An Approach for Fatigue Load Monitoring without Load Measurement Devices

Nicolai Cosack, Martin Kühn

Endowed Chair of Wind Energy, Universität Stuttgart, Germany +49 (0)711 685 68273, cosack@ifb.uni-stuttgart.de

Abstract: A novel approach for the monitoring of wind turbine fatigue loads has been developed. The method works without the installation of additional measurement devices. Instead, an empirical relationship between standard wind turbine control signals and wind turbine loading is established. Once this procedure has been established for one turbine, it should be suitable for the estimation of fatigue loads for all turbines of that type. This paper gives an overview of the basic approach as well as results of an estimation of single stage spectra and single stage distributions for some important load components of a state of the art wind turbine.

1 Introduction Routinely, load measurements at wind turbines are carried out only for a few prototypes as temporary measurement campaigns. The development of cost effective and reliable systems which can be used for continuous load monitoring of wind turbines has been proven to be a difficult task. Besides the high costs of measurement equipment and the large effort of post-processing and evaluating the collected data, the expected lifetime of a turbine might exceed the lifetime of standard measurement devices (e.g. strain gauges) by far and replacement might not always be easy. Besides information about energy yield, operating hours and maintenance or repair activities, a wind turbine’s performance and especially its dynamic behaviour is known only from the prototype testing. This prototype testing does not necessarily reflect the real conditions in the series at particular sites. As a consequence, very little or, in most cases, nothing is known about the load history of more than a few of the many existing turbines. Measuring loads in a continuous manner offers some significant benefits for the operation of a wind turbine and can help to produce energy at lower costs. Among the most obvious advantages are the adjustment of turbine operational control with respect to the current

loads, the adoption of maintenance cycles according to the load history and the realisation of a basic condition monitoring by means of trend analysis of the load data. Furthermore, the load information could also be used to compare wind turbines in a series not only on the basis of their energy production but also on their load history. Results of such a comparison might be useful to improve the planning of future wind farms. Therefore, the present research project investigates methods for using easily available turbine signals, like rotor speed, electrical power, pitch angle, etc., for fatigue load monitoring. The work aims to use these standard wind turbine signals for the estimation of simple load indicators, such as damage equivalent loads, but also for the more detailed fatigue spectra, e.g. multi stage load duration distributions and rainflow spectra.

2 System Specification A complete fatigue load estimation system does not only consist of an estimation procedure, but requires also a process control and a monitoring scheme. The general layout of such a system is shown in Figure 2 and described briefly in this section. Process Control System Identification Accurate estimation results can only be achieved, if the properties of the individual wind turbine are in good agreement with the design assumptions of the estimation system. Due to site specific conditions, such as soil properties, as well as to fabrication and assembly tolerances, the properties of wind turbines in a series can differ to some extend. Hence an exact match of the design assumptions is virtually impossible and system identification is required to check that the turbine’s properties lie within a suitable range. It should be performed at least once prior to the initialisation of the estimation system and periodically if significant system degradation over time can be assumed.

Figure 2: Layout of a load estimation system

The detection of immoderate rotor imbalances by system identification can serve as a practical example. If large imbalances are present but do not influence the standard signals used for the load prediction, their influence on the estimated loads will not be captured. On the other hand, if a standard signal is significantly influenced by an undetected disturbance, the prediction error is likely to be increased. Turbine status In order to give a complete picture, load predictions have to be performed for all turbine states relevant for the fatigue loading. The relation between standard signals and loads can be different for the various states such as normal power production, idling, starts and stops. It can therefore be reasonable to adopt the estimation procedure according to the current turbine state by treating the input data differently or switching to other estimation procedures. Load estimation procedure Statistical analysis Because standard signals are mainly used for control of wind turbines they are usually measured with high resolution. These continuous high resolution time series can either be applied directly for the estimation or divided into sections of equal length, usually 10 minutes, from which suitable statistical parameters can then be derived. The choice of the input data format depends also on the desired outcome of the estimation system. If the outcome is not supposed to be a high resolution time series statistical parameters are probably sufficient in most cases as input. Data Verification This step serves two main purposes. In the first place, the input data has to be checked

continuously for plausibility. Single outliers of input parameters as well as sensor malfunctions have to be detected in order to avoid corruption of the estimation results. Secondly, some estimation procedures can only handle data within a specific range, especially when the estimation is based on empirically derived relations which are not capable of extrapolation of data beyond the calibration range. If corrupted or unusable data has been found a suitable method of correction and handling of these data has to be defined to make sure that no periods of time are neglected for the fatigue load estimation. Transfer function The transfer function is the key part of the estimation. Some possible methods like regression models and neural networks are described and compared in the next section. Monitoring Load Monitoring The individual short-term fatigue load estimations would usually be cumulated to give the overall long-term fatigue load. Cumulated loads are then simply compared against the design loads of the turbine and allow for an assessment of the past operation of the turbine. With some additional assumptions regarding the long-term environmental conditions at a site it is also possible to extrapolate the fatigue loads to the design life of the wind turbine. However, this method requires choosing representative loads as basis for the extrapolation and is therefore more complicated than the simple load accumulation described above. If done correctly the life-time extrapolation allows for a better assessment of the turbine operation compared to the load accumulation especially at the beginning of the monitoring

period. It can be expected that the results from both methods approach each other after some time of monitoring, e.g. two to three years. Condition Monitoring Without much additional effort the above load estimation system can be extended to incorporate a basic monitoring that aims for the prediction of the overall turbine condition. Besides information from a periodically performed system identification also the result of the data verification can be analysed to safeguard the compliance of the wind turbine with the specification and hence the design assumptions of the wind turbine. Furthermore, the predicted loads can be analysed with respect to trends to detect wear and tear of the turbine as well as long-term degradation.

3 Load Estimation Procedures Four different load estimation procedures have been analysed and compared to asses their suitability for the proposed prediction scheme. These are classical regression methods, neural networks, physical model based approaches and state estimators. Classical regression techniques are often used to establish relations between two sets of data, in case that only limited information on the underlying processes is available [1]. Regression usually requires making some assumptions regarding the nature of the connection between input and target values, for example such as being linear. Furthermore, in a preceding step suitable input parameters have to be defined which will be related to the targets. Based on these a priori choices the input and target values are correlated to each other and the parameters of the assumed relation are derived. This relation is also referred to as the regression function and can be interpreted as transfer function which maps the input to the target values. If the relation between input and target values is very non-linear or depends on several input parameters the regression approach gets significantly more complex. It is likely that many correlations have to be tested and combined to a working regression model in this case. The process can be partly automated by means of more elaborate stepwise regression techniques [2] but still it can not be guaranteed that the found solution performs well. Another serious disadvantage of regression techniques is that they can generally not be used for extrapolation. Neural networks have been proven to be a very useful alternative to classic regressions [3]. As shown in Figure 3 a single neuron consists of

the weighted summation of inputs and a pre-defined function, the so called activation function, which is used to derive the output of the neuron. Many neurons can be combined in parallel or in line to build a neural network. The output of each activation function thereby serves as input to the following neurons. If the network is sufficiently large it is possible to approximate very complex relations by a combination of in fact relatively simple activation functions. One of the advantages of a neural network approach is that these networks can be trained to map the relation of input and output data if a suitable amount of training data is available. Using one of the many available training algorithms, the set-up of a neural network is often faster and easier than the set-up of a regression model, especially if complex non-linear relations have to be mapped. Furthermore, assumptions regarding the nature of the relation are required only in that respect that the network has to be sufficiently large to be able to approximate the relation with the available number of neurons. An a priori selection of suitable input parameters can improve the training process but is not compulsory. Input data which can not be related to the output will simply be assigned a relatively low weight during the training process. Just as with regression techniques, application of the neural network for predictions is only reliable if the input data are within the range which has been used for the training of the network. Detailed physical models, for example FE-or multi body models of structures, can also be used to relate input data to load quantities using observer based approaches as known from control theory. These models require very specific input data, like accelerations or deflections at specific points of the structure. Furthermore, detailed knowledge of structural properties of the physical system that governs the relation has to be available. Alternatively, classical grey-box system identification approaches can be applied to set-up suitable models [4]. Extrapolation, which is not possible with regression or neural network techniques, is not an issue with this approach. If the model reflects the real system behaviour correctly it can be applied at all turbine states. State estimation can be applied to classify wind turbine operation in terms of fatigue loads. For each identified state a corresponding load is read from an associated database and cumulated to an overall fatigue load. The state recognition approach requires an a priori classification of turbine operation into suitable

Figure 3: Single neuron and neural network

sub-states and the definition of representative loads for each sub-state. Once this has been achieved, the method is able to give results even for turbine states that are difficult to assess with other methods for example transient situations like starts or stops. Table 1 summarises the comparison of the above described estimation methods. In most cases, analysis of standard signals will probably not give such detailed input to employ physical models for the load prediction. Furthermore, information for setting up these models might not be fully available. Wind turbines operate under constantly changing wind conditions and the turbines themselves are very non-linear systems. Therefore, an excessive number of possible states and the respective representative loads would have to be defined, for state estimation methods. Because the presented work aims for an approach with a broad applicability and which requires as little information as possible on the wind turbine itself, regression techniques and neural networks both seem to be suitable. It is very likely that the transfer function which relates input and target values is highly non-linear and depends on several input parameters. This makes the use of classical regression techniques difficult and therefore a neural network based approach has been chosen for this work. The estimation scheme including input and target values is presented in more detail in the next section.

4 Description of the Applied Estimation Scheme

4.1 Overview

Fatigue loads can be described in various formats such as time series, multi stage fatigue spectra or single stage spectra, which can all serve as targets for an estimation procedure. The estimation of some of these formats has been investigated in previous publications, for

example the estimation of high resolution rotor thrust time series with regression models [2] or the estimation of multi stage rainflow spectra with neural networks [5, 6]. Here we focus on the prediction of single stage spectra based on standard signals and neural networks (Figure 4). The prediction of single stage spectra has already been discussed briefly in [5], but only with respect to the rotor torque. In this work we extend this approach also to other main load components. Because standard signals are usually measured in a fixed frame of reference behind the rotor they can be regarded as integral quantities and include cumulated aerodynamic and structural dynamic effects from all three blades. Here, special focus will be placed on the suitability of these integral quantities for the estimation of non-integral loads, such as blade root bending moments. Two main tasks have been performed for the set-up of the estimation procedure: 1. Calculation of statistical parameters and

single stage loads Because the spectra are estimated for fixed time periods of ten minutes we also use only statistical parameters of the standard signals as input to the estimation procedure. Suitable statistical parameters are derived from standard signals. They serve then as input to the neural network for the prediction of single stage fatigue load spectra.

2. Training of the neural network

Prior to the estimation the network has to be trained to map the relations between the input data and the single stage spectra. Common feed-forward networks with only one hidden layer have been used in this work. Training of the network was performed on basis of standard training algorithms such as backpropagation with moment term or resilient backpropagation [3].

Figure 4: Scheme for the estimation of single stage spectra from standard signals using neural

networks

Estimation Method Data Requirements Assumptions Coverage Miscellaneous

Regression Techniques

- Input and target values have to be available

- A priori choice of the most relevant input parameters required

- Assumptions regarding the nature of the regression function

- Extrapolation not possible; only valid for the design ranges

- Standard technique for linear problems

- Effort increases significantly for non-linear multivariate problems

- Regression function available as equation

Neural networks

- Many data sets of input and target values for training required

- Network architecture and training algorithms have to be chosen

- Extrapolation not possible; only valid for the design ranges

- Suitable for non-linear multivariate problems

- Relevant input parameters are found automatically during the training process

- Relation of input and target values ‘hidden’ in network, i.e. not directly accessible

Physical models

- Detailed information for the set up and validation of a physical model necessary

- Suitable input data for the model

- Model and input data are sufficiently complex and accurate to allow for predictions

- Coverage of all operational states

- Most suitable for specific component models, e.g. support structures or actuators

State estimation with database

- Input and target values are required

- Information on the turbine load characteristics and operational behaviour necessary

- Suitable sub-states of the operational conditions can be defined

- Representative loads for each sub-state can be derived

- Depends on the defined states only

- Accuracy of the results increases with the number of defined states

- Capable of load estimations during transients

Table 1: Comparison of estimation methods

Figure 5: Variation of skewness and kurtosis

Suitable statistical parameters and the derivation of single stage fatigue loads are discussed in the following sections.

4.2 Relevant Statistical Parameters

Most variable-speed pitch-controlled wind turbines monitor at least electrical power output, generator rotational speed, pitch angles and tower top accelerations. Furthermore wind direction deviations and yaw activities are recorded. Secondary signals like rotational accelerations or pitch rates can be derived from these primary data if necessary. In a pre-processing step adequate statistical parameters have to be calculated. These parameters have to be suitable to describe the turbine activities during the past time period. If the chosen parameters do not reflect the turbine behaviour well or if relevant information has been omitted the accuracy of the estimation result is likely to be decreased. Often a good description of the corresponding turbine operation is only possible if time and frequency domain related parameters are included. Time domain related parameters The mean values of standard signals can indicate the average operation point of a turbine while standard deviations or variances are basic measures of the variability of the operation around this point. A more detailed description of the variability is possible if additional higher order statistical parameters like the skewness and the kurtosis are taken into account. These parameters are calculated from the third and fourth central moments of a signal and can be used to describe basic deviations of the signal distribution from the normal distribution [1]. As illustrated in Figure 5, the skewness indicates the deviation of the distribution peak from the mean of the distribution, while the kurtosis is related to the relative flatness of the distribution.

Frequency domain related parameters Besides knowing the variability of a signal, the frequency content of the oscillations is also valuable information and can improve the estimation results. Similar to the central moments in the time domain, the spectral moments are basic parameters to characterise the distribution of the signal’s oscillations in the frequency domain. To derive the spectral moments, time series are usually transferred to the frequency domain to yield the power spectra density (PSD) of a signal as shown in Figure 6. Often traditional Fast Fourier Transform based spectral estimation methods, for example the periodogram or the correlation method, are applied for this task. Other approaches utilise autoregression models, where the autoregression coefficients are derived from the autocorrelation function of a signal. The coefficients can then be related to the power spectra density. These models are computationally more expensive but can give better results than the traditional approaches, especially if relatively short sequences of a signal are to be analysed. Furthermore they do not rely on the assumption, that the signal is composed of harmonically related sinusoids. [7]. If the PSD has been derived, the spectral moments can be calculated with cyclic frequency f and the order n of the spectral moment from

∫∞

⋅=0

)( dffPSDf nnλ

It should be mentioned that there are also methods to derive spectral moments directly from time domain representations of a process [8, 9]. However, from the above formula it is obvious, that the contribution of high frequencies to the spectral moment increases with increasing order of the moment. A comparison of moments of different order can therefore be used to conclude on the

Figure 6: Normalised generator rotational speed signal as time series and power spectral

characteristics of the PSD and hence on the distribution of energy of the process. Time series which feature significant oscillations with periods that are relatively large compared to the length of the time series are often denoted as being trended. Trends in wind speeds make the comparison of measured wind turbine data more complicated, because they can have for example a large influence on the variance of some signals while others are left almost unaffected. Therefore trended data sets are often excluded when measured data is analysed. In case of a load estimation system, excluding data sets is not an option. Instead the introduction of trend related parameters is preferred. Besides utilising spectral moments, it is also possible to compare for example the total variance of the signal to the variance of the same but low-pass filtered signal.

4.3 Output Data

Multi stage load spectra are determined from time series by appropriate counting procedures. An example is the rainflow counting procedure, which is used to count load cycles in a time series. The rainflow multi stage spectrum can be further simplified to a single stage spectrum, which under certain assumptions will give the same fatigue damage. It can be calculated from the number of cycles Ni associated with the load range Si, a reference load cycle number Nref and an exponent m. The exponent m is usually chosen as inverse slope of the S-N curve and thereby reflects material properties with respect to fatigue.

( )m

ref

ii

mi

kmNeq N

NSS

ref

∑ ⋅∆=∆ ,,,

From the above formula it is also obvious, that if the single stage spectrum is calculated with a large exponent, large load ranges will have a relatively higher impact on the result compared

to calculations with small values of m. Therefore a comparison of single stage spectra which have been derived from different exponents can indicate the ratio of large to small load ranges in the underlying multi stage spectra. Besides the rainflow spectra, multi stage load duration distributions are often used to characterise the loading of a wind turbine. These distributions are a measure of how long certain load levels are present. Similar to the above definition a single stage distribution can be calculated from the time Ti, the corresponding load level Li and a reference time Tref. The exponent p can be used again to indicate the ratio of large and small load levels in the distribution.

( )p

ref

ii

pi

kpTeq T

TLL

ref

∑ ⋅=,,,

The target values of the load estimation procedure are single stage spectra and distributions on the basis of ten minute time periods. They can be assembled to a single value if the same reference numbers and exponents have been used.

( )m

k

mkmNeqmNeq refref

SS ∑ ∆=∆ ,,,,,

( )p

k

pkpTeqpTeq refref

LL ∑= ,,,,,

5 Test and Validation

5.1 General

The above described approach for the estimation of single stage spectra and distributions from statistical parameters of

standard signals has been developed and tested on the basis of simulated wind turbine data first. In a second step, the method is validated with measured data from real wind turbines. Only results on the basis of measured data are given in this section. Since 2005 the Endowed Chair of Wind Energy is involved in a long-term measurement campaign that is still going on at the prototype of the Multibrid M5000 turbine in Bremerhaven. The M5000 is a state of the art multi-megawatt turbine with a rated power output of 5 MW, a rotor diameter of 116 m and a hub height of 102m. For the validation of the presented approach, about 150h of measured data have been extracted reflecting typical site conditions with wind speeds between 4 and 22m/s and turbulence intensities ranging from 3 to 17%. Only measured time series where the turbine was in normal power production mode are considered. Time and frequency domain related statistical parameters of electrical power, generator rotational speed, generator rotational acceleration, pitch angle and tower top accelerations have been calculated. Single stage loads of rotor torque, rotor thrust and blade root bending moments have been analysed using two exponents (4 and 10) for each load quantity. The blade root bending moments are estimated as in-plane and out-of-plane moments in a fixed coordinate system as well as edge- and flapwise moments in a pitching coordinate system. For each load quantity and each exponent a single neural network has been trained. About 120h of data have been used to train the networks. The trained neural networks have then been utilised to predict the single stage spectra on basis of the derived statistical parameters. This has been done for the remaining 30h of data, which have not been included in the training process. The estimation results of single stage spectra ∆Seq,Nref,m are given in the next section for two exponents, followed by the results for the single stage distributions ∆Leq,Tref,p. In both cases, the estimations have been compared with results from standard time series counting procedures and the errors have been computed.

5.2 Estimation of Single Stage Spectra

For each load the following quantities have been computed, in order to assess the accuracy of the estimation results:

• the overall error calculated from the

logarithmic sum of all estimations ∆Seq,Nref,m

• the linear average of all estimation errors ∆Seq,Nref,m,k

• the standard deviation of all estimation errors as measure of the average error of a single estimation

Exact values are listed in Table 2, while Figure 7 illustrates the data further. The mean error is relatively small for all estimations and decreases even further if the individual estimations are cumulated to an overall long-term spectrum. In this case the maximum deviation is about 4% only in the case of the out-of-plane blade root bending moment and an exponent of m=10. These accurate results seem at least to some extend to be due to the averaging of prediction results. The standard deviation of errors indicates that larger differences between predicted and real loads can be expected for a single estimation. Especially for large exponents an error of 10 to 13% is likely. The most accurate predictions have been derived for the in-plane and edgewise blade root bending moments respectively. These quantities are dominated by deterministic oscillations which are due to the self weight of the blade and the rotation of the rotor. As the weight is constant and the rotational speed is a direct input to the procedure a very good result can be expected. This holds true even for the standard deviations of the estimation error which are also higher for all other loads. The somewhat lower standard deviation for spectra calculated on the basis of the exponent of 4 indicates that these quantities can be predicted better compared to the spectra based on larger exponents. In general, the estimations of out-of-plane and flapwise bending moments comprise the largest errors. This is probably due to the fact, that all input signals are measured in a fixed frame of reference behind the rotor. They can therefore be regarded as integral quantities and include cumulated aerodynamic and structural dynamic effects from all three blades. Utilisation of these signals for the prediction of aerodynamically driven blade root loads results hence in relatively large scatter of the estimation results.

Figure 7: Comparison of single stage spectra estimation errors

Figure 8: Comparison of single stage distribution estimation errors

5.3 Estimation of Single Stage Distributions

The same estimation errors as described above have also been derived for the single stage distributions. Results are given in Table 3 and Figure 8. In general, the single stage distributions can be predicted with higher accuracy compared to the spectra. The estimation errors for the cumulated distributions are between -1.3 and 0.5% in any case. Unlike to the spectra, the largest standard deviations of the estimation errors occur for integral load quantities, i.e. the rotor torque and the rotor thrust. The most likely reason for this is the relatively large variation in the 10 minute mean value of these loads compared to the variations in the other quantities.

6 Conclusion and Outlook A method for the estimation of single stage fatigue loads from standard wind turbine signals has been developed. As the exact relationships between standard wind turbine signals and load quantities are in general unknown, an empirical approach has been applied. Here, statistical parameters of the standard signals are related to the main load components by trained neural networks. The focus is placed on the estimation of the most important load components, such as blade root bending moment, rotor thrust, rotor torque and tower bending moments, which are characteristic for the overall turbine load level. Measured data from a state-of-the-art multi megawatt wind turbine has been used for the validation of the approach. Results show relatively small estimation errors only, especially if they are cumulated to an overall long-term load.

Error from ∆Seq,Nref,m Mean error from ∆Seq,Nref,m,k

Standard deviation of error from ∆Seq,Nref,m,k

% % % Load quantity

m = 4 m = 10 m = 4 m = 10 m = 4 m = 10

Rotor torque 0.5 -1.2 1.1 2.3 6.7 13.2

Rotor thrust 1.8 0.6 3.7 2.8 7.9 9.9

In-plane bending moment 0.0 1.1 0.1 1.3 1.6 1.8

Out-of-plane bending moment 2.7 4.0 5.4 6.4 10.9 11.7

Edgewise bending moment 0.7 0.0 0.8 0.3 1.7 1.6

Flapwise bending moment 2.0 2.1 3.8 8.0 11.2 12.2

Table 2: Single stage spectra estimation errors

Error from Leq,Tref,p Mean error from

Leq,Tref,p,k Standard deviation of error from Leq,Tref,p,k

% % % Load quantity

p = 4 p = 10 p = 4 p = 10 p = 4 p = 10

Rotor torque -0.1 -0.3 0.8 -0.1 7.5 2.6

Rotor thrust -0.4 -1.3 1.4 0.2 5.7 4.8

In-plane bending moment 0.4 0.5 0.4 0.6 1.4 1.8

Out-of-plane bending moment 0.0 0.4 -0.1 0.5 2.1 2.1

Edgewise bending moment -0.1 0.2 0.0 0.5 1.6 1.9

Flapwise bending moment 0.0 0.6 -0.1 1.0 2.3 2.1

Table 3: Single stage distribution estimation errors

Further validation of the method with data from onshore wind turbines is planned. Emphasis will be placed on the robustness of the method and also on transferability of the established estimation procedure to other turbines of the same type. Application and improvement of the approach with data from the German offshore test site “alpha ventus” will begin as soon as measured data is available.

Acknowledgements The research is part of the Project ”Verification of Offshore Wind Turbines” (OWEA) at the German offshore test site ”alpha ventus” and is supported by the Federal Ministry for Environment, Nature Conservation and Nuclear Safety (BMU). The authors further acknowledge the cooperation with the Multibrid GmbH, Bremerhaven, and the possibility to validate the presented approach on the basis of measured data.

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