Pattern recognition of acoustic emission signals by Q235 steel corrosion in marine environment

2.1. Wavelet packet transform theory

Wavelet packet analysis adjusts the time-frequency window such that the time window becomes wider and the frequency window narrower at low frequencies, and vice versa at high frequencies. This provides excellent adaptability and time-frequency localization, making it highly effective for handling nonlinear and non-stationary signals.

The wavelet packet function can be expressed as:

where $j$ is the scale parameter, $k$ is the translation parameter, and $i$ is the modulation parameter.

The wavelet packet ${\psi }_i\left(t\right)$ can be obtained through the following recursion:

where ${\psi }_0\left(t\right)$ is the scale function, ${\psi }_1\left(t\right)$ is the wavelet basis function, $h\left(k\right)$ and $g\left(k\right)$ are the quadrature mirror filters associated with the scaling function and the wavelet basis function.

For signal $f\left(t\right)$, its wavelet packet decomposition coefficients can be defined as:

For the $i$-th node at the particular level $j$, its wavelet packet reconstruction coefficients can be expressed as:

The wavelet packet energy coefficient is an appropriate choice for analyzing the characteristics of acoustic emission signals, allowing for quantification of the frequency features of the signal. The analysis method involves performing a $j$-level wavelet packet decomposition on the detected signals. The signal is then divided into $2^j$ frequency bands, with the $i$-th frequency band defined as $\left(\frac{i-1}{2^j}{f}_{max},{\frac{i}{2^j}f}_{max}\right)$, $i=\mathrm{1,2},\dots ,2^j$. The original signal is represented as the sum of all wavelet packet components at the $j$-th level:

The energy of the wavelet packet components in the $i$-th frequency band can be expressed as:

The total energy of the signal is calculated as:

The energy coefficient of the $i$-th frequency band is defined as:

In such a manner, $P_i$ illustrates the energy coefficient distribution in each frequency band.

The flow process diagram of WPT is displayed in Fig. 1.

Fig. 1Flow process diagram of WPT

2.2. Principal component analysis

Principal Component Analysis (PCA) is an effective statistical technique to eliminate redundant information efficiently. The frequency band energy values obtained from the Wavelet Packet Transform are multidimensional feature data with strong correlations, which increase the computational load and complexity of data analysis. PCA performs an orthogonal transformation on these highly correlated multidimensional variables, yielding a smaller number of linearly independent principal components. This reduces the number of variables to be analyzed while preserving the maximum amount of information from the original data. The flow process diagram of PCA is described in Fig. 2.

Fig. 2Flow process diagram of PCA

First, the data must be centralized by calculating and removing the mean of each measurement, i.e.:

where $x_{ij}$ is the $j$-th feature of the $i$-th data and ${\overline{x}}_{ij}$ is the sample mean.

After centralizing the data, the new data matrix, $X_0$, is constructed. The next step is to calculate the sample covariance matrix, $R$:

Each element $R_{ij}$ of the covariance matrix R represents the covariance between the $i$-th and $j$-th features. To obtain the eigenvalues and corresponding eigenvectors of the sample covariance matrix $R$, the characteristic equation is solved, which is expressed as follows:

where $D$ is a diagonal matrix containing the eigenvalues arranged in descending order, i.e., $D=\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\left(t_1,t_2,\dots ,t_m\right)$, with $t_1>t_2>\dots >t_m$. $W$ is s the orthogonal matrix composed of the eigenvectors, with the $i$-th column of $W$ being the eigenvector corresponding to the eigenvalue $t_i$.

Next, the individual variance contribution ratio ($C$) and the cumulative variance contribution ratio ($F$) for each eigenvalue are calculated using the following formulas:

A larger variance contribution ratio ($C$) indicates a stronger ability of the principal component to explain the original variables. The first principal component usually has the largest contribution ratio. Similarly, a larger cumulative variance contribution ratio ($F$) corresponds to a greater proportion of the original information captured by the first k principal components. Typically, the first $k$ principal components are retained when the cumulative variance contribution ratio reaches 85 %.

Finally, the selected first $k$ principal components are used to construct the matrix, and the original data are projected onto the new principal component space as shown below:

3.1. Material and sample preparation

The material used in the experiment is Q235 low-carbon steel, with dimensions as shown in Fig. 3 as illustrated in Fig. 4(a), only a portion of the specimen is exposed to the corrosive environment, designated as the corrosion area, while the remainder of the surface in contact with the solution is covered with an anti-corrosion coating, including both sides and edges, ensuring full coverage. The experimental solution is a mixture of 5 % NaCl and 5 % Na₂SO₄ by mass, and the container used is a glass beaker.

As shown in Fig. 4(b), a substantial amount of reddish-brown corrosion products, mainly iron oxides, has formed on the specimen surface. Over time, the corrosion product layer thickens and accumulates due to gravity. Eventually, the adhesion between the product layer and the substrate becomes inadequate to support its own weight, causing the layer to peel off and form a downward sliding morphology. This phenomenon indicates that Q235 steel has experienced a relatively severe corrosion process in this environment.

Fig. 3Specimen dimension scheme

3.2. Experimental setup and test method

The acoustic emission detection equipment and α-series sensors from Physical Acoustics Corporation (PAC), USA, were used in the experiment. The threshold value is set at 45 dB to filter out most environmental noise, thus minimizing its impact. The filter range is simulated from 1 kHz to 1 MHz, covering the primary frequency band of the acoustic emission signals. The sampling rate is 1 MHz, and the maximum frequency of the collected acoustic emission signals is 500 kHz. The pre-trigger time is 100 µs, and the sampling length is 1k. The peak detection time (PDT), hit detection time (HDT), and hit lockout time (HLT) are 300 µs, 600 µs, and 1000 µs, respectively. The HLT value ensures that each collected acoustic emission signal avoids interference from reflected and late-arrival waves, capturing only localized changes in the material.

Fig. 4Pretreatment and corrosion samples

a) Pretreatment samples

b) Corrosion morphology samples

In the experiment, one end of the specimen is immersed in the solution to ensure complete coverage of the corroded area. A fixed magnet is used to position the sensor at the opposite end of the specimen, which is connected to the acoustic emission monitoring equipment and a computer for real-time monitoring of the corrosion signals. The corrosion process was monitored in real time for 10 days. And two parallel experiments were conducted. The experimental setup is illustrated in Fig. 5.

Fig. 5Schematic representation of the experimental setup

4.1. Feature extraction of AE signals

To investigate the relationship between the AE signals and the microstructural damage of Q235 steel under corrosion environment, 4-level wavelet packet decomposition using the db3 wavelet was applied to each collected AE signal.

For acoustic emission signals, it is essential to choose a discrete wavelet basis with properties similar to those of the signal, such as compact support, orthogonality, and regularity. The db3 wavelet basis meets these requirements and effectively preserves the signal's original features during the wavelet transform. It also performs well in signal compression and reconstruction, ensuring the accuracy of the analysis [25, 26].

After decomposition, the signals were decomposed into 16 frequency bands, ranging from low to high frequency at each scale, with a bandwidth of 31.25 kHz for each band. The energy coefficients were then calculated to analyze the frequency characteristics of the acoustic emission signals. Fig. 6 presents the typical acoustic emission signal waveform along with its corresponding energy coefficients obtained from the experiment.

Fig. 6The typical acoustic emission signal waveform and its energy coefficients

a) Acoustic emission signal waveform

b) Acoustic emission signal energy coefficients

Conducting a correlation analysis prior to cluster analysis enables a straightforward assessment of the degree of correlation among different WPT energy coefficients of acoustic emission signals. The formula for calculating the correlation coefficient between the energy coefficients is as follows:

where $r_p$ is the correlation coefficient, $\mathrm{cov}(P_i,P_j)$ is the covariance between variables $P_i$ and $P_j$, ${\sigma }_{P_i}$ and ${\sigma }_{P_j}$ is the standard deviation of each of the variables $P_i$ and $P_j$, $P_1$ to $P_{16}$ defined as the energy coefficients in the frequency bands 1-16.

The normalized data are substituted into Eq. (10), and the correlation coefficients of the energy values for each frequency band are presented in Table 1.

As shown in Table 1, the correlation between the energy coefficients varies, with certain parameters exhibiting generally higher correlation coefficients, such as those between $P_3$ and $P_7$, and between $P_4$ and $P_8$. Therefore, redundant information with high correlation should be eliminated.

PCA was applied to the energy coefficient data of each frequency band to achieve decorrelation and dimensionality reduction. The correlation matrix, eigenvalues, and eigenvectors were calculated, yielding the variance contribution ratios and cumulative variance contribution ratios for each principal component, as shown in Fig. 7.

Fig. 7The individual variance contribution ratios and cumulative variance contribution ratios of each principal component

As the number of principal components increases, the growth of the cumulative variance contribution ratio gradually slows. The cumulative variance contribution ratio for the first 6 principal components exceeds 86.96 %, capturing most of the information from the wavelet packet energy coefficients. Therefore, the first 6 principal components are selected as the feature set for each acoustic emission signal, and the original data are projected onto the new principal component space $X_{new}$. The eigenvectors corresponding to each principal component are presented in Table 2. The variables $t_1$ to $t_6$ represent the eigenvectors associated with the first six principal components extracted from the covariance matrix.

As illustrated in Table 2, these 6 principal components provide a comprehensive representation of the original data and are relatively independent. The proportions of the energy coefficient parameters are fairly balanced, with no significant bias, indicating that the processing results are satisfactory. The first principal component is strongly correlated with the $P_{11}$, $P_{12}$, and $P_{15}$ frequency bands, weakly correlated with the $P_9$, $P_{10}$, and $P_{16}$ frequency bands, and negatively correlated with the other frequency bands. In the second principal component, the $P_9$, $P_{10}$, $P_{16}$, and $P_{14}$ frequency bands show higher correlations.

Then using $X_{new}$ as the new matrix, cluster analysis of the signals was performed utilizing the $k$-means algorithm. The acoustic emission signals during the corrosion process are diverse, including signals from pit formation and expansion, bubble rupture, friction, detachment of corrosion products, and film rupture. Among these, the signals resulting from the friction-induced detachment of corrosion products shares a similar generation mechanism with that of the oxide film rupture, both resulting from activities such as creep, friction, and cracking between corrosion products and the membrane layer. Therefore, their signal characteristics are highly similar. Consequently, the number of clusters is set to 3, and clustering is performed on the dimensionality-reduced signals. The spatial distribution of each signal across the first three principal components is shown in Fig. 8. PCA 1, PCA 2, and PCA 3 refer to the first three principal components extracted through principal component analysis.

Fig. 8The spatial distribution of signals for each mode on the first three principal components

From Fig. 8, it can be observed that there are three signal modes in the corrosion process. The black color represents the signals of Mode 1, the red color represents those of Mode 2, and the blue color represents those of Mode 3. The data of each mode are relatively compact, with clear spatial separation between the modes, indicating good classification results. For signals of mode 1, the first principal component has a larger proportion and is negatively correlated with the third principal component, suggesting that the signals are characterized by a higher proportion of high-frequency bands, specifically the 11th and 15th frequency bands. For signals of mode 2, the first three principal components are more evenly distributed, indicating that the signals in this mode have a significant presence across all frequency bands. Compared to the signals of mode 2, the signals of mode 3 show greater correlation with the first and second principal components, indicating that the energy in the high-frequency bands is higher in Mode 3 than in Mode 2.

4.2. Relationship between AE signals and damage mechanisms correlated with Q235 steel corrosion

Corrosion of Q235 steel materials is a complex process. Chloride ions (Cl⁻) are aggressive and can penetrate the corrosion product film, reacting with the substrate, leading to surface damage and rupture of the film, thereby generating acoustic emission signals. Moreover, corrosion forms pits, and as these pits grow and expand, they also produce acoustic emission signals. Additionally, the accumulation of corrosion products and the friction and shedding between them can generate acoustic emission signals. Furthermore, gas bubbles are continuously formed during the corrosion process, and their rupture generates a small amount of acoustic emission signals.

The wavelet packet transform was applied to signals of different modes to obtain the energy coefficient plot. Typical acoustic emission signal waveforms and energy coefficient plots for three modes are shown in Fig. 9 and Fig. 10.

Fig. 9Waveforms of acoustic emission signals for three typical damage modes: a) mode 1; b) mode2; c) mode 3

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b)

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Fig. 10The energy coefficients distribution diagram of signals for three typical damage modes: a) mode 1; b) mode2; c) mode 3

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b)

c)

The quantity and variation of these signal for each mode collectively reflect the evolution of the entire corrosion process. By analyzing these variation patterns in detail, the specific signal mode can be determined. Fig. 11 presents the proportion of signals for each mode in each day.

By analyzing the variation in the quantity of signals for each mode in Fig. 11, the corrosion process is divided into three stages: early, middle, and late. During the early stage of corrosion (days 1-3), all signal types undergo changes. The signals of mode 1 decrease, with their proportion dropping from over 60 % on day 1 to around 20 % on day 3. The signals of mode 2 begin with a low proportion on day 1 but increase rapidly over the first three days, rising from 10 % to 50 %. The proportion of signals in mode 3 fluctuates between 20 % and 30 %. During the middle stage of corrosion (days 4-7), the signals of mode 2 consistently have the highest proportion, followed by those of mode 3, while the signals of mode 1 have the lowest. During this period, the signal proportions for all modes remain stable, at approximately 18 %, 48 %, and 34 %, respectively. The stability of all signal modes indicates that the system is gradually reaching equilibrium, and the corrosion process has entered a stable phase.

Fig. 11The proportion of the quantity of signals for each mode in each day

From the Fig 9 and 10, it can be seen that the signal of mode 1 is burst-type, characterized by a short rise time and duration. The energy distribution of this type of signal is relatively concentrated, with the energy proportions in the high-frequency bands of 312-343 kHz and 437-468 kHz both exceeding 25 %. In contrast, the energy proportions in the other frequency bands are all below 7.5 %. Bubble rupture is generally considered to occur instantaneously, lasting only a few dozen microseconds. The rapid release of pressure during rupture generates high-frequency elastic waves [27, 28]. Therefore, the signal of mode 1 is attributed to bubble rupture. In the early stage of corrosion, chloride ions (Cl⁻) in the sodium chloride solution cause localized areas on the Q235 steel surface to corrode, forming small pits or defects. These defect areas serve as the anode in electrochemical reactions, where metal dissolves and releases ions (e.g., Fe²⁺) into the solution. The non-corroded parts of the steel surface serve as the cathode. At the cathode, hydrogen ions (H⁺) are reduced to form hydrogen gas. This reduction reaction generates gas bubbles in the cathodic regions, leading to a higher number of bubble-related signals in the early stages. As corrosion progresses, corrosion products accumulate on the steel surface, slowing the corrosion rate. In addition, the concentration of the corrosive medium decreases due to ongoing reactions, reducing the rate of gas bubble generation and, consequently, the number of rupture signals.

The signal of mode 2 also exhibits burst characteristics, characterized by a slightly longer rise time and duration. The energy of the acoustic emission signal of mode 2 is relatively concentrated in the low-frequency bands, with the energy proportions in the frequency bands of 0-218 kHz reaching 60 %. The AE signal of pit growth is characterized by a short rise time and duration, with fewer high-frequency components. As a result, the signal of mode 2 is attributed to pit growth and expansion. During corrosion, these signals become the primary source of acoustic emissions, with their quantity significantly exceeding that of the other modes. In the early stage of pitting corrosion, the metal surface undergoes localized corrosion, leading to small holes or defects that gradually develop into pits. As corrosion progresses, corrosive ions in the solution react with the metal surface, causing the pits to expand and deepen. During this process, whenever the pit structure changes, such as cracking of the edges, increased depth, or formation of new defects, significant acoustic emission signals are generated. These signals reflect the microscopic damage to the material due to corrosion.

The signal of mode 3 is a continuous-type signal and has a long duration. Its energy distribution is more dispersed, with components present in the mid-to-low frequency bands of 0-125 kHz and 187-218 kHz, as well as the high-frequency bands of 312-343 kHz and 437-468 kHz. Signals from corrosion product shedding and oxide film rupture arise from interactions such as compression, friction, and cracking between the film layer and products, which is a gradual process. Thus, the signal of mode 3 is attributed to the detachment of corrosion products and the rupture of the oxide film. Due to the sample being placed at an inclined angle during the experiment, along with the small amount of corrosion products in the early stage and their weak adhesion in the solution, the corrosion products tend to slide off. What’s more, the mechanism of signals generated by oxide film breakdown is similar to that of signals from the shedding of corrosion products, as both phenomena result from activities such as creep, friction, and cracking between the corrosion products and the film layer. This leads to this mode signal exceeding 20 % in the early stage, with a similar proportion of approximately 32 % in the middle stage.

In the later stages of corrosion, as corrosion products accumulate, the thickness of the product layer gradually increases. This weakens the bond between the corrosion products, causing the previously tightly adhered product layer to become unstable. Large areas of the corrosion product layer begin to peel off, followed by the formation and accumulation of new corrosion products. This peeling phenomenon re-exposes parts of the metal substrate, previously protected by the corrosion product layer, to the corrosive environment, further accelerating material corrosion. This corresponds to the instability of the proportions of signals from different modes in the later stages of corrosion, as shown in Fig. 11. The proportion of mode 2 signals, representing the growth and expansion of pits, continues to increase, while the proportion of mode 1 signals decreases. The proportion of mode 3 signals decreases first, then increases.

4.3. Intelligent monitoring of steel corrosion condition based on convolutional neural network

After performing principal component analysis on the acoustic emission signals, a convolutional neural network (CNN) is applied to establish the nonlinear relationship between the AE signals and damage modes in the other set of experiments. The (CNN) is an architecture that utilizes convolutional layers for feature extraction and pooling layers for dimensionality reduction, combined with fully connected layers for classification. It excels in signal feature extraction and pattern recognition, which is why it has become a crucial tool in this field.

Fig. 12Schematic diagram of the convolutional neural network architecture

Fig. 12 illustrates the structure of the convolutional neural network adopted in this work. The input layer data comes from the 6 key principal components extracted by PCA. These principal components summarize and represent the core information of the signals. The CNN consists of two convolutional layers and one max-pooling layer. It utilizes the ReLU activation function and produces the final output through a fully connected layer, followed by a Softmax layer and a classification layer. The dataset is randomly shuffled and divided into training and test sets in a 7:3 ratio. The maximum number of iterations is set to 500, and the learning rate to 0.001.

Fig. 13Confusion matrix of the training results

a) Confusion matrix of the training set

b) Confusion matrix of the test set

Fig. 14Statistical analysis of corrosion damage modes based on convolutional neural network recognition results

Fig. 13 illustrates the confusion matrix of the convolutional neural network training results. The confusion matrix of the training set shows that with a large dataset, the neural network performs well. The recognition rates for mode 1 and mode 3 signals reach 98.6 % and 99.4 %, respectively, while the recognition rate for mode 2 signals, though lower, still reaches 97.9 %. When applied to the test set, the neural network demonstrates an accuracy of over 97 % in identifying the three damage modes in the acoustic emission signals. This result indicates that the convolutional neural network has excellent self-learning capabilities and strong generalization performance, enabling it to accurately identify different damage modes during the corrosion process based on the acoustic emission signal characteristics. The constructed convolutional neural network was utilized to perform pattern recognition on another set of acoustic emission signals collected during the corrosion process, and the recognition results were statistically analyzed, as shown in Fig. 14. The result provides an intuitive demonstration of the dynamic evolution behavior of Q235 steel during corrosion. The fluctuation in the curve shown in the figure reflects the transition of the corrosion state.