Dublin Institute of Technology From the SelectedWorks of Breiffni Fitzgerald Damage detection in wind turbine blades using time-frequency analysis of vibration signals Breiffni Fitzgerald, Dublin Institute of Technology Available at: https://works.bepress.com/breiffni_fitzgerald//
Damage Detection in Wind Turbine Blades Using Time-Frequency Analysis of Vibration Signals Breiffni Fitzgerald, John Arrigan and Biswajit Basu, Member, IEEE Abstract The dynamic behavior of modern multi-megawatt wind turbines has become an important design consideration. One of the major aspects related to the reliability of operation of the turbines concerns the safe and adequate performance of the blades. The aim of this paper is to develop a time-frequency based algorithm to detect damage in wind turbine blades from blade vibration signals. It is important that damage to blades is detected before they fail or cause the turbine to fail. A wind turbine model was developed for this paper. The parameters considered were the rotational speed of the blades and the stiffness of the blades and the nacelle. The model derived considers the structural dynamics of the turbine and includes the dynamic coupling between the blades and the tower. The algorithm developed uses a frequency tracking technique. Numerical simulations have been carried out to study the effectiveness of the algorithm. Index Terms Wind turbine blades, Tower blade coupling, Short Time Fourier Transform. I. INTRODUCTION ver the last decade, wind turbine technology has taken Ohuge leaps forward to become a leading alternative energy resource to traditional fossil fuels. Turbines with outputs as large as 5MW are being constructed with tower heights and rotor diameters of over 8m and m respectively. With the increased size of the blades comes increased flexibility making it important to understand their dynamic behaviour. Ahlstrom carried out research into the effect of increased flexibility in turbine blades and found that it can lead to a significant drop in the power output of the turbine []. Significant research has been carried out into the area of blade design and failure characteristics [, 3]. However, it is only over the last few years that research has started to focus on the dynamic behaviour of the turbine blades and the interaction that occurs between the blades and the tower. Two main types of vibration occur in wind turbine blades, flapwise and edgewise. Edgewise vibrations are vibrations Manuscript received March 6,. This work was supported by the Irish Research Council for Science Engineering and Technology (IRCSET) and the EU under FP7 Marie Curie project SYSWIND (Grant No. 3835). Breiffni Fitzgerald is with Trinity College Dublin, Ireland (phone: 353-896-389; e-mail: fitzgebr@tcd.ie). John Arrigan is with Trinity College Dublin, Ireland (e-mail: arriganj@tcd.ie). Biswajit Basu is with Trinity College Dublin, Ireland (e-mail: basub@tcd.ie). occurring in the plane of the rotor axis. Flapwise vibrations are vibrations occurring out of the plane of rotation of the blades. Flapwise vibrations are considered in this paper. Ronold and Larsen [4] studied the failure of a wind turbine blade in flapwise bending during normal operating conditions of the turbine while Murtagh and Basu [5] studied the flapwise motion of wind turbine blades and included their dynamic interaction with the tower. They found that the inclusion of the blade-tower interaction could lead to significant increases in the maximum blade tip displacement. The aim of this paper is to use Short Time Fourier Transforms (STFT) for damage detection in wind turbine blades. Wind turbine blades are vulnerable to cumulative fatigue damage owing to the periodic nature of the loading. Detecting damage to blades before failure is crucial. Simulations were run with the model developed. The stiffness of the blades was reduced in real-time during these simulations. This is essentially modelling the case where the blade loses stiffness due to delamination of its underlying composite structure. The responses obtained from the model simulations were then subjected to the STFT based tracking algorithm to identify blade damage. Nagarajaiah and Varadarajan [6] have developed algorithms to track the dominant frequencies of a system using STFTs. STFTs enable local frequencies to be identified in the response of the system that may only exist for a short period of time. Reducing the stiffness of the blade to simulate blade damage will alter the frequency of vibration of the blade and thus allow the damage to be detected by STFTs. II. LAGRANGIAN FORMULATION The dynamic model was formulated using the Lagrangian formulation expressed in equation below. () where: T = kinetic energy of the system, V = potential energy of the system, q i = displacement of the generalized degree of freedom (DOF) i and Q i = generalized loading for degree of freedom i. The kinetic and potential energies of the model were first derived including the motion of the nacelle and are stated in equations a and b. These expressions were then substituted back into the Lagrangian formulation in equation to allow the equations of motion to be determined. (a) 978--444-86-//$6. IEEE
(b) where: m b = mass of blade, L = length of the blade (= 48m) in this study, v bi = absolute velocity of blade i including the nacelle motion that causes blade tip displacement, this is a function of both the position along the blade, x, and time, t. M nac = mass of nacelle, E = Young s Modulus for the blade, I = second moment of area of blade, K nac = stiffness of the nacelle, q i is the displacement of the blade i and q nac is the displacement of the nacelle. Each blade was modelled as a cantilever beam with uniformly distributed parameters as can be observed from the expressions for the kinetic and potential energies in equations a and b. The relative displacement of the blades was expressed as the product of the dominant modeshape multiplied by the tip displacement, shown in equation 3 below., (3) where Φ(x) = modeshape and q i (t) = relative tip displacement of blade of blade i in the flapwise direction. The blades were assumed to be vibrating in their fundamental mode and a quadratic modeshape was assumed. This allowed reduction of the continuous beam to a single degree of freedom, a technique known as Raleigh s method [7]. The cantilevers were attached at their root to a large mass representing the nacelle of the turbine. This allowed for the inclusion of the blade-tower interaction in the model. A schematic of the flapwise vibration model is shown in Fig.. The degrees of freedom marked q, q, q 3 and q nac represent the motion of the blades and nacelle. The model consisted of a total of 4 DOF (one in each of the blades and one at the nacelle) expressed in the standard form as in equation 4 below. (4) where [M], [C] and [K] are the mass, damping and stiffness matrices of the system respectively. q, q and q are the acceleration, velocity and displacement vectors and Q is the loading. Centrifugal stiffening was added to the model as per the formula developed by Hansen [8]. Structural damping included in the system was assumed to be in the form of stiffness proportional damping. Fig.. Flapwise vibration model III. LOADING The loading scenario considered was a simple steady wind load varied linearly with height with an added random component modelling turbulent wind. The steady wind loading on blade is given by equation 5 below. The loads on blades and 3 are shifted by angles of π/3 and 4π/3 respectively. vnac A vnac L A v Q + = + + 3 v nac nac+ L A cos( Ωt) (5) where: v nac = wind speed at nacelle height, v nac+l = wind speed at the maximum blade tip height, i.e. when blade is in upright vertical position. A = area of blade, taken as to normalize the load, with Ω equal to the rotational speed of the blade. The loading on the nacelle was assumed to be zero so that all motion of the nacelle was due to the forces transferred from the blades through the coupling present in the system. The turbulent velocity component was generated at a height equal to that of the nacelle using a Kaimal spectrum [9] defined by equations 6, 7 and 8 below. Uniform turbulence was assumed for the blades., (6) where: H = nacelle height, S vv (H, f ) is the PSDF (Power Spectral Density Function) of the fluctuating wind velocity as a function of the hub elevation and the frequency,, is the friction velocity from equation 7, and c is known as the Monin coordinate which is defined in equation 8. (7) (8) where k is Von-Karman s constant (typically around.4 []), v H is the mean z =.5 (the roughness length), and ( )
wind speed. This results in a turbulence intensity of.5 in the generated spectrum. IV. STFT BASED TRACKING ALGORITHM STFT is a commonly used method of identifying the timefrequency distribution of non-stationary signals. It is widely used because it gives good time-frequency distribution for many signals. It allows local frequencies to be picked up in the response of the system that may only exist for a short period of time. These local frequencies can be missed by normal Fast Fourier Transform (FFT) techniques. The STFT algorithm splits up the signal into shorter time segments and an FFT is performed on each segment to identify the dominant frequencies present in the system during the time period considered. Combining the frequency spectra of each of these time segments results in the time frequency distribution of the system over the entire time history. The time segment is short compared to the whole signal therefore the process is called short time. The STFT algorithm developed in this study enables damage to be detected in wind turbine blades. When blades become damaged their stiffness is reduced. This causes the frequency at which the blades vibrate to change. Therefore, by tracking the frequency of the blades in real-time changes in frequency, and hence damage, can be detected. V. RESULTS Simulations were run with the flapwise model with a realistic stiffness value. The rotational speed (Ω) was assumed to be 3.4 rad/s. Fig. shows the response of Blade to turbulent load and Fig. 3 shows the frequency content. Fig. 3. Blade flapwise frequency spectrum, turbulent load, Ω = 3.4 rad/s Fourier Amplitude.5..5 -.5 -. -.5 5 45 4 35 3 5 5 5 X:.5 Y: 53.9 X:.66 Y: 468.4 X:.3 Y: 38.8.5.5.5 3 3.5 4 Frequency (Hz) -. 3 4 5 6 7 8 9 Fig. 4. Nacelle flapwise time history response, turbulent load, Ω = 3.4 rad/s.8.6.4. -. Fourier Amplitude 8 6 4 X:.37 Y: 7. X:.3 Y: 65.93 -.4 3 4 5 6 7 8 9 Ti me (s) Fig.. Blade flapwise time history response, turbulent load, Ω = 3.4 rad/s.5.5.5 3 Frequency (Hz) Fig. 5. Nacelle flapwise frequency spectrum, turbulent load, Ω = 3.4 rad/s Fig. 4 and Fig. 5 show the response of the nacelle to turbulent load and the nacelle response frequency content respectively. The model was then changed. A loss in stiffness in the blade and in the nacelle was simulated.
First a loss in blade stiffness was modeled. This is modeling the case where the blade loses stiffness due to delamination of its underlying composite structure. A simulation was set up for seconds. A loss in blade stiffness of % was applied 7 seconds into the simulation. Fig. 6 shows the time history response for Blade. It is clear from Fig. 6 that after 7 seconds the flapwise displacements observed at Blade increase dramatically. The next step was to use the STFT algorithm to track the dominant frequencies in the system with respect to time. Fig. 7 shows the dominant frequency of the system with respect to time. The STFT was applied at 4 seconds. It is clear that before the blade s stiffness was reduced (at 7 seconds) the dominant frequency in the system was roughly Hz. However, after the blade s stiffness has been reduced the dominant frequency in the system is reduced to roughly.5 Hz. STFT frequency tracking was thus successful in detecting a loss in blade stiffness and hence damage. Finally a loss in nacelle stiffness was modeled. The stiffness of the nacelle was reduced by 5% after 7 seconds. Fig. 8 plots the nacelle displacement time history. It is clear from this graph that there is a negligible increase in the nacelle displacement response after the loss in stiffness..5..5 -.5 -. -.5 Nacelle Displacement -. 3 4 5 6 7 8 9 Fig. 8. Nacelle displacement 5% loss in stiffness.6.4..8.6.4. -. -.4 Blade Displacement Dominant Freq (Hz).4.35.3.5..5..5 Dominant Freq (Hz).5.5 3 4 5 6 7 8 9 Fig. 6. Blade % loss in stiffness 3 4 5 6 7 8 9 Fig. 9. STFT loss in nacelle stiffness Fig. 9 shows the dominant frequency of the system with respect to time. The STFT was applied at 4 seconds. Before a loss in nacelle stiffness the dominant frequency was roughly.36 Hz. After 7 seconds the dominant frequency is reduced to roughly.3 Hz. The STFT again identified the change in frequency due to the loss in stiffness and can therefore be used for damage detection..5 3 4 5 6 7 8 9 Fig. 7. STFT loss in blade stiffness VI. CONCLUSION In this study the use of a STFT frequency tracking technique to detect damage in wind turbine blades was investigated. The model developed in this paper focused only on the structural dynamics of the turbine including the interaction between the blades and the tower. By reducing the young s modulus (stiffness value) of the blades damage was simulated. This in turn had an effect on the natural frequency
of the blades. By tracking the dominant frequencies present in the model over time, via STFTs, it was possible to detect this simulated damage. REFERENCES [] Ahlstrom A. Influence of Wind Turbine Flexibility on Loads and Power Production, Wind Energy 5; 9: 37-49 [] Tavner PJ, Xiang J, Spinato F. Reliability Analysis for Wind Turbines, www.interscience.wiley.com 7//6 [3] Sutherland HJ. A Summary of the Fatigue Properties of Wind Turbine Materials. Wind Energy ; 3: -34 [4] Ronold KO, Larsen GC. Reliability-based design of wind-turbine rotor blades against failure in ultimate loading. Engineering Structures ; : 565-574. [5] Murtagh PJ, Basu B, Broderick BM. Along-wind response of a wind turbine tower with blade coupling subjected to rotationally sampled wind loading. Engineering Structures 5; 7: 43-44 [6] Nagarajaiah S, Varadarajan N. Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD. Engineering Structures 5; 7: 43-44. [7] Clough RW, Penzien J. Dynamics of Structures. McGraw Hill: New York, 993. [8] Chaviaropoutos PK, Nikolaou IG, Aggelis KA, Sorensen NN, Johansen J, Hansen MOL, Gaunaa M, Hambraus T, von Geyr HF, Hirsch C, Shun K, Voutsinas SG, Tzabiras G, Perivolaris J, Dyrmose SZ. Viscous and Aeroelastic Effects on Wind Turbine Blades. The VISCEL Project. Part : 3D Navier-Stokes Rotor Simulations. Wind Energy 3; 6: 365-385. [9] J. C. Kaimal, J. C. Wyngaard, Y. Izumi, Coté OR. Spectral characteristics of surface-layer turbulence. Quarterly Journal of the Royal Meteorological Society 97; 98: 563-589. [] Simiu E, Scanlan R. Wind Effects on Structures. John Wiley & Sons: New York, 996..