Substructures of offshore wind turbines are becoming older and beginning to reach their design lifetimes. Hence, lifetime extensions for offshore wind turbines are becoming not only an interesting research topic but also a relevant option for industry. To make well-founded decisions on possible lifetime extensions, precise fatigue damage predictions are required. In contrast to the design phase, fatigue damage predictions can be based not only on aeroelastic simulations but also on strain measurements. Nonetheless, strain-measurement-based fatigue damage assessments for lifetime extensions have been rarely conducted so far. Simulation-based approaches are much more common, although current standards explicitly recommend the use of measurement-based approaches as well. For measurement-based approaches, the main challenge is that strain data are limited. This means that measurements are only available for a limited period and only at some specific hotspot locations. Hence, spatial and temporal extrapolations are required. Available procedures are not yet standardised and in most cases not validated. This work focusses on extrapolations in time. Several methods for the extrapolation of fatigue damage are assessed. The methods are intended to extrapolate fatigue damage calculated for a limited time period using strain measurement data to a longer time period or another time period, where no such data are available. This could be, for example, a future period, a period prior to the installation of strain gauges or a period after some sensors have failed. The methods are validated using several years of strain measurement data from the German offshore wind farm Alpha Ventus. The performance and user-friendliness of the various methods are compared. It is shown that fatigue damage can be predicted accurately and reliably for periods where no strain data are available. Best results are achieved if wind speed correlations are taken into account by applying a binning approach and if a least some winter months of strain data are available.
Although offshore wind energy is considered a relatively young industry, the oldest offshore wind turbines (OWTs) have been operating for more than 20 years. Some OWTs have even already been decommissioned
To enable safe and profitable lifetime extensions, the remaining useful lifetimes of the OWTs need to be determined. For this purpose, the first international guidelines for lifetime extensions for wind turbines have already been introduced
However, frequently, not only are the wind conditions known from SCADA data, but also additional data are available. For some OWTs, strain gauges at different relevant positions of the substructure measure the real load conditions the OWT is exposed to
Independent of the context of lifetime extensions, the first fatigue damage estimations based on measured strain data were conducted in the 1990s
Early approaches by
Spatial extrapolations can be extrapolations either to other positions on the same turbine or even to other turbines in the same wind farm. The former is done, for example, by
Finally, extrapolations in time – being the focus of this work – are analysed by
Hence, there are first approaches for temporal extrapolations of strain-measurement-based fatigue estimations. However, up to now, neither are the available procedures comprehensively validated nor is there a consensus regarding the most suitable methods. The approach of
Extrapolation approaches always feature some uncertainty. Therefore, for all methods considered, not only a deterministic extrapolation but also a probabilistic one is conducted. This enables an estimation of their uncertainty.
The rest of this work is structured as follows. In the next section, the underlying measurements are explained. This includes a description of the measurement setup as well as the presentation of some raw data. Moreover, the applied data processing is illustrated. In Sect.
In this work, offshore data from a measurement campaign in the German Alpha Ventus wind farm are utilised. The raw data are freely available for research purposes after signing an agreement concerning the data usage (
Farm layout of Alpha Ventus with the considered AV-07 turbine marked (adapted from OpenStreetMap).
Location of Alpha Ventus and the met mast FINO1 (adapted from OpenStreetMap).
Alpha Ventus was commissioned in April 2010. The measurement campaign started in 2011. Since then, not only have SCADA data been collected, but environmental conditions, strains, accelerations, etc. have also been measured as well. Further environmental data are available from the met mast FINO1 (
Properties of the investigated AV-07 turbine
Illustration of the AV-07 turbine (not to scale) and some of the installed sensors according to the sensor documentation
Positions of the strain gauges around the circumference of the tower.
Although measurement data are, in general, available for time periods since 2011, for many periods, the data quality is not sufficient for fatigue damage extrapolations. Many sensors have experienced defects, leading to missing or erroneous data. For fatigue extrapolations, it is important that data are recorded with a high availability for a continuous period of at least 1 year to cover seasonal effects properly. Since data of higher quality are available for the sensors on the tower compared to sensors on the substructure, this work only considers data from the previously mentioned strain gauges on the tower. Moreover, only the data from 3 specific years have a sufficient quality to be taken into account: 1 January to 31 December 2011 and 1 October 2015 to 30 September 2017. For these 3 years, raw data are post-processed as described in the next section before calculating fatigue damage.
For this work, three types of data are required: strain data, data regarding environmental conditions and data concerning operational conditions.
Strains are measured on the tower of the AV-07 turbine (see Fig.
Example strain data before post-processing, which include clearly erroneous measurements, i.e. physically unrealistic peak without any oscillation afterwards.
Example strain data. A wind direction of approximately
Operational conditions are taken from SCADA data from the AV-07 turbine. Environmental conditions are, in most cases, taken from the FINO1 met mast. Only if no data are available from FINO1, are the wind conditions included in the SCADA data from the AV-07 turbine taken into account. FINO1 data are available for approximately 95 % of all 10 min intervals. Another 3 % of the intervals are filled up using SCADA data, yielding a data availability for the environmental conditions of above 98 %. The reason for using FINO1 data whenever available is that they are of higher quality. There are no or at least fewer disturbance effects, e.g. no increased turbulence or reduced wind speed caused by the rotor. Still, all extrapolation methods applied in this work could also be used if no met mast data, i.e. only SCADA data, are available (see Appendix
Example wind speed data after the post-processing.
Correlation of wind speeds and logarithmised short-term damage values (
Correlation of wind speeds and wave heights. Histogram based on mean values of all 10 min intervals in 2016.
As stated in the Introduction, most extrapolation approaches are based somehow on correlations between fatigue damage and EOCs. This correlation is shown as an example in Fig.
In the following, a 10 min interval is only considered if strain and complete EOC data are available.
Assuming a linear damage accumulation according to the Palmgren–Miner rule, the overall damage, e.g. the lifetime damage of a structure, can be calculated as the sum of many short-term damage values. It is known that linear damage accumulation is a simplification of the real fatigue behaviour. For example, sequence effects are neglected. Moreover, the use of short-term intervals, e.g. 10 min intervals, for the damage calculation is a simplification as well. In this case, long-term fatigue cycles lasting several hours or even days are not taken into account
Assuming linear damage accumulation and a fixed location at which high-resolution strain data (
Results of the rain flow cycle count for a 10 min interval (18 March 2016; 00:10:00). Strain gauge at
Results of the rain flow cycle count for a 10 min interval (18 March 2016; 00:10:00). Strain gauge at
For nominal stresses at the position of interest (here: the measurement position), an overall safety factor (SF) is applied. It consists of several sub-factors. Using the safety factor, a representative value for the concentrated stresses at the structural detail is achieved. First, a stress concentration factor for the specific detail is used (here: SCF
The last step in calculating the damage sustained in a given interval is the application of the Palmgren–Miner rule, i.e. linear damage accumulation, and the application of S–N curves according to the DNVGL recommended practice
If strain data were available for the entire lifetime of the wind turbine, it would be possible to determine its fatigue lifetime by using the previously described approach of calculating short-term damage values. In this case, the lifetime damage (
However, normally, strain data are not available for the entire lifetime. Therefore, some kind of extrapolation procedure in time is necessary. In the following, three different approaches are presented: a simple linear extrapolation, an extrapolation based on bins of EOCs and an extrapolation based on machine-learning techniques. The latter two make use of the correlation of short-term damage and EOCs (cf. Fig.
In a real application, new data might come in continuously or discontinuously after having conducted a first extrapolation. Hence, updates of the extrapolation using additional data have to be possible. For all three approaches, such updates are feasible. Since the computing times of the approaches are relatively low in order to enable uncertainty assessments (cf. Sect.
The simplest extrapolation approach is a linear extrapolation. It assumes that the fatigue damage only depends on the elapsed time
For very long measurement periods (
A more advanced approach, which makes use of the correlation between fatigue damage and EOCs (cf. Fig.
The main difference is that bin probabilities (
As already discussed in the previous section, the correlation between short-term damage and EOCs can also be expressed as a functional relationship, i.e.
The accuracy of the prediction also depends on the EOCs considered. If too few EOCs are taken into account, important features might be missed. Too many EOCs might lead to some kind of overfitting.
In this work, GPR and ANN are investigated. Both methods are very powerful machine-learning techniques which have already been applied successfully in wind engineering
All configurations for ANN and GPR used in this work are based on recommendations in literature, e.g.
For ANN, inputs and outputs are normalised to values between 0 and 1. Two hidden layers with 10 neurons each are used. Hyperbolic tangent sigmoid transfer functions are applied in all layers to prevent unrealistic negative outputs, i.e. negative damage values. The network is trained using the Levenberg–Marquardt algorithm; 80 % of the input data are used as training data, and 20 % are used as validation data. Since the performance of ANN depends strongly on the randomly chosen initial weights for this problem, an automated control algorithm is implemented. It restarts the learning process using new initial weights if the relative prediction error is higher than
For GPR, inputs are normalised to values between 0 and 1. Outputs are standardised to achieve a mean value of 0 and a standard deviation of 1. A purely quadratic basis function and a Matérn kernel with a parameter of
Independent of the chosen extrapolation approach, the results will be uncertain, for example, due to unrepresented EOCs. Nonetheless, the main reason for this uncertainty is the limited amount of strain data and, therefore, of short-term damage values (
In the present case, short-term damage values (
In this section, the three methods for the temporal extrapolation of fatigue damage, which were presented in the previous section, are assessed using measurement data from the Alpha Ventus wind farm (see Sect. How should the parameters of each of the methods, e.g. bin sizes, be chosen to yield the most accurate results? Which method can predict fatigue damage for other time periods most accurately? How high is the uncertainty in the prediction? What amount of training data is required? How long is the minimum measurement period? Do the approaches still yield reasonable results if long-term extrapolations over several years are conducted? Do the approaches still yield reasonable results if extrapolations into the future are conducted, for which no EOC data are available?
Since high-quality strain data are only available for 3 years, for most steps, an extrapolation of measurement data from a single year to another year is conducted. For example, data from October 2015 to September 2016 are extrapolated to October 2016 to September 2017. Since strain and EOC data are available for both periods, the accuracy of the extrapolation can be determined by comparing the predicted damage (
For the three extrapolation methods considered in this work, different parameters must be chosen, for example, the number of EOCs to be taken into account. To determine the most suitable parameters, the extrapolation from a single year to another year is analysed. Since the choice of the parameters might be influenced by the period investigated, several periods should be analysed. However, only 3 years of data is available, with only 2 of these being consecutive years. For the third, non-consecutive year (2011), long-term effects – being analysed in Sect.
Visualisation of the 13 different 1-year periods for statistical evaluations.
For the simple extrapolation, no parameters have to be chosen. First results for the simple extrapolation are presented in Fig.
Moreover, a box plot shows some summary statistics: the median (red centre line), the 25th and 75th percentile (box), the minimum and maximum values (excluding any outliers), and possible outliers of 13 different 1-year measurement periods. Hence, the box plots visualise the variation in the accuracy of the predictions depending on the period considered. All box plots in the following sections show the same summary statistics. To judge the conservatism of the approach, signed errors are more informative. For such results, the reader is referred to Sect.
Percentage errors of predicted yearly damage values using a simple extrapolation method compared to real yearly damage values. Prediction from a year to a second year for 13 different years. Box plot shows summary statistics.
Clearly, the prediction does not yield precise results. Nonetheless, it is remarkable that even such a simple extrapolation leads to results with errors of less than 35 %.
For the extrapolation based on bins of EOCs, the number and type of EOCs to be taken into account and the bin size must be selected. In contrast to previous work by
Some example results for the binning approach are presented in Fig.
Percentage errors of predicted yearly damage values using a binning method compared to real yearly damage values. Comparison of various bin types and sizes (
Percentage errors of predicted yearly damage values using a functional relationship compared to real yearly damage values. Comparison of GPR and ANN and different EOCs:
The optimal choice always depends on the turbine considered, the measurement period and the extrapolation period. Hence, an automated selection method would be beneficial. Ideally, different choices would be assessed automatically for the predicted period and the best choice selected. However, strain data from the predicted period are normally not available; otherwise no extrapolation would be required. This is why automated selection must be based on cross-validation, i.e. splitting up the measurement period. One part of the data is used as training data to determine the mean damage in all bins. Another part replaces the prediction period. It is used to evaluate the accuracy of the extrapolation for the chosen settings. This procedure reduces the amount of training data significantly. As a result, predictions become less accurate. In most cases, due to the limited training data, the automated selection yields bin sizes which are too fine, i.e. overfitting. Hence, although automated selection is desirable, it is not suitable for “short” measurement periods. For example, measurement periods of 1 year or less – as used in this work – are not sufficient.
Therefore, it can be summarised that the choice of the bin dimension and size is of minor importance as long as empty bins do not occur at all or only in some rare cases. For most applications, simple wind speed bins with a size of 2 to 3 ms
For the extrapolation based on a functional relationship, only the number and type of EOCs to be taken into account are relevant. The same six environmental conditions as before are considered. Operational conditions are taken into account separately in a second step. Some example results for the functional relationship are presented in Fig.
A slight improvement in the accuracy might be achieved for ANN if additional environmental conditions are taken into account. However, this improvement is not significant, especially when considering the previously mentioned uncertainty due to the random selection of the initial weights. At least for wave conditions, it definitely does not justify the effort needed to measure them.
Therefore, in the following, only results using a single environmental condition, i.e. the wind speed, are shown.
In contrast to the environmental conditions, the turbine status, i.e. the sole considered operational condition, is not defined continuously. This makes the definition of a functional relationship complicated. Hence, in this work, the turbine status is treated differently from the environmental conditions. For all three methods, in a first step, all data are split up according to the turbine status. This means that some kind of binning based on the turbine status is applied for all three approaches. This has the advantage that in each turbine status bin, the extrapolation approach remains unchanged. Finally, the extrapolation results of each turbine status bin are weighted according to the occurrence probability of this turbine status. For the simple extrapolation this yields the following:
Similar to the challenge of determining a suitable bin size, an adequate number of different turbine statuses and the type of statuses must be found. The most simple differentiation is normal production operation and others (two statuses). This was already proposed by
Percentage errors of predicted yearly damage values using simple extrapolation. Data separated according to turbine statuses: no separation (1), normal production operation and others (2), idling below cut-in and above cut-off (4), and service (5).
Percentage errors of predicted yearly damage values using a binning method (1D wind speed bins) compared to real yearly damage values. Data separated according to different turbine statuses (cf. Fig.
Percentage errors of predicted yearly damage values using an ANN compared to real yearly damage values. Data separated according to different turbine statuses (cf. Fig.
To summarise, splitting up the data according to operational conditions can help to improve the extrapolation. However, it is not straightforward to determine the best separation, as it depends on the period considered and probably on the turbine as well. Moreover, if the measurement period is relatively short and/or many environmental conditions are taken into account, e.g. 3D binning, clustering according to operational conditions becomes more challenging. In this case, the amount of data for each turbine status might become insufficient.
Hence, as improvements are not always pronounced, for many applications it can be sufficient not to cluster the data according to operational conditions. This is especially the case either if the relation of operational to non-operational data is similar in the measurement and the extrapolation period or if the short-term damage values in operational and non-operational do not differ significantly. Since these two prerequisites are fulfilled for the present data, in the rest of this work, clustering according to operational conditions is not performed. In a real application, the two prerequisites should be checked. For example, the second prerequisite can easily be tested by analysing the difference between the mean short-term damage during operational and non-operational conditions in the measurement period.
In the following, the performance of the extrapolation approaches with respect to the accuracy of the prediction, the computing time, and the required data and knowledge is evaluated. For all methods, no clustering according to operational conditions is applied. For the binning approach, only wind speed bins with a bin size of 3 m s
In Fig.
Percentage errors of predicted yearly damage values using all extrapolation methods compared to real yearly damage values. Predictions from a year to a second year for 13 different years.
It becomes apparent that the binning approach reduces the percentage error on average by about 60 % compared to the simple extrapolation (cf. red centre lines of the box plots). Moreover, the binning approach outperforms ANN and GPR. However, two facts about ANN and GPR should be mentioned. First, the initial weights used by ANN and the subsets used by GPR are chosen randomly. Hence, the performance of both is not deterministic but features some kind of model uncertainty that should not be confused with the uncertainty due to limited strain data (cf. Sects.
The second performance criterion evaluated in this work is the computing time. For deterministic predictions using wind speed as the only EOC, all methods are more or less suitable. For a prediction from a single year to another, the simple approach and the binning approach require less than 0.1 s on a standard desktop computer. ANN requires a few seconds, and GPR needs about 30 s. If ANN and GPR are run 100 times to rule out the model uncertainty, their computing times are significantly longer. For ANN, the computing time is still sufficiently short, i.e. only a few minutes. For GPR, 100 runs take nearly an hour. For probabilistic predictions, i.e. assessing the uncertainty due to limited strain data (cf. Sects.
The last criterion, i.e. the user-friendliness and required data, is a more vague criterion. Clearly, the simple extrapolation does not require any additional data (e.g. SCADA data) and is straightforward to apply. The binning approach, especially if only wind speed bins are used, is also quite user-friendly and does not rely on detailed data. For the machine-learning approaches, first of all, much more expert knowledge is required to achieve adequate results. Moreover, the two previous criteria demonstrated that machine-learning approaches perform better with respect to accuracy and computing time if additional data (e.g. additional EOCs or 1 s SCADA data) are available.
To summarise, the simple extrapolation works relatively well. However, if 10 min SCADA data are available, the binning approach clearly outperforms the simple extrapolation with respect to accuracy, while computing time and user-friendliness are comparable. For expert users and high-quality data, ANN and GPR might be alternatives. For the current application, they are less accurate. Moreover, the machine-learning approaches, especially GPR, have significantly longer computing times. The long computing time of GPR makes probabilistic predictions nearly unfeasible on a standard desktop computer. This is why GPR is not considered in the rest of this work.
The box plots in the previous sections showed that the performance of the various extrapolation approaches depends on the period considered, as there is a significant scatter of the percentage error across the 13 different years. Since 13 different years are not enough for a well-founded assessment of the uncertainty of the prediction due to the limited available strain data, this uncertainty is approximated by applying bootstrapping, i.e. resampling with replacement. Therefore, for all three extrapolation approaches, bootstrapping is conducted using
Empirical distribution for the (signed) percentage error of predicted yearly damage using different extrapolation methods. Prediction from a single year (1 October 2015 to 30 September 2016) to another year (1 October 2016 to 30 September 2017). PDF: probability density function.
Empirical distribution for the (signed) percentage error of predicted yearly damage using different extrapolation methods. Prediction from a single year (1 August 2016 to 31 July 2017) to another year (1 October 2015 to 31 July 2016 and 1 August to 30 September 2017). PDF: probability density function.
Overall, even the highest errors are below
In theory, the three extrapolation methods can be used to extrapolate from any period to another. However, if the measurement length is too short, the extrapolation will be biased
Measurement lengths of 2 to 12 months are used to predict the fatigue damage expected to occur in a second year. This means that, for example, 1 October to 30 November 2015, 1 October to 31 December 2015 and so on are extrapolated to the second year, i.e. 1 October 2016 to 30 September 2017. Again, to enable a statistical interpretation of the results, these predictions using different measurement lengths are repeated using the 13 different years that have been used before, e.g. 1 November to 31 December 2015 is extrapolated to October 2015 and 1 November 2016 to 30 September 2017 (cf. Fig.
Convergence of the percentage error of predicted yearly damage values using simple extrapolation for increasing measurement lengths. Box plot shows data from 13 different measurement periods.
Convergence of the percentage error of predicted yearly damage values using the binning approach for increasing measurement lengths. Box plot shows data from 13 different measurement periods.
Convergence of the percentage error of predicted yearly damage values using the ANN for increasing measurement lengths. Box plot shows data from 13 different measurement periods.
For the simple approach, no complete convergence is achieved even for measurement lengths of 12 months. There is a small increase in the percentage error for measurement lengths of more than 9 months. This is probably a statistical artefact due to the limited number of different measurement periods. Nonetheless, for measurement lengths greater or equal to 9 months, relatively low percentage errors are achieved. This is not only in accordance with results from
For the binning approach, convergence is achieved for measurement lengths of approximately 8 to 9 months. After this period, all bins – especially those for high wind speeds are critical – are filled with enough data for an accurate extrapolation. However, for the binning approach, this time can be reduced if the measurement period starts during the winter. Figure
Convergence of the percentage error of predicted yearly damage values using the binning approach for increasing measurement lengths. Box plot shows data from five different measurement periods starting in the winter.
For ANN, fairly accurate results can be achieved using data from a few months. Here, the advantage of determining a functional relationship becomes obvious if data are scarce. Starting the measurement campaign in winter can further reduce the required measurement length (not shown). Nonetheless, it should be noted that even for a measurement length of only 2 months, ANN and the binning approach perform similarly well.
So far, all extrapolations of fatigue damage have been conducted for 2 consecutive years, i.e. short-term extrapolations. This has the advantage that long-term changes not only in the environmental conditions but also in the turbine can virtually be ruled out. However, for real damage assessments used for lifetime extensions, an extrapolation over several years might be necessary. For example, if strain gauges failed after 5 years of operation and an lifetime extension is planned after 15 years, extrapolations over 10 years, i.e. long-term extrapolations, are required. Such long-term extrapolations might be more challenging, as the “learned” correlation between environmental conditions and fatigue damage might have changed. If it has changed, which might even happen within the first year after the measurement campaign ended, extrapolations based on all three methods are impossible. It is important to be aware of this fact. Otherwise such effects might lead to an underestimation of the fatigue loads.
In the following, a single year of measurement data is extrapolated to a second year which occurred several years earlier or later. For this purpose, data from the 3 years of 1 January to 31 December 2011 and 1 October 2015 to 30 September 2017 are used. Similar to before, the starting dates of the 2 years are shifted month by month in order to realise a higher number of different years. This means that the year of 1 January to 31 December 2011 is extrapolated forwards to 1 October 2015 to 30 September 2016, 1 November 2015 to 31 October 2016 and so on. In addition, 1 October 2015 to 30 September 2016, 1 November 2015 to 31 October 2016 and so on are extrapolated backwards to 1 January to 31 December 2011, i.e. vice versa. This procedure yields 26 different years. A visualisation of this shifting procedure is shown in Fig.
Visualisation of the 26 different periods for statistical evaluations in the context of long-term extrapolations.
The results of the long-term extrapolation for the three extrapolation approaches, using the same settings as before, are shown in Fig.
Percentage errors of predicted yearly damage values using all extrapolation methods compared to real damage values. Data concern both short-term (13 different consecutive years) and long-term predictions (1 year extrapolated to a non-consecutive second year for 26 different years).
For all three extrapolation approaches, the resulting percentage errors are in a similar range for both short-term and long-term extrapolations. For the binning approach, the approximation even improves slightly for long-term extrapolations. However, it can be assumed that this improvement is only due to some random effects in the varying environmental conditions across the different years. Nonetheless, for this data set, it can be concluded that long-term changes in the structural behaviour seem to be less pronounced compared to variations in environmental conditions. Therefore, depending on how severe structural changes are, i.e. whether the learned correlation is still valid, long-term extrapolations are possible, especially if the binning approach is applied. Certainly, it must be asked where the boundaries of these long-term extrapolations lie. Is it still possible to use them if the structure has changed significantly (e.g. rotor blades have been exchanged)? This question cannot be answered conclusively by this work, as much more data would be needed and since the answer will always be case-specific to some extent. Nonetheless, although the exact changes to the AV-07 turbine may not be mentioned here for reasons of confidentiality, it should be said that the AV-07 turbine has been significantly modified during the period considered. Despite this significant modification, the learned correlation seems to be still valid. Hence, long-term extrapolations are probably possible for more situations than expected, sometimes even if moderate to severe modifications to the turbine have been made. In a real industry application, it would be necessary to test the validity of the correlations every few years. For this purpose, for example, a small measurement campaign with only strain gauges at a single location for a few weeks could be conducted.
In all previous sections, it has been shown that the use of EOC data, i.e. SCADA data, is beneficial compared to a simple extrapolation based on pure strain data. However, it was always assumed that EOC data are available for the predicted period. This is a valid assumption for nearly all predicted periods in the past, since SCADA systems feature a high availability and data quality. However, for extrapolations into the future, this is no longer valid. Extrapolations into the future are especially relevant for lifetime extensions. Hence, in this section, the last question of Sect.
For approaches using functional relationships, the adaptation for future periods is similar. Here, Eq. (
For the simple extrapolation, there is no difference between extrapolations to periods in the past (with available EOC data) and the future (without EOC data), since the simple extrapolation is based on strain data from the measurement period only.
Results of all three approaches are shown in Fig.
Percentage errors of predicted yearly damage values using all extrapolation methods compared to real yearly damage values. Results of predictions into the future using long-term EOC data are compared to previous results for which EOC data are available (short-term predictions of past periods); 13 different years are used in both cases.
By definition, for the simple extrapolation, an extrapolation into the future is equally accurate compared to an extrapolation to a period for which EOC data are available. For all other approaches, the results demonstrate that the quality of the prediction decreases slightly for extrapolations into the future. Nonetheless, predictions are still reasonable and yield lower percentage errors compared to the simple extrapolation. Just like before, the binning approach also leads to the smallest percentage errors for extrapolations into the future.
In summary, extrapolations to future periods, for which no EOC data are available, are still possible with a relatively high accuracy provided that past long-term EOC data are used instead. Again, the binning approach is most suitable. Certainly, it must be kept in mind that the accuracy will decrease if long-term changes in the EOCs, e.g. due to climate change, become relevant. Hence, an accurate extrapolation of a few years into the future is possible, but an extrapolation 20 years into the future might be unreasonable.
To enable well-founded lifetime extensions for OWTs, the remaining useful lifetime has to be determined. Although several simulation-based and strain-measurement-based approaches for determining the remaining useful lifetime already exist, especially for strain measurement concepts, additional research is required. This work addresses the research gap regarding extrapolations of strain-measurement-based fatigue damage calculations to other time periods.
Regarding the extrapolation in time, several approaches making use of the correlation of EOCs (10 min mean values) and short-term fatigue damage values are enhanced, assessed and validated using real offshore measurement data. The approaches are a simple extrapolation, a binning approach and two machine-learning approaches. A summary of the most important results is as follows.
User-friendly binning approaches yield accurate results. More complex machine-learning approaches do not yield better results for the given data type, i.e. 10 min EOC data. It is sufficient to consider wind speed correlations only. Other environmental conditions do not need to be taken into account for locations at the tower. Consideration of different turbine statuses can improve the accuracy of the prediction. However, as it is not straightforward, careful consideration should be given to the question of whether it is beneficial. The uncertainty of the prediction is moderate, and no systematic bias occurs. It is sufficient to measure strains for only a few months, if these months are winter months. Long-term extrapolations over several years might be possible, even if the OWT is moderately to heavily modified in this time period if the learned correlation between EOCs and fatigue damage is still valid, which has to be checked.
For extrapolations into the future, the accuracy of the prediction decreases, since EOCs have to be approximated using long-term EOC data. Still, reasonable predictions are possible.
Therefore, the results of this work demonstrate that user-friendly binning approaches are a suitable alternative or addition to simulation-based lifetime extensions, even if only limited strain data are available. However, some limitations of this work should be discussed. First, spatial extrapolations, i.e. extrapolations to other locations on the same turbine and/or to other turbines in the same wind farm, are not addressed. For spatial extrapolations, the reader is referred to current research, e.g.
Some of the previously mentioned limitations of this work immediately lead to future work.
First, the results of this work should be assessed for other turbine types, for example, in other regions of the world or onshore. This would increase the general validity of the results. Certainly, here, the availability of open-access strain measurement data is a limiting factor.
Second, an analysis of extrapolation approaches for turbine blades would be valuable. The presented binning approach is quite user-friendly and based on limited data. Hence, it could be interesting for industry applications. If such a “simple” approach were available for blades and other components as well, this could be a useful extension. However, before applying the binning approach to rotor blades, two simplifications of the short-term damage calculations should be investigated in more detail. The relevance of sequence effects of stress cycles has to be investigated. Moreover, the effect of long-term fatigue cycles lasting more than an hour should be analysed. For such cycles,
Third, the value of additional data, e.g. data of continuous operational conditions like power output or pitch angle or 1 s SCADA data, should be analysed. For machine-learning approaches, additional data are valuable. However, it is not known whether it also improves the accuracy of binning approaches, since these are normally based on aggregated EOC data.
Fourth, a thorough comparison with the probabilistic approach of
Finally, a combination of temporal and spatial extrapolation methods would be an interesting addition. In this context, spatial extrapolations cover predictions for other positions on the same turbine and also for other turbines in the same wind farm.
In this work, environmental conditions are taken from the FINO1 met mast. Only if no data are available from FINO1, are the wind conditions included in the SCADA data from the AV-07 turbine taken into account. The reason for using FINO1 data is that they are of higher quality. Still, in industry applications, met mast data are normally not available. Hence, the proposed methods have to yield accurate results even if only SCADA data are used. In theory, this should be the case, since EOC data are only used for the correlation, e.g. binning. The practical applicability is demonstrated in Fig.
Percentage errors of predicted damage values using a binning method compared to real damage values. Comparison of predictions using met mast plus SCADA data and SCADA data only. Results only for 1D bins, i.e. wind speed (
After signing an agreement for the data usage, the raw data of the RAVE (Research at Alpha Ventus) data archive – operated by the Federal Maritime and Hydrographic Agency (BSH) – are freely available for research purposes (
CH conceptualised the project and its methodology, performed the investigation, provided the formal analysis, used relevant software, and visualised and validated the data. CH and RR administered the project, and RR acquired funding. CH wrote the initial draft of the paper, and RR reviewed and edited the paper.
At least one of the (co-)authors is a member of the editorial board of
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We gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation; ENERGIZE, Effizienzsteigerung unscharfer Strukturanalysen von Windenergieanlagen im Zeitbereich; grant no. 436547100). Moreover, we would like to thank the RAVE (Research at Alpha Ventus) initiative for making the data available. The RAVE initiative was funded by the German Federal Ministry for Economic Affairs and Energy on the basis of a decision by the German Bundestag and coordinated by Fraunhofer IWES (Institute for Wind Energy Systems; see
This research has been supported by the Deutsche Forschungsgemeinschaft (grant no. 436547100, ENERGIZE). The publication of this article was funded by the open-access fund of Leibniz Universität Hannover.
This paper was edited by Michael Muskulus and reviewed by Wout Weijtjens and two anonymous referees.