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This paper demonstrates the effectiveness of a nondestructive diagnostic technique used to determine the location and size of delamination in laminated coatings of wind turbine blades. This is realized based on results of numerical and experimental investigations obtained by the use of the finite element method (FEM) and laser scanning vibrometry (LSV). The proposed method is based on the one-dimensional continuous wavelet transform of vibration parameters of a wind turbine blade. The investigations were conducted for a 1 : 10 scaled-down blade of a 36 m rotor wind turbine. Glass fibres and epoxy resin were used as laminate components. For numerical studies, a simple delamination model was proposed. The results obtained by the authors were used to determine the optimal set of parameters of the continuous wavelet transform. The application of high-quality LSV for experimental measurements allowed determining the optimal conditions of measuring procedures. At the same time the capabilities and limitations, resulting from the nature of the measurement method, were identified. In order to maximize the effectiveness of the detection method, preliminary signal processing was performed. Beside base wavelets also different waveform families were tested. The results obtained by the authors showed that it is possible to identify and localize even relatively small damage.

For every technical device, there are many various factors that can start irreversible processes changing its condition and gradually deteriorate its operating characteristics. This also applies to wind turbines, where rotor blades are particularly sensitive to different kinds of defects. Rotor blades are the most important subassembly of wind turbines, which are responsible for converting the wind kinetic energy into mechanical energy. Thanks to aerodynamic forces acting on rotor blades, it is possible to generate torque, which is necessary to drive electric generators. The efficiency of wind turbines is directly related to the effective swept area of rotor blades. The simplest way to increase the power of wind turbines is to increase the diameter of their rotors [

The detection method proposed by the authors in this paper assumes measurements and analysis of vibration parameters of a scaled-down composite wind turbine rotor blade, which allows for early damage detection. A universal nature of this method also allows for its application to existing installations, regardless of their locations, the size, or type of rotor blades, as well as without the necessity for rotor stopping.

The main objective of the investigation presented in this paper is the development of a nondestructive diagnostic method in order to determine the location and size of damage in a laminated coating of a wind turbine rotor blade. A general research methodology is schematically depicted in Figure

A scheme of a general research methodology.

Selection of useful modal parameters resulted from the requirements for the detection and localization of delamination in a relatively small area. The literature indicates that vibration frequency analysis is effective in the case of damage lengths greater than 15% of the total length of specimens [

Figure

A scheme of detailed research methodology.

A scheme of a scaled-down wind turbine rotor blade.

Investigations were carried out for a 1 : 10 scaled-down blade of a real wind turbine rotor, 36 m in diameter. The blade under investigation, 1.74 m in length, was based on a ClarkY aerodynamic profile. The blade was strengthened by one longitudinal spar, as shown in Figure

In order to avoid any sudden changes in the blade stiffness, a linear change in the coating thickness between the sections was ensured, which have a great effect of the results of wavelet analysis.

In general, the motion of wind turbine blades can be characterized by three types of vibrations: bending in the plane perpendicular to the rotor plane in the direction of the axis of rotation, bending in the rotor plane, and torsion, as shown in Figure

Fundamental types of vibrations of wind turbine blades.

The rotor blade was modeled by the FEM. The shell finite elements used by the authors had eight nodes and six degrees of freedom at each node. The total number of finite elements of the blade numerical model was 5,409. It was also assumed that the blade was fixed at one of its end. Numerical calculations included computations of the first 10 bending natural frequencies and modes of vibrations of the blade, with and without damage. It should be mentioned here that the current study was focused on delamination detection and localization, which is one of the most common type of damage in laminates. As a result of the forces acting on the blade during its motion, particular layers of the blade coating can be separated, leading to delamination. Figure

A scheme of delamination initiation.

Characteristic features of delamination include no material loss, two possible states of damage (open and closed), and the occurrence at different depths within the laminate. This makes it difficult to develop numerical models of delamination with realistic influence on dynamic behaviour. In general, numerical models of delamination can be divided according to the research purpose. Models based on specific criteria, such as Hashin’s failure criteria [

The main purpose of experimental measurements was validation of the numerical model of a wind turbine rotor blade proposed by the authors. Glass fibres and epoxy resin were used as laminate components. The reinforcing fibres were symmetrically arranged as

The experiment conducted a series of measurements in order to determine natural frequencies and modes of vibrations of the wind turbine rotor blade under consideration at a certain initial reference state as well as three locations of simulated damage. Measurement data were collected from 200 points. A steel element fixed to the blade surface was used to simulate damage in the form of a stiffness change in the composite coating, as shown in Figure

A scheme of a laboratory stand:

Correct interpretation of the results of experimental data is dependent on the level of measurement noise. High noise values can mask information about the damage presence and consequently can prevent its detection. Therefore, during laboratory tests, appropriate measurement conditions were ensured, in order to maximize the signal level received by the vibrometer (the blade surface was coated by a special retroreflective foil) as well as isolate the blade from any external vibrations. The results of measurements are frequency response functions (FRFs), used to determine the values of natural frequencies and corresponding modes of induced vibrations. The induced vibrations of the blade were excited by a sinusoidal force of a constant amplitude and a linearly varying instantaneous frequency, as presented in Figure

A typical form of an excitation signal used during experimental measurements.

A typical frequency response function measured experimentally.

For this reason, in order to minimize the noise level, a

The first mode of blade natural vibrations measured experimentally: FFT (black) and FastScan (red).

Based on measured frequency response functions, presented in Figure

Comparison of the first 10 natural frequency values obtained experimentally and numerically.

Lp. | | | | |
---|---|---|---|---|

| 7,03 | 6,69 | 0,34 | 5,10 |

| 20,78 | 22,48 | 1,70 | 7,56 |

| 44,84 | 51,07 | 6,23 | 12,19 |

| 75,94 | 91,55 | 15,61 | 17,05 |

| 114,69 | 142,37 | 27,68 | 19,44 |

| 159,84 | 206,18 | 46,34 | 22,47 |

| 214,22 | 273,06 | 58,84 | 21,55 |

| 285,16 | 350,80 | 65,64 | 18,71 |

| 360,63 | 430,97 | 70,35 | 16,32 |

| 445,78 | 513,01 | 67,23 | 13,10 |

Calculated differences for individual vibration modes up to 22.5% were primarily due to the lack of precise information about the arrangement of additional masses and local stiffeners within the blade coating. Possibly, they are all related to the bonding technology used to join the high and low pressure surfaces of the blade. However, in the case of the diagnostic method proposed in this work the source of information about the presence of damage is carried primarily by the modes of natural vibrations rather than the values of natural frequencies. Assessment of individual mode shapes, which are shown in Figure

Selected modes of natural vibrations: (a) I mode, (b) III mode, (c) V mode, and (d) VII mode (experimental data: dashed line, computational data: continuous line).

A wavelet transform was used by the authors in order to analyse the data obtained experimentally. A wavelet transform represents a process of signal decomposition into, and subsequent representation by, a linear combination of base functions called wavelets. This transformation can be seen in the context of five types of wavelets: orthogonal (Haar, Daubechies, and Symlets), biorthogonal (BiorSplines, ReversBiors), with scaling function (Meyer), without scaling function (Morlet, Mexican hat, and Gaussian), and complex (Shannon, Complex Gaussian, and Complex Morlet). Members of each family are shown in Figure

Selected examples of basic wavelet functions: Daubechies, Bior, Meyer, Morlet, and Shannon.

Wavelets are mathematical functions characterized by zero-mean, a finite signal strength, as well as a limited range and rapid decay. These characteristics determine that wavelets are well-localized both in time (or space) and frequency domains. For this reason they are particularly useful in representing signals with singular points or discontinuities. The wavelet analysis can be continuous (CWT) or discrete (DWT). In the case of DWT signal decomposition is iterative and in each iteration the original signal is decomposed into components of lower resolution. Each iteration decreases signal resolution by half. For this reason the DWT has a limited number of decomposition levels and is ineffective for low sample rates. Contrary to that the CWT makes it possible to decompose signals for any scale and allows for smooth shifting. Due to these features the CWT was used by the authors in this study. Its application leads to certain coefficients determining the similarity between a selected wavelet and the signal under investigation. These coefficients are defined by the following formula:

The scale and shift coefficients

Typical scalograms obtained using different wavelet functions: (a) Morlet; (b) Haar; (c) Gauss.

The efficiency of the wavelet analysis is determined by the correct selection of signal preprocessing parameters and wavelet transform attributes. In the case of signals located in the spatial domain, such as are modes of natural vibrations, an even distribution of measurement points has overriding importance. It should be stated here that in the case of signals of uneven distributions of measurement points the results of wavelet analysis can be falsified. If measurements cannot be carried out for even distribution of measurement points, interpolated signals should be produced first. Interpolation is also very useful in the case of signals with small numbers of samples.

Another problem is the effect of high wavelet coefficients at the beginning and end of signals. This prevents detecting and localizing damage properly. The solution to this problem is to extrapolate signals under examination at their ends, so that the zones of increased coefficient values, resulting from boundary effects, stay outside the range of interest. The type of applied interpolation and extrapolation algorithms, such as linear, polynomial, or different, depends on the form of source signals and should be chosen carefully not to introduce any additional discontinuities.

Another important aspect presents the appropriate selection of correct base wavelets. It turns out that the wavelets of orders lower than 4 generate nonzero wavelet coefficients in the entire signal lengths [

Numerical results obtained by the use of the FEM model were employed to determine preprocessing parameters of signals and wavelet transform parameters such as the type of wavelet and scale. Proper interpretation of computed scalograms, in terms of damage detection, localization, and estimation its size, was obtained for

linear extrapolation in order to extend the representation of selected modes of natural vibrations from initial 200 samples to 230 samples by adding 15 extra points on both signal ends,

cubic spline interpolation in order to supplement selected modes of natural vibrations with additional samples by adding 10 extra points between each two subsequent signal samples,

fourth-order Gauss base wavelet.

Scalograms for the second mode of natural vibration in the case of the intact, as well as three damage scenarios, are shown in Figures

Numerical results of wavelet analysis of the 2nd mode on natural vibrations in the case of the intact and three damage scenarios.

For a majority of natural vibration modes the location of damage was identified correctly. However, for small defects of blade coating it is impossible to indicate accurately defect edges. For the 10th mode of natural vibrations detection was practically impossible, as shown in Figure

Numerical results of wavelet analysis of the 10th mode of natural vibrations in the case of Gauss4 (a) and Gauss6 (b) wavelet functions.

The right side of the scalogram indicates nonzero wavelet coefficients as dark and blurry trails, that is, as the location of possible damage, whereas this part of the blade remains intact. This effect, which is noticed mainly for higher modes of natural vibrations, may obfuscate the scalogram and consequently can prevent proper damage localization. A solution to this problem is to adjust wavelets individually with higher order numbers, as seen in Figure

Through the analysis of scalograms, in the case of one mode of natural vibrations, for all three damage locations, it can be seen from Figure

Numerical results of wavelet analysis in the case of three damage location scenarios.

In the first stage of the analysis of experimental signals, data processing and the analysis of CWT parameters were based on the results of numerical simulations. Figure

Scalograms obtained from measured data in the case of all modes of natural vibrations.

The second conclusion concerns the noise level observed, which is directly related to the quality of measurement signals. High noise levels make it difficult to interpret results, as local stiffness changes can result in an increase in wavelet coefficients in the same range as noise. Therefore it was necessary to modify the approach proposed by the authors to extract sharper information about the location and size of defects. It should be noticed that limited methods available to increase the accuracy of measurements make it necessary to modify signal analysis parameters.

The main element of signal preprocessing that influences the performance of wavelet analysis is interpolation. It separates one sample of the original signal from the other by increasing signal resolution, which can be described by a one-dimensional vector. The consequence is sharpening the boundaries of any discontinuities on scalograms, which may include measurement distortions. The level of details can be reduced by reducing the number of interpolation points, thus exposing the sought after changes in a wider range, as shown in Figure

Scalograms of the 7th mode of natural vibrations in the case of different numbers of interpolation points: (a) 2; (b) 4; (c) 6; (d) 8.

Thanks to the approach proposed scalograms were obtained also in the case of the remaining damage location scenarios. Figure

Scalograms of the 8th mode of natural vibrations obtained in the case of six interpolation points.

It can be seen that the reduction in the number of interpolation points enabled the authors to detect damage very accurately. However, this process can cause loss of precise information about the width of the damage zone. Figure

Scalograms of the 7th mode of natural vibrations obtained in the case of three different damage sizes.

The analysis of the experimental results shows that the key element for correct interpretation of scalograms is a low noise level as well as precise knowledge about the structure of the object under investigation. For this reason, reference signals are indispensable. Figure

Scalograms of differential signals (damaged to reference) obtained for the 9th mode of natural vibrations for three damage locations.

Based on the results obtained for all considered cases, it can be concluded that measured signals should be analysed and assessed in a multistage manner with respect to a reference state by

starting from a small number of interpolation points,

registering global changes (damage identification),

gradual increasing of the number of interpolation points, narrowing the window of determination of the damage nature and its exact boundaries.

The paper presents certain results of numerical simulations and calculations as well as experimental measurements aimed at developing a method for delamination detection and localization in composite wind turbine blades. Numerically and experimentally determined modes of natural vibrations of a wind turbine blade were assessed for local changes that may indicate the presence of damage. For numerical simulation a simple delamination model was proposed that allowed the authors to calculate eight simulated damage levels in three different locations. Next the results obtained were used to determine an optimal set of parameters of the continuous wavelet transform (CWT). The second stage of the analysis included experimental research in order to verify both finite element method (FEM) based model predictions as well as the damage detection method developed. The use of high-quality Scanning Laser Vibrometry allowed the authors to determine the optimal conditions and measuring procedures, which led to the required accuracy of measurement. At the same time the capabilities and limitations resulting from the nature of the measurement method were identified.

The main challenge in the practical implementation of a diagnostic system based on the proposed method comes from low levels of signal distortions that are sought after. The damage detection method presented can be used on an operating wind turbine based on data obtained from a system of piezoelectric or fibre optic sensors. Vibration measurements can also be performed by means of laser vibrometry supplemented by additional devices, such as is a derotator equipped with a special optical system, whose rotational motion is fully synchronized with the rotation of the object under investigation, such as are wind turbine blades.

The results of the research presented in this paper confirm the effectiveness of wavelet methods in detection of signal discontinuities. Based on them the following conclusions can be made:

For best results, wavelet transform analysis should be proceeded by some signal preprocessing in the form of extrapolation and interpolation. Extrapolation reduces effects of increased values of wavelet coefficients at signal ends, while interpolation increases signal resolution.

Analysis of modes of natural vibrations and corresponding scalograms makes it possible to correlate the damage location and size with characteristic points of source signals. Only in the case when damage zones coincide with local signal extremes, it is possible to detect damage.

In the case of experimental data that are subjected to measurement noise, too many interpolation points block proper interpretation of scalograms. For this reason signals obtained experimentally should be analysed in a multistage manner, starting from a small number of interpolation points in order to observe more general changes. A gradual increase in the number of interpolation points allows determining the type of damage and its precise location.

Signal windowing increases the sharpness of the damage zone. This solution may be particularly important in the case of damage that has a small effect on the object dynamics.

Both experimental and numerical data indicate that the key to the correct interpretation of CWT analysis results, in the case of complex structures, is the knowledge about initial, undamaged state of the object under investigation. In the case of experiments carried out the availability of reference signals made it possible to reduce the influence of noise on the results of subsequent CWT computations.

The authors declare that there are no conflicts of interest regarding the publication of this paper.