• condition monitoring system;
  • load monitoring;
  • shaft torque;
  • Kalman filter;
  • gearbox


  1. Top of page
  2. Abstract

Improvement of condition monitoring (CM) systems for wind turbines (WTs) and reduction of the cost of wind energy are possible if knowledge about the condition of different WT components is available. CM based on the WT drive train shaft torque signal can give a better understanding of the gearbox failure mechanisms as well as provide a method for detecting mass imbalance and aerodynamic asymmetry. The major obstacle preventing the industrial application of CM based on the shaft torque signal is the costly measurement equipment which is impractical for long-term use on operating WTs. This paper suggests a novel approach for low-cost, indirect monitoring of the shaft torque from standard WT measurements. The shaft torque is estimated recursively from measurements of generator torque, high speed shaft and low speed shaft angular speeds using the well-known Kalman filter theory. The performance of the augmented Kalman filter with fading memory (AKFF) is compared with the augmented Kalman filter (AKF) using simulated data of the WT for different load conditions, measurement noise levels and WT fault scenarios. A multiple-model algorithm, based on a set of different Kalman filters, is designed for practical implementation of the shaft torque estimator. Its performance is validated for a scenario where there are frequent changes of operating points. The proposed cost-effective shaft torque estimator overcomes all major problems, which prevent the industrial application of CM systems based on shaft torque measurements. Future work will be focused on validating the method using experimental data and developing suitable signal processing algorithms for fault detection. Copyright © 2013 John Wiley & Sons, Ltd.


  1. Top of page
  2. Abstract

The worldwide wind energy production is increasing rapidly, and the total installed capacity reached 238 GW in the beginning of 2012. [1] Despite the positive trend in wind capacity growth, one of the biggest challenges in the wind industry is the reduction of the Cost of Energy (CoE). Reduction of the CoE of already installed wind turbines (WTs) can be achieved by increasing availability and/or by reducing operational costs (OPEX). In order to compare influences of the availability and OPEX on CoE, GAMESA conducted a study [2] showing that a 1% decrease in OPEX leads to a 0.16% decrease in the CoE, whereas an increase in availability of 1% decreases the CoE by 1.5%. The results of this study highlight the importance of developing new techniques that will increase the availability of turbines. Some of the promising approaches for reducing the amount of WTs downtime include maintenances and inspections in low wind conditions, predictive and customized maintenance programmes, and further automation and innovation of condition monitoring (CM) systems.

Industrial CM systems for WTs are commonly designed using monitoring systems developed primarily for other rotating machinery. [3, 4] However, the efficiency of these CM systems is limited as WTs are nonlinear, complex dynamic structures which are exposed to rapidly varying wind and wave loads. Through the development of CM systems specialized for WTs, it is hoped that one can increase WT efficiency and improve fault prediction and early fault detection thus allowing the use of condition-based operation and maintenance strategies. The actual trend in the development of CM systems is focused on monitoring the most vulnerable components of the WT. Statistical reliability analyses of reported WT failures [5, 6] show that the majority of WT failures are initiated in the gearbox, the main shaft and bearings, the generator, the rotor brake and the blades.

The development of CM systems for WTs based on measurements of the shaft torque was initiated during the last decade, and the potential of this approach was highlighted in some recently published state-of-the-art papers. [4, 7, 8] One relevant measurement campaign was performed in a wind park in Spain where DEWI [9] validated the shaft torque loads entering the gearboxes of different WTs under the same operational conditions. The aim was to compare the 1 Hz equivalent loads of different WTs under the same operating conditions and to find the root causes of frequent gearbox failures. The campaign was time-limited, and the results were used to indicate a specific WT with potentially less operating lifetime. The study illustrates the use of the shaft torque signal in practice for only a limited period and shows the potential benefit that could be achieved by continuous monitoring of the shaft torque.

The research group from Durham University validated CM systems on the basis of the shaft torque measurements in the laboratory environment using a mechanical test rig. The aim of their studies was to extract certain fault signatures from the measured shaft torque by using signal processing techniques. The extracted fault signatures are the rotor imbalances [10-12] and the electrical asymmetry on rotor of induction generator. [10, 11] The relations between specific faults and the shaft torque will be further discussed in the coming sections, and the previously mentioned works will be commented on in more detail.

The potential of monitoring different WT components using only the shaft torque signal is significant, but the use of shaft torque measurements for CM systems is still limited to the laboratory environment, and industrial validation and application of this kind of CM systems is currently a topic of future work. One of the obstacles preventing the application of CM systems based on shaft-torque data is the expensive and impractical nature of the required measurement equipment. Torque transducers based on strain gauge sensors are suitable only for laboratory use and for prototype machines as their application to operational WTs would be costly and impractical with the accuracy around 5%. [11, 13] Also, practice shows that strain gauges are not suitable for long-term application.

An alternative to direct shaft torque measuring is its estimation from low-cost, standard and reliable WT measurements. An indirect method [14] compares angular displacements of the low speed-side and the high speed-side shafts. The shaft torque is further directly calculated from the terminal electrical quantities. In a recent paper, the indirect measuring of shaft torque is investigated by Perišić et al.. [15] The shaft torque is recursively estimated from the standard WT measurement signals using a model-based approach and augmented Kalman filter (AKF). [16] Good estimation results were achieved for the above-rated wind speed, but degradation of the estimation accuracy was present for below-rated wind speeds, indicating that the assumptions required for optimal running of Kalman filter are not fulfilled in this operating region. Also, the standard Kalman filter is not able to adapt to changes in operating conditions, thus preventing it from being directly implemented on real WTs.

In the current paper, it is proposed that the augmented Kalman filter with fading memory (AKFF) be used for the indirect measuring of the shaft torque from the measurements of the generator torque, the rotor angular speed and the generator angular speed. The AKFF assigns more weight to the most recent portion of measurements than the standard Kalman filter. Making the filter more responsive to new measurements makes it less sensitive to modelling errors. A drawback of weighting the measurements is a loss of the optimality of the Kalman filter. However, as practise showed, when the optimal filter does not converge, it is better to use a suboptimal filter that is relatively robust to modelling errors and changes in operating conditions. Also, by using a more robust algorithm, simpler and more general models of the system can be used.

The performances of two different observer structures, the AKF and the AKFF, are tested for different load conditions, i.e. for below-rated, around-rated and above-rated wind speeds. Robustness of the algorithms is tested by adding artificial noise to simulated WT measurement data. The AKF and the AKFF cannot adapt to straightforward changes of operating points as they are designed on the basis of a system model specific for a single-operating point. In order to allow practical implementation, multiple-model (MM) shaft torque estimator [17] based on a set of the AKFs and the AKFFs working in parallel is tested on WT-simulated data for a case when operating points change very frequently.

The paper is organized as follows. Section 2 is focused on the design of the shaft torque observer. Drive train model structures, model identification and the optimal structures of the shaft torque estimator are discussed. Also, the solution for practical implementation of the algorithm for load monitoring of operating WTs is proposed, and the implementation issues are addressed. Section 3 presents the potential applications of the estimation algorithm in CM systems for WTs. This section provides physical explanations on how different WT components can be monitored by using the shaft torque measurements. Section 4 is focused on testing the performances of the shaft torque estimators. Investigation of the shaft torque load estimators performance in the presence of various faults is investigated by modelling WT faults in the turbine model used for simulations. The MM estimation algorithm is further tested for the case when the operating conditions change frequently.


  1. Top of page
  2. Abstract

Design of a low-cost estimator of the shaft torque consists of the following steps:

  1. Physical-law based model of the drive train
  2. State-space model of the drive train
  3. Model identification: Grey box model
  4. State estimator design: AKF
  5. State estimator design: AKFF
  6. Multiple-model algorithm for shaft torque estimation
  7. Tasks and challenges in practical implementation

2.1 Physical-law based model of the drive train

The role of the drive train system in the geared WT is to transfer mechanical energy from the low-speed rotor side to the high-speed generator side where the electrical energy is produced. The term ‘drive train’ is used to refer to all rotating parts from the rotor hub, through the low-speed shaft and the gearbox, to the high-speed shaft and the generator. The driving force of the system is the aerodynamic load on the low-speed side of the drive train, where the reaction force is due to the generator torque on the high speed shaft. As a result of mechanical and electrical losses in the drive train system, these two torques are not equal. Because of the shaft's elasticity, torsional torque causes twisting in the shaft. The angle of twisting is proportional to the unit of the applied torque, thus torsional torques in the shaft are increasing with excitation level (i.e. with the wind speed acting on the turbine).

In order to model the drive train system, a variety of physical models with different levels of complexity are available. Decision on the level of complexity is mostly based on the further application of the model. For instance, a one-mass turbine drive train model, where all components of the drive train are lumped together, can be used for power analysis of variable speed WTs. In variable speed WTs, mechanical rotor speed and electrical frequency of the grid are decoupled, so the simplest drive train model is sufficient for analysis of the system. On the other hand, this model is not sufficient for power analysis of the fixed speed WTs where two, three or six mass models are usually used. [18, 19] For the purpose of design of drive train system, very complex and accurate finite element models are used where each component is modelled in detail. [20]

In the system identification field, the best model has the lowest number of degrees of freedom necessary to model all important system dynamics. Modelling of all important system dynamics is especially important in the case of the Kalman filter, as the accurate system model is required for the filter optimality. However, even when the model provides filter optimality in a simulation environment, it may happen that it will not work well in the real operating conditions. Usually, it is not possible to obtain the exact model of the real system in practise because of, for instance, the complexity of the structure, non-modelled system dynamics, non-modelled nonlinear effects, over-fitting to simulated data, very dynamic excitation, non-Gaussian noises, etc.

In this work, only simulated WT data is available for the estimation of the shaft torque. One of the performance goals is that shaft torque estimator should converge even when the model structure is not the exact representation of the real physics of the system dynamics. Thus, in order to make a realistic test of the shaft torque estimator using simulated data, a model of the drive train is used, which includes all necessary torsional dynamics. However, the model is less complex than the turbine model used for obtaining simulated data. This model should be validated using real data, and, if necessary, extended and updated.

The two degree of freedom models, Figure 1, includes two mass moment inertias: Jr, which represents the equivalent inertia of the blade and the hub, and Jg, which represents the equivalent inertia of the gearbox and the generator rotor. Mass moment inertias are interconnected by a spring and a damper. Viscous damping is present on each of the inertias, and cr and cg are respectively viscous damping for the rotor and generator. The equivalent viscous damping and the stiffness coefficients of the drive train system are denoted as cdrt and kdrt, respectively. The external forces exerted on the system are aerodynamic torque Qa on the low-speed shaft and generator reaction torque Qg on the high-speed shaft. Qst is unknown shaft torque. The ordinary differential equations that approximate the dynamic motion of this system around operating point are given in equations (1),(2) and (3).

  • display math(1)
  • display math(2)
  • display math(3)

The tilde symbol above a signal, for example in inline image, inline image and inline image, indicates a dynamic signal, i.e. displacement of the signal from the operating point. Θr and Θg are absolute angular displacements of rotor and generator shaft, ωr is the rotor angular speed and ωg is the generator angular speed.


Figure 1. Reduced order model of drive train.

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2.2 State-space model of the drive train

Differential equations (1), (2) and (3) can be transformed to only one equation in matrix-form, also known as a state-space representation of the system. By defining inline image and inline image as the state variables of drive train system, the state-space equation describing how the state variables propagate in time is given in the succeeding equation:

  • display math(4)

Ac is the system matrix, and Bc is the input matrix in continuous time. WT signals assumed measurable are ωr,ωg and Qg, so the measurement equation has the following form:

  • display math(5)

C is the measurement system matrix, equal in continuous and discrete time. Physical equations representing the dynamics of the real processes are usually in continuous time, and that is the reason why the drive train system is modelled in continuous time. However, measurements are sampled in discrete time, and a state estimation algorithm is applied in discrete time to allow straightforward computational implementation. Therefore, it is more convenient to discretize the model given by equations (4) and (5) and to use a discrete drive train model obtained by, for instance, a zero-order hold discretization method. The size of the discretization step Ts is chosen to correspond to the sampling time of the measurements.

  • display math(6)
  • display math(7)

In order to implement the state estimator, input and output vectors should be available at every time step. In this work, aerodynamic torque, which is one of the inputs, is not measurable. One way to deal with the unknown input is to augment the state vector with all unavailable input signals. By augmenting the state vector, it is assumed that a model of the unknown input is available. In this work, the unknown input inline image is represented as the output of the first order dynamic system in discrete time [equation (8)].

  • display math(8)

As the mean value of the dynamic signal inline image is zero, ζk is a zero-mean stationary, stochastic process that accounts for the aerodynamic torque increment. The covariance matrix of ζk is S, and it represents the tuning matrix which needs to be experimentally determined for a specific problem.

2.3 Model identification: Grey box model

The physical parameters of the previously defined drive train models can be either determined by taking values from the technical specifications of the specific WT or they can be identified using system identification techniques. [21] Model identification can be conducted offline using test measurements or simulated data of the WT, or it can be achieved online by continuous updating of the model with new data. In this work, all the required WT simulated data is available, so the chosen approach is offline identification of the model for different operating points. The aim of the identification procedure is to find the best model which is able to predict outputs of the system. Different parameter sets θ = [JrJgcrcgcdrtkdrt] produce various, in this case, state-space models and consequently different predictions of output inline image for the same inputs. In order to make a comparison between models with different θ, a prediction error is computed [equation (9)].

  • display math(9)

The model for which the time sequence of prediction errors is the lowest is chosen as the best possible model. A variety of methods [21] have been developed for finding the optimal θopt . The least-squares (LS) method proved to work very well for systems linear in the parameters. The LS method involves finding the minimum of the criteria function, equation (10), by taking its derivatives with respect to θ. θopt is where the derivative of the criteria function is equal to zero and is therefore the optimal parameter set, which ensures the best possible model:

  • display math(10)

where N is the number of measured data and S is a weighting matrix. S is chosen in this work as a diagonal matrix. In the case where physical knowledge about the system is available, relations between parameters in vector θ can be held fixed during minimization of VN. In this work, coupling between parameters is required because it guarantees the desired state vector in the state-space model.

As already mentioned, WTs are nonlinear, complex and time varying dynamic systems, but WT dynamics can be modelled by linear models valid around the specific operating points. Thus, the parameters of the linear drive train models are identified using an LS method around three different operating points corresponding to below-rated, around-rated and above-rated wind conditions. In order to keep the straightforward physical meaning of the parameters in the model, identification is performed in continuous time using simulated WT data with constant wind speeds. The identified state matrices are denoted inline image and inline image, where V 0 indicates the corresponding operating point.

2.4 State estimator design: augmented Kalman filter

The identified augmented state-space model for each of the operating regimes has the following form:

  • display math(11)
  • display math(12)

where wk is the process noise vector at time k with the same dimensions as inline image, and vk is the measurement noise at time k with the same dimensions as the measurement vector. Process and measurement noises are assumed to be a stationary, stochastic process with zero means and covariance matrices Q and R, which have appropriate dimensions. Matrix R can be derived from the noise characteristic of the measured data, where the matrix Q is a control variable tuned to represent the accuracy of the system model.

The augmented state vector inline image, the augmented system matrix F, the augmented output matrix G and the augmented measurement matrix H are given by

  • display math(13)

where inline image and inline image are column matrices of the discretized, estimated input matrix inline image. In order for the Kalman filter to converge, the matrix pair (F,H) must be observable.

For the identified linear drive train model, the aim is to design a causal filter that outputs the estimation of the augmented state vector, inline image. If the process and measurement noises are zero-mean, uncorrelated and white, then the optimal linear filter, which minimizes the statistical variance of the state estimation error, is the Kalman filter. Because of its recursive and discrete time nature, the Kalman filter is well suited for real-time application on linear systems.

The Kalman filter uses a priori knowledge about the state-space model, new measurements at every time step and propagates the mean and covariance of the state through time. The algorithm consists of the following steps:

  • Prediction: The aims of the prediction or time updating is to obtain a priori state inline image from the previous a posteriori state inline image, and a priori covariance inline image from the previous a posteriori covariance inline image if measurement at the time k is not available. The state inline image and covariance inline image are progressed through the known dynamics of the linear system [equations (14) and (15)].

    • display math(14)
    • display math(15)

    Prediction of the measurement is given by

    • display math(16)
  • Correction: The aim of the Correction step is to update estimations of states and covariance inline image and inline image when new measurements yk become available. Updated estimations of states and covariance are inline image and inline image. The state vector is updated with the increment proportional to the measurement prediction error, often called innovation or residual. The updated state vector is derived by using the following recursive equation:

    • display math(17)

    where Kk is the Kalman gain matrix and it defines the amount of the innovation in the new state vector. An optimal value of Kalman gain is found by minimizing the sum of the variances of the state estimation errors at time k:

    • display math(18)
    • display math(19)

    A posteriori covariance is derived from equation (17):

    • display math(20)
  • Initialization: The measurements are taken from time k = 1 so no measurements are available for the estimation of the state at the initial time k = 0. The initial state inline image is defined as the expected value of the initial state, where the uncertainty of the estimated state is quantified by the covariance of the estimation error, Pk.

    • display math(21)
    • display math(22)

    The initial covariance inline image represents uncertainty in the initial guess about the state of the system. If inline image is chosen randomly, inline image tends to infinity, where in the case when the initial state vector is well known, inline image tends to be zero.

Assuming that the the accurate model of the system and the stochastic properties of the process and measurement noises are known, the Kalman filter represents an optimal, linear filter. Verification of the performance of the Kalman filter can be conducted by using knowledge about statistics of the residuals, i.e. performing residual analysis. [22] If the mathematical model of the system is an exact representation of the real system, and if the process and measurement noises are Gaussian, white and uncorrelated, then the residual sequence, inline image, should be zero-mean white random process with a covariance equal to inline image.

In practise however, it is very difficult to have all of the optimality requirements fulfilled, and every model is only a simplified representation of some aspects of the real system. Therefore, in order to mimic the real operating environment, the used drive train model is a simplification of the turbine model used for obtaining WT simulated data. For this reason, the residual test cannot show that the applied Kalman filter is an optimal, but only a suboptimal filter. However, if the Kalman filter is applied on the best available model, this filter should still be the best linear filter for the observed system. Sometimes though, non-compliance of the assumptions may cause divergence or even instability in the implementation of the Kalman filter on the real turbine. In order to avoid this, the next section presents another suboptimal Kalman filter, more robust to modelling errors than the standard Kalman filter.

2.5 State estimator design: augmented Kalman filter with fading memory

In the situation where the system model does not match reality, the Kalman filter may diverge from the true state. This can explain the poor results obtained for some wind conditions by using the Kalman filter and the simple drive train model. In order to test if the poor estimation results are due to mismodelling, the Kalman filter is modified to give greater emphasis to more recent data. This Kalman filter modification is also known as the Kalman filter with fading memory, and it represents a suboptimal filter that is more robust to modelling errors than the standard Kalman filter. The main difference between these two filters is in the form of the cost function used for the estimation of the sequence of the state that minimizes the cost function. The cost function used by the Kalman filter is given by the equation (23).

  • display math(23)

The cost function of the Kalman filter, equation (23), is a special case of the cost function of the Kalman filter with fading memory, equation (24), when the forgetting factor α is equal to 1. In the case where one wants to completely ignore the model, α tends to infinity.

  • display math(24)

The purpose of the forgetting factor α ≥ 1 in the first part of equation (24) is to minimize the weighted covariance of the residuals where more weight is put on the recent time samples. By doing this, the filter is forced to converge to state estimations considering the most recent measurements. The forgetting factor in the second part of equation (24) does not have a significant role and is added to further simplify the mathematical derivation. The complete procedure for the derivation of the filter with the fading memory can be found in. [22] The structure of the Kalman filter with fading memory is almost identical to the structure of the Kalman filter, with two crucial exceptions:

  1. inline image is substituted with which is not the real covariance of the estimation error, but is the weighted covariance.

  2. Equation (15) is modified as follows:

    • display math(25)

where α2 increases the estimation-error covariance. In other words, it increases the uncertainty in the state estimations and it puts more faith in the measurements. This approach is equivalent to increasing the process noise, so the filter gives more trust to measured data.

2.6 Multiple-model estimation: implementation of the load estimator in a dynamic environment

The previously defined AKF and AKFF can be directly implemented on real turbines only if the system is stationary, i.e. if the WT operates in a specific wind operating condition. However, this is not practically feasible as WTs are exposed to very dynamic wind and wave loads that result in very frequent changes of operating conditions. Therefore, instead of having only one model of the system implemented in the shaft torque estimator, it would be beneficial to consider models for all possible operating points. This can be done by using MM algorithm in which one runs different Kalman filters in parallel. An MM algorithm fuses estimations of those filters for an overall state estimation.

In this work, in order to account for frequent changes of operating conditions, the MM algorithm runs in parallel the AKF and the AKFF filters for each possible drive train model, i.e. for below-rated, around-rated and above-rated wind conditions, to obtain estimations of the system states. The overall estimation is calculated using a Bayes-optimal combination of individual estimates. Summary of the MM algorithm is given in the following.

Filtering the states of the multiple model systems requires running filters denoted by F = {f(1),f(2), … ,f(M)}, for all possible models M1,M2,..,MM. The probability pi,j that the model structure will change in MM algorithm, in two sequential time steps, is given by

  • display math(26)

where δ(i − j) is the sigma function, and inline image denotes the event that filter f(i) matches the best available filter structure for the system mode in effect at time k. The probabilities pi,j are assumed to be known for each time step k, and in a general case, they can have any value from the interval [0,1]. The matrix with elements pi,j can be seen as a transition probability matrix of the first-order Markov chain that characterizes the transition between modes.

Each filter f(i) is determined with a system model, i.e. system matrices [equation (11)], and the parameter α which defines the filter structure (α = 1 defines the AKF, where α = 1.01 defines the AKFF). The MM algorithm runs independently the AKF and the AKFF for each drive train model corresponding to specific operating conditions. No information is exchanged among filters, and the overall estimates is only the output of the MM algorithm. If the filter with index i calculates the state estimate inline image and covariance inline image, the overall state estimate and covariance at time k are given by

  • display math(27)
  • display math(28)

The posterior probability inline image for each filter f(i) is calculated recursively from Bayes rule as a sum of the conditional estimates weighted by their corresponding model probabilities:

  • display math(29)

where L(i) is the likelihood function with a Gaussian distribution inline image.

2.7 Tasks and challenges in practical implementation

It is very important to consider all potential practical issues before implementing the proposed shaft torque estimator on the operating WT. Some of the most important steps to be taken in the shaft torque estimator design procedure for practical implementation are:

  1. Wind turbine data: Measurements of all relevant data for all relevant operating points prior to the designing and calibrating the shaft torque estimator have to be available. This requires a very extensive measurement campaign of forces and dynamic responses in different operating conditions on at least one of the WTs in the wind farm. In order to measure all necessary WT dynamics and to avoid correlation between measured data and measurement noises, the measurement campaign should be well planned and performed in the period of the year when it is expected that the WT will experience all wind operating conditions.

  2. The model structure, complexity and accuracy: This is a critical step in the design procedure, and its outputs have direct effects on the success of the practical implementation of the shaft torque estimator. From the available measured data, parameters of the drive train model should be estimated and validated. If needed, the system identification procedure should be changed, and the structure of the drive train and aerodynamic torque models should be expanded. Also, all WT measured data should be analysed to quantify the statistical properties of the measurement noises.

  3. Shaft torque estimator calibration: When the drive train model and noise statistics are determined, parameters of the shaft torque estimator should be calibrated using the measured data for each of the operating points. The performances of the AKF and the AKFF should be compared and the set of filters for each operating point should be selected and further included in the MM shaft torque estimator. Also, if one has a priori knowledge about the most probable operating conditions or preferable model structures, this can be included in the multi-model algorithm by changing the probabilities of switching from model to model.

Even though the theory is correct and one is able to successfully implement all steps of the required procedure, the shaft torque estimator may not work on the real turbine. The common reasons for failure of the Kalman filter are numerical and modelling errors. As only a limited number of bits is used for storing the numbers in the Kalman filter, accumulated numerical errors may cause divergence or even instability. If this problem occurs, the straightforward solution is to increase the arithmetic precision, which should not be a problem with modern computer technology. However, if this is not possible, some form of square-root filtering can be used in the Kalman filter algorithm, which will increase the computational time.

With respect to modelling errors, the standard Kalman filter assumes that the noises are pure white, zero mean and completely uncorrelated and that the system model is exactly known. If any of these assumptions are violated, the filter may not work. As it was already explained, the Kalman filter with fading memory is one way to handle modelling errors. If the exact statistics of the measurement and process noises are not known, the MM estimator can be expanded to consider more filters with different noise models.

As it will be seen later, very high measurement noise may affect the shaft torque estimations. This may limit some applications of the shaft torque estimations. Namely, if the post-processing of the shaft torque includes a rainflow count algorithm, the accuracy of the calculated 1-Hz equivalent loads is directly affected by the accuracy of the estimations of the peaks and pits in the shaft torque time-series. On the other hand, if one is intending to conduct damage detection on the basis of the frequency signatures, then only accurate estimations of the energy in the signal around the relevant frequencies is important so the high measurement noise is not an obstacle.


  1. Top of page
  2. Abstract

The aim of this section is to show the potential application of the shaft torque measurements in fault detection strategies, where the future work will address the development of a fault detection algorithm with special attention given to determining the least set of signals sufficient for providing unique and reliable fault detection.

3.1 Gearbox fatigue load monitoring

The gearbox is the WT component that causes the highest annual downtime among all turbine components. [23, 24] This is because of high failure rate combined with a time-consuming, highly expensive and difficult replacement procedure. To better understand the causes of these failures, much research has been conducted in academia and industry. Unfortunately, the latest studies in this field show that the majority of gearbox failures happen due to some unexpected events whose physics are still not understood. [23, 25]

The most often used gearbox CM systems in wind industry are based on vibration analysis algorithms. The overall idea is to use measurements of dynamic responses such as acceleration measurements, as inputs to the algorithms. In the best case scenario, successful algorithms should be able to asses the health of the gearbox and detect the presence of faults at their early stage. Some of the advanced algorithms can quantify the faults size and the stage, but the prediction of fault propagation is very difficult in the case of gearboxes. Thus, vibration-based algorithms can detect the presence of some faults; however, they cannot predict if and when the faults will occur in the gearbox and neither when to expect the complete failure if the fault is already detected. The limiting factor in the application of these algorithms can also be the position of the installed sensors as the fault signatures are usually present in vibrations measured around the fault appearance.

Description and application of some of the often used vibration-based algorithms for gearbox CM on measured data can be found in the National Renewable Energy Laboratory gearbox CM Round Robin project report. [26] In this study, data collected from the test gearbox in a healthy condition and in a faulty condition were given to 16 academic and industrial partners so they could analyse them and detect faults without knowing a priori if and which faults were present. The results obtained using standard practises in industry and academia for gearbox monitoring showed more missed faults than false alarms, stating that despite the fact that available algorithms are powerful in diagnosing faults, there is still room to improve them.

In order to develop CM algorithms for gearbox fault prediction, better knowledge about events that are root-cases of different gearboxes faults is needed. A new approach in the wind industry for recognition of the possible damaging events for gearbox failures is based on measuring the fatigue loads inputting the gearbox. Continuous monitoring of the gearbox shaft torque on all WTs in one wind park, and recording transient events and operating regimes which differ from the normal operation of the WT, can provide information about gearbox structural changes caused by each of these events. In this way, the gearbox failure mechanisms can be better understood, and the obtained information can be used for improving gearbox design and for developing a predictive maintenance strategy.

One example of this approach was in the study by Soker et al., [9] when input loads on the gearbox were monitored in order to investigate the possible reasons of repeated damages to the gearboxes in a wind park in Spain. Measurements were post-processed, and rainflow cycle distributions were produced for two WTs. During the monitored period, it was noticed that the WT, which experienced four times more full stops than the other turbine, had a considerable number of load cycles with large load ranges under the same operating conditions. In order to quantify this difference, 1-Hz equivalent loads were compared for these two turbines, and a difference of 38% was noticed in the shaft torque equivalent loads, indicating that the WT which experienced more full stops suffered from more structural changes than the other one.

In order to illustrate the load ranges inputting the gearbox during normal operation and manual full stops, Figures 2 and 3 show the 250-kHz shaft torque measurements obtained in the Vattenfall measurement campaign that was performed during 2008 and 2009. The corresponding shaft rotational speeds are reconstructed from the bending load measurements with a sampling frequency of 2 Hz. It is very important to notice an almost immediate increase in load range when the full stop of the turbine is initiated during normal operation (Figures 2 and 3). Unfortunately, still no research study was performed to quantify the structural changes of the gearbox due to particular events like this or manual stop or frequent shut downs and start-ups, etc. One of the main reasons is a lack of measurement equipment for long-term measuring of the shaft torque. Usually, the shaft torque is measured using strain gauge sensors, but as was mentioned before, these sensors are not suitable for long-term application on operating WTs. Also, their mounting on low-speed and high-speed shafts is very challenging and sometimes not even feasible.


Figure 2. Measurements of high-speed shaft torque and corresponding shaft speed during normal operation of the test wind turbine in Tjaereborg, Denmark.

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Figure 3. Measurements of high-speed shaft torque and corresponding shaft speed during manual stop of the test wind turbine in Tjaereborg, Denmark.

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For instance, Vattenfall obtained these measurements during a time-limited field test campaign on a gearbox in a Vestas (Vestas Wind Systems A/S Hedeager 44 8200 Aarhus N Denmark) V80 2 MW WT situated in Tjaereborg, Denmark. This specific WT was a prototype for the Horns Rev offshore WTs with identical design and configuration. The WT was instrumented with intensive measurement equipment, and measurements were performed during normal production and during different WT maneuvers such as normal stop, manual stop and start-up.

In the future, standard vibration-based CM can be expanded to monitor the loads inputting the gearbox. When the fault is detected using standard vibration-based fault detection CM, shaft torque signals can be examined and deviations from the normal operation detected. Combining different monitoring systems can provide a better insight in the effects of certain load-input patterns on the gearbox and recognizing critical events causing faults. The overall benefit of expanding standard CM with the gearbox transient loads monitoring systems can result in a better understanding of gearbox failure mechanisms, thus making possibilities for more reliable gearbox design and gearbox predictive maintenance strategies.

3.2 Rotor imbalance monitoring based on shaft torque

Wind turbine faults causing rotor imbalance are common in practice, but they can be very challenging to detect, quantify and localize. With respect to the effect on the WT, the rotor imbalance can be divided into two groups: blade mass imbalance and aerodynamic asymmetry.

  • Blade mass imbalance happens when an uneven rotor mass distribution is present. Some of the root causes of mass imbalance are manufacturing inaccuracies, including water inside the blades, unequal icing, etc. Also, the centre of rotor mass can move if some of the unfixed parts inside the rotor start to move towards the tip of blades. As a consequence of mass imbalance, transverse oscillations at the rotor rotational frequency and its subharmonics are amplified. The vibration intensity increases with the size of the mass imbalance fault.

    In order to illustrate the influence of the mass imbalance on the shaft torque, separate 10-min long simulations were obtained with no mass imbalance (reference or baseline simulations) and with the mass of one blade changed by + 1%, + 2% and + 3%, whereas the masses of the other two blades were not changed. These simulations were repeated for the below-rated, around-rated and above-rated wind speeds. In order to illustrate fault signatures for rotor imbalances, time-domain simulations of the shaft torque are transformed in the frequency-domain using the Fourier transform. Power spectrum density (PSD) plots are generated to compare the shaft torque of the healthy WT and the shaft torque of the WT with modelled mass imbalances.

    Figure 4 compares PSDs of the simulated shaft torque for different health conditions of a WT, for the below-rated and the above-ratedwind speed. The most evident change, i.e. fault signature, is detected at 1 P rotational frequency confirming the physical explanation given in the previous text. The same pattern is noticed for all wind conditions. The frequency of the fault signature is defined by the mean angular rotational speed of the low-speed shaft. Consequently, the angular rotational speed will also need to be monitored in variable speed WTs.

    It is beneficial if one notices that the Fourier transform assumes a stationary signal during the period when the transformation is applied. In practice however, WTs are exposed to dynamic environmental changes and excitations, so more appropriate methodology for monitoring the PSD of the shaft torque signal should be based on time-frequency analysis. For instance, Wavelet time-frequency analysis [27] can be used to track the frequency spectrum of the signal in time (and therefore the fault signature).

    In the work of Yang et al., [10] the mass imbalance is detected by monitoring the shaft torque and the shaft speed. The fault indicator signal is based on the ratio of the torque and the speed time series, and it is shown how it oscillates in the presence of the mass imbalance. The oscillations can be explained by the increase of energy at 1 P rotational frequency. The fault signature can be extracted using the method proposed in the work of Yang et al. [10] or some other signal processing methods. After extracting the fault signature, the challenge is to set the right threshold so as to avoid the false alarms and to be able to detect even small changes in the blade mass.

  • Aerodynamic asymmetry is characterized by uneven distribution of thrust loads on the blades. The thrust loads imposed by wind can have an uneven distribution on the turbine rotor because of an offset in the angles of attack of individual blades and/or different blade profiles. Some of the common root causes of the aerodynamic asymmetry are manufacturing inaccuracies, permanent deformation of the blade profile during operation, icing of blades, faults in the control system and blade bearing fault. A long-term global consequence of the aerodynamic asymmetry is a reduction in annual WT production.

    The influence of the aerodynamic asymmetry on the shaft torque is illustrated by modelling a WT with pitch offset. Separate simulations are obtained with no pitch offset (reference or baseline simulations) and with changed pitch angle of one blade by + 1, + 2 and + 5 degrees, whereas the pitch offset of the other two blades were equal to zero. These simulations were repeated for the below-rated, around-rated and above-rated wind speeds.

    Power spectrum densities of shaft torque with and without pitch offset are compared and shown in Figure 5. The most evident fault signature is noticed at 1 P frequency; however, its delectability increases with the average wind speed. From the simulations, it is very difficult to notice it at the below-rated wind speed. However, at the above-rated wind speeds, the aerodynamic asymmetry results in changes of the energy at the same frequency as the rotor mass imbalance. Thus, the fault signature is at the same 1 P frequency as in the case of the rotor mass imbalance, but its appearance differs with respect to the operating condition. As in the case of blade mass imbalance, the angular rotational speed will also need to be measured and the shaft torque signal need to be analysed using time-frequency techniques.


Figure 4. Comparison of shaft torque PSDs plots with and without mass imbalance faults around 1 P frequency for below-rated operating conditions (plot on the left) and above-rated operating conditions (plot on the right).

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Figure 5. Comparison of shaft torque PSDs plots with and without aerodynamic asymmetry faults around 1 P frequency for different operating conditions.

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From performed simulations, a rotor imbalance fault detection algorithm based on the shaft torque measurements can be made by analysing the pattern in which energy content around 1 P frequency in the shaft torque signal changes with the operating conditions. It is possible to detect rotor imbalance and to distinguish between mass imbalance and aerodynamic asymmetry. In the case of the mass imbalance, changes in the PSD at 1 P frequency is present at all wind speeds, where in the case of the aerodynamic asymmetry, changes are present in high wind speeds but disappear in lower levels of mean wind speed. In the development of a reliable fault detection algorithm, it would be beneficial to consider all relevant, available signals such as shaft speed, shaft torque, pitch angles and annual electrical production. A final decision should be made considering all extracted fault features, with the aim to make a robust and reliable decision.


  1. Top of page
  2. Abstract

4.1 Wind turbine model

The performance of the estimator is tested by using WT-simulated data obtained using a high-fidelity, aero-elastic simulator LACflex. LACflex was developed by the consulting company LAC engineering and is an improved version of the well known simulation software FLEX5, developed by the Danish Technical University.

The simulated WT is a generic 2 MW type. The hub height of the turbine is 60 m, with a rotor diameter of 80 m. The turbine is driven by ambient wind loads corresponding to offshore load conditions, and the wind field model is obtained by Sandia methods. Average wind speeds of 6, 14 and 22 m s  − 1 and with 10 % turbulence level are used for 10-min long simulations with a sampling time Ts equal to 0.02 s. Wind turbine models with no faults and with different rotor imbalances are used for creating artificial data for testing the performance of the estimator.

In order to use stochastic data for estimations, measurement noise is added to the simulated data. The artificially added measurement noise v(t) is Gaussian, zero-mean noise with the variance equal to 1%, 2% and 3% of the variance of the simulated data. These noise levels are relatively high and correspond to a signal-to-noise ratio (SNR) of 100, 50 and 30, respectively. In practice, it is expected that the error in the measured low-speed shaft is 1%, where the error of high-speed shaft is 5%, [28] which corresponds to a much higher SNR then simulated, thus lower noise intensity.

In order to compare the quality of the estimations, the normalized mean square error function (NMSE) is calculated for the estimated shaft torque time-series. The NMSE compares the measured time series inline image with the estimated shaft torque inline image signal, where inline image is the variance of the simulated shaft torque. Generally, an NMSE of under 5% indicates good estimations.

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The performances of the AKF and the AKFF are compared for three operating points when there is no fault in the WT and when the rotor imbalances faults are present. The AKF and the AKFF are designed to work around single operating points, so they are tested for the case when changes of operating points are not present. To allow practical implementation of the estimator, an MM algorithm based on the AKF and the AKFF is tested for the case when frequent changes of operating conditions happen. Data for this test was obtained by merging randomly selected data sets from all three simulated wind conditions. In this way, changes of operating points happen immediately, which is usually not the case in reality where the transient period is longer. However, when unable to simulate more realistic data, this is still a good example for testing the performances of the estimator and how well the algorithm can track changes of the operating conditions.

4.2 Shaft torque estimation: normal operating conditions

In order to test the performance of the AKF, AKFF and the benchmark estimations for different noise and wind load conditions, the estimated shaft torque time-series were compared with simulated data, both in the time and frequency domains. Simulated data was obtained using a model of the healthy conditioned WT. During all simulations, the forgetting factor of the AKFF was held fixed with a value close to 1 in order to put more emphasis to recent measurements but still takes the system model into consideration. This value of the forgetting factor showed the best performance in the practice.

Table 1 compares the NMSE of the estimations using the AKF and the AKFF for different wind and measurement noise conditions for a WT without faults. In order to illustrate the ability of the AKFF to track the energy around the most significant low-frequencies, simulations and estimations of the shaft torque by the AKFF for the mean wind speeds of 6, 14 and 22 m s  − 1 are presented in the time and frequency domains in Figures 6, 7 and 8, respectively. Estimations are obtained in the presence of high measurement noise with SNR (SNR = 30), which represents the worst assumed scenario.

Table 1. NMSE of shaft torque estimations for different mean wind speeds and noise levels for the case of healthy WT.
V0(m s−1)inline imageAKFNMSE(%)AKFFNMSE(%)

Figure 6. Shaft torque estimation in time and frequency domains for the mean wind speed of 6 m s  − 1 and measurement noise with SNR = 30.

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Figure 7. Shaft torque estimation in time and frequency domains for the mean wind speed of 14 m s  − 1 and measurement noise with SNR = 30.

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Figure 8. Shaft torque estimation in time and frequency domains for the mean wind speed of 22 m s  − 1 and measurement noise with SNR = 30.

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4.3 Shaft torque estimation: rotor imbalances

In order to test the performances of the AKF and the AKFF for the WT with rotor imbalances, mass imbalance and pitch asymmetry were modelled and simulated separately as previously described. The estimations are obtained using simulated data of a WT with mass imbalances of 1% and 5%, and with pitch offsets of 1, 2 and 5 degrees. For each of the estimations, the NMSE was calculated and presented in Tables  2-5 and 6.

Table 2. NMSE of shaft torque estimations for different mean wind speeds and noise levels for the case of WT with 1% mass imbalance.
V0(m s−1)inline imageAKFNMSEAKFFNMSE
Table 3. NMSE of shaft torque estimations for different mean wind speeds and noise levels for the case of WT with 5% mass imbalance.
V0(m s−1)inline imageAKFNMSE(%)AKFFNMSE(%)
Table 4. NMSE of shaft torque estimations for different mean wind speeds and noise levels for the case of WT with one degree pitch offset.
V0(m s−1)inline imageAKFNMSE(%)AKFFNMSE(%)
Table 5. NMSE of shaft torque estimations for different mean wind speeds and noise levels for the case of WT with two degrees pitch offset.
V0(m s−1)inline imageAKFNMSE(%)AKFFNMSE(%)
Table 6. NMSE of shaft torque estimations for different mean wind speeds and noise levels for the case of WT with five degrees pitch offset.
V0(m s−1)inline imageAKFNMSE(%)AKFFNMSE(%)

4.4 Shaft torque estimation: dynamic, normal operating conditions

The performance of the MM shaft torque estimator is illustrated on a case when the operating points (and consequently the 1 P frequency) are changing fast in time. In the observed period of less than half a minute, the operating point changes three times. During the first 4 s, data are obtained for the below-rated wind operating conditions. During next 16 s, data are simulated for the above-rated wind conditions. In the last 10 s, simulations are performed for the around-rated wind conditions. Data obtained in different operating regimes were simulated separately, where sets of data from each of the regimes are randomly selected and merged together to present immediate changes of operating points. Changes of the frequencies of the referent shaft torque signal in time are illustrated in Figure 9.


Figure 9. Spectrogram of the reference shaft torque signal obtained using time windowing and Fast Fourier transformation.

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Figure 10 represents the dynamic component of the shaft torque estimations obtained by multiple model algorithms and assuming different measurement noise levels. Estimations are compared with the dynamic component of the reference signal. The first plot in the figure corresponds to the case when there is almost no noise in the measurements, i.e. it is assumed that the relative measurement error is only 0.1%. The two plots below correspond to more realistic assumptions about measurement noise. If one assumes that low-shaft speed is measured using low-cost inductive proximity sensors, the expected accuracy of the system is 1%. [28] If the high-shaft speed is measured using the same type of the sensor, the accuracy of the measurements is 5%. Thus, the plot in the middle of Figure 10 is obtained under these assumptions about the measurement noise. The third plot is obtained under the assumption that accuracy of the high-speed shaft is 10%, where the accuracy of low-shaft speed remained at 1%.


Figure 10. Shaft torque estimations in dynamic operating conditions using multi-model algorithm, assuming different measurement noise levels. More precisely, very low measurement noise (top plot) and two possible cases of real measurement noises. Expected measurement noise error is 1% of the low-speed side shaft and 5% (plot in the middle) and 10% (lowest plot) of the high-speed side shaft, depending on the equipment.

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4.5 Discussion and the future work

The performances of two different shaft torque estimation algorithms based on the well-known Kalman filter are tested for different wind speeds, different measurement noise levels and different health conditions of a WT using simulated data. More precisely, the performances of the standard AKF and the AKFF were tested for WT simulated data obtained around single operating points. The performance of the multi-modal estimator, based on a set of the AKFs and the AKFFs, is tested on simulated data when the operating point was frequently changing. In the following is discussed the robustness of the AKF and the AKFF in the presence of the measurement noise for different operating regimes. The performance of the MM algorithm, the application limitations and the future work are discussed as well.

The AKFF showed to be more robust to measurement noise than the AKF. The NMSE of estimations is always either under or just slightly above 5%, which indicates good estimations. However, as it can be seen from Figures 6, 7 and 8, estimations in the presence of very high measurement noise may have a limited application. More precisely, if the aim is to extract fault signature at 1 P frequency, these estimations can be used as the AKFF provides almost perfect estimations of the energy contained around this frequency for all wind speeds and measurement noise levels. However, if the further application involves a rainflow count algorithm, then the use of the shaft torque estimations obtained in the presence of very high measurement noise is not suitable, especially in the below-rated wind condition, Figure 6, where the torque estimation error is a result of a poorly tuned Kalman filter. In order to find the source of the tuning error, results presented in Tables 1- VI are analysed, and it can be seen that the most significant improvement of the estimations using the AKFF compared with the AKF is achieved in below-rated wind conditions, indicating that the mismodelling error is the highest in this range. Despite the fact that the AKFF improves estimations, they are still not good enough for calculation of 1-Hz equivalent loads in the presence of high measurement noise. In practise, the expected level of measurement noise is much lower than the noise assumed in this work. However, if high measurement noise is present in experimental data, a more complex model of drive train system might be required.

The approach proposed for the practical implementation of the shaft torque estimator, i.e. multi-modal estimation algorithm shows good performance on simulated data and the ability to follow immediate changes of the operating points that are expected on real WTs. In the case with very low measurement noise, the estimated signal is almost perfect, and the convergence of the algorithm is immediate. In the case with the realistic assumptions about the measurement noise, the convergence time increases, especially when the mean wind speed declines. However, the estimations do not have any phase delay, and they are still good. This algorithm should be further tested using experimental data on cases that differ from the normal production. More precisely, it is important to check its performance on cases such as normal stop, WT start-up or manual emergency stop.

Future work should include validation of the presented method on experimental data, the development of an understanding of structural changes in the gearbox due to events and regimes that differ from normal WT production and the development of the failure detection algorithm for identification of the rotor imbalances.


  1. Top of page
  2. Abstract

The proposed estimation algorithm for the cost-effective, accurate and indirect measuring of the shaft torque from measurements of the generator torque, the rotor angular speed and the generator angular speed, decreases the price of measurement equipment required for direct measuring of the shaft torque, additionally allowing long-term, continuous monitoring of loads. In other words, the proposed estimation algorithm overcomes the majority of problems that were limiting industrial application of CM systems based on measurements of the shaft torque. However, in order to implement this algorithm on the real WT, there are many practical issues which will have to be considered. The most important of these issues were summed in the end of Section 2.

On the basis of the results and discussion presented in the previous section, the following conclusions can be made:

  • The overall results provide very good matching between the predicted and the simulated shaft torque signals, where the accuracy of the estimations is comparable with the expected accuracy of the direct measurements of the shaft torque signal.

  • The MM estimation algorithm, which runs multiple AKFs and AKFFs in parallel, shows the ability to track the immediate changes of the operating points in a very prompt way, assuming realistic measurement noise.

  • Generally, both single-model estimators, the AKF and the AKFF, show almost equally good performance for around-rated and above-rated wind speeds, where the AKFF achieved slightly better results than the AKF on average. An NMSE value under 5% indicates good estimation results, and all estimations obtained using the AKFF have a NMSE under this value.

  • For below-rated wind speeds, the AKFF has much better results compared with the AKF. However, the degradation of the estimation results of the AKF is present with the decrease of wind speeds. More precisely, the achieved improvement is in between 20% and 50%. This indicates that the linear drive train model does not model the exact dynamic of WT for lower wind speeds, and the price for using AKF are high values of NMSE.

  • The performances of the estimation algorithms are equally good, with simulated data of WT model without faults and with different rotor imbalance faults.

  • The energy of the shaft torque estimations is almost perfectly tracked around the relevant frequencies such as rotational frequencies and torsional frequency despite the measurement noise level and the operating wind conditions. This is very important for further extraction of the fault signatures as the most significant fault signatures are present there.

  • Degradation of the estimated shaft torque is present in higher frequencies and it increases with the measurement noise indicating that the filter is not well tuned in this region due to modelling errors. Thus, if high measurement noise is present, the described method has limited application for below-rated wind speeds if the shaft torque estimation should be further used for rainflow count algorithm. In order to provide better estimation of the signal for higher frequencies, a more complex system model should be used.


  1. Top of page
  2. Abstract

The financial support by the SYSWIND project, funded by the Marie Curie Actions under the Seventh Framework Programme for Research and Technology Development of the European Union, is gratefully acknowledged. Special thanks to Jesper Runge Kristoffersen and Vattenfall for providing the WT measurements and data for calibration of the LACflex WT model.


  1. Top of page
  2. Abstract
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