Wavelet analysis of acoustic emission signals from thermal barrier coatings

 YANG Li(杨 丽), ZHOU Yi-chun(周益春)

Key Laboratory for Advanced Materials and Rheological Properties of Ministry of Education,

Faculty of Material Photoelectron Physics, Xiangtan University, Xiantan 411105, China

Received 10 April 2006; accepted 25 April 2006

Abstract: The wavelet transform is applied to the analysis of acoustic emission signals collected during tensile test of the ZrO₂-8% Y₂O₃ (YSZ) thermal barrier coatings (TBCs). The acoustic emission signals are de-noised using the Daubechies discrete wavelets, and then decomposed into different wavelet levels using the programs developed by the authors. Each level is examined for its specific frequency range. The ratio of energy in different levels to the total energy gives information on the failure modes (coating micro-failures and substrate micro-failures) associated with TBCs system.

Key words: wavelet transform; acoustic emission; tensile test; thermal barrier coatings; failure modes

1 Introduction

Acoustic emission(AE) technique for non-destructive evaluation of material failure has been widely used to study the fracture behavior of thermal barrier coatings[1-4]. The fundamental characteristics of acoustic signals, such as the attenuation, event count, ring-down count, peak amplitude distribution and energy count are investigated to describe the initiation and propagation of cracks in thermal barrier coatings. In the fracture process of the TBCs, the number of AE events is in a good agreement with the number of micro-failures[5], the amplitude or energy count are commonly used to estimate the deformation degree[1-4], and the waveform is occasionally introduced to analyze the failure mode of TBCs[1]. In fact, the amplitudes attenuate greatly with the increment of the propagation length and the distance of sensor, moreover, an AE signal may be the result of multi-failure, while the frequencies of AE signals from the certain failure modes are almost unchanged. This proves that the frequency analysis is an effective way in processing AE signals.

Another point motivating the development of frequency analysis is the stochastic noise mixed in AE signals. The signals obtained during the recording of AE events and storing their waveforms are usually not

recorded in a way to apply more sophisticated analysis tools. The so-called raw data have to be processed in a way to extract detailed information about the source terms of fracture analysis. To do so, all influences not related to source information have to be eliminated. The data processing can include several steps. One can be the application of a band-pass filter to cut-off frequencies out of the frequency range of interest as well as suppressing alias effects. There is also a demand to eliminate artifacts caused by the sensor transfer functions (sensor frequency response). A more effective way to filter the void information is the use of frequency analysis by reducing the noise mixed up with signal parts related to the fracture process and enhancing the signal-to-noise ratio.

In frequencies analysis to AE signals, one method is the fast-Fourier transform (FFT) to identify various failure modes, etc. [6-8]. However, the noise information can not be eliminated because of its randomicity, and the time information of failure modes can not be obtained. A more sophisticated way of denoising AE signal and discriminating failure modes is using wavelets. Wavelet techniques have been suggested to enhance the signal-to-noise ratio[9]. Wavelets are mathematical functions that cut up data into different frequency components, and then reconstruct the useful components by thresholding policy[10-15]. In this study, the tensile test and AE monitoring are performed on TBCs. The AE signals are de-noised using wavelet technique, and the de-noised AE signals are decomposed into different frequency levels by wavelet to discriminate the failure modes by the ratio of energy at different levels to total energy.

2 Wavelet transform

A wavelet ψ(t) is an oscillating function of short duration, temporarily localized around the center t=1/2, Its spectrum  concentrates in a bilateral band 0<ω₁<ω<ω₂. This mother function, by means of dilatations and displacements, generates a family of elemental functions or atoms, ψ_j,k(t) with localization in time–frequency, varying in an inverse proportion:

Ψ_j,k(t)=2^j/2ψ(2^jt-k)  j>0, k∈Z                  (1)

The wavelet transform can be considered a correlation between the signal under study s(t) and the wavelets. For a given a signal s(t), it is possible to represent it by the series:

                        (2)

where c_j,k is the wavelet coefficients.

Assuring that the set {ψ_j,k(t), k∈Z} is the orthonormal basis of W_j. Let φ(t) is the scale function the wavelet ψ(t), and the set {φ_j,k(t), k∈Z} (where

φ_j,k(t) are obtained by expanding and translating ofφ(t)) is the orthonomal basis of V_j. According to the scale and wavelet function, a low-pass filter and a high-pass filter construct, and their response function h(k) and g(k) are defined as

h(k)=＜ψ_j(t), ψ_j-1,k(t)＞                        (3)

g(k)=＜φ_j(t), φ_j-1,k(t)＞                   (4)

A space V_j-1 is decomposed a lower resolution space V_j plus a detail space W_j, W_j is the orthogonal complement of the spaces V_j and V_j-1, and , thus

V_j-1=V_j⊕W_j                                 (5)

The orthogonal projection of a signal on V_j-1 is decomposed as the sum of projections on V_j and W_j, which can be obtained by the convolution between the orthogonal projection on V_j and low-pass filter, high-pass filter, respectively. Thus, the coefficient c_j,k and d_j,k can be expressed as

               (6)

              (7)

h(m-2k) and g(m-2k) are the new response functions reconstructed by inserting j-1 zeros between each near two coefficients of h(k) and g(k), respectively.

Defining C_js(t) and D_js(t) are the lower and higher resolution at jth order, respectively. They are can be represented as

                      (8)

                      (9)

Thus, the wavelet decomposition of a given signal , is then expressed as:

s(t)=C₀s(t)

C₀s(t)=C₁s(t)+D₁s(t)

C_J-1s(t)=C_Js(t)+D_Js(t)                     (10)

Namely

.         (11)

Let  and  be the accumulative energy at low frequency of  order and that at high frequency of jth order at any time t during the test, respectively. Namely

                        (12)

,  j=1, 2, ??? , J            (13)

With the total energy given by

                  (14)

To be more precise, the ratio of energy in different levels to the total energy is more important in discriminating how the energy is displayed in different levels. Let

                 (15)

By tracing the values defined by the level energy distribution coefficient  and , the energy variation of each fracture mode is expected to be evaluated.

Although there are many types of wavelets, we restrict ourselves in this study to the Daubechies[16], which is good enough for the purpose of engineering applications.

3.1 specimen preparation

The TBCs used for this research project were provided by Beijing Institute of Aeronautical Materials. First, Ni based superalloy DZ125 which consisted of multiple elements Cr_8.9C_0.1Co₁₀W₇Mo₂Al_5.2Ti_0.9Ta_0.8- Hf_1.5 B_0.015Ni was used as substrate, its geometry is 5 mm in width, 3 mm in thickness and 60 mm in length with a gage length of 40 mm. Next, a NiCrAlY bond coat about 50 μm thick was deposited on one surface of the beam substrate by vacuum plasma-spray technology using Sulzer-Metco systems (where the powder feed rate is 45  g/min). Last, electron beam physical vapor deposition technique applied to manufacture ZrO₂ stabilized with 7%-8%Y₂O₃ ceramic coat in a total thickness of approximate of 10 μm on the top of bond coat, during this deposition, the power of electric gun is 15 kW, and the surface temperature of the gun is 1 173 K.

3.2 Tensile test monitored by acoustic emission

The tensile test was carried out to understand the microscopic failure behavior of thermal barrier coatings using AE technique. The experiment was carried out under load control at a rate of. Two AE sensors with resonance frequency of 600 kHz were used. The AE sensors were attached firmly to the surface of substrate by an elastic cord and sealed with butter a thin film of butter to ensure maximum ultrasonic signal transmission. AE signals traveled through TBCs, were received by sensors, were filtered and magnified by DB16 AE analyzer, and then recorded automatically by a computer.

4 Result and discussion

4.1 Micro-failure mechanism and AE characteristic

Fig.1 shows typical stress-strain curves and the relationship between the load increment and the AE events. The deformation behavior and corresponding AE response of TBCs can be described in three different steps

1) All layers of TBCs system are fully elastic, and no AE signals are observed because no irreversible deformation behavior occurs.

2) The YSZ layer deform plastically, but the substrate and the bond coat deform elastically, AE events increase gradually because the YSZ ceramic is so brittle that it begins to fracture in the plastic region.

3) All layers of TBCs deform plastically till ultimate fracture occurs, AE event count increases rapidly compared with region 2) due to the occurrence of micro-failures in each layers of TBCs, for example, the fractures of YSZ coat, the delemination between YSZ coat and bond coat, as well as the plastic deformation and fracture of the substrate and those of the bond coat.

Fig.2 shows the cross-section of the TBCs specimen at the end of stage Ⅰ and stage Ⅱ, respectively. No

Fig.1 Relationship between AE events and loading time

Fig.2 Cross-section of TBCs specimen at end of stage Ⅰ(a) and  stage Ⅱ(b)

cracks has been found in YSZ layer in Fig.2(a), but serious fractures in YSZ layer have been found and some of these has penetrated into the bond coat in Fig.2(b). The small magnification is applied for Fig.2(b) in order to exhibit the panorama of TBCs. In addition, the great mass of YSZ layer has spalled after the ultimate fracture of TBCs, thus the cross-section is absent.

4.2 Denoising of AE signals

AE data are usually disturbed by noises of different frequency ranges. On the one hand, AE data contain a lot of high-frequency noise, mainly caused by the measurement equipment (preamplifier etc.) and the surrounding. On the other hand, due to the testing process itself, a low-frequent signal caused by the testing device (loading machine) often superimposes AE signals additionally. When a signal is transformed into the wavelet domain, the noise in the signal often corresponds to the coefficient whose absolute value is relatively small. This noise can be excluded easily because of its small absolute coefficient compared with the threshold. Once the threshold is obtained, one can apply soft thresholding policy: for each wavelet coefficient , the soft thresholded value is calculated as

C_j,k=sgn(c_ij)(|c_j,k|-th)  if  |c_j,k|≥th              (16)

c_j,k=0  if |c_j,k|＜th                           (17)

It can be observed that, when a testing device disturbance occurs, the absolute values of wavelet coefficients at the final scale level would become very large and exceed the threshold more. Extracting this coefficient, disturbance due to the testing device is erased.

The computations were performed with Matlab for Windows version 7.0[17], using our own programs. Each of the wavelet function has different characteristic. The wavelet filter which is optimal for a given signal, is not necessarily the best for another type of signal. Improper choice of filter can cause distortions and artefacts in the reconstructed signal. By comparing the original and reconstructed signals, such as, signal-to-noise ratio, neatness without white noise, the wavelet function DB7 with level 7 was used in AE signal denoising. A filtering example of AE signal for TBCs is shown in Fig.3. Specifically, soft thresholding with universal threshold and the last level of decomposition was restored for all of the signals.

Fig.3 Original AE signal and denoised AE signal using wavelet technique

4.3 Signal classification using energy analysis

  Base on the theoretical ground of the work discussed in section 2, the denoised AE signals are decomposed into six different levels. The decomposed AE signals in each level and corresponding frequency spectrum is shown in Fig.4. Each level represents a specific frequency range from 0-156.25 to 2 500-5 000 kHz. Visually, none of these is similar to white noise, and none of these exhibits abrupt change. The features of these waveforms, such as, duration time, amplitude and frequency spectrum are useful to illustrate the characteristics of AE signal and distinguish the different AE signals from various possible failure modes in TBCs. Given the AE signal that decomposed in Fig.4, it is seen that the duration of each level shows no obvious difference; the amplitudes distributing is that it is higher in D2, D3 and D4 than in the rest levels; corresponding energy intensities are high in these three levels with the maximum in D3. The results show that the signal can be distinctly identified with its character concentrate in D2 to D4.

   Information shown in Fig. 4 can give immediate access to AE signal and are always convincing. But due to the large number of AE events, analyzing by this way is very time consuming. Note that the ratio of energy defined as Eqn.(15), which includes not only the time information such as duration and amplitude but also the frequency information, is a favorable index to discriminate the AE signals. The automatic application of wavelet algorithms for distinguishing is simple as long as the AE signals can be classified in a certain way, i.e. typical models for AE signals exist.

In this work, one hundred AE signals from TBCs during tensile test are chosen and analyzed using wavelet transform. Three typical models are found and the distributions of their energy ratios at different levels are shown in Fig.5. From the figure, it can be seen that the energy is concentrated on scale D4, D3 and D2 (with a frequency range from 312.5-625 kHz, 625-1 250 kHz and1 250-2 500 kHz) as the same result shown in Fig.4. The histograms in Fig.5 also reveal that the biggest value of energy ratio for each type exceeds , such as, at scale 2 for model 1, at scale 3 for model 2 and  at scale 4 for model 3. Thereafter, a given signal can be discriminated by comparing the biggest value of energy ratio with  and confirming which level of the biggest value occurs in. Specially, for some signals can’t be regarded as any one of the existed modes, such as, the values of energy ratio at all levels are small than , the biggest one exists not in D2-D4 but in D1 or C5, discriminating should be practiced again to find another possible model. In case of our work, no else model can be established because of small quality of these cases.

The accumulative AE event counts of each model at different stage of tensile test are illustrated in Table 1.

Among, stage Ⅰ is absent in that no AE signal recorded,  stage Ⅱ is divided into two period at its

Fig. 4 AE waveforms and corresponding frequency spectra in different wavelet levels

Table 1 Percentage of each model for AE signals of TBCs at different deformation stages

approximate midpoint, named as stage Ⅱ (F) and stage Ⅱ (L), respectively. According to Table 1, AE signals of model 1 and model 2 are active during the whole tensile test, with a total percentage of 73%. It can also be seen that the percentage of model 2 and model 3 keeps rising, but that of model 1 keeps declining with the deformation of TBCs increasing. Table 1 also displays that a decrease trend in AE count of the others with the increase of the TBCs deformation. Considering the AE characteristics and the micro-failing process discussed in section 4.1, AE signals are mainly caused by the plastic deformation and fracture occurred in YSZ layer in stage Ⅱ, but those in stage Ⅲ are induced by the micro-fractures of both YSZ coat and substrate. As we know, the frequencies of AE signals resulted from the plastic deformation are commonly higher than those caused by the fracture of a certain material[18]. These results show that AE signals induced by micro-failures of YSZ layer are mainly of model 1 or model 2, associated with the plastic deformation and micro-fractures respectively; most AE signals caused by the micro-failures in substrate belong to model 2 or model 3. The rapid increase of AE signals in model 3 indicates the fracture of substrate give the rise to AE signals with low frequencies consisting. In addition, it can be deduced that the model of AE signals associated with the micro-failures in the interface between the YSZ layer and the bond coat, like delemination, is one of the three models because no other model has be found.

The characteristics of AE signals induced by the same micro-failure type from the same source may be different from each other due to different micro-mechanism. In terms of the cracking behavior of YSZ layer, the difference may be caused by the different crack direction, crack initiation or propagation. The further discrimination should be discussed in future work

Fig.5 Three typical models of AE signals

1)AE event count changes with the deformation of TBCs. Hence, AE technique is an effective way to monitor the micro-failing of TBCs.

2) The wavelet transform can be a useful way to analyze AE signals by decomposing the signal into different wavelet levels. The ratio of energy at different wavelet component is a reliable and convenient index to different modes of AE signals.

3) AE signals of TBCs submitted to tensile test can be classified into three types associated with micro-failures in YSZ layer and substrate.

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(Edited by CHEN Ai-hua)

Foundation item: Project(10525211, 50531060) supported by the National Natural Science Foundation of China.

  Corresponding author: ZHOU Yi-chun;  Tel: +86-732-8293568; Fax: +86-732-8292468; E-mail: zhouyc@xtu.edu.cn