Detection of Diffusion Interlayers in Dissimilar Welded Joints in Processing Pipelines by Acoustic Emission Method

Abstract

The paper considers the neural network application to detect microstructure defects in dissimilar welded joints using the acoustic emission (AE) method. The peculiarity of the proposed approach is that defect detection is carried out taking into account a priori information about the properties of the AE source and the acoustic waveguide parameters of the testing structure. Industrial process pipelines with dissimilar welded joints were studied as the testing object, and diffusion interlayers formed in fusion zones of welded joints were considered microstructure defects. The simulation of AE signals was carried out using a hybrid method: the signal waveform was determined based on a finite element model, while the amplitudes of AE hits were determined based on a physical experiment on mechanical testing of dissimilar welded joints. Measurement data from industrial process pipelines were used as noise realizations. As a result, a data sample was formed that considered the parameters of the AE source and the parameters of the acoustic waveguide with realistic noise parameters and a signal-to-noise ratio. The proposed method allows for a more accurate determination of the waveform, spectrum, and amplitude parameters of the AE signal. Greater certainty in the useful signal parameters allows for achieving a more accurate and reliable classification result. When using a backpropagation neural network, a percentage of correct classification of more than 90% was obtained for a data set in which the signal-to-noise ratio was less than (−5 dB) in 90% of cases.

1. Introduction

Modern trends in improving industrial structures’ strength lead to increased requirements for the applied structural materials and the quality of their welded joints. Weld structures made of dissimilar materials are used in cases where operating conditions (temperature, medium, mechanical load level) vary for different sections of the structure. Welding of dissimilar metals has a few features associated with the different chemical composition and mechanical properties of the materials being welded. During welding, subsequent heat treatment or long-time operation of dissimilar welded joints at high temperatures, diffusion processes occur in the fusion zones of the joint, due to which the formation of diffusion interlayers is often observed along the fusion lines [1]. Diffusion interlayers can be considered as welded joint microstructure defects, as their formation can cause premature failure of products under high-temperature operating conditions [2].

Acoustic emission (AE) is a nondestructive testing (NDT) method that makes it possible to detect defects in structures using elastic stress relaxation waves. Due to its sensitivity to changes in the microstructure parameters of the materials being tested, the AE method, unlike other NDT methods (such as X-ray diffraction [3], eddy-current testing [4], ultrasonic testing [5,6]), allows detecting not only continuity defects but also microstructure defects.

In previous research, the authors demonstrated the possibility of detecting diffusion interlayers in welded joints of pearlitic to austenitic steel using the AE method under both static and cyclic loading [7]. Unlike cracks, which are characterized by a variety of shapes and an uneven nature of propagation, diffusion interlayers have a regular microstructure and are characterized by predictable parameters. For example, under cyclic loading, diffusion interlayers generate AE hits with a certain constant activity level, and AE hit amplitudes correspond to a power law [8].

This paper examines the practical application of the previously obtained results, namely, the detection of defects in dissimilar welded joints in field conditions against the technological interference background. The method for detecting microstructure defects proposed in this paper differs from known ones in that it attempts to provide more reliable and universal solutions for detecting diffusion interlayers in dissimilar welded joints of pipelines.

The disadvantage of the AE method is the large number of factors affecting the diagnostic results. The diagnostic data depends on the AE source function, the waveguide transfer function, and the measuring system transfer function [9,10]. In the case of oblong industrial structures testing, it is difficult to assess the influence of the AE source function and the acoustic waveguide parameters on the diagnostic data, so, as a rule, the defect detection criteria are formulated empirically by identifying differences in the AE data features obtained by comparison of defective and defect-free structural elements [11,12,13]. When using the empirical method of diagnostic criteria, it is difficult to assess the reliability and accuracy of defect detection [14,15], and due to the close connection of the obtained defect detection method with the specific characteristics of the testing structure, it is impossible to extend such a solution to similar structure with other geometric parameters or with other operating conditions.

However, in the problem under consideration, the AE data parameters predictability during the diffusion interlayer deformation and the certainty of its location (on the fusion line of the welded joint) reduce the AE data variability and uncertainty, which is a favorable factor that facilitates the task of AE monitoring system constructing. The proposed approach seems to be more reliable since the defect detection procedure is not empirical but is based on the calculation of realistic models of AE signals and the development of methods for their detection against the background of noise obtained in field conditions [16].

Realistic signal models are obtained by considering the AE activity and the AE hits amplitude values obtained during the experiment on cyclic tension of specimens with dissimilar welded joints and also by determining the signal waveform using numerical modeling of signal propagation along the acoustic waveguide. Such a hybrid modeling method is justified since, during mechanical testing of specimens, the AE source parameters are determined quite accurately, but the signal waveform is distorted due to an increase in duration and rise time caused by multiple reflections of the AE waves from the specimen edges [17].

Numerical, analytical and hybrid modeling are widely used to calculate the propagation of AE signals along waveguides of various shapes to determine the signal onset time [18], refine the location procedure [19], and implement waveguide testing methods [20]. A comparison of modeling and experimental signals shows high accuracy in the modeling results. The use of an acoustic waveguide numerical model allows us to consider the size and shape of the testing structure and welded joint and to form a set of AE signals for different source parameters and mutual arrangements of the AE source and AE sensor.

Neural networks are used to identify signals obtained from simulations against noise background measured in the field conditions. The advantage of neural networks in AE data processing compared to statistical classifiers and machine learning methods is the formalization of the pre-processing stage. The use of statistical classifiers usually requires pre-processing data, searching for patterns and identifying informative features associated with certain physical processes [21]. AE data, both useful signals and noises, are random in nature and are characterized by significant variability [22], so the search for informative parameters is a complex and labor-intensive task that does not always lead to a reliable result. Due to the more complex nonlinear structure of the classifier, the use of a neural network allows for simplifying the process of preliminary processing by shifting the search for patterns and data generalization from the pre-processing stage to the classification stage. With the help of neural networks, it is possible to use an excessive number of features to apply standard AE parameters or the actual time realizations and AE signal spectra as informative features [23].

Thus, in this paper, we propose an approach to AE data neural network classification adapted for use in AE monitoring systems, providing greater flexibility and the possibility of universalization of approaches compared to existing methods. The universality of the proposed method is achieved through the hybrid formation of a training data sample: the values of AE hits amplitudes, and activity are formed because of a physical experiment, the acoustic waveguide of the test object is considered using numerical modeling, and when forming a sample of noise realization of technological interference, data obtained in field conditions are used.

2. Materials and Methods

2.1. General Approach to Data Classification

The advantage of the proposed approach to constructing a neural network classifier consists in the method of forming a representative training sample which takes into account all aspects of the AE control procedure: the parameters of the AE source, the characteristics of the acoustic waveguide and the parameters of the interferences in the controlled object. The general scheme of the proposed algorithm is shown in Figure 1.

The interference sample is formed based on the realizations of acoustic noise obtained as a result of calibration acoustic measurements in field conditions on the testing object under various operating modes. AE signals waveform is obtained through modeling: the waveform is calculated based on the finite element model (FEM) of the testing object. AE source parameters obtained from the experiment (mechanical tests with AE signal registration) are used to model stochastic parameters—activity values and amplitude distributions of AE hits.

As a result of modeling and calculation, two samples are formed—a sample of noise and a sample of “signal + noise”, the latter consisting of AE waveforms obtained as a result of modeling and noise obtained during calibration measurements.

2.2. AE Source Characteristic

Dissimilar welded joints of grade 20 steel (carbon steel with a ferrite-pearlite structure) and 12Kh18N10T steel (austenitic stainless steel) were the objects of the research. The welded joints were fabricated from sheets of grade 20 steel and 12Kh18N10T steel with a thickness of 3 mm. The chemical compositions of the 12Kh18N10T and grade 20 steel are provided in

Table 1. Chemical compositions of grade 20 steel and 12Kh18N10T steel, % wt.

Steel Grade	C	Si	Mn	Ni	S	P	Cr	Cu	Ti	Fe
12Kh18N10T	max 0.12	max 0.8	max 2	9–11	max 0.02	max 0.035	17–19	max 0.3	0.4–1	bal.
20	0.17–0.24	0.17–0.37	0.35–0.65	max 0.3	max 0.04	max 0.035	max 0.25	max 0.3	max 0.08	bal.

. The sheets were cut into strips 1000 mm long and 200 mm wide and were welded together using MIG welding (Figure 2a).

Welding was performed with a double-sided butt joint, using Sabaros O101 wire as the filler material. The chemical composition of the filler wire is provided in

Table 2. Chemical composition of the Sabaros O101 filler wire for MIG welding, % wt.

C	Si	Cr	Ni	Mn	Fe
0.10	0.50	19.0	9.0	6.0	Base

. The use of Sabaros O101 wire provides the formation of an austenitic microstructure in the weld metal, which is optimal in terms of its mechanical and operational properties. Additionally, the chromium content in the wire contributes to the formation of carbide and decarburized diffusion interlayers during the heat treatment of the welded joints.

The preparation of specimens for tension tests was carried out by cutting the welded sheets with a laser. The shape and sizes of the test specimens were selected in accordance with the recommendations of tension test standards and the specific requirements of the AE tests being conducted. The width of the specimen gauge section was set at 20 mm to securely attach an AE sensor with a diameter of 15 mm to its surface. The weld was in the center of the specimen gauge section. The width of the grip section was set at 50 mm to prevent plastic deformation of the 12Kh18N10T steel in the grip area during tension testing (Figure 2b,c).

To form diffusion interlayers, which typically occur in the welded joints during long-term operation under high temperatures, a few of the weld specimens were subjected to subsequent heat treatment to simulate the effect of long-term operation under high temperatures. Heat treatment was conducted in a Nabertherm P180 furnace at a temperature of 650 °C with different holding times (1 h, 5 h, and 25 h). Different holding times were necessary to form diffusion interlayers of different thicknesses. Increasing the heat treatment duration and temperature intensifies the diffusion of carbon from grade 20 steel into the weld metal, resulting in the thickening of the diffusion interlayers in the area of the fusion line—both carbide (in a weld metal) and decarburized (in grade 20 steel). The average values of interlayer thicknesses are presented in

Table 3. The average thickness of diffusion interlayers in welded joints of grade 20 steel and 12Kh18N10T steel, obtained by MIG welding after heat treatment.

No. of Heat Treatment Mode	Holding Time at 650 °C, h	Thickness of Decarburized Interlayer, µm	Thickness of Carbide Interlayer, µm
1	1	145	20
2	5	225	45
3	25	600	65

. The microstructure of welded joints after heat treatment is shown in Figure 3.

The samples were tested for cyclic tension by zero-triangular cycles with a maximum stress of σ_max = 200 MPa, which corresponds to the elastic region of the weld joint tensile stress diagram. The tests were carried out on an Instron 5982 testing machine with a frequency of about 0.2 Hz. A photo of the experimental setup is shown in Figure 4. The AE data were recorded using an A-Line 32D system with GT200 AE transducers installed at a distance of 200 mm from each other symmetrically relative to the welded joint. A digital filter with a passband of 100…300 kHz and an amplitude discrimination threshold of 32 dB was used to suppress the noise of the testing machine during data collection.

2.3. Acoustic Waveguide Simulation

Experiments conducted on the samples of dissimilar welded joints allow us to estimate the AE activity and the values of the AE hit amplitudes, but the signal waveform is distorted. Due to multiple reflections from the specimen boundaries, the rise time and duration of the signal are several times higher than in the case of extended objects. In order to obtain the correct signal waveform and ensure the possibility of determining the signal waveform at a point remote from the AE source, the authors use a finite element model of the acoustic waveguide of the testing object.

The testing object was a dissimilar section of a process pipeline welded from austenitic and pearlitic steels, with an external diameter of 100 mm and a wall thickness of 3 mm. The model was calculated using the finite element method (FEM) in the Comsol Multiphysics software (version 5.5) Solid Mechanics module. The modeling was carried out in the time domain. The parameters of the steels used in the modeling are given in

Table 4. Material parameters used when modeling.

Steel Grade	Density, g/cm3	Young’s Modulus, GPa	Poisson’s Ratio
12Kh18N10T steel	7.9	200	0.3
Grade 20 steel	7.8	210	0.3

.

The weld width of 10 mm and the reinforcement bead height of 3 mm for FEM were selected in accordance with the parameters of the real welded joint made of grade 20 and 12Kh18N10T steels. For the filler material with an austenitic microstructure, the same properties were specified for 12Kh18N10T steel. To prevent multiple reflections, the length of the FEM pipeline model was chosen to be 5 m. The defect was specified as a point source generating a single displacement oriented out-of-plane. The form of the source was a “cosine bell” with 1 μs duration. The location of the source corresponded to the location of the diffusion interlayers—along the fusion line on the side of grade 20 steel.

Figure 5a shows a general view of the model with a finite element mesh that was set finer in the area of the welded joint and coarser at a distance from it; Figure 5b shows the area of the welded joint in more detail.

Since the occurrence of AE impulses is caused by the action of microscopic sources associated with the movement of dislocations, the emission of an AE impulse can occur at any point of the deformed volume. Therefore, the location of the AE source relative to the surface of the object varied; it is located on the surface of the pipeline, in the area of the weld root and at a depth equal to half the wall thickness.

Also, for each of the models, AE signals were calculated at different distances from the source in the axial and azimuthal directions; the general list of variable model parameters is given in

Table 5. Variable model parameters.

Parameter	Range of Values
AE sensor axial coordinate, m	0.1; 0.15; 0.2; 0.25; 0.3; 0.35; 0.4; 0.45; 0.5
AE sensor azimuthal coordinate, °	0°; 45°; 90°; 135°; 180°
Source depth below the surface, mm	0; 1.5 (middle-depth)

. The limited number of signals corresponding to the in-plane and oblique orientation of the AE source were also calculated.

2.4. Data Sample Formation and Feature Calculation

The training sample was formed based on the results of waveguide modeling, considering the data from experiments on cyclic loading of specimens of dissimilar welded joints. The set of AE signal waveforms was calculated with the help of the FEM model by placing the AE source in depth along the fusion line and around the circumference of the weld joint. The amplitudes of AE signals in the data set were modeled in accordance with the parameters of the amplitude distributions obtained as a result of the experiment on cyclic loading of the samples.

Long-term signals recorded in the field conditions were used as noise. To ensure greater reliability of the results, two types of process noise were considered. The first type of noise was measured on the body of a chemical reactor (Figure 6a); it has a nonstationary character with an impulse component of short duration and a broadband frequency spectrum (Figure 6b). Noise of this type is often recorded when monitoring heat exchangers, chemical reactors, and process pipelines, and it can be caused by the presence of solid dispersed particles in the flow of liquid or gaseous medium.

The second type of noise (Figure 7b) corresponds to the noise of a loading device (compressor); it was measured on the body of a process pipeline (Figure 7a) with a turbulent flow of gaseous product and a high vibration level. The noise has a quasi-stationary nature with slow trends in the change of the standard deviation and is characterized mainly by a low-frequency spectrum.

Filtering such types of noise seems to be the most difficult since nonstationary stochastic noise processes have a form and frequency spectrum similar to AE signals. However, the use of the FEM model allows us to estimate the parameters of the AE signal and bring the signal detection procedure closer to the parametric version.

Classification features are calculated based on the continuous wavelet transformation [24], which allows us to clearly identify the features of signals with impulse components simultaneously in time and frequency domains.

3. Results

3.1. AE Source Study Results

To determine the parameters of the AE source, cyclic tension tests were performed on samples of dissimilar welded joints. Defect-free specimens and specimens with diffusion interlayers of different thicknesses were examined. A total of 16 samples were tested, including 4 defect-free samples (not subjected to additional heat treatment) and 4 samples with different heat treatment modes, with diffusion interlayers of different decarburized interlayer thicknesses of 145, 225 and 600 µm.

From the point of view of AE data, the cyclic loading of samples is a stationary process with a constant level of AE activity. Figure 8 shows the dependences of AE activity on time for a specimen of a dissimilar welded joint without diffusion interlayers and with diffusion interlayers of an average thickness of 225 μm. In all experiments, the AE activity was quite low since the nature of loading of the specimens corresponded mainly to the region of elastic deformation. The average value of activity in the test series changed insignificantly in the range from 0.18 to 0.52 imp/s, with a tendency to rise up with an increase of the diffusion interlayer thickness.

The presence of diffusion interlayers also influences the values of the AE hit amplitudes. When loading the welded joint samples with diffusion interlayers, the amplitude level was 40–50 dB, while when testing the defect-free samples, the AE hits mainly had an amplitude of less than 40 dB. The values of the AE hit amplitude over time are shown in Figure 9: Figure 9a corresponds to the results of testing a defect-free specimen, and Figure 9b corresponds to testing a specimen with a diffusion interlayer of about 225 μm thickness.

The values of AE activity and the level of AE hit amplitudes differed significantly for defect-free samples and samples with diffusion interlayers, but no direct correlation was found between the thickness of the diffusion interlayer and the values of AE parameters.

Table 6. AE parameters of specimens of dissimilar welded joints under cyclic loading.

Type of Specimen	Defect Free	With Diffusion Interlayers
		~145 μm	~225 μm	~600 μm
AE activity, 1/s	0.12	0.38	0.52	0.43
Quantile 95% of amplitude distribution, dB	34.3	41.2	44.1	43.1

shows the average values of AE activity and the quantile 95% order of amplitude distribution.

When analyzing the distribution of AE hit amplitudes, it was found that the presence of diffusion interlayers leads to a qualitative change in the type of AE hit amplitude distribution. For specimens without diffusion interlayers, the distribution corresponds to the exponential law, which is confirmed by the value of the determination coefficient R² > 0.92. For specimens with diffusion interlayers, the nature of the amplitude distribution acquires a power-law character and corresponds to the Gutenberg–Richter law. The minimum value of the determination coefficient R² for distributions corresponding to specimens with diffusion interlayers is 0.93. Figure 10a shows examples of amplitude distributions for defect-free specimens, and Figure 10b shows the specimens with interlayers of different thicknesses.

To form a description of the AE source parameters, it is rational to use the averaged non-normalized distribution of AE impulse amplitudes, which gives an idea of both the process activity and the AE hit amplitude values.

Figure 10c shows the sample-averaged amplitude distributions for a defect-free specimen (red-point graph) and for a specimen with diffusion layers (blue-point graph). As can be seen from the graphs, AE hits with an amplitude of more than 42 dB are important for diagnosing diffusion interlayers; the probability of such impulses appearing for defect-free specimens is less than 0.5%, and for specimens with diffusion interlayers, it is an order of magnitude higher than 6%.

The frequency table of the amplitude distribution was used as a characteristic of the AE source when forming a data set for training and verifying the neural network classifier.

3.2. Acoustic Waveguide Modeling Results

Acoustic waveguide modeling allows for determining the waveform and spectrum of the AE signal when diagnosing dissimilar welded joints of process pipelines. To confirm the correctness of the modeling results, Figure 11 shows the distribution of the object surface displacements. The displacement map is shown at different moments in time relative to the moment of generation of the probing impulse. The modeling result corresponds to the case when the AE source is located on the pipeline surface along the fusion line on the side of grade 20 steel. Five microseconds after acting, the source (Figure 11a) at the wavefront was localized in the source location zone; after 50 and 100 μs (Figure 11b,c), the propagation of the spherical wavefront along the acoustic waveguide of the monitored object can be observed.

To verify the results, a comparison was made between the time-frequency parameters of the signals obtained by simulation and the signals measured experimentally. The experiment was performed on a laboratory model of a pipeline with a welded joint; the diameter and wall thickness of the pipeline corresponded to the model parameters (outer diameter 100 mm, wall thickness 3 mm). The AE signals were simulated using a Hsu–Nielsen source at different distances from the AE sensor. Measurements were performed using the A-Line 32D system in the same configuration as in mechanical tests. To ensure a correct comparison, the signals obtained by simulation were subjected to additional processing, including the convolution with the impulse response of the AE sensor. The comparison results are shown in Figure 12.

As can be seen from Figure 12, the signal obtained as a result of simulation (Figure 12a) and the measured signal (Figure 12b) have a similar waveform, and the wavelet spectrograms show a correct dispersion structure characteristic of Lamb wave propagation. The similarity of the signals obtained as a result of modeling and the measured signals confirms the reliability of the finite element model.

Analysis of signals obtained with different modeling parameters showed that variations in the position of the source and receiver do not lead to significant changes in the signal waveform. The greatest influence on the waveform is exerted by a change in the coordinate of the signal recording point in the axial direction. Figure 13 shows signals recorded at a distance of 0.1, 0.3, and 0.5 m from the emission point; with an increase in the distance of signal propagation along the waveguide, signs of a change in waveform characteristic of dispersive propagation are noted—a decrease in amplitude and an increase in the rise time (Figure 13a–c), on the wavelet spectrograms one can also notice a shift in the spectrum to the low-frequency region (Figure 13d–f).

Changing the azimuthal coordinate also does not have a significant effect on the signal waveform; Figure 14a,b show signals measured at a distance of 0.3 m from the source; the signal shown in Figure 14a has the same azimuthal coordinate as the source, and the signal shown in Figure 14b is shifted by 180°. As can be seen from the figures, the signals have a similar waveform; the wavelet spectrograms (Figure 14c,d) only show a change in the phase spectrum of the signal.

Changing the source position by depth, as well as source orientation, should change the ratio of energies of the asymmetric (A0) and symmetric (S0) Lamb wave modes. However, in the considered frequency range of 30–300 kHz, typical for industrial AE testing, the S0 mode is significantly attenuated [25] and, as a rule, has several times smaller amplitude than the A0 mode. As a result, the location of the source by depth and the change in its orientation did not lead to significant changes in the signal waveform.

3.3. Classification Features Choice

Detection of defects in dissimilar welded joints by the AE method is reduced to the problem of recognizing time realizations containing a useful AE signal in a noise flow. Since the AE signals corresponding to the propagation of a defect have an impulse waveform and are characterized by a fairly low activity (see Section 3.1), and noise is recorded continuously, it is advisable to divide the data into two classes: “noise” and “signal + noise”. To determine the parameters that allow us to identify the differences between the classes, a wavelet analysis of the noise and AE signals against a noise background was performed.

Figure 15 shows the results of wavelet analysis for the case of impulse noise: realization of noise is shown in Figure 15a, and the AE signal against the noise background in Figure 15b. Figure 15c,d show wavelet spectrograms of these signals. The Morlet wavelet was used as a wavelet function; the resolution of the wavelet spectrogram is 10,000 samples along the time axis (10,000 μs with a sampling interval of ΔT = 1 μs) and 150 samples by frequency (300 kHz with a frequency resolution of 2 kHz). The amplitude values were selected so that the signal-to-noise ratio was approximately equal to 3 dB. The noise spectrogram visualizes areas corresponding to the impulse components of noise, localized in time (up to 50–100 μs) and stretched along the frequency axis. The AE signal against the background of noise (Figure 15d) is characterized by greater energy in the low-frequency region, up to 100 kHz, and a greater duration of the impulse.

Figure 16 shows the results of wavelet analysis for the noise of the loading device. As can be seen from the wavelet spectrogram, the noise of this type is continuous and low-frequency, corresponding to the frequency band of 50–100 kHz. The AE signal against the background of noise is revealed on the wavelet spectrogram as a time-localized region of interest corresponding to the low-frequency range.

The wavelet transform is a signal decomposition at different scale levels; when choosing a long observation interval (longer than the stationarity interval of stochastic noise), the wavelet decomposition character remains similar for different intervals of long-term noise implementation. Signal detection using the wavelet transform is possible since a short-term impulse signal introduces a change point in the time-frequency decomposition character of the noise signal.

Therefore, even though in the cases under consideration, the frequency ranges of the noise and useful signals significantly overlapped, and in the case of impulse noise, the signal and noise had close parameters in the time domain, the use of the wavelet transform made it possible to identify the differences between useful AE signals and noise. Various parameters of the time and frequency projections of the wavelet transform coefficients were considered as parameters for detecting the AE signal. The most informative parameter turned out to be the wavelet kurtosis, which represents the kurtosis calculated for wavelet coefficients corresponding to different frequencies (temporal wavelet kurtosis) and different times (frequency wavelet kurtosis) [26,27].

Figure 17a shows the dependence of time wavelet kurtosis vs. frequency for impulse noise (blue graph) and for the AE signal against the background of impulse noise (red graph). Due to the fact that impulse noise has a broadband spectrum, the kurtosis value remains high from 5 to 15 in the entire frequency range; the presence of a signal leads to the appearance of an additional extremum in the frequency band of 50–100 kHz. Figure 17b shows the same data for the stationary noise of the loading device.

Figure 18 shows the dependences of the wavelet frequency kurtosis on time. Figure 18a corresponds to the case of impulse noise, and Figure 18b to the case of stationary noise. Since the impulse components of noise are extended in the frequency domain and localized in time, and the continuous components of the stationary noise, on the contrary, are extended in the time domain and localized in the frequency domain, the frequency kurtosis for stationary noise is higher than for impulse noise. The frequency range of the useful AE signal is broader than that of stationary noise but narrower than that of impulse noise, so the presence of a useful signal increases the kurtosis of impulse noise and decreases it for continuous stationary noise.

The full list of features selected for classification is given in

Table 7. Classification features.

	Parameter	Parameter’s Equation	Initial Dimension	Pre-Processing Method	Final Dimension
1	Wavelet coefficients averaged in time	$S_f(f)={\displaystyle \frac{1}{N}}{\displaystyle \sum _{t=0}^{t_{max}}}W(t,f)$ N—number of samples	250 × 1	Compresses 26 times with the help of DWT approximation order 6	62 × 1
2	Frequency wavelet kurtosis	$E_f\left(f\right)=E\left(W\right(t,f\left)\right)$	250 × 1	Compresses 26 with the help of DWT approximation order 6	62 × 1
3	Wavelet coefficients averaged in frequency	$S_t\left(t\right)={\displaystyle \frac{1}{N_f}}{\displaystyle \sum _{f=0}^{f_{max}}}W\left(t,f\right)$ Nf—number of frequency coefficients	10,000 × 1	Compresses 26 times with the help of DWT approximation order 6	161 × 1
4	Time wavelet kurtosis	$E_t\left(t\right)=E\left(W\right(t,f\left)\right)$	10,000 × 1	Compresses 26 times with the help of DWT approximation order 6	161 × 1

. For classification, it is proposed to use wavelet coefficients averaged over time and frequency, as well as time and frequency wavelet kurtosis. Compression is used to reduce the dimensionality of the selected parameters. Compression is performed using the discrete wavelet transform (DWT) with the Daubechies wavelet ‘db6’. The parameters depending on the frequency are compressed by 4 times (up to the A2 approximation), and those depending on the time are compressed by 64 times (up to the A6 approximation).

3.4. Neural Network Classifier

The data sample for training the neural network was generated according to the approach presented in Section 2.1. The data set for the “noise” class was generated based on long-term noise realizations (Figure 6b and Figure 7b) by reducing them to a certain peak level (from 40 to 60 dB). The data sample for the “signal + noise” class is generated in a more complex way. In the first stage, the acoustic signals obtained using FEM are converted from displacement units to voltage units using convolution with the impulse response of the AE sensor. Then, using weighting coefficients, the signal amplitudes are brought into conformity with the power-law distribution typical of welded joints with diffusion interlayers (Figure 10c—blue-point graph), and at the final stage, noise is added to the signals. The flow chart of the data retrieval algorithm is shown in Figure 19. On the basis of this algorithm, a training sample was formed, consisting of 1000 data sets—500 realizations of noise and 500 realizations of “signal + noise”.

A neural network of radial basis functions (RBF) and a multilayer perceptron (MLP) with different activation functions were considered as a neural network for constructing the classifier. The best classification result was achieved using an MLP with a sigmoid activation function of a neuron. The architecture of the neural network, the number of hidden layers and the number of neurons in each layer were determined by selection to minimize classification errors. The best result with classification error was achieved for a neural network with one hidden layer of 32 neurons (MLP 446-32-2); however, when varying the number of neurons in the hidden layer from 19 to 41, the classification error changed by no more than 2%. Figure 20 reveals the best training results for neural networks for the case of impulse noise (Figure 20a) and for the case of stationary noise (Figure 20b) for the different noise levels.

At a noise level of no more than 50 dB, the classification accuracy was at least 90%; at a noise level of up to 55 dB, the classification accuracy decreased to 80%. The classification results for both types of noise are approximately the same: at a low noise level, the result is higher for stationary noise due to its lower similarity to the useful AE signal; at a high noise level of 55–60 dB, the accuracy of signal detection against the background of impulse noise is higher, due to the probability that the AE impulse and the impulse components of the noise do not overlap.

Figure 21 shows the classification matrices for the case when the noise level is 50 and 55 dB, class zero corresponds to noise signals, and class 1—to “signal + noise”. As can be seen from the presented matrices, at a noise level of 50 dB, the classification error is low, both for impulse noise (Figure 21a) and stationary noise (Figure 21b). With an increase in the noise level (Figure 21c,d), the error for class 0 turned out to be greater than for class 1, which indicates that the probability of a false detection is greater than the probability of missing a defect.

4. Discussion

The majority of studies devoted to the issues of AE data analysis and processing are vulnerable to criticism since, due to the features of the method related to its structural sensitivity and remoteness, there are numerous factors influencing the nature of the diagnostic data. A significant difficulty is also that most of these factors are random in nature or highly variable, so their influence is difficult to take into account or predict. Therefore, when attempting to universalize data processing algorithms or generalize the results to a certain class of objects, problems related to the influence of unaccounted factors arise. Studies based on the results of mechanical tests do not consider the factors related to the attenuation and the features of dispersive propagation of AE waves. Studies devoted to the analysis of data obtained in the field are focused on defects with certain parameters and do not take into account the influence of the size and topography of defects or the influence of various loading modes.

The current research proposes an approach that does not offer a radical solution to the problem but allows for some progress in this direction due to the procedure of complex modeling of various AE testing factors. A method for classifying AE data is proposed, which, with some assumptions, allows for taking into account the AE source and acoustic tract parameters, as well as the nature of the technological noise of the equipment under control.

The paper considers the defects of a dissimilar welded joint, specifically the carbon and decarburized interlayers that form during the long-term operation of the object under high-temperature conditions, as a source of AE. The presence of diffusion interlayers leads to a decrease in the elastic limit and ultimate tensile strength of the weld joint [1].

Microstructure defect detection is a unique diagnostic feature of the AE method, which distinguishes it from a number of traditional nondestructive testing methods. The detection of microstructure defects is not a typical task, but it is a more favorable case in terms of determining the parameters of the AE source. In contrast, to crack propagation in a jump-like manner, the deformation of diffusion interlayers occurs continuously and leads to continuous generation of AE hits with an approximately constant level of activity and amplitudes belonging to a fairly narrow range of values.

In addition, diffusion interlayers are a defect, the location of which is known as a priori; therefore, when determining the AE signal waveform, the uncertainty associated with the unknown length of the acoustic waveguide is significantly reduced. In the paper, the acoustic waveguide parameters are taken into account using the FEM model and the AE signal propagation along a single-layer cylindrical waveguide is considered; such a model corresponds to the case of an uninsulated pipeline filled with a gaseous medium. The modeling took into account various possible source locations in the azimuthal direction along the line and in-depth, as well as various positions of the AE sensors. Analysis of the data obtained during the modeling showed an insignificant variability in the AE signal waveform for different positions of the AE source and the AE sensor compared to the variation of the noise parameters, which is a favorable factor in identifying useful signals against a noise background. However, it should be noted that the modeling did not take into consideration the influence of random factors associated with possible changes in the acoustic parameters of the material, the presence of a liquid medium inside a pipe and various wall thicknesses.

Long-term realization of technological noise measured in the factory conditions was considered as noise. Two types of noise signals with different parameters in the frequency and time domains were selected for analysis. Nonstationary impulse noise with a broadband spectrum and the duration of impulse components shorter than the duration of the useful AE signal, as well as stationary noise with continuous components and a narrow-band low-frequency spectrum, were studied. In both cases, a significant intersection of the frequency ranges of noise and useful signal was observed. The differences between noise and useful signals were determined using wavelet transformation. The choice of wavelet analysis as a method for presenting data is explained, firstly, by the high time and frequency resolution in the analysis of impulse signals and, secondly, by the possibility of universalizing the feature extraction procedure for various types of noise [28].

An effective solution was the use of wavelet kurtosis. Kurtosis is the fourth standardized moment of probability distribution, often used to detect a signal and determine the time of arrival [29]. In this study, kurtosis is used more effectively since it analyzes the coefficients of wavelet decomposition in time and frequency projections, which allows more reliable detection of the presence of a useful signal since the signal-to-noise ratio increases with wavelet decomposition. Secondly, the simultaneous assessment of time kurtosis and frequency kurtosis allows the detection of change points associated with the presence of useful signals, both in the time and in the frequency domain. The effectiveness of using wavelet kurtosis for signal analysis and detection of disorder moments is confirmed by a number of researchers [26,27].

A network with backpropagation of errors was used as a neural network, and an alternative solution could be to use a convolutional neural network to recognize a wavelet spectrogram without additional feature extraction. However, the use of classical neural network architecture made it possible to achieve the desired classification result due to the effective selection of features considering the useful signal parameters.

5. Conclusions

The paper demonstrates the possibility of detecting diffusion interlayers in dissimilar welded joints of pearlitic to austenitic steel using the AE method in structure health monitoring systems.

Diffusion interlayers under loading close to operating conditions do not generate AE hits with high amplitude and energy, but taking into account a priori information about the AE source parameters and the influence of the acoustic waveguide made it possible to achieve high reliability in detecting AE signals corresponding to a defect against a background of noise.

Considering a priori information in combination with the use of a wavelet pre-processed neural network classifier made it possible to ensure a correct classification result of about 90% in cases when the SNR ratio is less than −5 dB and about 80% in cases when the SNR ratio is less than −10 dB.