Wideband Vibro-Acoustic Modulation for Crack Detection in Wind Turbine Blades

<jats:p>Wind turbines (WT) are a popular method used in energy production, but blade failure and maintenance costs pose significant challenges for the industry. Early detection of blade defects is vital to prevent collapse. This paper examines the modulation of blade vibrations via low-frequency blade rotation, mirroring the vibro-acoustic modulation (VAM) method. Specifically, we study the modulation of blade vibrations, which are generated via blade interactions with air turbulence and have a wide frequency range. These vibrations are modulated by the alternating bending stress experienced during blade rotation. For the simulation of VAM, we employ a simple breathing crack model, which considers a mechanical oscillator with parameters that are periodically changed in response to low-frequency blade rotation. The modulation of the wideband signal by blade rotation can be extracted using the detection of envelope modulation on noise (DEMON) algorithm. This model was applied for the estimation of the modulation of a large (52-m-long) WT blade. Steel specimens have been used in laboratory experiments to demonstrate the feasibility of VAM using a probe broadband noise signal. This paper presents the first work to experimentally and theoretically apply wideband signals in VAM. It further explores the analysis of the use of natural vibrations within VAM for the SHM of WT blades.</jats:p>

section_content: WT are among the most vital sources of clean energy production, owing to their low installation costs and the abundance of wind energy. To enhance their energy production capabilities, assessing the health of all WT blades is important. Blades play a significant role in energy generation; they are the most dynamic part of the WT and exposed to harsh environments. As a result, a variety of structural health monitoring (SHM) and non-destructive evaluation (NDE) methods have been developed to assess damage caused to WT blades [1] [2] [3] [4]. 

The vibro-acoustic structural health monitoring (SHM) technique is one of the most pragmatic methods used to identify damage in blades. Various vibration measurements can be applied to WT blades, such as active vibrations [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] and passive vibrations [1, [20] [21] [22] [23] [24]. In active vibrations, the vibrations are artificially generated using an electrodynamic shaker or actuator. Meanwhile, in passive vibration measurements, the blade vibrations are naturally excited. These excitations can be produced by the aerodynamic force acting on the blades as they rotate in the wind. A common mechanism is vortex shedding, which occurs when alternating vortices are shed from the blade's trailing edge [25]. 

Numerous methods have been used to operate turbines passive and active vibration on blades, as reported in various studies [10, [13] [14] [15] [16] [17] 20]. These investigations have primarily focused on the operational conditions of the blades while they are rotating, thus evaluating real-time performance and damage that might occur during the rotation. 

Meanwhile, laboratory testing methods have also been crucial to assessing the health of turbine blades. Studies such as [5] [6] [7] [8] [9] 12, 18] have conducted thorough active vibration assessments of blades separated from the turbine system. The laboratory investigations of passive vibrations were conducted using windmill models, with electrical motors being used to enable blade rotation [21, 24]. Blade vibration and their variations in the presence of cracks have been examined using finite element software, as shown in [22, 26]. As depicted in Figure 1, various types of vibrations are categorized based on their method and the condition of vibration measurement. Damage and cracks result in the modification of the natural frequencies, damping coefficients, frequency response characteristics, and mode shapes, as well as their derivative functions. These changes can be assessed via various analysis methods; for example, the operational modal analysis (OMA) can be used [22, 23, [27] [28] [29] [30]. This method measures natural blade vibrations in windy environments to identify and predict crack locations based on changes in frequencies, damping ratios, and frequency response functions [28]. Other methodologies, including operational deflection shapes (ODS) [8, 31], as well as statistical methods, aim to characterize WT blades by utilizing vibration measurements and statistical models. Table 1 demonstrates the effect of damage on the resonance frequencies of blades, notably emphasizing the percentage change in frequencies between damaged and undamaged blades. Damage and cracks result in the modification of the natural frequencies, damping coefficients, frequency response characteristics, and mode shapes, as well as their derivative functions. These changes can be assessed via various analysis methods; for example, the operational modal analysis (OMA) can be used [22, 23, [27] [28] [29] [30]. This method measures natural blade vibrations in windy environments to identify and predict crack locations based on changes in frequencies, damping ratios, and frequency response functions [28]. Other methodologies, including operational deflection shapes (ODS) [8, 31], as well as statistical methods, aim to characterize WT blades by utilizing vibration measurements and statistical models. Table 1 demonstrates the effect of damage on the resonance frequencies of blades, notably emphasizing the percentage change in frequencies between damaged and undamaged blades. 

However, the functional applications of vibro-acoustic SHM methods are limited because they rely on comparing the vibrations of damaged and undamaged structures. Cracks and damage inclusions to the initially intact materials change materials' elasticity properties and lead to the non-linear relationship between stress and strain. This nonlinearity can be detected based on non-linear effect in the acoustic waves. Non-linear vibro-acoustic SHM techniques have high sensitivity to cracks and do not necessitate a comparison between damaged and undamaged structures for integrity assessment. The sample is excited using a signal generator and a shaker device. 

12. 4 12

[12] 43. 8 9 112. 9 5

A 5-m blade length Cracks of varying sizes (small, medium, and large) in a WT blade at 72% of the blade's length. 

• Simulation;
section_name: Introduction

section_content: The simulation was conducted for blades excited via wind forces. A 1300-cm Vestas V27 WT blade

In the blade used in the three-month field tests, an artificial defect was introduced to simulate adhesive joint failure between the skins, specifically using a trailing edge opening.
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section_content: Operation condition; • An electromechanical actuator, placed near the root of the blade, prompts the blade by hitting it every five minutes. The application of non-linear acoustics (NA) to detect damage within materials began in the 1970s. One early method employed to assess material cracks is harmonic distortion. This method evaluates the material by measuring the non-linear distortion of a primarily sinusoidal acoustic signal, which represents the harmonic distortion [32, 33]. Since then, significant research has been conducted into techniques and methods using the NA approach. Various NA, NDE, and SHM techniques utilize a broad range of NA effects. A comprehensive summary of current NA, NDE, and SHM research can be found in [34], as well as in [35] [36] [37] [38] [39] [40]. 

Currently, the method most widely adopted and used to assess damage is VAM. This technique applies the modulation of a high-frequency probe wave by a lower-frequency pump wave. The majority of VAM methods evaluate non-linearity by measuring the level of sideband components with sum and difference frequencies, which are typically quantified as the ratio of sideband peaks to the amplitude of the carrier wave. More recently, the count of sideband peaks has been utilized as a measure of non-linearity [41] [42] [43] [44]. 

The generation of low-frequency vibrations in VAM techniques has been accomplished through two methods: (1) utilizing harmonic sources and (2) applying mechanical impact. The first method has several options for excitation, such as piezoceramic transducers [45, 46], speakers [47, 48], lasers [49], and loading machines [50]. 

A limited number of publications have considered VAM applications for WT SHM. The periodic load change due to blade rotation can serve as the low-frequency wave used for the modulation of the high-frequency wave. Refs. [10, 11] presented VAM experiments using actual WT blades. The chosen spot for the fracture was the back edge of the blade, which was 0. 3048 m away from the blade's tip, where the highest stress occurs. A quick force was applied to the blade's tip to cause a break while it was held steady at this predetermined break point. In the tests, high-frequency probe signals were radiated and received using micro fiber composite (MFC) transducers with frequencies ranging from 5 to 10 kHz. At a rotational frequency of 3. 1 Hz, the modulation of these signals, along with corresponding harmonic frequencies, was detected. 

There are many more publications about theoretical study of non-linear vibrations of objects with breathing defects. In [51], the resonant frequency and the non-linear stiffness of the blade with a defect were studied using a finite element model via centrifugal loading. The outcomes revealed that the resonant frequencies of the blade with cracks were greater for the rotating case than for the static case. Furthermore, the distinction between the resonant frequencies of the non-linear and linear cases became more apparent as the crack length increased. 

Ref. [52] presented the simulation of the non-linear dynamic characteristic of a rotating blade with breathing damage. The results showed that the defect length had a significant effect on the resonant frequency and the vibration behavior contains damping and stiffness. Research presented in [53] used a numerical model to analyze the forced response of the blade under alternating loads. The model considers the impacts of the crack on the blade's natural frequencies, mode shapes, and damping characteristics and calculates the resulting vibrations. The results of the study indicate that the resonant frequencies of the blade are significantly affected by the presence of a crack, with the natural frequencies decreasing and the damping ratio increasing as a result of the crack. Also, the vibration response of the blade is highly dependent on the increase in the alternating loads. 

In this study, we explore the VAM technique, in which the harmonic or broad-spectrum vibrations of the probe blade are influenced by the rotation of the blades. The simulation of this effect is conducted based on the oscillator model, in which the resonance frequency and attenuation vary under altered loads produced via the rotation of the WT blades. We used published experimental data regarding changes in resonant frequencies and attenuation to estimate the impact of cracks on non-linear blade vibration parameters. The suggested methods used to measure wideband signal modulation are based on the DEMON algorithm, which is widely used in submarine detection. Laboratory tests were conducted using small steel samples (10 inches in length) under cyclic loading. These tests demonstrated the feasibility of measuring the modulation of the wideband signal in laboratory conditions using the DEMON algorithm. 

The structure of the article and steps performed are illustrated in Figure 2.
section_name: •

section_name: VAM Model for Detecting Cracks in WT Blades

section_content: To describe the VAM on the WT blade, we consider a mechanical oscillator model (comprising spring, mass, and damping elements), as illustrated in Figure 3. This model can be applied to various blade resonance modes, each of which has its unique resonance frequency and damping parameters (Q factor). Numerous studies have utilized this mechanical oscillator model to perform WT blade analysis. For example, this model was described using Equation (1) in [8] and Equation (34) in [54]. The rotation of the blade generates internal stress due to its weight, altering the elasticity and damping of any existing cracks. A unique aspect of our model is that it incorporates time variation into the model parameters (resonance frequency and Q factor). This variation is driven by the blade load and gravitational load during its rotation. The mechanical oscillator model is presented in Figure 3. 

The model describes the blade material displacement x under the action of external force in Equation ( 1 ) [8, 54]. 

where m is the mass, σ is the applied force, k is the model stiffness that depends on the blade material and include the non-linear crack stiffness, and c is the damping (attenuation) coefficient. Thus, Equation ( 1 ) can be written in the following form:

. . 

where the resonance frequency ω 0 = k m and attenuation decrement

The classical solution shown in Equation ( 2 ) can be presented for use in spectral components of the displacement X(ω) = FFT[x(t)]. The same solution was presented in Equation ( 3 ) in [8] and in Equation ( 56 ) in [55]. 

where P(ω) = FFT(σ(t)/m) is the spectrum of the external applied force. 

The proposed VAM model is based on the slow modulation of the oscillator parameters by the internal loading generated via the blade rotation. This effect is illustrated in Figure 4, where the crack can be opened to a horizontal blade position when the crack is on the upper side (Figure 4a ) and closed when the crack is on the lower side (Figure 4b ). The model contemplates a linear oscillator, where elasticity and damping parameters are slowly varied under the gravitational force acting in line with the blade rotation frequency F. This model is applicable if the decay time of the oscillator T is much shorter than the blade rotation period. 

In the model, two time scales are considered: Fast time t describes high-frequency wideband vibrations in the frequency band 100-5000 Hz. In the simulation, the sampling rate at this time is 10 kHz. 

Slow time τ is used for the description of the blade rotation with the frequency F = 0. 05-0. 2 Hz. In the simulation, the sampling rate for the slow blade parameter variations was 10 Hz. 

We assume that two parameters of the model oscillator exhibit minor variations in the rotation frequency and can be described using the following formulas:

where Ω = 2πF, non-inear parameters α, β << 1, and ∼ ω o and δ o are the resonance frequency and the damping coefficient without application of the rotation load, respectively. 

The small non-linear parameters α and β represent the shift in the resonance frequency and changes in attenuation upon the application of the rotational load. It is assumed that these parameters can be estimated based on known information about blade resonance frequency and damping variation due to the presence of a crack.
section_name: Description of the Proposed Model for WT Blade Crack Detection

section_content: There are many publications about the amplitude frequency response measured for blades, both with and without cracks, and some of them are presented in the Table 1. For the demonstration of the suggested model ability to predict VAM parameters, we have chosen several examples demonstrating clear frequency response variations in the damaged blades. 

Figure 5 presents the frequency response measured in a test using an 8-foot blade section [8]. The interpolations of the measured response by Equation ( 3 ) are represented by dashed lines. The resonance frequency of the model was chosen to be the same as the measured resonance frequency, and the Q factor of the model was chosen as it provided the minimal averaged difference between the experimental frequency response and the interpolation. This interpolation allows the determination of the resonance frequency and Q factors for a blade without a crack (Q 2, f 2 ) and with a crack (Q 1, f 1 )

For rough estimation of the non-linear parameters, it is assumed that the non-linear parameters of an uncracked blade are closely aligned with those of a cracked blade when the crack is nearly completely closed. It is speculated that under particularly high loads, both the resonance frequency and the Q factor could exhibit variations, which reside in the ranges f 1f 2 and Q 1 -Q 2, respectively. To account for the partial closure of the crack due to oscillating blade rotation loads, a minor parameter γ is introduced. This parameter indicates which part of the crack is closed under the influence of the alternating load. In this model, γ is considered to be quite small, having an estimated value of around 0. 1 for the estimation of the non-linear parameters presented in Table 2. This methodology allows the provisional estimation of the parameters α and β of the non-linear model. The same interpolation of the resonance responses measured for the 52-m WT blade [6] is presented in Figure 6. The results of these estimated parameters are presented in Table 2. 

In this exploration of VAM effects, we focus on the following two distinct scenarios: Active VAM, in which the external excitation is produced by a harmonic wave. This method could involve a shaker, as presented in [6], or a piezoceramic actuator, as used in [8]. Passive VAM uses the natural excitation of blade vibrations, which forms the basis for the OMA, as described in [23].
section_name: Extract Non-Linear Parameter Derived from the Published Data

section_content: This model considers the application of the probe wave with the frequency f. 

where ω = 2π f. In our model, it is assumed that the vibrations in the blades are measured via accelerometer, the electrical signal of which is directly proportional to the acceleration of the blade. This obtained signal is then presented in the following form:

The amplitude and phase are defined using the following Equations:

The constant C is frequency-independent coefficients, reflecting the amplitudes of the externally applied force and accelerometer sensitivity. The resonance frequency and attenuation undergo slow modulation, as described in Equations ( 5 ) and ( 6 ). Consequently, the spectrum of the signal u(t) will contain a main component with an excitation frequency f and two sideband components with frequencies f + F and f -F. 

In this paper, we evaluate the modulation of the harmonic probe wave or noise blade vibrations, and results are presented in normalized form. Therefore, the signal spectrum will display the relative level of sideband components. 

In the VAM method using harmonic probe wave, the Modulation Index (MI) is often used as a measure to assess the level of non-linearity [50, 56]

where U o is the received spectral component of the probe wave, and U + and U -are the sideband components in dB. 

Applying Equations ( 11 ) and ( 12 ) enables the calculation of signal spectra with side components produced via modulation. Figures 7 and 8 illustrate examples of these calculations for a blade rotation frequency of 0. 2 Hz and various probe wave frequencies. For the comparison of various blades, in this calculation, we used the normalized frequency ζ calculated by subtracting the probe wave frequency f from the from the resonance frequency f 0, before dividing the solution by the resonance frequency f 0. It can be observed that the 8-foot blade section exhibits a higher level of side band compared to the 52-m blade, which occurs due to the higher Q factor in the 8-foot section of the blade. 

The MI response dependencies on the probe frequency were also calculated, and the results are shown in Figure 9. It reveals a significant dependency of the MI on the frequency when using the VAM model, and the case with lower attenuation shows stronger variation in the MI.
section_name: Comparison between Traditional VAM (Active Vibration) and Proposed VAM (Passive Vibration) 2.3.1. Active Method

section_content: For the simulation of the VAM effect to create wideband noise excitation signals, we employed Equations ( 1 ) and ( 3 ), where P(ω) represents the wideband noise spectrum with random amplitude and phase. An example of the spectrum of the blade vibrations for case 1, without additional rotational loads, is shown in Figure 10. Variations in the signal spectra due to resonance frequency and attenuation changes during the blade rotation are not typically seen in the signal spectra, and we will consider the modulation of the total signal energy E(τ). Here, the slow time variance τ is used. In our modelling, the sampling rate for this slow time was 10 Hz, while the sampling rate for the description of the resonance blade vibration was 10,000 Hz. 

where ω o = ∼ ω o (1 + αcosΩ 0 τ), and δ = δ o (1 + βcosΩ 0 τ). The frequency band for energy calculation was chosen around the blade resonance frequency:

The calculations of the slow time variation in the signal energy and its spectra form the basis of the DEMON signal processing, which is widely applied in the field of submarine detection [55, 57]. 

The spectra of the DEMON signal are as follows:

In the DEMON spectra, a peak will appear at the rotation frequency F representing a crack or other non-linearities that may occur on the WT blade. This peak can be detected when it is higher than the surrounding spectral noise components. In this wideband VAM model, the signal-to-noise ratio (SNR) is computed as the difference between the frequency component with the rotation frequency and the maximal spectral component outside of the rotation frequency. Figure 11a illustrates the SNR of the DEMON spectra of the rotating blade excited via wideband noise. The SNR is calculated using the following formula:

where the A F is the amplitude of the DEMON component with the rotation frequency, and A max is the maximum of the noise peak outside of A F. Figure 11 displays the DEMON spectra of the three cases summarized in Table 3. The analysis of the signal is conducted within a time window of 10,000 s. The influence of the non-linear parameters describing the resonance frequency shift (a) and amplitude dependable attenuation (β) was investigated by comparing the SNR and MI for cases with and without amplitude-dependable attenuation (β = 0). This comparison is presented in Table 3. 

As can be seen in the table, damping non-linearity is particularly important for wideband signal modulation. The SNR of the DEMON signal decreases with the absence of damping non-linearity (β = 0). 

In contrast, damping non-linearity does not significantly influence the MI parameters of the harmonic probe wave. 

The conducted modelling allows the prediction of the measured SNR of the processing time. Increasing the time window of signal analysis leads to an increase in the SNR. Figure 12 presents the dependence of the SNR on the signal-processing time, which is up to 10,000 s (about 2. 8 h), for the 52-m blade (case 2 in Table 2 ).
section_name: Passive VAM

section_content: An experimental study was conducted in the lab to examine the use of wideband VAM for detecting cracks, using the experiment outlined in reference in [58] and the harmonics outlined in [50, 59]. The sample used in the experiment was a 10-inch A36 bar with a crosssection of 1 × 1 /8 inches. In order to manage the expected position of the fatigue crack, a central hole with a 1 /4 inch diameter was created. Two piezoelectric disks were affixed to the sample to transmit and receive signals. We used piezoceramic with a thickness of 1 mm and a diameter of 10 mm produced by PI Ceramic (www. piceramic. com (accessed on 16 August 2023)). The specimen was installed in the material test system (MTS). The experimental arrangement is depicted in Figure 13. 

Two conditions were imposed on the specimen: assessment and damaging until it completely split. The MTS was used to apply the cyclic tensile load, aiming for a setpoint of 10. 5 kN and a magnitude of 10 kN. 

While evaluating with VAM, the material test system (MTS) was utilized to stimulate the specimen using pumping waves at a frequency of 10 Hz and an amplitude of 0. 5 kN. Together, a wideband noise signal was transmitted into the sample through one of the piezoelectric discs. An NIUSB 6361 data acquisition (DAQ) board was utilized to activate the pump wave, and its signal was increased 50 times using a piezo driver power amplifier. As a result, the notch location witnessed an interaction between the noise signal and the pump wave, which occurred in the presence of a defect. The other piezoelectric disc received the modulated signal, which was then directed to a bandpass filter with a frequency range of 110-220 kHz before being received by the DAQ board. Finally, the spectral modulated signal was analyzed using a computer. 

In this experiment, two types of signals were sent to the sample during the damaging process: (1) harmonic signals and (2) wideband noise signals. 

Figure 13. The experimental setup for VAM using a wideband probe wave [58]. Figure 13. The experimental setup for VAM using a wideband probe wave [58]. 

For comparison between the analysis of the VAMs of the noise signals and the sinusoidal signals, a harmonic high frequency of f = 189 kHz and a low frequency of F = 10 Hz were selected. Figure 14 shows the modulated signal spectra of both the intact sample and the same sample after developing a crack. In the traditional VAM method, the MI is used to assess the non-linearity. When a crack occurs in the sample, an increase in the amplitude is observed in the two sidebands with frequencies F + f and Ff. This MI measurement is defined in Equation (13). As seen in Figure 14a, when the sample is at the 5000-cycle point (undamaged state), the sidebands exhibit low amplitude, resulting in a low MI. Conversely, in a 48,004-cycle load (damaged state), as illustrated in Figure 14b, the high sideband amplitude results in a high MI measurement. 

To evaluate the MI for each load point for this examined steel sample, we present the normalized cycle fatigue lifetime versus MI measurement in Figure 15. In undamaged conditions, the MI remains relatively low and begins to rise when minor cracking occurs in the sample due to the tensile cycle load produced by the MTS machine. MI measurement is a conventional method used to assess cracks in materials. To compare this method to the previous example, we propose a new wideband signal, with the frequency band of 150-200 kHz incorporated into the VAM method analyzed via the DEMON technique. In the normalized cycle fatigue lifetime versus SNR, the same cycle load point at MI (5000-cycle load) displays a low SNR value, while a high SNR level is observed at the 48,004-cycle load. This observation is based on a 10-hertz modulated frequency calculated with a time window of 10 s, as presented in Figure 16a, b. In Figure 17, the level of the DEMON component is shown in relation to the normalized number of cycles. This normalized load cycle number can be considered to be the sample's lifetime. This diagram demonstrates two phases of the sample's lifetime. In the first phase, there is no damage to the sample that shows a low value of SNR. In the second phase, the damage is not visible; however, the elevated level of the SNR using the 10-hertz component signifies the existence of a crack. The accuracy levels of the conducted measurements of SNR and MI parameters were estimated via the processing of the recorded signal in 10 windows. This processing was performed for a 48,004-cycle load. The average value of SNR was 16. 4 dB, with the standard deviation being 0. 7 dB. The accuracy of the MI measurements was higher, as the average MI was -23 dB, with the standard deviation being 0. 04 dB. 

Comparing the plots in Figures 15 and 17 reveals that both methods exhibit similar levels of sensitivity regarding crack detection. The wideband signal method is more convenient for real WT blade SHM, as it does not require a probe wave emitter that transmits sinusoidal waves. 

The conducted test demonstrated the applicability of the VAM to crack detection in the steel sample, and we hope that a similar demonstration for the WT scaled model and the real turbine will be conducted in the near future.
section_name: Laboratory Investigation of Damage Accumulation in Steel Due to Cyclic Loading

section_content: The present research introduces a new approach to crack and damage detection in WT blades based of the modulation of the naturally excited blade vibrations by the altered load during blade rotation. The developed model allowed the estimation of the non-linear signal SNR based on the known data of the resonance frequency and the damping variations occurring in the presence of cracks. 

As far as we know, this study was the first work that experimentally and theoretically applied a wideband signal in VAM and analyzed the application of natural vibrations in the VAM SHM of WT blades. 

The suggested VAM method for crack and damage detection in WT blades can be implemented via the currently used SHM systems. This implementation does not require additional hardware and can use algorithms for the extraction of the non-linear effects that are described in this paper. Future works will be conducted using WT blades employing wideband blade modulation on a small-scale model, with the blade being 2 m in length.
section_name: Conclusions

section_name: Conflicts of Interest:

section_content: Data Availability Statement: Not applicable.

section_content: The authors declare no conflict of interest.
section_name: Conflicts of Interest: