Multiphysics surrogate-based model updating of a jacket-supported offshore wind turbine using measured vibration and SCADA data

Abstract

Multiphysics models are often utilized for structural design, condition assessment, and response prediction of a system, such as the support structure of offshore wind turbines. Although multiphysics models are considered to be of high fidelity, discrepancies are often observed between the model predictions and actual data measurements from the real structure. The model updating process reduces the model parameter uncertainty by minimizing the differences between the model and the measured data through an optimization procedure. In this paper, such a procedure is applied to an instrumented GE Haliade 6-MW jacket-supported offshore wind turbine by updating the tower and substructure modulus of Elasticity (E) to minimize differences between modal parameters identified from 1 month of measurements and those obtained from the OpenSees model or predicted from surrogate models. Surrogate models, including a neural network and a polynomial regression fit, are used to replace the OpenFAST simulations. The results indicate that the fully coupled OpenFAST model provides a more physically consistent representation in the medium power range (0.5–4.5 MW) by reducing variability in the updated E, whereas the OpenSees model is more suitable for low and high categories, where pitch control and reduced aerodynamic loading limit the influence of aero-hydro-servo-elastic effects.

1 Introduction

The development of more offshore wind farms worldwide demands the implementation of structural health monitoring (SHM) techniques to assess the state of health and performance of OWTs (Svendsen et al., 2022; Ramboll, 2022). Vibration-based SHM techniques relying on acceleration and strain measurements, such as system identification (Song et al., 2023a), finite-element model updating (Liu et al., 2018/12; Augustyn et al., 2020), input load and parameter estimation (Song et al., 2023b), virtual sensing (Tarpø et al., 2020; Iliopoulos et al., 2016), damage detection (Shid-Moosavi et al., 2025), and fatigue-life estimation (Bradshaw et al., 2024/05; Partovi-Mehr et al., 2024) have been applied to OWTs. That can be achieved through the physics-based model updating or digital twinning process, where a physics-based model of the structural system is integrated with measured data (Larsen et al., 2019; Tygesen et al., 2019; Graves et al., 2023). A digital twin of an OWT is a living, continuously updated virtual representation of the physical structure. The digital twin is updated over time to reflect the real-time state, behavior, and performance of the actual structure, e.g., an OWT (Tao and Qi, 2019). This allows us to continuously assess the structure’s integrity, detect damage, estimate the remaining lifetime, and support predictive decision-making (Grieves and Vickers, 2016).

Modern OWT engineering increasingly relies on high-fidelity and mid-fidelity numerical simulations to capture the complex aero-hydro-servo-elastic behavior of turbines. Mid-fidelity tools such as OpenFAST offer computationally efficient coupled aeroelastic simulations suitable for design and operational analyses (OpenFAST/openfast: OpenFAST v4, 2025; Partovi-Mehr et al., 2022). These models support the prediction of turbine responses under stochastic wind, wave, and operational conditions and are essential for load assessment, fatigue analysis, and decision-making throughout the turbine lifecycle. However, OpenFAST simulations can become computationally expensive when multiple model evaluations are required, as in real-time model updating and digital twin applications. Surrogate models address these challenges by providing fast approximations of these simulations through learning input–output relationships from carefully selected datasets (Benner et al., 2015). Common surrogate-modeling strategies include Gaussian process regression, polynomial regression, radial basis functions, neural networks, and physics-informed reduced-order approaches (Benner et al., 2015). By substantially reducing computational cost while preserving predictive accuracy, surrogate models enable efficient, data-driven engineering workflows for OWT design and operation (Dimitrov et al., 2018; Haghi, 2024; Haghi and Crawford, 2024).

In parallel, the accuracy and reliability of OWT simulations depend on the accuracy of the underlying physics-based models. So, model updating plays a critical role in refining aero-servo-hydro-elastic models to ensure simulated responses match the structural behavior from the observed measurements (Friswell and Mottershead, 1995; Marvala, 2010; Moynihan et al., 2023). This process typically involves adjusting model parameters—such as stiffness distributions, damping properties, soil–structure interaction characteristics, and boundary conditions—to reduce discrepancies between measured and predicted turbine responses. Model updating is fundamental in structural dynamics, damage identification, and SHM of OWTs, where mismatches between predictions and measurements may indicate modeling error, environmental variability, or structural degradation. SHM studies have shown that temperature and operational variations can influence identified modal parameters in vibration-based monitoring systems (Han et al., 2021/02). Model-updating approaches rely on optimization or stochastic sampling in Bayesian inference and can become computationally expensive. Implementation of surrogate models will accelerate the process by replacing expensive simulation calls with computationally efficient approximations (Ramancha et al., 2022; Schneider et al., 2022).

The combination of surrogate modeling and physics-based model updating is a powerful paradigm for offshore wind applications that require rapid or near real time assessments—including digital twin development, reliability based design, operational performance optimization, and condition based maintenance planning (Augustyn et al., 2021). Integration of computationally efficient surrogate models with sensor and monitoring data, for instance, updating foundation parameters from vibration measurements in monopile supported turbines (Delgado-Trujillo et al., 2025; Moynihan et al., 2025/12), or tower load estimation in a validated floating turbine digital twin (Branlard et al., 2024), allow the creation of accurate, scalable, and adaptive predictive frameworks for the next-generation of OWT systems. As OWTs become larger and more complex, such integrated modeling strategies will be increasingly important for improving structural reliability, reducing operational costs, and enabling data-driven long-term asset management.

Most applications of model updating in offshore wind turbine research have focused on standstill conditions or simplified structural models, rather than fully coupled aero-hydro-servo-elastic representations. For instance, deterministic and data-driven updating approaches have been applied to jacket or monopile substructures using finite-element models under idling, without explicitly accounting for operational effects such as aerodynamic loading, or controller dynamics (Augustyn et al., 2020; McAdam et al., 2023). Similarly, Bayesian and optimization-based model updating methods have been used to calibrate selected parameters, particularly foundation stiffness and soil–structure interaction properties, using measured response data (Moynihan et al., 2025/12). However, these studies generally rely on reduced-order or decoupled models and do not evaluate whether an updated aero-hydro-servo-elastic model can reproduce observed operational frequency variations.

Previous studies by the authors identified modal parameters using system identification methods and demonstrated that aero-hydro-servo-elastic models can capture a portion of operational variations in modal parameters, including changes in natural frequencies associated with wind speed, rotor speed, and control effects (Song et al., 2023a; Partovi-Mehr et al., 2023). These studies focused on identifying and interpreting stiffening and softening behavior using multiphysics simulations and measured data. In the present study, the aero-hydro-servo-elastic OpenFAST model is integrated, together with surrogate models, into a physics-based model updating framework using field measurements from an operating offshore wind turbine. The updating framework is examined to assess whether these models can account for observed frequency variations during operation without requiring large adjustments to structural model parameters such as the modulus of elasticity or soil stiffness. Partovi-Mehr et al. previously showed that soil–structure interaction effects are negligible for the rigid jacket-supported OWT foundation in BIWF (Partovi-Mehr et al., 2023); therefore, only the modulus of elasticity is updated in this work. To establish a baseline, an OpenSees finite element (FE) model and a standstill OpenFAST model are first updated and compared with the fully coupled OpenFAST operational model.

The novelty of this study lies in integrating a fully coupled aero-hydro-servo-elastic model (OpenFAST) and surrogate models into a physics-based model updating framework using field measurements from an operating OWT. The framework evaluates the OpenFAST model against a structural-only model (OpenSees) and quantifies how incorporating multiphysics effects reduces the need for large adjustments to the structural stiffness parameter during model updating, thereby improving the physical consistency. In addition, surrogate models based on polynomial regression and neural networks are implemented to replace computationally expensive simulations, enabling efficient and stable stiffness parameter estimation under varying operational conditions.

2 Wind turbine and dataset

The OWT in this study is GE Haliade 6 MW, and it is one of the five 6 MW OWTs located in the Block Island Wind Farm (BIWF), as shown in Figure 1, with a water depth of roughly 30 m. The substructure is a four-leg jacket. The measured position OWT is instrumented with accelerometers, strain gauges, and one inclinometer along its tower. The monitoring system has been recording data since 2021 (Hines et al., 2023). Data is stored in 10 min windows with a sampling frequency of 50 Hz. In this paper, acceleration data is used, and the layout of the accelerometers is shown in Figure 1.

FIGURE 1

The datasets selected for this work consist of 4,319 consecutive 10 min data sets during the month of September 2022 from triaxial accelerometers A1-A6 on the tower, a triaxial A9 and a biaxial A10 in the data acquisition (DAQ) cabinet on the tower bottom, and a biaxial accelerometer A7 on the platform. Supervisory Control and Data Acquisition (SCADA) has also been available during this timeframe. The SCADA data includes 10 min averages of wind speed, power, ambient temperature, rotor speed, yaw angle, wind direction, and blade pitch angle. There was an approximately 20 min lag in the DAQ clock, so the DAQ measurements are compared with those 20 min ahead in the SCADA data.

The acceleration data is filtered using a low-pass finite impulse response (FIR) filter with a cut-off frequency of 0.8 Hz. The cut-off frequency is chosen such that the cleaned filtered data contains only the first structural mode of the OWT system, which is discussed more in Sections 3.1.

3 Methods

This section presents the system identification analysis to extract the first FA and side-to–side (SS) vibration modes. The models developed in OpenFAST and OpenSees are then described. Next, the surrogate models—comprising a polynomial fit and a neural network—used to replace the models within the model updating process are introduced. Finally, the model updating framework is presented.

The workflow flowchart is shown in Figure 2 to illustrate the logical sequence of the research. The figure summarizes the OpenFAST model updating framework, including data acquisition, system identification, surrogate modeling, and convergence of the updated parameter.

FIGURE 2

3.1 System identification

In this section, a system identification process using data-driven Stochastic Subspace Identification (SSI-DATA) is explained.

Prior to system identification, the measured acceleration time histories are preprocessed to improve the system identification results. The raw acceleration measurements are low-pass filtered to isolate the frequency range containing the dominant structural first modes while suppressing high-frequency noise and filtering out the higher modes. A 512th-order FIR lowpass filter with a cutoff frequency of 0.8 Hz is designed. To reduce computational cost and improve numerical efficiency, the filtered acceleration data are subsequently down-sampled to 10 Hz which still preserve the dynamic content of interest.

The SSI-DATA method (Peeters, 2000) fits a linear stochastic state-space model to output-only measurements and provides estimates of the system matrices A and measurement matrix C in the state-space formulation, See Equation 1. From these estimated matrices, the modal parameters of the system—including natural frequencies, damping ratios, and mode shapes—are subsequently estimated (Overschee and De Moor, 1996). The SSI-DATA method was implemented by Song et al. (Song et al., 2023a) for 1 year system identification of the same instrumented OWT with some minor differences in hyper-parameters used.

The structural dynamics are represented in discrete-time stochastic state-space form as

Where is time index, is the state vector, is the measured acceleration vector, and are the system and measurement matrices, and and represent process and measurement noise, respectively.

For each 10 min data, a block Hankel matrix is constructed using Equation 2 from the measured outputs and partitioned into past and future components, and , respectively.

For each 10 min data, a block Hankel matrix is constructed using Equation 2 from the measured outputs and partitioned into past and future components, and , respectively.

Where contains the acceleration time histories, is the number of rows and is the number of columns in the matrix. and should be chosen such that the output measurement matrix use all the measurements, provide accurate results and have reasonable computational efficiency. In this study, in which 25 is the number of acceleration signals and 5949 is the number of data measurements in each 10 min window after filtering and down-sampling. should be chosen by the user not more than what is shown in Equation 3, which in our case would be , so the maximum of 114 is used to construct the Hankel matrix.

In this study, H consists of for all 25 accelerometer signals, so the number of rows would be , and the number of columns is calculated as Equation 4, equal to 5722.

After constructing the Hankel matrix , the algorithm one described in (Overschee and De Moor, 1996) is used in this study. First, the projection of the Hankel matrix with and and the projection of the same Hankel matrix but with one row moved down ( and ) are calculated as Equation 5.Where is shorthand for the projection of the row space of the matrix on the row space of the matrix . The RQ decomposition is used for this orthogonal projection. R matrix is defined as the upper-triangular R factor of the RQ decomposition , as described in (Overschee and De Moor, 1996). R matrix is then truncated to a square matrix with rows and the first columns of it. In this study, R factor matrix is . then would be the and columns of R matrix.

The singular value decomposition (SVD) of the unweighted projection is calculated because an unweighted principal component (UPC) algorithm is used in this paper. The order of the system is chosen as 24 in this study and then used to obtain and as the first diagonal values of . Then the extended observability matrices can be calculated as shown in Equation 6.

Where is the extended observability matrix without the last rows.

The forward Kalman filter state sequences and are calculated from Equation 7.

Then the matrices and in Equation 1 can be solved as shown in Equation 8.

Where is a block Hankel matrix with only one row of outputs.

An eigenvalue decomposition of provides the eigenvalues and eigenvectors as , where is the eigenvalue matrix and is the eigenvector matrix. Natural frequencies are calculated as where is the diagonal component of and is the time step size in the filtered down-sampled measurements ( second in this study). The subscript denotes selection of alternating eigenvalues, as the eigenvalues appear in complex-conjugate pairs, with each pair representing one physical vibration mode. Damping ratios are calculated as and mode shapes are computed as .

As the first FA and SS modes are closely spaced in frequency and persist across operating conditions, reference-based mode tracking is used. First, all identified mode shapes are rotated from the global (x, y) to the local (FA, SS) coordinate system using Equation 9 and the yaw angle, as shown in Figure 1. The rotated mode shapes in the (FA, SS) coordinate system is calculated as

Where and are the orthogonal mode shapes in (x, y) coordinates, and are the rotated orthogonal mode shapes in (FA, SS) coordinate system, respectively, and θ is the yaw angle measured clockwise from the magnetic North. A reference dataset during the monitoring period, along with its modal parameters, is chosen. The rotated mode shapes are then compared with the reference mode shapes and classified as FA or SS modes accordingly. A reference FA and SS mode shape is selected, and identified modes in each 10 min window are classified by maximizing the Modal Assurance Criterion (MAC). MAC value quantifies the correlation between two mode shapes, indicating how well they align. The MAC value ranges from 0 to 1, with 1 indicating an excellent match and 0 indicating poor correlation. MAC value between two mode shapes and is calculated as Equation 10.

Only modes with sufficiently high MAC values relative to the reference modes are retained, ensuring consistent tracking of the FA and SS modes over time.

3.2 Physics-based models

OpenFAST and OpenSees models represent the OWT at two different levels of physical fidelity. OpenFAST is a time-domain aero-hydro-servo-elastic solver that couples specialized modules through a glue code that exchanges loads and motions at each time step. ElastoDyn for the rotor-nacelle assembly and drivetrain dynamics, SubDyn for the finite-element tower and jacket substructure, AeroDyn for blade-element/momentum aerodynamics, HydroDyn for hydrodynamic loading on the submerged jacket members, InflowWind for the turbulent wind field, and ServoDyn for the generator-torque and blade-pitch controller. This coupling reproduces the operational mechanisms—centrifugal stiffening, aerodynamic damping, and pitch-induced thrust changes—that drive the observed variation of the FA natural frequency. OpenSees model, in contrast, is used here as a structural-only FE baseline that solves the equations of motion for the tower and jacket geometry alone, without aerodynamic, hydrodynamic, or control modules, and is therefore unable, by construction, to reproduce variation of dynamic properties due to operations.

In this subsection, two numerical models of the instrumented OWT, that are developed using the OpenSees, and OpenFAST platforms, are discussed. Within OpenFAST, two models are studied: the standstill condition and the operational condition, which includes the turbine controller. WISDEM is used to develop the OpenFAST model (WISDEM/WEIS: WEIS, 2025; Haghi et al., 2026). The simulations used to build the surrogate models from OpenFAST simulations are also discussed in this section.

The role of each modeling tool within the study is defined as follows. OpenSees is used as the structural FE baseline model to represent the tower and jacket substructure and to perform model updating under simplified structural assumptions. OpenFAST is used as the fully coupled aero-hydro-servo-elastic model to simulate the turbine under operational conditions and to evaluate how multiphysics effects influence modal parameters and reduce the need for stiffness adjustments.

3.2.1 OpenFAST

In OpenFAST, the tower and foundation are modeled in the SubDyn module. The jacket and tower FE model is built in SubDyn using the same methodology that was described in (Partovi-Mehr et al., 2023). While a typical OpenFAST configuration for onshore turbines models the tower using the ElastoDyn-Tower module, in which the tower mode shapes are predefined and remain fixed, in the present study the tower is modeled within the SubDyn module together with the foundation, as is common practice for offshore wind turbines in OpenFAST. In this configuration, the structural representation is based on a finite-element formulation, allowing the mode shapes and associated structural properties to vary during the model-updating process. Therefore, the tower in the OpenFAST model of this study is not constrained to fixed modal properties but is included in the finite element model updating framework. The FE model in SubDyn was built using 116 Timoshenko beam elements. The concentrated masses are added to the locations that the designers provided in the design document. Bradshaw et al. reported that the soil conditions at the instrumented offshore wind turbine location consist primarily of sand with a stiff clay layer (Bradshaw et al., 2024/05). Based on this information, the jacket substructure is modeled as fixed at the sea level, assuming a sufficiently stiff foundation.

3.2.1.1 OpenFAST simulations

The main goal of numerical simulations in this study is to create a database to train our surrogate models. These surrogate models are extensively explained in Section 3.3. The input to these surrogate models is the modulus of elasticity and wind speed, and the output is the first mode natural frequency in Fore-Aft (FA) direction. As model updating is an iterative optimization process, the multi-physics model should be run in each iteration. This is expensive and time-consuming; therefore, we substitute the OpenFAST model with surrogate models.

In this study, an OpenFAST model is developed for the GE 6 MW OWT for which the data is accessible to the authors. For developing the model, the WISDEM (WISDEM/WEIS: WEIS, 2025) framework is used to match the model outputs to measurements. This model development, which is mainly a model calibration process, starts from a publicly available reference wind turbine and the initial design. Afterwards, using the measurement at hand and employing WISDEM, the rotor is optimized to provide similar thrust, torque, and power. More details about the calibration process in WISDEM are provided in (Haghi et al., 2026).

After calibrating the OpenFAST model, it was used to run two sets of simulations to build two databases. First, to compare directly with the OpenSees model, the simulations were run with the rotor’s rotational speed set to zero. To build this database, OpenFAST simulations were run with the modulus of elasticity varied from 1.5e11 Pa to 2.5e11 Pa in 128 equal steps. Then, the first natural frequency for each of the runs was obtained from the linearized model (Jonkman and Jonkman, 2016). Figure 3 shows the modulus of elasticity E versus the first FA frequency of the simulations for the OpenFAST model in the standstill condition.

FIGURE 3

The second set of simulations mimic the turbine operation and wind speed measurement. For that purpose, simulations with two sets of variables were run: one environmental and one structural. The environmental variable is wind speed, ranging from 3 m/s to 17 m/s during the monitoring period (September 2022). This band of wind speed was divided into a resolution of 0.1 m/s to ensure coverage of all environmental conditions. For each considered wind speed value (3–17 at 0.1 intervals resulting in 141), the modulus of elasticity was changed in the same fashion as the standstill conditions, i.e., 128 values. This means running and linearizing for 141 × 128 = 18,048 OpenFAST simulations to obtain the first FA frequency. Utilizing Tufts University computational resources, the 18,048 OpenFAST simulations run in batches of ∼1,000 parallel jobs. The parallelization of the OpenFAST simulations reduced the computation time significantly and made building the OpenFAST database possible. The linearization was performed every 10° of the azimuth angle from 0° to 360°, and the average of over 36FA frequencies was used as the FA frequency for that condition. The controller is a variable-speed controller (Hansen and Henriksen, 2013), which means the turbine’s operational conditions (pitch angles for each wind speed) are defined by the user, and the controller determines the wind turbine’s rotational speed to generate the torque required to generate power in a specific wind speed. Figure 4 presents the simulated dependence of the modulus of elasticity (E) and FA frequency on wind speed, with further discussion provided in Section 4.

FIGURE 4

3.2.2 OpenSees

The details of the standstill OpenSees model are provided in (Partovi-Mehr et al., 2023). The major difference between the OpenSees and OpenFAST models is that a lumped mass and inertia at the tower top are used in the OpenSees model to represent the rotor-nacelle assembly (RNA), whereas a detailed RNA representation is used in the OpenFAST model. Additionally, the ServoDyn module in OpenFAST is used to represent the turbine controller during operation, whereas the OpenSees model is unable to simulate the OWT’s operating condition. The controller used in this study had not been developed in (Partovi-Mehr et al., 2023).

3.2.3 OpenSees and OpenFAST model validation

The OpenFAST and OpenSees models are validated by comparing the natural frequencies and mode shapes obtained from them with those identified from data measurements. The comparison between the OpenSees and OpenFAST mode shapes with those from system identification results for a dataset from 1 September 2022, is shown in Figure 5. The dataset is referred to as the reference mode discussed in Section 4.1. The mode shapes are shown in the local (X, Y, Z) coordinate system, where Z is vertical direction, X is the FA, and Y is the SS. The MAC value between the FA mode shapes of the OpenFAST and OpenSees models is 0.999, indicating strong agreement between the mode shapes obtained from the two models. Similarly, the MAC value for the SS mode is 0.999. The MAC values between the numerical models and the system identification ones are 0.995 in both FA and SS directions, as shown in Table 1. Therefore, the mode shapes of the numerical models are verified through their strong agreement with the system identification results.

FIGURE 5

Regarding the first mode, the FA frequency of the OpenSees and OpenFAST models is 0.293 Hz and 0.294 Hz, respectively, as shown in Table 1 for a standstill turbine, corresponding to a 0.3% difference. This condition serves as the initial state for the model updating process in both OpenSees and OpenFAST under standstill conditions. The natural frequency identified for the specific reference mode is 0.306 Hz, which is approximately 4% higher than the numerical model predictions because the measurements correspond to an operating turbine, where aerodynamic and rotor effects introduce stiffening behavior. The FA frequency over September 2022 has a mean of 0.290 Hz and a standard deviation of 0.011 Hz, as shown in Table 2. Therefore, the frequencies predicted by the numerical models fall within the range of mean ± standard deviation of the measured values. Furthermore, as illustrated in Figure 6c, the OpenFAST simulations conducted at several wind speeds produce FA frequencies that remain within the same range of mean ± standard deviation observed during September 2022. The SS frequency is 0.289 Hz and 0.293 Hz for the OpenSees and OpenFAST models, respectively, with the OpenFAST model exhibiting a 1.4% higher frequency. The system identification SS frequency is 0.290 Hz, corresponding to approximately a 1.0% difference from the OpenFAST prediction. Altogether, the OpenSees and OpenFAST models show strong agreement with the system identification results and are validated through comparison of the modal parameters.

FIGURE 6

3.3 Surrogate modeling

Surrogate models are simplified, computationally efficient representations of complex physical or numerical simulations, designed to approximate input–output relationships with minimal computational cost. They are beneficial for physics-based model updating where multiple OpenFAST simulations are time-consuming. In this paper, two surrogate models are used to represent the OpenFAST models at different conditions: a polynomial regression model and a neural network, representing the OpenFAST standstill and operation OWT models, respectively. Polynomial regression provides a classical approach, fitting an explicit algebraic relationship between inputs and outputs, which is easy to interpret and fast to evaluate. Neural networks, on the other hand, offer a flexible, data-driven framework capable of capturing highly nonlinear and multidimensional behaviors that are difficult to model with simple polynomials.

3.3.1 Polynomial

For the OpenFAST standstill model, where aerodynamic loading and control effects are absent, the relationship between the stiffness updating parameter and the modal response is smooth and weakly nonlinear. Therefore, a second-degree polynomial surrogate model is employed to approximate the dependence of the FA natural frequency on the Young’s modulus . The polynomial surrogate is defined in Equation 11.where denotes the predicted first FA natural frequency and , , and are regression coefficients obtained through least-squares fitting to a set of OpenFAST standstill simulation results generated over a prescribed range of E. This polynomial surrogate provides a computationally efficient and differentiable approximation suitable for optimization-based model updating. The quality of the polynomial fit is quantified using the root mean squared error (RMSE), which measures the average deviation between the surrogate predictions and the corresponding OpenFAST simulation results.

In contrast, for the OpenFAST operational model, the presence of aero-hydro-servo-elastic coupling and control-system dynamics introduces more substantial nonlinearities and interactions between operating conditions and structural parameters. As a result, a polynomial surrogate is insufficient to capture the system’s behavior. Instead, a neural network surrogate model is employed to represent the operational OpenFAST response, as described in Section 3.3.2. This separation allows the surrogate modeling strategy to be matched to the underlying physics and complexity of each simulation case.

3.3.2 Neural network

A feedforward neural network architecture (Goodfellow et al., 2016) is developed as the surrogate model for the operational OpenFAST model. This simple Neural Network takes the wind speed and modulus of elasticity as inputs from the database built earlier, and maps them to the FA frequency. The database of the simulations from the operational OpenFAST model is divided into 95% for training and 5% for testing. Then, a k-fold cross-validation methodology is used (for this case, 5-fold) to prevent overfitting. The trained neural network with the smallest error out of the 5-fold is used as the surrogate model in the continuation of this work. A schematic presentation of the utilized neural network is shown in Figure 7. TensorFlow (Abadi et al., 2016) is employed for building and training the neural network.

FIGURE 7

A model for 2,000 epochs per cross-validation fold is trained to ensure convergence. The neural network activation function was set to tanh, and a 20% dropout rate was set during training. Before training, data was normalized to have a mean of zero and a standard deviation of one. The training and testing loss function is set to Relative Root Mean Squared Error (RRMSE).

3.4 Model updating

The dynamic properties of the models in OpenSees or OpenFAST differ from the measurements due to differences in modeling and measurement errors. To minimize differences between the model’s properties and the measurements, specific model parameters are tuned. An objective function, as shown in Equation 12, is defined and optimized to find the best model parameters that can fit the data.where is the objective function, and are the weights of frequency and mode shape residuals, respectively, is the natural frequency residual, and is the mode shape residual, both are scalar in this study. is the model updating parameter corresponding to the modulus of elasticity, and is the initial value of the updating parameter . is the L2 regularization term, which is weighted by the regularization parameter . The regularization term adds a penalty proportional to the square of the parameter change (). It discourages large deviation from the prior value of parameter . The frequency and mode shape residuals are calculated as Equation 13 and Equation 14.where index 1 refers to the first FA mode, and and are the first FA radial natural frequencies of the identified and the FE model, respectively, and MAC₁ is the MAC value between the identified and the FE model’s first FA mode shapes.

In this paper, the updating parameter is the Young’s modulus for steel used in the tower and substructure. The initial value of the updating parameter () is 200.00 GPa, and the weights are , , . is obtained from the FE model in OpenSees and predicted using a surrogate model, discussed in 3.3, for the standstill and operating models in OpenFAST.

In this work, the modulus of elasticity is treated as a global stiffness parameter representing the overall structural stiffness of the tower and substructure. The approach is adopted to maintain parameter identifiability and numerical stability. A segmented or spatially distributed parameter updating is not the focus of this paper. Introducing multiple segmented stiffness parameters would increase the dimensionality of the optimization problem and could lead to non-unique solutions without sufficient spatial measurement resolution. Furthermore, the primary goal of the model updating procedure in this study is not to produce a detailed spatial calibration of structural properties, but rather to assess how different modeling assumptions (e.g., inclusion of aero-hydro-servo-elastic effects) influence the required stiffness adjustments during operation.

3.4.1 Rotation of numerical mode shapes

In the case that a dynamic system has two vibration modes with identical or closely-space frequencies (i.e., symmetric geometry), the two numerical mode shapes will remain perpendicular are non-unique and but can be rotated in a plane (Daniz et al., 2024). To improve the match between numerical and identified mode shapes, i.e., increase the MAC value, small rotations of the numerical coordinate system result in mode shapes that remain essentially unchanged in form. So, the numerical mode shapes are slightly rotated counterclockwise using the angle α calculated in Equation 15, and the corrected mode shapes are obtained as shown in Equation 16.Where and are the numerical model’s mode shapes in (X, Y) coordinate system, and are the rotated numerical mode shapes, and and are the identified mode shapes in (FA, SS) coordinate system. The schematic rotation of mode shapes is shown in Figure 8.

FIGURE 8

4 Results and discussion

In this section, results of the system ID, surrogate models and the model updating are discussed.

4.1 System identification results

As explained in Section 2, acceleration signals are recorded in 10 min windows. After analyzing these signals using the SSI-DATA method, modal parameters—namely natural frequencies, damping ratios, and mode shapes—are identified for every 10 min window.

As the frequency values are very close and the mode shapes are similar, a reference mode is chosen to distinguish between the FA and SS modes. A reference mode in September 2022 is selected such that the first FA and SS mode shapes align with the x and y directions of the sensors. The selection is important because it eliminates the yaw rotation of mode shapes. When FA and SS are in the x and y directions, the mode shapes can be directly used from the system identification results. In addition, this reference mode provides a convenient and consistent baseline for numerical model validation. Another criterion for selecting this reference mode is that the turbine is operating around the rated conditions, with a rotor speed of 11.09 rpm at a wind speed of approximately 9.05 m/s, making the reference state representative of a stable and well-defined operational regime. This reference mode is used to consistently separate the FA and SS modes throughout the entire month. The first FA and SS frequencies of the reference mode are 0.306 and 0.290 Hz, respectively, with mode shapes vibrating on the diagonals of the platform, as shown in Figure 9.

FIGURE 9

The MAC values between each identified mode shape and its corresponding reference mode shape are shown in Figure 10a, where all SS and FA MAC values exceed 0.7, indicating a strong agreement between the identified mode shapes and the reference counterparts. The damping ratios and natural frequencies of the first FA/SS modes are shown in Figures 10b, c, respectively.

FIGURE 10

Out of 4,319 datasets, 246 SS modes and 729 F A modes could not be identified with MAC > 0.7; 22 datasets could not be identified as either FA or SS were missing. Therefore, 3,116 datasets are identified with both FA and SS modes, which are shown in Figure 6a. For datasets corresponding to an idling or a standstill turbine in low wind, the FA and SS designations are not physically meaningful, since the blades are feathered and the yaw controller does not align the nacelle with the wind. As a result, the FA and SS modes cannot be reliably distinguished when the pitch angle is close to 90°, corresponding to fully feathered blades. Therefore, out of 3,116 datasets, only those with pitch angle<70° and power≥0 (operating condition), totaling 2,816 datasets, are retained for further analysis. The results are shown in Figure 6b with the power color bar. As mentioned previously, the SS frequency remains relatively constant, whereas the FA frequency varies under different operational and environmental conditions.

In general, turbine structures are designed such that the first natural frequency does not resonate with the blade-passing frequencies of 1P and 3P (Van Der Tempel, 2006). For the instrumented OWT, a limited number of instances are observed where the rotor speed results in resonance with the tower and substructure’s natural frequency. However, these occurrences are relatively rare, as shown more clearly in Figure 11a. In the zoomed view, the turbine controller is designed to avoid sustained operation in the rotor speed range of approximately 5–6.5 rpm, as shown in Figure 11b, corresponding to 0.250–0.325 Hz at the 3P frequency where the FA frequency lies. The upper bound is very close to the maximum FA frequency observed in this study (0.320 Hz), so it is suggested that the avoided range of rotor speed would be increased for similar substructures. Of the 2,816 operating datasets, an additional 30 datasets within this resonance range are excluded from the subsequent analysis. These datasets are selected such that the difference between the FA frequency and 3P frequency is less than 0.01 Hz. As a result, only 2,790 datasets are ultimately considered for model updating. This is still a very rich dataset encompassing the common operating conditions of the turbine.

FIGURE 11

As summarized in Table 2, the SS mode exhibits a highly consistent frequency, with a mean value of 0.290 Hz and a standard deviation of 0.001 Hz, along with a mean damping ratio of 0.2% and a mean MAC value of 0.95 throughout the monitoring period. In comparison, the first FA mode has a mean frequency of 0.296 Hz with a standard deviation of 0.011 Hz, a mean damping ratio of 1.5% with a standard deviation of 0.7%, and a mean MAC value of 0.94. Overall, the FA mode exhibits noticeably greater variability than the SS mode.

The mean and standard of the identified first FA frequency within each wind speed bin are calculated and shown in Figure 6b. Under similar wind speed conditions, the OpenFAST simulation results are compared with the identified ones in Figure 6c. This initial comparison suggests that the OpenFAST model captures a portion of the frequency variation trend, which is expected to improve the subsequent model updating process by reducing the amount of frequency discrepancy that must be compensated through parameter updates. Further analysis of this behavior is presented in Section 4.3.

One observation from the SCADA data is that the rated rotor speed does not happen at the rated wind speed. It is observed that maximum power of 6 MW is generated at the rated wind speed of approximately 11 m/s, as expected. Whereas, the rotor speed reaches its maximum at a lower wind speed, around 9.5 m/s. The latter wind speed corresponds to the peak in the FA frequency peaks, as shown in Figure 6b. This is because of the centrifugal effect of the operating rotor that causes stiffening in the wind turbine structure. So, the maximum FA frequency peak is where the rotor speed reaches its rated value. The variation in FA frequency after the wind speed of 9.5 m/s can be due to several factors such as pitch control and lower thrust force.

The stiffening behavior is primarily observed as rotor speed and aerodynamic loading increase toward rated operating conditions. In this regime, increased rotor speed leads to centrifugal stiffening of the OWT system. As the rotor spins, centrifugal forces pull the slender blades outward. This tension straightens the blades, increasing their structural stiffness and raising their natural frequency and the natural frequency of the system (Hang et al., 2022). The largest stiffening is observed in the medium power operating range, where rotor speed increases with wind speed and aerodynamic interaction is strongest.

The dynamic softening is referred to as spin softening. This occurs due to the interaction between the blade’s rotation and its own curved geometry (Chen et al., 2023). Beyond the rated rotor speed, the turbine controller activates blade pitch control to regulate power production. As the blade pitches, geometric changes and inertial effects reduce its flexural rigidity, softening the structure and lowering the increased natural frequency in the rated operating regime.

4.2 Surrogate models results

This section presents the train and test results of the two surrogate models.

4.2.1 Polynomial surrogate model for OpenFAST-standstill

Figure 12 presents the results of the polynomial surrogate model fitted to the OpenFAST standstill simulations. The OpenFAST simulations are performed with the AeroDyn and Inflow modules off and a fixed blade pitch angle of 0°, such that aerodynamic and control effects are excluded. A design of experiments consisting of 128 equally spaced values of the Young’s modulus , as discussed in 3.2.1.1, is used to generate the training dataset. The second-degree polynomial surrogate captures the relationship between and the first FA natural frequency, which is expressed as shown in the figure. The root mean squared error (RMSE) of the fit is 0.0003 Hz, indicating excellent agreement between the surrogate predictions and the high-fidelity OpenFAST standstill simulations. This level of accuracy demonstrates that the polynomial surrogate provides an efficient and reliable representation of the OpenFAST standstill response for subsequent model updating.

FIGURE 12

4.2.2 Neural network surrogate model for OpenFAST-operational

After building the database for the operational OpenFAST model and training the neural network on 95% of the data with 5-fold cross-validation, the best model is selected from the 5-fold results. This model is then tested on the 5% of the data, which consists of 894 data points that are not utilized during training. The training dataset was normalized to have a mean of zero and a standard deviation of one. Afterwards, the testing data set was normalized using the mean and std deviation of the training dataset, to prevent data leakage and ensure the test data is transformed consistently with what the model learned from. The test results are presented in Figure 13.

FIGURE 13

The results show that the neural network can predict the test results very accurately. With an R² value of 0.9983, the model predicts variation in the data with high precision. This guarantees that minor errors in our surrogate model predictions do not propagate into our optimization process and affect the model update results.

4.3 Model updating results

The three numerical models—OpenSees, OpenFAST under standstill conditions, and OpenFAST under operational conditions (using a controller)—were successfully updated using the proposed optimization-based model updating framework. The improvement in frequency matching is confirmed in Figure 14. The time history in Figure 14a shows that the first FA frequency error (model minus identified frequency) remains small (between and after updating, whereas the initial error was between −0.03 and 0.03 Hz, as shown in Figure 14b. The histogram in Figure 14c indicates that the error distribution is tightly clustered near zero. Among the three models, the mean FA frequency error is closest to zero for the OpenFAST model under operational conditions (with a Controller), indicating slightly better overall bias reduction than the other two updated models.

FIGURE 14

Figure 15 presents the MAC values between the identified mode shapes and those obtained from the updated OpenSees (blue) and OpenFAST (red) models, all of which are greater than 0.6. This indicates that the rotated mode shapes can provide an improved, though not perfect, representation of the measured modal behavior and supports the use of limited rotation as a practical step for comparing numerical and identified mode shapes. In addition, the OpenSees and OpenFAST mode shapes match well, as evidenced by their MAC values lying on top of each other in Figure 15, which is consistent with Figure 5 where the OpenSees and OpenFAST mode shapes were shown to agree with a MAC value of approximately 0.999.

FIGURE 15

Figure 16 presents the modal frequencies obtained from the system identification results together with those from the updated OpenSees, OpenFAST–Standstill, and OpenFAST–Control models. The comparison shows that the frequencies from the numerical models closely match the identified frequencies throughout the monitoring period, with no systematic deviation. This consistency is in line with the small FA frequency errors reported in Figure 14a, where the differences between the updated model frequencies and the identified values remain below .

FIGURE 16

Figure 17 shows the time history of the updated Young’s modulus for the three models. The updated parameter varies over time, consistent with the temporal variability observed in Figure 14, reflecting changes in the identified modal properties and the operating and environmental conditions across the monitoring period. The updated varies between approximately 170 GPa and 240 GPa over short time periods. Although the variability range becomes smaller when using the OpenFAST-control model, the magnitude of this variation remains difficult to justify from a purely physics-based perspective, since the material property cannot realistically change to such an extent in practice. Instead, this apparent variation indicates that even the aero-hydro-servo-elastic representation in OpenFAST does not fully capture all mechanisms influencing the natural frequency of the BIWF offshore wind turbine. Therefore, additional factors—such as unmodeled operational conditions, environmental effects, or uncertainties in system dynamics—likely contribute to the observed softening and stiffening behavior of the turbine.

FIGURE 17

Figure 18 further relates the updated Young’s modulus to the first FA natural frequency for the three updated numerical models and provides additional insight when considered together with the statistical results summarized in Table 3. As shown in Table 3, the OpenSees and OpenFAST–Standstill models exhibit very similar levels of variability, with standard deviations of 14.49 GPa and 14.68 GPa, respectively, and their mean updated values differ by only about 2 GPa. This close agreement indicates that, despite differences in modeling framework, both models capture similar effective stiffness characteristics after updating.

FIGURE 18

Consistent with these statistics, Figure 18 shows that the trends between updated and FA frequency for OpenSees and OpenFAST–Standstill are highly similar, with both models exhibiting comparable relationships between stiffness and dynamic response. In contrast, the OpenFAST–Control model displays a different pattern, with the updated showing dependence on rotor speed, power, and wind speed, reflecting the additional influence of aero-servo-elastic effects under operational conditions. These results indicate that while the OpenSees and OpenFAST–Standstill models primarily reflect structural stiffness effects, the OpenFAST–Control model captures the combined influence of structural, aerodynamic, and control-related dynamics. For this reason, subsequent discussion focuses on comparing the OpenSees and OpenFAST–Control results, with OpenFAST–Standstill considered largely representative of the structural-only response with minor differences.

Figure 19a shows that the updated modulus of elasticity (E) in the OpenSees model exhibits a trend similar to that of the first FA natural frequency shown in Figure 11b as wind speed varies. As the rotor speed reaches its rated value at a wind speed of approximately 9.5 m/s, both the FA frequency in Figure 11b and the updated (E) values reach their maximum around this wind speed, followed by a decrease at higher wind speeds. Figure 19b shows the OpenFAST–Control model exhibits less variability in the updated E values around a wind speed of approximately 9.5 m/s, indicating a more stable response under operating conditions. The tiled histogram plots in Figure 19d further show that the highest counts of updated E values in the OpenFAST–Control model are clustered closer to 200 GPa, corresponding to the nominal Young’s modulus of steel, whereas the OpenSees results, as shown in Figure 19c, display a broader distribution and larger positive bias to account for stiffening effects in 7–10 m/s wind speed range.

FIGURE 19

Regarding the observed trend, the inclusion of aero-elastic behavior enables the model to reproduce the operational stiffening of the turbine as rotor speed increases toward the rated condition. This effect arises from the combined influence of aerodynamic loading, increased thrust, and dynamic coupling between the tower and the rotating RNA, which modify the effective system stiffness and natural frequency. Beyond the rated rotor speed, blade pitch control reduces aerodynamic loading and alters the dynamic interaction between the rotor and tower, leading to lower stiffening of the OWT.

Building on the trends observed in Figures 19, 20 provides a binned statistical summary of the updated Young’s modulus E as a function of wind speed and power for the OpenSees and OpenFAST models. For the two operational parameters, both models exhibit similar qualitative behavior, with the mean updated E generally increasing with wind speed, and power until the maximum rpm is reached and after that drops. This consistency indicates that both modeling approaches capture the same overall directional relationship between the effective structural stiffness and turbine operating conditions. However, notable quantitative differences are observed. Between the two parameters, OpenSees exhibits a larger range of change in the mean updated E compared to OpenFAST. Although the aero-hydro-servo-elastic behavior in OpenFAST captures some changes in modal parameters (e.g., FA frequency), the model does not fully reproduce all observed variations, and the remaining discrepancies are compensated through adjustments to the modulus of elasticity E.

FIGURE 20

The updated parameter E, as shown in Figure 20a, ranges from 187.8 to 214.1 GPa in the OpenSees model and 189.7–204.7 GPa in the OpenFAST model when wind speed changes from 4 to 9 m/s. This shows that the variability in E decreases when using OpenFAST. Furthermore, the standard deviation of E for the OpenFAST model is slightly less than that of the OpenSees model.

For a more detailed analysis of model updating results, we consider the results in 3 groups of power generations: low (0–0.45 MW), medium (0.5–4.5 MW), and high (4.5–6.04 MW). As shown in Figure 20b, the mean updated Young’s modulus E in the OpenFAST model remains closer to the nominal steel value of 200 GPa compared to the OpenSees model over the medium power operating range, whereas the OpenSees model stiffness parameter has consistently higher mean values across most power levels. Over the same range, the standard deviation of E is slightly lower for OpenFAST than for OpenSees, indicating reduced variability in the updated stiffness estimates. The lower standard deviation of the updated modulus of elasticity E observed in the OpenFAST results occurs because a portion of the measured frequency variability is explicitly captured by the aero-hydro-servo-elastic physics included in the OpenFAST model. By accounting for rotor–tower coupling, controller and pitch effects, as well as gyroscopic and centrifugal stiffening, OpenFAST naturally reproduces frequency stiffening and softening trends associated with changes in wind speed, rotor speed, and power. Consequently, these operational effects appear directly in the model response, reducing the need for compensatory stiffness adjustments during model updating. In contrast, the structural-only OpenSees model cannot represent these operational influences, and discrepancies between measured and predicted frequencies are therefore absorbed through larger and more variable updates to the stiffness parameter E, resulting in a higher standard deviation.

Figure 21a illustrates the variation of the updated E vs. rotor speed, showing that as the rotor speed increases, a stiffening effect is observed on the instrumented OWT system up to approximately the rated rotor speed of 11.5 rpm. Near the rated rotor speed, E exhibits increased variability without a clear trend, which may be attributed to changes in blade pitch angle and reduced aerodynamic coupling with the structural vibration.

FIGURE 21

To characterize the increase in the updated Young’s modulus E with rotor speed in the medium power category, linear regression lines are fitted to the filtered data (retaining only data points with power between 0.5 and 4.5 MW) for both the OpenSees and OpenFAST models, as shown in Figure 21. For both models, the root mean squared errors (RMSEs) are similar, at approximately 9.4–10 GPa. The intercept of the fitted line increases from 169.9 GPa in the OpenSees model to 183.8 GPa in the OpenFAST model, corresponding to an increase of 13.9 GPa. In contrast, the changes in slope are more pronounced; the slope decreases from 4.1 to 1.9 when using the OpenFAST model, corresponding to a reduction of 53%. The results indicate that the fitted linear trends confirm a systematic increase in the updated stiffness with rotor speed in the medium power range, while also showing that the multiphysics-based model updating yields a substantially flatter slope than OpenSees, reflecting reduced sensitivity of the updated modulus of elasticity to the frequency changes in medium-power operational condition.

Figure 22 illustrates the individual histogram plots of the updated E distributions within each operational bin. For most operational bins, the updated values in both the OpenSees and OpenFAST models exhibit bell-shaped, near-normal distributions, with the fitted normal curves providing reasonable approximations. This suggests that the variability within each operational bin is random and can be statistically characterized using the mean and standard deviation.

FIGURE 22

Figure 23 further illustrates the inter-variable relationships through the Kernel Density Estimation (KDE) joint distribution plots. They provide a holistic view of the interrelationships between updated E in the OpenSees and OpenFAST models, wind speed, power (MW), and rotor speed (rpm), categorized by power (low, medium, high).

FIGURE 23

The off-diagonal scatter plot (or distribution plot) for versus shows a strong positive correlation, indicating that as one increases, the other generally increases. However, as discussed before, subtle differences in their distributions and magnitudes are visible. The KDEs highlight regions of higher density, confirming that these models generally track each other’s predictions, but with noticeable offsets in certain operational ranges.

The diagonal subplots in the first two rows (i.e., – and –) provide the marginal distributions of the updated modulus E for each power category and form the primary basis for assessing proximity to the nominal steel value of 200 GPa. In these diagonal panels, the OpenFAST distribution for the medium power category is more tightly clustered around the dashed 200 GPa reference line than the corresponding OpenSees distribution. In addition, the off-diagonal joint subplots relate E to wind speed, power, and rotor speed (e.g., –Power and –Power subplots in the second and fourth rows). In these subplots, OpenFAST shows relatively compact contours around GPa across a wide range of power and rotor speed, particularly in the medium power regimes, whereas OpenSees exhibits larger dispersion and a more substantial upward shift in E with increasing operational demand. For the low power category, both OpenSees and OpenFAST exhibit broader and more scattered distributions of the updated Young’s modulus E, reflecting increased uncertainty under lightly loaded operating conditions which could be caused by system identification variability. In the high-power category, both models show increased spread due to pitch-regulated operation, but OpenSees remains slightly more centered near the 200 GPa reference line.

Altogether, the observations from the individual histogram plots (showing the modulus of elasticity E distributions per bin) in Figure 22 and the KDE joint distribution plots in Figure 23, show that the E predictions from OpenSees and OpenFAST are highly correlated with operational intensity in the medium power category. The histograms provide detailed insights into the distribution characteristics (mean, standard deviation, and normality) within discrete operational bins, while the KDE joint distributions offer a broader view of the inter-variable relationships and how these vary across macro-level operational categories like wind speed ranges. The differences in variability and magnitude between the models remain a key finding, with OpenSees generally showing a slightly higher spread and range in its elastic modulus predictions.

5 Conclusion

This study developed a multi-physics model updating framework for a jacket-supported offshore wind turbine using long-term vibration measurements. An SSI-DATA system identification method was applied to extract modal parameters, which were used to update numerical models in OpenSees and OpenFAST. Surrogate models enabled efficient optimization-based updating under both standstill and operational conditions. All three models were successfully updated, and the updated OpenFAST operational model captured a portion of the observed FA frequency variations associated with changing wind and operating conditions in the medium power category (0.5 MW–4.5 MW). The medium power category is associated with rotor speed between 6 and 11.5 rpm and wind speed between 5 and 9.5 m/s. Observed from the SCADA data, the rotor speed reaches its maximum at a wind speed of 9.5 m/s, where the turbine generates 4.5 MW. Then, at the same 11.5 rpm but with an increased wind speed of 11 m/s, power generation is 6 MW.

The results demonstrate that incorporating aero-hydro-servo-elastic effects in the model updating process reduces the adjustments to structural stiffness parameters, e.g., modulus of Elasticity E, compared to an OpenSees model, especially in the medium power operation. The results indicate that incorporating aero-elastic behavior enables the model to reproduce the operational stiffening of the turbine as rotor speed increases toward rated conditions due to increased aerodynamic loading and tower–RNA coupling, while reduced aerodynamic interaction from blade pitch control beyond rated speed leads to diminished stiffening effects.

The fully coupled OpenFAST model showed reduced variability in the updated modulus of elasticity E, in the medium power category, indicating improved physical consistency under operational conditions. However, using only a structural tool like OpenSees would be similar to OpenFAST for low (0–0.5 MW) power category. In the high power category, due to the pitch control and low aerodynamic loads, the updated E does not increase that much, however it varies between the low and high E values (160–240 GPa). Despite the improved physical representation of operational effects, the observed variation of the updated modulus of elasticity (approximately 160–240 GPa) indicates that even the aero-hydro-servo-elastic OpenFAST model does not fully capture all mechanisms influencing natural frequency changes, suggesting that additional sources contribute to the softening and stiffening behavior of the turbine.

5.1 Scope and limitations

This study focuses on model updating of a full-scale, jacket-supported offshore wind turbine using field measurements and physics-based simulations. The primary objective is to evaluate how different modeling frameworks—specifically a structural-only finite element model (OpenSees) and a fully coupled aero-hydro-servo-elastic model (OpenFAST)—influence the updated global stiffness parameter under varying operational conditions. The work emphasizes system-level dynamic behavior, operational effects on modal parameters, and the feasibility of using surrogate models to improve computational efficiency in the updating process. The methodology is intended for applications such as structural health monitoring, digital twin development, and operational performance assessment of offshore wind turbines.

Several limitations should be noted. First, the model updating process considers a single global stiffness parameter (modulus of elasticity) rather than spatially distributed parameters; therefore, the results represent system-level stiffness changes rather than localized structural variations. In addition, the conclusions are based on data from a single turbine and a specific site condition; while the proposed methodology is generalizable, quantitative results may vary for different turbine types, support structures, or operational environments.

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