A damage detection and location scheme for offshore wind turbine jacket structures based on global modal properties

Structural failures of offshore wind turbine substructures might be less likely than failures of other equipment of the wind turbine generator, but they pose a high risk due to the possibility of catastrophic consequences. Significant costs are linked to offshore operations like inspections and maintenance, thus remote monitoring shows promise for cost-efficient structural integrity management. This work is aimed to investigate the feasibility of a two-level detection, in terms of anomaly identification and location, in the jacket structure of an offshore wind turbine. A monitoring scheme is suggested by basing the detection on a database of simulated modal properties of the structure for different failure scenarios. The detection model identifies the correct anomaly based on three types of modal indicators, namely natural frequency, the modal assurance criterion between mode shapes, and the modal flexibility variation. The supervised Fisher’s linear discriminant analysis is applied to transform the modal indicators to maximise the separability of several scenarios. A Fuzzy clustering algorithm is then trained to predict the membership of new data to each of the scenarios in the database. In a case study, extreme scour phenomena and jacket members ’ integrity loss are simulated, together with variations of the structural dynamics for environmental and operating conditions. Cross-validation is used to select the best hyperparameters, and the effectiveness of the clustering is validated with slight variations of the environmental conditions. The results prove that it is feasible to detect and locate the simulated scenarios via the global monitoring of an offshore wind jacket structure.


INTRODUCTION
The increasing need for reduced operation and maintenance costs has led to focused research on monitoring concepts and frameworks for assessing the health status of wind turbine generator (WTG) systems [1]. Based on the different reliability levels [2], much focus has been on drivetrain components and the electronics of the control systems [1], [3]- [6]. With regard to structural failures, the damage to the turbines' blades are relatively common in the offshore environment [7]. Concerning offshore WTG's tower and foundation, although structural failures are relatively unlikely due to design conservatism, their presence could result in dramatic consequences if undetected [8]. It might also not always be possible to design the support structure in an inspection-free estimation of location and severity of simulated structural damage in onshore WTG towers. The main findings outlined that a detection algorithm trained on frequencies only performed better for the assessment of the severity.
In terms of indicators of the damage, the modal curvatures have been extensively investigated for experimental and numerical studies of beam-and plate-like structures [30], [31]. Therefore, in the context of civil engineering for the wind energy sector, curvature-based methods found an application for the detection of blades damage mainly [32], [33]. However, as concerns the monitoring of the global modal properties of a wind turbine structure, Richmond et al. [28] argued that the detection via the mode curvature could be challenged by the generally limited amount of sensors installed.
Extensive research was also conducted for the detection of structural failures in offshore (oil and gas) jacket platforms. Liu et al. [34] suggested a modal flexibility-based method using a finite element (FE) model updating technique. Modal flexibility detection approaches belong to a family of traditional vibration-based methods, together with frequency-based and mode shape ones [35]. The modal flexibility is influenced by the low-order modes mainly, being thus suitable for the offshore wind structural health monitoring applications, where higher modes are generally difficult to extract. Liu et al.
applied a gradient-based method for the minimisation of the Frobenius norm of the matrix representing the residual of the flexibility between the damage condition and a healthy reference (cf. [12] and Section 2.2). Another model updating approach applied to an offshore truss structure was proposed by Malekzehtab and Golafshani in [36]. For their updating procedure they applied a genetic algorithm to optimise a cost function defined ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering Special Issue on Probabilistic Approaches for Robust Structural Health Monitoring of Wind Energy Infrastructure (SI047B) model updating -, to instruct data-based monitoring algorithms to identify and locate the damage. As the feasibility of the suggested approach is the main concern of this work, the investigation is limited here to the turbine idling state for simplicity.
Starting from the findings of [28], six types of localised structural damage and several levels of scour are simulated for the case study presented in Section 3. The feasibility of the detection is discussed in Section 4, together with a consideration of the set of features to derive and track. Finally, in Section 5, the challenges and limitations of the current approach, prior a field application, are outlined.

METHODOLOGY
The flow of data and processes for the field employment of this monitoring approach is given in Section 2.1. In Section 2.2, details are provided on the simulation setup to extract the modal properties of the structure and calculate their deviations. The machine learning algorithms and the processes for their training, testing and validation are presented in Section 2.3.

Monitoring approach
An overview of the workflow for the suggested health monitoring of the WTG structure and damage detection is given in Figure 1. The pillar of this strategy is the model-based digital twin technology [40]- [42]. Passing through the screening and diagnostics of the structure (level 1), the FE model updating (level 2), the load calibration (level 3), and the quantification of the uncertainties (level 4), the digital twin can finally be employed to continuously monitor the accumulated fatigue damage in the hot spots The modal properties of the system in its normal behaviour -depending on the environmental and operational conditions (EOC) -and in its damaged status, are then retrieved from natural frequency analysis (NFA) simulations. By comparing the derived modal properties with those of a reference healthy scenario, modal indicators, such as the modal assurance criteria (MAC) and the modal flexibility variation ( ), are calculated and employed to track the system's dynamics evolution and deviation. This set of information, stored into a database, is used for instructing detection models to identify and locate (detection levels I and II) the system's anomalies (in red). The instructed algorithms can then be used on the modal data calculated from the field vibrational data, to raise alarms if the pattern of one of the simulated damage scenarios is recognised (in yellow).
In contrast to the approaches of [34] and [36], where a further model updating is used to detect location and severity (level III) of the damage, a classification-based detection is suggested here. The reason for this decision is related to the fact that, for offshore wind applications, several types of damage are potentially critical for the structure. The approach proposed can easily be extended to set up the detection of anomalies of every type, while the studies in [34], [36] find their application for the detection of damage controlled by a single model parameter -e.g. elements' and joints' stiffness. Additionally, the uncertainty of the simulated data is introduced by a slight variation of the environmental parameters (e.g., scour and tidal phenomena), rather that adding several levels of white noise to the signals.

Data acquisition
The study of the dynamics of the WTG structure in its healthy conditions, and in response to anomalies in the system, is obtained via NFA of an FE-updated model, set up in Ramboll's in-house ROSAP (Ramboll Offshore Structural Analysis Package) software.
This implementation does not allow the integration of moving and/or rotating parts, and thus represents only the WTG dynamics in idling condition. The rotor-nacelle-assembly is, however, integrated for its contribution in terms of mass and inertia. The methodology suggested can be applied independently of the type of software used for the analysis. It is worth mentioning that, if the modes extraction is carried out via an aero-hydro-servoelastic tool, it would be possible to extend the analyses to account for the interference of the rotor dynamics and the effect of the different WTG operating regimes.
The eigenfrequencies and their corresponding mode shape vectors are derived for several integrity scenarios of the WTG jacket and for varying environmental conditions.

Modal Assurance Criteria (MAC)
The MAC provide a comparative value between two vectors, giving a measure of their level of consistency. A value closer to 1 means that the vectors are consistent and a value at or close to 0 means that the vectors are inconsistent. MAC are calculated between two modal vectors (e.g. {φ r } and {φ s }), according to the following equation [44].

Modal flexibility variation per sensor location
The modal flexibility matrix ([F]) is derived according to equation (2) The residual matrix of the modal flexibility ([ΔF]) is measured by calculating the flexibility matrices before and after the damage ([F*]) and subtracting them, as in equation (3). The absolute maximum of each j-th column of the [ΔF] -as for equation (4) -is the modal flexibility variation in each DOF (δ j ̅ ). It indicates where the maximum variation in flexibility is produced. This quantity has been historically used to estimate changes in the static behaviour of the structure from the dynamically measured modal properties of the system [45].

Machine learning processes and algorithms
This section introduces to the selected machine learning algorithms and features, by explaining the criteria and the decision-making process behind their selection. Finally, the processes for the training and testing of the detection models and their validation is detailed.

Selection of the features
For the investigation of this paper, three sets of features are analysed: a set of frequencies only, a set consisting of frequencies and MAC values, and a set including frequencies and δ j ̅ . Frequencies, rather than relative difference of frequencies, are selected and normalised, together with other possible features, during the pre-processing phase. By adding the MAC values, the algorithm is also informed on the deviation of the shapes of vibration. However, being used as a mode-goodness indicator during the postprocessing of the OMA results, it can happen that modes with a low MAC value get filtered out of the analysis, although potentially signalling the presence of damage. An alternative measure of the modes' deviation can be given by the δ j ̅ , which additionally provides a higher level of information because of being not only sensitive to the mode, but also to the sensor location.

Selection of the algorithms
Allowing data samples to belong to two or more class types, with different levels of membership, is the main criterion for the selection of the detection algorithms to be tested in this feasibility analysis. This requirement reduces the choice to soft-classification models, to explicitly estimate the class conditional probabilities, and discard the more complex-to-interpret deep learning and tree-based models. Either fuzzy-or Bayesianbased models inform on the degree of membership of each data sample to the given classes. Targeting a multi-class classification, a predictive model based on the linear discriminant analysis (LDA) theory is deemed more suitable than setting-up multi-class logistic regression models. However, the particular set of data in analysis violates the LDA assumptions of normally distributed data and identical covariance matrices for every class [46]. For this reason, fuzzy-based models only are investigated further.
Fuzzy logic is an organised and mathematical approach, able to handle inherently imprecise concepts through the use of membership functions. In their simplest application, then, these functions are manually defined setting the truth values and a set of fuzzy rules is given to describe how one or more fuzzy variables relate to another.
Although such a transparent approach would be preferred, the mapping by hand of variables and rules is not straightforward for this detection application. Therefore, the fuzzy logic principles are automatically applied to cluster the multidimensional data, according to the so-called fuzzy c-means (FCM) method [47]. The algorithm works by assigning membership to each data point corresponding to each cluster centre on the basis of distance between the cluster and the data point. This unsupervised method is controlled by specifying the number of clusters to identify, the fuzzy exponent and a termination tolerance [48]. Specifically, the Python open-source version of [49] is used for the purpose of this paper.

Training, testing and validation processes
A sketch of the flow of data and processes for the training, testing and validation of the FCM model is given in Figure 2. The cross-validation procedure [50] is employed to verify the independency of the prediction on the WTG operating condition (yaw angle rotation). Although the supervised LDA was not considered suitable for the application,

WTG measurements and FE model
The chosen wind turbine belongs to the 10% of the structures with an SHM system installed. The set-up of the monitoring systems, and the sensors' and elements' naming conventions are illustrated in Figure 3. As it is generally recommended for offshore WTG structures [51], the accelerometers are installed at 3-4 levels, including the tower-top Based on these measurement data, together with information from the 10-minute SCADA data on the turbine's operating condition, Augustyn et al. [52] updated the FE model of the WTG to match at best the real system dynamics in its as-installed condition.
After the update, the discrepancy between the measured and modelled global frequency is reduced as follows: from the initial design discrepancy of 6% to 0.3% for the 1 st tower modes, and from 30% to 1.0% for the 2 nd tower modes. Furthermore, the MAC values with respect to the measured mode shapes generally improved after the update, reaching a value of 0.99 for the 2 nd FA mode from the initial 0.85 of the design. Although the 1 st torsional mode of the jacket was not used for this model calibration, it will be included in the following analysis to investigate whether its monitoring is beneficial for detection purposes.

Simulation of the scenarios
Scenarios for the healthy and the damaged status are simulated on the FEupdated WTG model described in Section 3.1. Given that, from the design specification, the site accounts for only a few centimetres of variation in the water level for tidal phenomena, the measurements' uncertainty is introduced solely by varying the local scour depth within the design limit. In regard to the operating regimes, idling-only conditions are mimicked, accounting for the impact of the rotor-nacelle-assembly yawing on this asymmetric system inertia, and thus on its modal properties.
The damage scenarios are simulated following the recommendations of Scheu et al. [8]. They prioritised the following failure modes for an offshore wind substructure: excessive corrosion, fatigue, deformation and buckling, grout connection and bolted connection. As the design of this WTG sub-structure is fatigue-driven, extreme scour events can be of concern for fatigue damage [53], bringing the utilisation of the jacket is worth pointing out that, in the case of the presence of local scour, a higher δ j ̅ is recorded by the tower's top sensors.

Loss of structural integrity in the brace elements
The localised structural damage is implemented in the ROSAP model of the substructure by varying the Young's modulus (E) of its elements and sub-elements. The damage types that could be associated with a variation in stiffness of the structural members of the jacket are corrosion, material softening due to cyclic loading, and loosening of the connection between elements. The simulation of the full integrity loss of the jacket leg would not lead to representative results, due to the fact that either full or partial integrity of the legs is required for the substructure's survivability. In contrast, it was observed that the substructure might survive the loss of integrity of the brace members.
In Figure 5, the E of each of the brace elements of the jacket structure connecting to a leg element is reduced to 1% of the design value. The results are reported with respect to the several levels of Figure 3, and in terms of the relative difference in frequency, the MAC values, and the δ j ̅ . For each brace level, eight values are reported, corresponding to the eight brace-to-leg connections, two per leg, of this 4-legged jacket structure. Because of this, and due to the fact that the results in Figure 5 are relative only to a single rotor-nacelle-assembly position, it is possible to observe some analogies in the results at each level, with slight differences that are caused by the damage locations and system's asymmetry between the legs. By reporting the thresholds identified in Figure 4 to Figure 5 (light grey shaded areas), it is evident that the ranges of variability due to the EOC overlap with the deviations caused by the structural failures, emphasizing how this poses a challenge on damage detection and location.
In general, it can be observed in Figure 5 (a), that the frequencies of the 1 st torsional mode and the 2 nd tower modes are mainly affected by the presence of the disconnection. These modes grow in difference with respect to the reference healthy scenario -almost up to 2.5% for the 1 st torsional mode -if the damage is closer to the splash-zone, and thus to the sensorized area of the WTG jacket -cf. Figure 5 (b). The changes in the mode shapes, shown in Figure 5

Training, testing, and validation datasets
The data samples for training, testing, and validating the detection algorithms are simulated, as explained in Section 2.2, by introducing the anomalies described in Section 3.2. The detection algorithms then try to cluster the data into as many clusters as the number of simulated WTG status, corresponding to the following labels: • eoc, reproducing the structure behaviour for local scour depth up to the design threshold, • scour, modelling scour phenomena over the design allowance, • D55, D50, D25, D20, D15, and D13, mimicking the integrity loss of brace members at the leg K or Y joints, for the levels from 55 to 13, as reported in Figure 3. label is assigned to each data sample based on the highest membership predicted by the fuzzy clustering model.

Training and testing on the operational variations
The focus of this preliminary analysis is on the identification of the optimal number of the LDA transformed component, for the reduction and rotation of the modal indicators into features separating at best the eight classes. The cross-validated estimates are reported in terms of macro averages of the accuracy and of the F1-score [54]. The accuracy gives an indication of the total amount of correct predictions over the total amount of samples in the dataset tested. The F1-score is the harmonic mean of the precision -defined as the percentage of correctly detected damaged cases with respect to the total amount of cases predicted to be damaged -and recall -defined as the portion of correctly detected damaged cases with respect to the total amount of damaged cases in the dataset tested. For multiclass classification, the macro average (arithmetic) of these metrics can be calculated by aggregating the contributions of all classes [54], with c being the number of classes, as indicated in equation (5).
The fuzzy clustering models are trained to identify all eight centres on uniform, but randomly selected, subsets of the training set -according to the cross-validation process explained in Section 2.3.3. In Figure 6, the box plots of the fuzzy clustering results, for the three feature combinations, are presented for varying numbers of the LDA components. The random selection of the subsets for this training and testing phase is the reason for the predictions' variance.
It can be observed, in Figure 6 (a), that the detection based on the tracking of frequency only has already quite satisfactory performances. The macro accuracy and F1score reach median values above 93% and 74%, respectively, by selecting the first two LDA components. Slight improvements -with a median macro accuracy of about 94% and a median macro F1-score of 76% -are achieved by including the features relative to the MAC values of the modes. As shown in Figure 6 (b), this is achieved by additionally extending the number of LDA components (from three to five). It is finally evident, in confidence intervals, are reported in Table 1.   The goodness of the detection, based on the features' combination including the frequencies and the δ j ̅ , can also be observed in the generally high values of the fuzzy partition coefficient of Figure 7 (right). The coefficient represents how cleanly the data are separated into the selected number of clusters [49]: it ranges from 0 to 1, with 1 being the best separation. The scatter in the results is again given by the training and testing of several models on subsets of the dataset. Although the models do not reach their best performances by clustering into eight groups of behaviour -but into six -, it is observable that the detection achieved by using the δ j ̅ generally outperforms the one by using the MAC values, in Figure 7 (left). indicate the density of the data sample for each pair of true-predicted labels, with dark grey being 1 (or 100% data samples) and white being 0. The diagonal of the confusion matrix, in dashed lines, represents the correctly labelled predictions, which is supposed to be populated by density 1 (thus in a dark grey colour). To ease the interpretability of the results, the validation outcomes are presented here only for the best performing models on the training and testing sets (cf. Figure 6). In Figure 9, the algorithms trained on MAC values and δ j ̅ are further validated on the second validation dataset replicating the brace disconnections, together with higher depths of local scour, yet within the scour allowance. In Figure 9 (a), it can be observed that the algorithm relying on frequencies and MAC values transfers all its predictions to the extreme scour scenario. In contrast, the algorithm trained on frequencies and δ j ̅ correctly identified the disconnection damages as such. Nonetheless, as shown in Figure   9 (b), the addition of extra scour caused the mislocation of the damage for levels 55, 20, 13 and 15. To show the benefit of the probabilistic monitoring approach, the membership predictions of the fuzzy clustering are reported in Figure 10 as histograms of probabilities for case D50 of Figure 9. It is evident, in Figure 10 (a), that the misclassification into extreme scour scenario for the algorithm trained on frequencies and MAC values, is associated to generally low membership to any of the simulated labels. Even if the assigned label -i.e. "scour" -has clearly the highest predicted probability, its value is below 0.3. Concerning the detection via frequencies and δ j ̅ , it can be observed, in Figure   10 (b), that although the damage scenario D50 has the highest probability, the true scenario label D55 shows a probability higher than the remaining scenarios.

TOWARDS FIELD APPLICABILTIY: CHALLENGES AND LIMITATIONS
The results, shown and discussed in Section 4, prove of the feasibility of the suggested approach for the detection and location of failure events in the jacket sub-structure of the offshore wind turbine in analysis. The monitoring strategy outlined in Figure 1 is achieved to the extent of the "Detection Model Training -based on the simulated data. This detection algorithm fulfils the criteria of (i) diagnostic capability, (ii) low-cost -as opposed to any other ad-hoc monitoring system and field inspections -, and (iii) transparency of reasoning process, as required for the industrial needs delineated in Section 1.3. As concerns the eventual use of this probabilistic models for decision making (iv) of maintenance actions, the fuzzy clustering method allows to judge the prediction for the membership of the data to all the possible classes. However, this will be not as easy to interpret for the real-time data and the raising of alarms. Instead, it should be considered to make some engineering judgment on the evolution of the predictions in time. The implementation for real-time field monitoring (v) requires, as a next step, to verify the accuracy of its predictions to a set of data from the real structure.
Some of the challenges of dealing with modal data extracted from field measurements -especially in the case of offshore wind structures -come from their scatter and fluctuation in time caused by complex loads and rotating mass. As a first step one could apply the detection algorithm on only the data from the idling turbine -as here However, it must be noted that this filtering procedure, as well the lack of excitation and thus poor OMA performance, can quite often lead to a lack of some required modes. In this respect, multiple detection models should be setup for adapting the prediction to the varying number of features available. This approach and the likely drop in accuracy caused by the removal of modes in the training phase must be yet investigated.

CONCLUSIONS AND FUTURE WORK
This study has demonstrated the feasibility of the identification of damage scenarios and their location based on the tracking of the modal properties for an offshore wind jacket structure. The approach suggested is based on the training of an unsupervised fuzzy clustering algorithm, after having applied a supervised features transformation technique (i.e. LDA), on a reduced set of data, for obtaining the maximum separability of the clusters. The detection scheme fulfils the identified needs in low-cost equipment, Figure 11. Illustration of the detection algorithm capability -trained on frequencies and the δ j ̅ -, to locate (a) each anomaly scenarios for slight variations of scour depth, and (b) the integrity loss of brace members for local scour depths close to the design allowance.
The results from applying the trained algorithm on the validation datasets showed the correct detection of all anomalies with promising capabilities to identify the location of the brace integrity loss. The healthy status and extreme scour scenarios were always classified correctly. Additionally, the brace disconnection-damage was always classified as such. Best damage location capabilities were seen by combining frequencies and δ j ̅ as training features, followed by the combination of MAC and frequencies. The frequenciesonly detection showed the most mistaken results as concerns the location of the anomalies. A summary of the damage location capability of the best feature combination is further visualised in Figure 11. Each anomaly is indicated with a circular sign, coloured in green if the location is correctly identified, and in red otherwise. The arrows are used to point to the mistaken location of the damage. It can be seen that a good identification of the location of the brace integrity loss is possible for small variations of scour depth - Figure 11 (a). Mistaken identification of the damage location is likely for higher scour depth variations - Figure 11 (b). Yet, it is worth noticing that the algorithm correctly distinguishes the damage locations between above and below the water level.
It should be noted that the methodology suggested in this paper can potentially be applied to any offshore wind substructure type as long as all information and processes

Figure 1
Processes and data flow for the suggested monitoring strategy Figure 2 Processes and data flow for training, testing, and validating the detection algorithms Figure 3 Wind turbine geometry and SHM system. The x and y axes are oriented along north and west directions, respectively.

Figure 9
Confusion matrix of the fuzzy clustering prediction of the dataset for the combination of single brace damage and scour depth approaching the design allowance. Results are reported for the detection models trained on, (a) frequencies and MAC values, (b) frequencies and δ j ̅ .

Figure 10
Histogram of soft clustering membership predictions on the dataset for the combination of single D50 brace damage and scour depth approaching the design allowance. Results are reported for the detection models trained on, (a) frequencies and MAC values, (b) frequencies and δ j ̅ .

Figure 11
Illustration of the detection algorithm capability -trained on frequencies and the δ j ̅ -, to locate (a) each anomaly scenarios for slight variations of scour depth, and (b) the integrity loss of brace members for local scour depths close to the design allowance. Table 1 Summary of the optimal number of LDA-transformed features and estimated metrics on the test set