ≥ 0.90, imposing a minimum alarm reliability constraint consistent with practical wind turbine operation, where unnecessary maintenance dispatches carry an asymmetric cost relative to the consequence of delayed detection of gradual mild-severity degradation [2,6]. The complete grid-search results are reported in

Table 8. Threshold grid-search results across all 15 parameter combinations.

Setting	TP	TN	FP	FN	Acc.	Prec.	Sens.	Spec.	F1
P95/1%	27	0	9	0	0.750	0.750	1.000	0.000	0.857
P95/2%	27	1	8	0	0.778	0.771	1.000	0.111	0.871
P95/3%	27	1	8	0	0.778	0.771	1.000	0.111	0.871
P95/4%	27	1	8	0	0.778	0.771	1.000	0.111	0.871
P95/5%	27	4	5	0	0.861	0.844	1.000	0.444	0.915
P97/1%	27	0	9	0	0.750	0.750	1.000	0.000	0.857
P97/2%	27	1	8	0	0.778	0.771	1.000	0.111	0.871
P97/3%	26	4	5	1	0.833	0.839	0.963	0.444	0.897
1  P97/4%	24	8	1	3	0.889	0.960	0.889	0.889	0.923
P97/5%	18	9	0	9	0.750	1.000	0.667	1.000	0.800
P99/1%	23	4	5	4	0.750	0.821	0.852	0.444	0.836
P99/2%	13	9	0	14	0.611	1.000	0.481	1.000	0.650
P99/3%	7	9	0	20	0.444	1.000	0.259	1.000	0.412
P99/4%	6	9	0	21	0.417	1.000	0.222	1.000	0.364
P99/5%	5	9	0	22	0.389	1.000	0.185	1.000	0.312

Note: ¹ denotes the selected operating point.

and illustrated in Figure 10.

Figure 10 and Table 8 reveal a clear monotonic trade-off between sensitivity and alarm reliability with increasing percentile and exceedance threshold. At aggressive settings (P95/1–4%), sensitivity reaches 100%, but at least eight of the nine healthy test cases are misclassified as faulty (precision = 0.750, specificity = 0.000 at the most permissive setting), rendering these settings operationally unacceptable. As the decision threshold tightens toward P99, precision and specificity improve at the cost of sensitivity, ultimately reaching precision = 1.000 at P99/2–5%—but at the cost of missing 14–22 of 27 faulty cases.

The selected operating point P97/4.0% (highlighted in Table 8) achieves the highest F1-score (0.923) among all settings with precision ≥ 0.90, balancing a sensitivity of 0.889 (24 of 27 faulty cases detected) against alarm reliability (precision = 0.960; only one false positive from nine healthy cases). This setting was adopted as the primary operating point for all subsequent fault classification evaluations.

Detection performance also varied with operating wind speed. Complete fault detection was achieved at 12 m/s, while only a single fault case remained undetected at 8 m/s. In contrast, most false-negative cases occurred at 6 m/s. This behaviour suggests that low-severity torsional degradation faults operating under below-rated wind conditions generate structural responses that remain closer to those of healthy, turbulence-driven variability. Consequently, residual distributions exhibit reduced separation from the healthy baseline, making classification more challenging. The wind-speed-stratified detection rates are summarized in

Table 9. Fault detection performance by wind speed.

Wind Speed	Detected	Missed	Total	Detection Rate (%)
6 m/s	7	2	9	77.8
8 m/s	8	1	9	88.9
12 m/s	9	0	9	100.0
Overall	24	3	27	88.9

.

3.4. Fault Classification Performance

3.4.1. Case-Level Residual Exceedance Behaviour

Figure 11 illustrates the case-level fault score fws for all 36 test cases. The nine healthy test cases cluster below the 4.0% decision threshold, confirming that the P97 threshold effectively characterises the tail of the healthy residual distribution under all three wind speed regimes. The faulty cases exhibit clear progressive amplification with increasing degradation severity. The most extreme 20% GJ reduction case at 6 m/s reaches an exceedance fraction as high as 37.3%, representing a 12.4× amplification relative to the mean healthy exceedance at the same wind speed. This amplification is physically consistent with the bending–torsion coupling disruption described in Section 2.3: reduced torsional stiffness alters the aeroelastic twist response of Blade 1, modifying the coupling between B1RootMxr, BldPitch1, RotSpeed, and the target B1RootMyr, and thereby generating amplified virtual sensor prediction residuals that serve as the detection signal.

3.4.2. Confusion Matrix and Classification Metrics

Applying the P97/4.0% threshold configuration to all 36 test cases yields the classification results summarised in

Table 10. Confusion matrix at the P97/4.0% operating point.

	Predicted Healthy	Predicted Faulty
Healthy	TN = 8	FP = 1
Faulty	FN = 3	TP = 24

and illustrated in Figure 12. The classification metrics were computed as follows:

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}={\displaystyle \frac{(TP+TN)}{(TP+TN+FP+FN)}}$$

(36)

$$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{TP}{(TP+FP)}}$$

(37)

$$\mathrm{S}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}={\displaystyle \frac{TP}{(TP+FN)}}$$

(38)

$$\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}={\displaystyle \frac{TN}{(TN+FP)}}$$

(39)

$$\mathrm{F}1=2\times {\displaystyle \frac{Precision\times Sensitivity}{(Precision+Sensitivity)}}$$

(40)

The framework achieves an F1-score of 0.923, an AUC of 0.951, and an overall accuracy of 88.9%. The full set of classification performance metrics is provided in

Table 11. Fault classification performance at the selected P97/4.0% operating point.

Metric	Value
Accuracy	0.889
Precision	0.960
Sensitivity (Recall)	0.889
Specificity	0.889
F1-score	0.923
AUC–ROC	0.951

Note: Bold value indicates the primary classification metric used for model evaluation.

.

The framework achieves a sensitivity of 0.889, successfully identifying 24 of 27 faulty cases spanning all three degradation severity levels. Precision of 0.960 confirms that 24 of the 25 issued alarms correspond to genuine structural degradation, with only one false positive arising from a healthy seed-specific turbulent realisation whose absolute residual distribution marginally exceeds the P97 threshold. The F1-score of 0.923 reflects a strong operational balance between detection coverage and alarm reliability. The ROC curve (Figure 12b, AUC = 0.951) confirms a strong discriminative capability substantially above the random classifier baseline (AUC = 0.500). The step-wise ROC character reflects the discrete 36-case evaluation set; the curve reaches TPR = 1.00 once the FPR reaches 0.56, confirming that complete faulty-population detection is achievable at more permissive threshold settings.

3.4.3. Detection Rate by Fault Severity

Table 12. Fault detection rates stratified by degradation severity level (3 seeds × 3 wind speeds = 9 cases per severity level; P97/4.0% threshold).

Severity	Detected	Missed	Total	Detection Rate
5% GJ reduction	7	2	9	77.8%
10% GJ reduction	8	1	9	88.9%
20% GJ reduction	9	0	9	100.0%
Overall	24	3	27	88.9%

reveals a clear and physically meaningful monotonic increase in the detection rate with degradation severity. The framework achieves 100% detection of all severe 20% GJ reduction cases across all wind speeds and turbulent seeds, without requiring any faulty data during training. The detection rate for moderate 10% degradation reaches 88.9% (eight of nine cases detected), while mild 5% degradation yields 77.8% (seven of nine detected). This severity-dependent detection pattern is physically expected: larger torsional stiffness reductions introduce stronger bending–torsion coupling disruption, producing proportionally greater amplification of the virtual sensor prediction residuals and correspondingly higher exceedance fractions relative to the P97 healthy threshold.

3.5. Analysis of Undetected Fault Cases

Despite the overall strong classification performance, three faulty simulations were not detected (Figure 13,

Table 13. Undetected (false-negative) fault cases at the P97/4.0% operating point.

Case (Abbreviated)	Wind Speed	GJ Reduction	RMSE (N·m)	Exceedance f_ws
5MW…6m/s_100_10pct	6m/s	10%	162,236	3.4%
5MW…6m/s_100_5pct	6m/s	5%	152,823	2.8%
5MW…8m/s_100_5pct	8m/s	5%	223,629	3.5%

). All three missed cases exhibit exceedance fractions between 2.8% and 3.5%, marginally below the 4.0% decision boundary, and are concentrated at 6 m/s (5% and 10% GJ reduction), with one additional case at 8 m/s (5% GJ reduction).

Three physically interpretable factors explain the pattern of false negatives. First, the mild-to-moderate GJ reduction at 6 m/s (5% and 10%) generates a comparatively small bending–torsion coupling disruption at this below-rated wind speed. At 6 m/s, aerodynamic loading is modest and blade structural responses are primarily rotor-speed-driven; torsional stiffness reductions in this magnitude produce only a small perturbation in the flapwise–torsional–edgewise coupling, insufficient to push more than 4% of residual samples above the P97 threshold in two of these three missed cases (3.4% and 2.8% exceedance, respectively). Second, the 8 m/s missed case (5% GJ reduction) has an exceedance fraction of 3.5%, only 0.5 percentage points below the threshold, a marginal miss that could be recovered with a slightly more permissive decision boundary (e.g., δ = 3.0%), as Table 8 demonstrates for the P97/3% setting, where sensitivity rises to 0.963 (26 of 27 faulty cases detected). Third, mild-severity torsional degradation operating at below-rated wind speeds can generate structural responses that more closely resemble normal, turbulence-driven healthy behaviour, a known limitation of healthy-data-based anomaly detection that is addressable through expanded healthy baseline datasets or multi-blade asymmetry indicators in future work.

Although

Table 14. Comparison between case-level RMSE thresholding and sample-level residual exceedance classification.

Method	TP	TN	FP	FN	Accuracy	Precision	Sensitivity	F1-Score	AUC
RMSE Threshold	17	9	0	10	0.722	1.000	0.630	0.773	0.774
Residual Exceedance	24	8	1	3	0.889	0.960	0.889	0.923	0.951

compares two decision strategies within the proposed framework, the contribution of this study extends beyond threshold selection. Conventional normal behaviour models (NBMs) are typically developed using SCADA-derived temperature, power-production, or drivetrain signals, which provide indirect indicators of structural degradation. In contrast, the proposed framework operates directly on blade-root structural-load responses reconstructed through virtual sensing. Because blade-root loads provide direct access to the physical mechanisms governing stiffness loss and aeroelastic degradation, they represent a fault domain that indirect SCADA-derived signals are not structurally positioned to observe. Furthermore, the virtual-sensing architecture enables structural behaviour to be monitored without requiring extensive additional instrumentation, thereby supporting future digital-twin-based condition-monitoring applications.

Compared with the initial case-level RMSE thresholding strategy, the proposed residual exceedance framework substantially improves the fault detection capability. Sensitivity increased from 63.0% to 88.9%, while the F1-score improved from 0.773 to 0.923. Similarly, the AUC increased from 0.774 to 0.951, indicating superior discrimination between healthy and faulty operating conditions. These improvements demonstrate the advantage of preserving sample-level residual information rather than reducing each simulation case to a single RMSE value.

4. Discussion

The excellent predictive accuracy achieved by the virtual sensor can be attributed to the capability of Random Forest regression to capture highly nonlinear aeroelastic relationships without requiring explicit structural governing equations. Rotor speed, blade pitch angle, azimuth position and bending dynamics interact through complex aerodynamic and structural coupling mechanisms that are difficult to represent using conventional analytical models. The ensemble-learning architecture enables these interactions to be learned directly from simulation data while maintaining robustness against noise and overfitting [11,29].

A key contribution of the proposed framework is the use of sample-level residual exceedance statistics rather than conventional case-level RMSE thresholding. Traditional RMSE-based approaches compress thousands of residual samples into a single scalar metric, potentially masking short-duration fault-induced deviations. In contrast, the exceedance fraction formulation preserves temporal information contained within the residual distribution, enabling subtle changes in structural response to remain detectable. This characteristic explains the significant improvement in sensitivity and F1-score observed relative to the original RMSE threshold method [6,30].

From an industrial perspective, the direct measurement of blade-root loads remains expensive and challenging due to sensor installation, maintenance and reliability constraints. The proposed virtual sensing framework therefore offers a practical alternative by reconstructing structural loads from readily available operational signals while simultaneously providing a fault detection capability. Such a framework aligns naturally with emerging digital-twin architectures for next-generation wind turbine condition monitoring and predictive maintenance systems [6,31].

The results demonstrate that the proposed physics-informed virtual sensing framework successfully integrates high-fidelity aeroelastic simulation, healthy-only machine learning, and residual-based diagnostics within a unified condition-monitoring architecture. The virtual sensor achieved excellent predictive performance (R² = 0.9820, MAPE = 3.67%) while maintaining strong generalisation across unseen operating conditions and stochastic turbulent seeds, with a train–test R² gap of only 0.0155 [29,30].

Feature importance analysis confirmed that the model learned physically meaningful aeroelastic relationships dominated by rotor speed (61.4% MDI) and blade-pitch angle (11.3% MDI), validating that the edgewise loading is primarily inertia- and pitch-control-driven, which underpins the fault detection architecture. When deployed as a healthy digital twin, the trained virtual sensor generated residual signals capable of distinguishing healthy and faulty structural states with an AUC = 0.951 and F1-score = 0.923, representing improvements of 22.9% in AUC and 19.4% in F1-score over initial case-level RMSE formulations. These improvements are attributable to the transition from case-level RMSE thresholding which compresses all sample-level residual information into a single statistic and is sensitive to the small healthy sample pool (n = 3 seeds per wind speed) to sample-level exceedance fraction scoring, which explicitly captures the proportion of the residual distribution that departs from the healthy statistical envelope [30,31].

Most importantly, the framework achieved 100% detection of all severe 20% GJ torsional stiffness degradation cases and 88.9% detection of moderate 10% degradation cases without requiring any faulty data during training. These findings confirm the feasibility of using healthy-data-driven virtual sensors as practical digital twins for wind turbine rotor condition monitoring and early torsional fault detection. Although the proposed framework achieved reliable detection performance across most degradation scenarios, lower sensitivity was observed for the 5% stiffness-reduction cases, where the structural response remained closer to healthy turbulence-driven variability. This effect is most pronounced at 6 m/s, where the healthy baseline was estimated from a comparatively smaller turbulent seed population (n = 10) than at 8 m/s and 12 m/s (n = 50 and n = 100, respectively), limiting the precision of the corresponding residual threshold. Future work will therefore expand the simulation campaign to include additional turbulence seeds, operating conditions and degradation severities, particularly at below-rated wind speeds, thereby increasing the diversity of fault samples available for model evaluation [6,30,31]. Furthermore, validation using field-operational datasets will be pursued to assess the robustness and engineering applicability of the proposed virtual sensing framework under real-world operating conditions.

We note that detection sensitivity is comparatively lower for mild 5% torsional degradation at 6 m/s, despite the healthy baseline dataset being balanced across all three wind speeds (Table 6). This reduced sensitivity instead reflects the smaller absolute aeroelastic loading present under below-rated conditions: both the mean healthy residual and the corresponding P97 decision threshold scale with wind speed (88,579 N·m and 407,981 N·m at 6 m/s, rising to 151,330 N·m and 734,264 N·m at 12 m/s, respectively, so a fixed percentage reduction in torsional stiffness produces a proportionally smaller deviation from the healthy residual envelope at 6 m/s than at 8 or 12 m/s. Future work will expand the simulation campaign with additional turbulence seeds and degradation severities, particularly at below-rated wind speeds, to improve detection robustness under this operating condition.

Nevertheless, several limitations remain. The present study considered simulated torsional stiffness degradation within the OpenFAST environment and, therefore, does not yet incorporate sensor uncertainty, environmental variability or operational inconsistencies typically encountered in field measurements. Future work will focus on validation using SCADA and condition-monitoring datasets obtained from operational wind turbines, as well as extension toward continuous stiffness-degradation estimation and physics-informed neural-network-based virtual sensing [6,29,30,31].

Although the proposed threshold-selection procedure demonstrated strong fault-classification performance, this performance was evaluated on a limited number of simulation cases (nine healthy, 27 faulty), and the operating threshold was selected and evaluated using the same dataset. Given these small per-condition sample sizes, the reported classification metrics—including instances of 100% detection—carry wide statistical uncertainty and should be interpreted as proof-of-concept evidence of feasibility rather than as a definitive or precise estimate of operational generalisation performance. Future work will evaluate threshold robustness using substantially larger simulation datasets, additional turbulent realisations, independent validation datasets and field measurements, enabling confidence intervals and out-of-sample threshold validation to be established for practical deployment. Future work will also investigate the blade asymmetry index formulated in Section 2.7 as a complementary blade-localisation indicator alongside the proposed residual-based virtual sensing framework.

5. Conclusions

This study presents a physics-informed virtual sensing framework for detecting wind turbine blade torsional degradation using OpenFAST–BeamDyn simulations and healthy-only machine learning. A Random Forest virtual sensor was trained exclusively on healthy operating data to reconstruct the blade-root edgewise bending moment (B1RootMyr) from structural-response features. The model achieved high predictive accuracy under healthy conditions (R² = 0.9820, MAPE = 3.67%), demonstrating that edgewise loads can be reconstructed reliably without direct measurement.

Fault detection was performed through residual-based analysis, where torsional stiffness degradation altered the learned aeroelastic relationships and produced amplified prediction residuals. The proposed sample-level residual exceedance method improved detection performance compared with conventional RMSE thresholding, achieving an overall classification accuracy of 88.9%, a precision of 96.0%, a sensitivity of 88.9%, a specificity of 88.9%, an F1-score of 0.923, and an AUC of 0.951. All severe degradation cases (20% torsional stiffness reduction) were successfully detected, while moderate degradation cases achieved an 88.9% detection rate.

The results demonstrate that healthy-data-driven virtual sensing provides a practical and scalable approach for blade structural health monitoring without requiring additional blade instrumentation or labelled fault data. Future work will focus on validation using operational wind turbine measurements and the extension of the framework towards real-time digital-twin applications and continuous structural degradation assessment.