Recognition of Intergranular Corrosion in AISI 304 Stainless Steel by Integrating a Multilayer Perceptron Artificial Neural Network and Metallographic Image Processing

Abstract

The correct management of operations in thermoelectric plants is based on the continuous evaluation of the structural integrity of its components, among which there are elements made of stainless steel that perform water conduction functions at elevated temperatures. The working conditions generate progressive wear that must be monitored from the perspective of the microstructure of the material. When AISI 304 stainless steel is subjected to a temperature range between 450 and 850 °C, it is susceptible to intergranular corrosion. This phenomenon, known as sensitization, causes the material to lose strength and generates different patterns in its microstructure. This research analyzes three different patterns present in the microstructure of stainless steel, which manifest themselves through the following characteristics: the absence of intergranular corrosion, the presence of intergranular corrosion, and the precipitation of chromium carbides. This article shows the development of a methodology capable of recognizing the corrosion patterns generated in stainless steel with an accuracy of 98%, through the integration of a multilayer perceptron neural network and the following digital image processing methods: phase congruence and a gray-level co-occurrence matrix. In this way, an automatic procedure for the analysis of the intergranular corrosion present in AISI 304 stainless steel using artificial intelligence is proposed.

1. Introduction

Stainless steels are alloys containing approximately 12% chromium [1]. In an oxidizing atmosphere, this percentage of chromium (Cr) is sufficient for the formation of an adherent layer of chromium oxide (Cr203), also called chromite, which protects the steel from corrosion. Considering their metallurgical structure, stainless steels are classified into austenitic, martensitic, and ferritic [2].

Austenitic stainless steels are used daily in the power generation industry, particularly in thermoelectric plants because of their excellent corrosion resistance and structural stability. The alloy AISI 304 is an austenitic stainless steel with a cubic structure with centered faces; the large amounts of chromium and nickel give the stainless steel an excellent resistance to corrosion caused by oxidizing agents [3] (see

Table 1. AISI 304 stainless steel composition. ASTM A240.

C	Mn	S	P	Si	Cr	Ni	N
0.07	2.0	0.03	0.045	0.75	17.5–19.5	8.0–10.5	0.10

).

AISI 304 steel is used to manufacture boiler conductors in thermoelectric plants, which translates into elevated temperature working conditions and attack from external oxidizing agents such as humidity. The permanence of the steel in the temperature zone between 450 and 850 °C causes the precipitation of carbon through the generation of chromium-abundant carbides of the M23C6 type [4]. The main change that occurs after stainless steel’s exposure is the appearance of susceptibility to intergranular corrosion, linked to the modification of the structure and the alteration of the mechanical properties of the material and, consequently, the generation of unexpected failures in the conductors and equipment in service [5].

In AISI 304 stainless steel, there are different states that are related to the duration and temperature of heat to which the material has been subjected; at temperatures close to 500 °C, carbides are manifested at the grain boundary as a thin and continuous sheet, i.e., at that time, there is no intergranular corrosion; see Figure 1a. When the steel is in operating conditions with temperatures close to 700 °C, the carbides take dendritic forms that develop at the intersection of the grain boundaries, where they start their agglomeration; under this morphology, intergranular corrosion starts; see Figure 1b. With increases in the working time and temperatures near 850 °C, the fine dendritic form of chromium carbide gradually transforms into a sizable nucleation that precipitates toward the grain boundary, giving way to a compromised condition for the material to continue operation [6]; see Figure 1c.

This paper presents the development of a methodology that allows for the recognition of intergranular corrosion patterns generated in stainless steel from the integration of a multilayer perceptron artificial neural network (ANN) and the following digital image processing methods: phase congruency and gray-level co-occurrence matrix (GLCM), which will give way to an automatic diagnosis of the condition of stainless steel based on artificial intelligence. This study provides a comparison of the processing methods applied on metallographic images of AISI 304 stainless steel, to identify the appropriate characterization method for the task of recognizing the distinct stages of intergranular corrosion present in the material.

After a brief introduction in Section 1, this article proceeds with a literature review of the topic addressed and is organized as follows: Section 2 contains a description of the methods used for digital image processing, as well as the data generated to train and test the ANN. The results of the experiments and validation are presented in Section 3. Finally, the discussion of the results and conclusions from the proposed methodology constitute Section 4 and Section 5, respectively.

Bibliographic Review

Research has been conducted demonstrating the benefits of artificial intelligence in the field of materials to develop expert systems focused on data analysis and failure diagnosis [7,8,9]. Artificial neural networks have been present in stainless steel to solve classification, recognition, and estimation tasks. In the work shown by Yetim et al. [10], the wear rate of 316L stainless steel was predicted by using artificial neural networks. The results showed that the CrN and γ’-Fe4N phases of the steel are present at temperatures above 400 °C, while the S-phase formed at temperatures below 400 °C.

In the research developed by Desu et al. [11], the mechanical properties of 304L and 326L austenitic stainless steels subjected to elevated temperatures were studied using artificial neural networks trained to predict different mechanical properties, such as the elongation and strength coefficient. Lakshmi et al. [12] demonstrate the efficiency of an artificial neural network to predict the flow stress of austenitic stainless steel 304 during its heat deformation from the perspective of the following variables: voltage and temperature.

The work presented by Gupta et al. [13] addresses the implementation of deep learning technologies to predict the tribological characteristics of 316 stainless steels versus a 100 Cr6 alloy. The coefficient data and friction forces from the experiments were used to develop the different deep learning models, and the performance of the learning model demonstrated higher levels of accuracy. In Mohamed et al. [14], the development of a system based on an artificial neural network to detect cracks in steel and estimate their depth from 2D images was reported. Automatic crack detection is needed to reduce costs and improve the quality of surface inspection for infrastructure maintenance. The performance of the system is comparable to the state of the art and provides an applicable and affordable inspection device. The research by Ai et al. [15] shows the development of an automated method for damage localization in stainless steel structures using acoustic emission signals and a convolutional neural network based on weighted ensemble regression. A data fusion approach was designed to integrate the waveform information into three types of images. A convolutional neural network supported by weighted ensemble regression was proposed to analyze the images and calculate the damage coordinates.

In the area of study related to stainless steel, artificial neural networks have covered tasks such as wear estimation, crack detection, and damage localization generated in stainless steel. Regarding the integration of digital image processing and artificial neural networks applied to the recognition of wear patterns generated in metallographic images, the following works have been presented: In Prasad et al. [16], the classification of machined surfaces was performed using image processing and machine learning techniques. The images were preprocessed to extract GLCM-based features and sent to a classifier such as a support vector machine. The research by Gapsari et al. [17] analyzes the corrosion inhibition efficiency of carbon steel specimens based on images characterized using a gray-level co-occurrence matrix (GLCM) and a support vector machine. Darnton and Ruzzene [18] employ phase congruency processing to visualize the extent of subsurface damage in aluminum structures. Sommer et al. [19] used binarization-based digital image processing from illumination and contrast invariant measurements to quantify the porosity of AISI 316L stainless steel. Küllaç and Çuvalcı [20] applied the principles of phase congruence by implementing Fourier transform on turned surfaces to identify their wear.

As can be seen, the main digital image processing techniques used for the characterization of microstructures in steels that have suffered different types of damage are phase congruence and feature extraction based on GLCMs. Regarding classification and recognition tools, the use of classifiers such as the support vector machine is highlighted; however, in the studies developed by Guerrero et al. [21] and Bennett-Lenane et al. [22], it is shown that multilayer artificial neural networks classify patterns more efficiently than the support vector machine, in terms of sensitivity, specificity, and accuracy. Based on the above, the research methodology is structured according to the literature review; it is necessary to compare the characterization techniques used so far to digitally process metallographic images and evaluate their performance with a classifier such as a multilayer artificial neural network, and establish a mechanism capable of recognizing intergranular corrosion from microstructural images at different stages of degradation. The presented study describes a methodology capable of automatically identifying the presence of intergranular corrosion in stainless steel and recognizing the phase in which the corrosion is found in AISI 304 stainless steel, with only the digital processing of the information contained in the metallographic image under the pattern recognition approach.

2. Materials and Methods

The intergranular corrosion generated in AISI 304-type stainless steel as a consequence of working in high-temperature environments manifests itself in the microstructure of the material in an iterative way from the beginning to the end of its useful life; in this way, it is possible to recognize three different metallographic patterns present in the microstructure of AISI 304 stainless steel (see Figure 1a showing no intergranular corrosion (NIC), Figure 1b showing the presence of intergranular corrosion (PIC), and Figure 1c showing the precipitation of chromium carbides (PCC)).

The metallographic images containing the microstructure of stainless steel was obtained from optical microscopy techniques for further processing. There is a standardized process for obtaining a metallographic image that consists of consecutive activities [23]. It starts with cutting the stainless steel to examine a section of the material; the stainless steel section is placed in a specimen that is sanded and a 4% concentration of Nital solution is applied. As a last step, the specimen is placed under an inverted microscope so that the user can visualize the microstructure of the material at 100× magnification and determine the presence or absence of intergranular corrosion.

The methodology for the development of the research consists of two stages: the first corresponds to the digital processing of the metallographic image and the second stage corresponds to the development of an artificial neural network focused on the recognition of the different corrosion phases present in the microstructure of stainless steel. In the first stage corresponding to the digital processing of the metallographic image, two efficient characterization methods are applied: phase congruence and GLCM. The main objective of digital processing is to provide a correct input signal to the ANN for its subsequent recognition stage.

2.1. Digital Processing of the Metallographic Image Using the Phase Congruency Method

Digital image processing involves a set of computer algorithms that is applied to digital images with the aim of processing, visualizing, and improving their quality. By applying digital image processing methods, it is possible to extract key features describing the texture of an image for further processing [24]. According to [25,26], phase congruence in terms of Fourier series provides an efficient characterization of digital images through the application of different filters and is expressed as shown in Equation (1).

$$PC\left(x\right)=ma{x}_{\overline{\varphi }\left(x\right)ϵ\left[\mathrm{0,2}\pi \right]}\frac{{\sum }_n{A}_{n}cos({\varphi }_n\left(x\right)-\overline{\varphi }\left(x\right))}{{\Sigma }_n{A}_n}$$

(1)

where $A_n$ represents the amplitude of the $n$ Fourier component. ${\varphi }_n\left(x\right)$ is the local phase of the Fourier component at position $x$. $\overline{\varphi }\left(x\right)$ represents the angle-weighted average amplitude of the local phase of all Fourier terms; see Figure 2. On the other hand, the local energy function is defined in Equation (2):

$$E\left(x\right)=\sqrt{F{\left(x\right)}^2+H{\left(x\right)}^2}$$

(2)

where F(x) is the luminance signal I(x) with its congruency difference component removed, and H(x) is the transform of F(x), with a phase increment of 90 degrees.

In [27,28,29], it shown that employing logarithmic Gabor filters are extremely useful for image rendering. In the present study, the logarithmic filter functions are employed using a Gaussian transfer function, as suggested by [30]. Therefore, the response vector for each of the filter pairs is determined through Equation (3). As mentioned above, $I\left(x\right)$ represents the luminance signal, and $M_n^e$ and $M_n^o$ symbolize the even (cosine) and odd (sine) symmetric wavelets at scale n, respectively; therefore, the results of each quadrature filter pair constitute a response vector. The wavelet amplitude transforms at a given scale for each component $n$ and is defined in Equation (3).

$$A_n\left(x\right)=\sqrt{{(I\left(x\right)*M_n^e)}^2+{(I\left(x\right)*M_n^o)}^2}$$

(3)

The phase is determined by Equation (4).

$${\varphi }_n\left(x\right)=atan2\left(I\left(x\right)*M_n^e,I\left(x\right)*M_n^o\right)$$

(4)

At each point $x$ of any signal, a matrix of response vectors generates one vector for each filter scale. These response vectors form the localized representation of the signal and are used in the same way as the Fourier components to estimate the phase congruency. The construction of the wavelet filter bank should ensure that the transfer function of each filter overlaps sufficiently with its neighbors so that the sum of all the transfer functions forms a uniform coverage of the spectrum. Care should be taken to preserve a wide range of frequencies in the signal, because phase congruency is only significant when it occurs over a wide range of frequencies. On the other hand, $F\left(x\right)$ can be estimated by summing the convolutions of the even filters using Equation (5). Similarly, $H\left(x\right)$ can calculated from the convolutions of the odd filters using Equation (6).

$$F\left(x\right)=\sum _{n}I\left(x\right)*M_n^e$$

(5)

$$H\left(x\right)=\sum _{n}I\left(x\right)*M_n^o$$

(6)

The sum of the amplitudes of the frequency components in F(x) is determined using Equation (7).

$${\sum }_n{A}_n\left(x\right)={\sum }_n\sqrt{{(I\left(x\right)*M_n^e)}^2+{(I\left(x\right)*M_n^o)}^2}$$

(7)

It is of vital importance to consider that phase congruency can compromised due to noise present in the input signal. The incidence of noise in the calculation of $E\left(x\right)$ can be deduced under the following conditions: the image noise is additive; the noise power spectrum is constant; and the features originate only in isolated areas of an image. The energy is the magnitude of a vector sum. If the noise exhibits Gaussian behavior with random phase, each vector of this sum will consist of two normally distributed independent variables. Thus, the distribution of the position of each vector will be a two-dimensional Gaussian centered at the origin. It is possible to establish an expected value of energy due to noise, as an evaluation of the mean ${\mu }_R$ in the energy distribution and, therefore, to determine its variance ${\sigma }_R^2$. With the intention of decreasing the effects, a noise factor $T$is considered, and is expressed as shown in Equation (8).

$$T={\mu }_R+k{\sigma }_R$$

(8)

where k is the number of standard deviations in a range from 2 to 3; in the present work, a value of 2 is considered. On the other hand, the mean of the distribution ${\mu }_R$ and the variance ${\sigma }_R^2$ are obtained using Equations (9) and (10), respectively [31].

$${\mu }_R={\sigma }_G\sqrt{\frac{\pi }{2}}$$

(9)

$${\sigma }_R^2=\frac{4-\pi }{2}{\sigma }_G^2$$

(10)

where ${\sigma }_G^2$ is the variance of the normal distribution describing the position of the total energy vector.

Finally, the phase congruence of the image is obtained using Equation (11).

$$PC\left(x\right)=\frac{⌊E\left(x\right)-T⌋}{\sum _n{A}_n\left(x\right)+\epsilon }$$

(11)

The digital processing of the metallographic image is exemplified in Figure 3. Figure 3a shows the original metallographic pattern, which will subsequently be set to grayscale function and the median filter will be applied to it. Finally, a threshold is necessary to perform binarization of the metallographic pattern that is present in the stainless steel microstructure (Figure 3b) [32].

Phase congruence is applied in five scales to each of the six orientations established for the filter bank, which generates the characterization vector of thirty components.

Table 2. Vectors generated by the phase congruence method.

Component	Metallographic Patterns Generated in the Microstructure of AISI 304 Stainless Steel
	NIC	PIC	PCC
1	5.3159	4.9938	0.9298
2	7.9265	9.7508	1.6579
3	8.5655	14.3055	2.7167
4	7.5030	13.4716	4.8411
5	5.4449	8.8230	7.2431
6	5.6887	4.9894	0.9540
7	8.3048	9.5880	1.6770
8	8.8012	14.1052	2.7884
9	7.6352	13.4266	5.0512
10	5.3438	8.9049	7.5339
11	6.1157	4.9800	0.9552
12	8.8028	9.5746	1.6814
13	9.1595	14.0507	2.8174
14	7.8581	13.3929	5.1690
15	5.5829	8.8504	7.7330
16	6.1266	4.9564	0.9377
17	8.9701	9.6936	1.6947
18	9.4814	14.2718	2.8464
19	8.1151	13.6235	5.2423
20	5.7155	8.9897	7.5972
21	6.1105	5.1438	0.9102
22	8.8957	9.9253	1.6098
23	9.3805	14.4633	2.7363
24	8.0535	13.8608	5.0907
25	5.6936	9.1759	7.5296
26	5.6720	5.1510	0.9024
27	8.3202	9.9727	1.5837
28	8.8045	14.5427	2.6544
29	7.6466	13.7590	4.8481
30	5.6399	9.0081	7.2917

shows the components of the characterization vector of three different metallographic patterns processed by the phase congruence method. It is necessary to digitally process each of the metallographic images of the stainless steel that contain a pattern representative of the damage generated in the material, with the purpose of storing the vectors in a database so that they can later be converted into input information for the artificial neural network.

2.2. Digital Processing of the Metallographic Image Using the Gray-Level Co-Occurrence Matrix Method

Texture analysis is an important task in digital image processing operations; texture analysis refers to the characterization of certain sections present in an image by their texture content. A statistical procedure for examining texture that considers the spatial relationship of pixels is the gray-level co-occurrence matrix (GLCM). The GLCM method is based on characterizing the texture of an image by calculating how often pairs of pixels that reveal specific values and are in a specific spatial relationship occur in an image, generating a GLCM and subsequently extracting statistical parameters from this matrix [16]. In the works presented in [33,34], the advantages of the GLCM method for texture analysis in images are demonstrated. Within the focused statistics for the study of texture, fourteen equations will be employed that extract texture properties of diverse types of images, considering their statistical nature from the GLCM and the texture statistical parameters presented in Equations (12)–(25):

Second angular momentum/energy:

$$f_1=\sum _i{\sum _j\left\{p\left(i,j\right)\right\}}^2$$

(12)

where

$$p\left(i,j\right)=\mathrm{normalized} \mathrm{co}\text{-}\mathrm{occurrence} \mathrm{matrix}.$$

Contrast:

$$f_2={\sum }_{n=0}^{N_{g-1}}{n}^2\left\{\begin{array}{c}\sum _{i=1}^{N_g}\sum _{j=1}^{N_g}p\left(i,j\right)\\ \left|i-j\right|=n\end{array}\right\}$$

(13)

where

$$N_g=\mathrm{number} \mathrm{of} \mathrm{discrete} \mathrm{intensity} \mathrm{levels} \mathrm{in} \mathrm{the} \mathrm{image}.$$

Correlation:

$$f_3=\frac{\sum _i\sum _j\left(ij\right)p\left(i,j\right)-{\mu }_x{\mu }_y}{{\sigma }_x{\sigma }_y}$$

(14)

where ${\mu }_x,{\mu }_y,{\sigma }_x$, and ${\sigma }_y$ are the means and standard deviations of $p_x$ and $p_y$.

Variance:

$$f_4={\sum }_i{{\sum }_j\left(i-\mu \right)}^{2}p\left(i,j\right)$$

(15)

Moment of inverse difference:

$$f_5={\sum }_i\frac{1}{1+{\left(i-j\right)}^2}p(i,j)$$

(16)

Sum of averages:

$$f_6={\sum }_{i=2}^{2N_g}i{p}_{x+y}\left(i\right)$$

(17)

where

$$p_{x+y}={\sum }_{i=1}^{N_g}{\sum }_{j=1}^{N_g}p\left(i,j\right); \left|i+j\right|=2,3\dots 2N_g$$

Sum of variances:

$$f_7={\sum }_{i=2}^{2N_g}{\left(i-f_8\right)}^2{p}_{x+y}\left(i\right)$$

(18)

Sum of entropies:

$$f_8=-{\sum }_{i=2}^{2N_g}{p}_{x+y}\left(i\right)\log \left\{p_{x+y}\left(i\right)\right\}$$

(19)

Entropy:

$$f_9=-{\sum }_i{\sum }_{j}p\left(i,j\right)\log \left(p\left(i,j\right)\right)$$

(20)

Variance Difference: The texture variance difference is a measure of the variation in pixel intensity between a given set of pixels. High variance difference values indicate that there is a significant variation in pixel intensity between a given set of pixel gray levels. In case of low variance difference values, they reveal that there are fewer transitions between the values of gray level pairs. Visually, a texture with a higher variance difference value may appear noisy, while a texture with a lower variance difference value will appear more homogeneous.

$$f_{10}=varianzade{p}_{x-y}$$

(21)

where

$$p_{x-y}={\sum }_{i=1}^{N_g}{\sum }_{j=1}^{N_g}p\left(i,j\right); \left|i-j\right|=0,1\dots N_g-1$$

Entropy Difference: This indicator quantifies the randomness or unpredictability of the distribution of differences between the gray levels of pixel pairs. It is a measure of the entropy of the histogram of differences between pixel pairs, which captures the granularity of the texture. Logarithms are an alternative for handling exponential values and a logarithmic scale allows for better visualization of the variations and patterns of randomness between the gray levels of pixel pairs. The sum product between a normalized matrix and a logarithmic expression generates a measure of entropy dispersion present in the histograms between pixel pairs, and the negative value refers to the difference between the two entropy values.

$$f_{11}=-{\sum }_{i=0}^{N_{g-1}}{p}_{x-y}\left(i\right)\log \left\{p_{x-y}\left(i\right)\right\}$$

(22)

Correlation measures (23) and (24):

Equation (23) evaluates the correlation between the probability distributions of$i$ and $j$, weighting the texture complexity. The numerator is defined as $HXY-HXY1$, and, consequently, is $\le 0$. In the case of the denominator, it is divided by the maximum of the 2 marginal entropies, where, in case of a total dependence, a value of $f_{12}=-1$ will be reached, since $HX=HY$. In a scenario where a flat region is analyzed, an arbitrary value of 0 is set.

$$f_{12}=\frac{HXY-HXY1}{max\left\{HX,HY\right\}}$$

(23)

where

$$HX=-{\sum }_{i=1}^{Ng}{p}_x\left(i\right){log}_2\left(p_x\left(i\right)\right)$$

$$HY=-{\sum }_{i=1}^{Ng}{p}_y\left(j\right){log}_2\left(p_y\left(j\right)\right)$$

$$HXY=-{\sum }_{i=1}^{Ng}{\sum }_{j=1}^{Ng}p\left(i,j\right){log}_2\left(p\left(i,j\right)\right)$$

$$HXY1=-{\sum }_{i=1}^{Ng}{\sum }_{j=1}^{Ng}p\left(i,j\right){log}_2(p_x\left(i\right)*p_y\left(j\right))$$

Equation (24) also weights the correlation between the two probability distributions of the image. A value of 0 represents the case where the two distributions are independent, i.e., there is no correlation in the information. A value close to one represents a scenario where the two distributions are dependent.

$$f_{13}={\left(1-exp\left[-2.0\left(HXY2-HXY\right)\right]\right)}^{1/2}$$

(24)

where

$$HXY2=-{\sum }_{i=1}^{Ng}{\sum }_{j=1}^{Ng}{p}_x\left(i\right)*p_y\left(j\right){log}_2(p_x\left(i\right)*p_y\left(j\right))$$

Maximum correlation coefficient:

$$Q\left(i,j\right)=\sum _k\frac{p\left(i,k\right)p(j,k)}{p_x\left(i\right)p_y\left(k\right)}$$

(25)

The descriptors are applied to each of the metallographic images of the stainless steel containing an intergranular corrosion pattern in its microstructure, with the objective of storing the vectors in a database to consecutively convert the input signal to the artificial neural network.

Table 3. Vectors generated using the gray-level co-occurrence matrix method (GLCM).

Component	Metallographic Patterns Generated in the Microstructure of AISI 304 Stainless Steel
	NIC	PCI	PCC
1	0.6892	0.8341	0.3379
2	0.1568	0.0377	0.1270
3	0.7584	0.9059	0.9525
4	33.9203	34.6487	39.3598
5	0.9462	0.9818	0.9406
6	11.6236	11.7699	12.3639
7	119.3224	129.0370	125.8385
8	0.7525	0.4440	1.3812
9	1.2512	0.6807	2.1270
10	0.1435	0.0441	0.1126
11	0.3699	0.1580	0.3759
12	−0.4078	−0.6376	−0.6365
13	0.6879	0.6864	0.9288
14	0.7645	0.9083	0.9772

shows different examples of characterization vectors for each of the intergranular corrosion patterns using the GLCM method.

2.3. Training of the ANN Using the Phase Congruence Method

The human brain is made up of interconnected neurons and can think and interpret information to provide an efficient solution to the problems posed. Scientists have tried to computationally model qualities related to the functioning of the human brain; the result has been artificial neural networks. Currently, artificial neural networks present a series of characteristics of the brain, for example, they learn from experience, have generalization capacity, and abstract important characteristics of data sets [35].

The multilayer perceptron artificial neural network used in the present investigation employs supervised training from the vectors generated by the characterization methods. The set of metallographic images containing the microstructures with the damage patterns generated in stainless steel is used to train and test the ANN with a total of 538 metallographic images previously recognized by experts; see

Table 4. Training and testing matrix.

	Phase Congruence Method		GLCM Method
	Training	Test	Training	Test
Images	411	127	411	127
Metallographic pattern	Dimension		Dimension
NIC	145 × 30	45 × 30	145 × 14	45 × 14
PCI	167 × 30	50 × 30	167 × 14	50 × 14
PCC	99 × 30	32 × 30	99 × 14	32 × 14

.

The hyperbolic tangent activation function is implemented in the multilayer perceptron neural network so that the input signal values are efficiently transformed over an interval ranging over [−1, 1]. The hyperbolic tangent activation function achieves symmetric and balanced outputs, which allows for the modeling of nonlinear relationships between data more accurately [36]. Recognizing and classifying intergranular corrosion patterns in AISI 304 stainless steel from digital processing of metallographic images is a scenario where the relationships between variables are of the nonlinear type, thus justifying the use of the hyperbolic tangent activation function. On the other hand, since the ANN will be trained and tested to perform the task of classifying and recognizing three types of corrosion patterns, it was decided to proportionally divide the output interval of the activation function; thus, the objective values will be balanced with an equivalent distance.

The target values required by the artificial neural network to perform the task of classification and recognition of the metallographic patterns present in AISI 304 stainless steel are assigned as follows: (−1) for materials with precipitation of chromium carbides (PCC), (0) for materials with presence of intergranular corrosion (PCI), and (1) for materials that do not present intergranular corrosion (NIC); therefore, the activation function used is a sigmoidal tangent. The ANN performs the estimation based on the synaptic weights and the bias generated from an iterative process, and according to [37], the general operation of the multilayer perceptron artificial neural network is based on Equation (26):

$$\mathrm{m}=({\omega }_i*p_i)’+\mathrm{b}$$

(26)

where ${\omega }_i$ is the weight factor that the network assigns to the input information, $p_i$ corresponds to the input signal, and $b$ is the bias determined by the network. The activation function is expressed in Equation (27) and provides an output in the interval [−1, +1].

$${\mathrm{f}}_{\mathrm{k}}\left(\mathrm{m}\right)=\frac{{\mathrm{e}}^{\mathrm{m}}-{\mathrm{e}}^{-\mathrm{m}}}{{\mathrm{e}}^{\mathrm{m}}+{\mathrm{e}}^{-\mathrm{m}}}$$

(27)

The neural network architectures were developed dynamically by constructing an algorithm based on exhaustive experimentation conditioned to cycles to test the total number of possible combinations of topologies. The first parameter considered is the number of neurons in the hidden layer with an interval of [5, 200]. The second parameter is the learning rate with an increment factor of 0.001 [0.005, 0.9]. The allowed error was set to only two possibilities: 1 × 10⁻⁴ and 1 × 10⁻⁵. Finally, a stop in training was set through the down-gradient method if the error function did not improve by at least 0.0001 for 150 iterations. For each architecture, its output is recorded in a database to proceed to calculate the mean squared error against the previously established target values and this was the mechanism for selecting the winning topology. The advantage of the proposed procedure is to ensure a global minimum and avoid falling into local minima.

The ANN topologies proposed in

Table 5. Topologies of artificial neural networks developed for the training phase.

Topologies	1	2	3	4	5	6
Number of neurons	54	54	55	55	56	56
Learning rate	0.01	0.005	0.01	0.005	0.01	0.005
Allowed error	1 × 10−4	1 × 10−5	1 × 10−4	1 × 10−5	1 × 10−4	1 × 10−5
Number of iterations	1293	2420	1457	1632	1050	2130
MSE	0.091	0.106	0.095	0.088	0.095	0.103

adequately fit the 411 target values of the corresponding metallographic pattern in the training phase, which is why the mean squared error (MSE) used to determine which ANN architecture should be selected for the test phase with the remaining 127 images.

The ANN 4 topology presented a better fit in the training phase by registering a lower MSE index (0.088); therefore, it will used in the test phase. See

Table 6. Selected topology.

Parameter	Specification
Neurons hidden layer	55
Activation function	Sigmoidal tangent
Learning rate	0.005
Allowed error	1 × 10−5
Number of iterations	1632
MSE	0.088
Convergence time	00:01:13

.

Once the information is processed through ANN, the following weights and bias matrices are obtained:

W₁: synaptic weights of the first layer (55 × 30):

$${\mathrm{W}}_1=\left[\begin{array}{ccccc}-0.0767& -0.0553& \cdots & -0.0477& -0.0235\\ 0.1308& -0.0414& \cdots & 0.0383& 0.0386\\ ⋮& ⋮& \ddots & ⋮& ⋮\\ 0.0514& 0.0064& \cdots & -0.0094& -0.2929\\ -0.0671& -0.0197& \cdots & 0.0684& -0.0362\end{array}\right]$$

b₁: bias of the first layer (1 × 55):

$${\mathrm{b}}_1=\left[\begin{array}{ccccc}2.7675& -2.7125& \cdots & 2.6527& -1.8140\end{array}\right]$$

W₂: synaptic weights of the hidden layer (1 × 55):

$${\mathrm{W}}_2=\left[\begin{array}{ccccc}-0.2024& -0.0995& \cdots & -0.5504& 0.2546\end{array}\right]$$

b₂: hidden layer bias (1 × 1):

$${\mathrm{b}}_2=\left[-0.0523\right]$$

2.4. ANN Training Using the GLCM Method

For the textural characterization method of the GLCM, the topologies of artificial neural networks developed in the training phase that present a correct efficiency are shown in

Table 7. Topologies of artificial neural networks.

Topologies	1	2	3	4	5	6
Number of neurons	80	80	90	90	100	100
Learning rate	0.005	0.01	0.005	0.01	0.005	0.01
Allowed error	1 × 10−4	1 × 10−4	1 × 10−4	1 × 10−4	1 × 10−4	1 × 10−4
Number of iterations	15,125	22,921	18,450	18,419	14,349	14,413
MSE	0.0192	0.1268	0.0323	0.0251	0.1064	0.0219

, and again, the selection criterion is the MSE statistic.

The ANN 6 topology presented a better fit in the training phase by registering a lower MSE index (0.0219); therefore, it will used in the test phase. See

Table 8. Selected topology.

Parameter	Specification
Neurons hidden layer	100
Activation function	Sigmoidal tangent
Learning rate	0.01
Allowed error	1 × 10−4
Number of iterations	14,413
MSE	0.0219
Convergence time	00:07:06

.

After the iterative process, the ANN provides the following matrices:

W₁: synaptic weights of the first layer (100 × 14):

$${\mathrm{W}}_1=\left[\begin{array}{ccccc}-3.0273& 4.3698& \cdots & 3.3214& -4.4911\\ 2.3262& 2.1168& \cdots & 1.3786& -4.3327\\ ⋮& ⋮& \ddots & ⋮& ⋮\\ 1.0979& -0.2433& \cdots & -5.1740& 4.6218\\ -2.3543& -5.0160& \cdots & -2.5376& 5.6513\end{array}\right]$$

b₁: bias of the first layer (1 × 100):

$${\mathrm{b}}_1=\left[\begin{array}{ccccc}25.4275& 7.5885& \cdots & -9.7822& -17.0344\end{array}\right]$$

W₂: synaptic weights of the hidden layer (1 × 100):

$${\mathrm{W}}_2=\left[\begin{array}{ccccc}0.2244& 0.5309& \cdots & 0.0876& -0.1545\end{array}\right]$$

b₂: hidden layer bias (1 × 1):

$${\mathrm{b}}_2=\left[0.0331\right]$$

3. Results

To verify the performance of the ANN in the recognition task, 127 metallographic images not included in the training process were introduced, and in this way, the artificial neural network was subjected to the testing stage. To validate both processing methods, it was necessary to verify that the characterization of the metallographic image was correct and provided detailed information to the ANN. Both the characterization methods compared the phase congruence and GLCM.

3.1. Recognition of Metallographic Patterns from the Phase Congruency Method

The recognition process performed by ANN from the characterization using the phase congruence method is exemplified by analyzing a metallographic image with the presence of intergranular corrosion that was not included in the training phase.. Considering the general operation of the multilayer perceptron ANN and the sigmoidal tangent activation function, Equations (28) and (29) are defined, respectively, as follows:

$${\mathrm{m}}_1=({\mathrm{W}}_1*\mathrm{P})’+{\mathrm{b}}_1$$

(28)

$${\mathrm{m}}_2=\frac{{\mathrm{e}}^{{\mathrm{m}}_1}-{\mathrm{e}}^{-{\mathrm{m}}_1}}{{\mathrm{e}}^{{\mathrm{m}}_1}+{\mathrm{e}}^{-{\mathrm{m}}_1}}$$

(29)

Substituting the values in Equations (28) and (30) generated, as a result, a vector with dimensions of [1 × 55].

$${\mathrm{m}}_1=\mathrm{f}{\left(\left[\begin{array}{ccc}-0.0767& \cdots & -0.0062\\ 0.1308& \cdots & 0.0227\\ 0.1235& \cdots & -0.0151\\ ⋮& \ddots & ⋮\\ 0.0514& \cdots & -0.2929\\ -0.0671& \cdots & -0.0362\end{array}\right]*\left[\begin{array}{c}4.9938\\ 9.7508\\ 14.3055\\ ⋮\\ 14.5427\\ 13.7590\\ 9.0081\end{array}\right]\right)}^{’}+[2.7675-2.7125\cdots 2.6527-1.8140]$$

$${\mathrm{m}}_1=\mathrm{f}\left[\begin{array}{ccccc}2.7732& -2.3202& \cdots & -1.0063& -2.7400\end{array}\right]$$

(30)

Substituting in Equation (29) for each value obtained from vector $m_1$, we calculate (31), which results in a vector [1 × 55].

$${\mathrm{m}}_2=\frac{{\mathrm{e}}^{2.7732}-{\mathrm{e}}^{-\left(2.7732\right)}}{{\mathrm{e}}^{2.7732}+{\mathrm{e}}^{-\left(2.7732\right)}}=0.9922$$

$${\mathrm{m}}_2=\left[\begin{array}{ccccc}0.9922& -0.9809& \cdots & -0.7642& -0.9917\end{array}\right]$$

(31)

Finally, the response issued by the methodology was generated by substituting in the general ANN function the matrices of weights ${(\mathrm{W}}_2)$, bias ${(\mathrm{b}}_2)$, and the transpose of the resulting vector of the first layer ($m_2$); see Equation (32).

$${\mathrm{m}}_3={\mathrm{f}\left(\left[\begin{array}{cc}-0.2024& \begin{array}{ccc}-0.0995& \begin{array}{cc}0.00040& \cdots \end{array}& \begin{array}{cc}0.4164& \begin{array}{cc}-0.5504& -0.2546\end{array}\end{array}\end{array}\end{array}\right]*\left[\begin{array}{c}0.9922\\ -0.9809\\ \begin{array}{c}⋮\\ \begin{array}{c}-0.7642\\ -0.9917\end{array}\end{array}\end{array}\right]\right)}^{’}+\left[-0.0523\right]$$

$${\mathrm{m}}_3=\left[-0.0067\right]$$

(32)

The variable $m_3$ corresponds to the value that the ANN assigned to the metallographic image used in the test phase, recognizing the presence of intergranular corrosion in the stainless steel. The output value assigned to the ANN in the training phase to recognize such a state in the microstructure of the stainless steel is equal to (0), so the ANN achieved the efficient recognition of the metallographic pattern present in the microstructure of the material.

3.2. Recognition of Metallographic Patterns from the GLCM Method

To illustrate the recognition process conducted by the ANN based on the characterization of the metallographic image from the GLCM method, a microstructure with a metallographic pattern showing intergranular corrosion in stainless steel was considered. Replacing the corresponding matrices in Equations (28) and (33) generated, as a result, a vector with dimensions of [1 × 100].

$${\mathrm{m}}_1={\mathrm{f}\left(\left[\begin{array}{ccc}-3.0273& \cdots & -4.4919\\ 2.3262& \cdots & -4.3327\\ 2.6176& \cdots & 1.4167\\ ⋮& \ddots & ⋮\\ 1.0979& \cdots & 4.6218\\ -2.3543& \cdots & 5.6513\end{array}\right]*\left[\begin{array}{c}0.8341\\ 0.0377\\ 0.9059\\ ⋮\\ -0.6376\\ 0.6864\\ 0.9083\end{array}\right]\right)}^{’}+[25.42757.5885\cdots -9.7822-17.0344]$$

$${\mathrm{m}}_1=\left[\begin{array}{ccccc}0.2767& -1.3042& \cdots & 6.3857& -2.3669\end{array}\right]$$

(33)

Substituting in Equation (29) each value obtained from vector $m_1$, Equation (34) is generated, resulting in a vector [1 × 100].

$${\mathrm{m}}_2=\frac{{\mathrm{e}}^{0.2767}-{\mathrm{e}}^{-\left(0.2767\right)}}{{\mathrm{e}}^{0.2767}+{\mathrm{e}}^{-\left(0.2767\right)}}=0.2698$$

$${\mathrm{m}}_2=\left[\begin{array}{ccccc}0.2698& -0.8628& \cdots & 1.0000& -0.9826\end{array}\right]$$

(34)

The response generated by the ANN to classify and recognize the metallographic pattern present in the stainless steel microstructure is achieved by solving Equation (35), substituting in the general function of the ANN the matrices of the weights ${(W}_2$), bias ($b_2$) and the transpose of the resulting vector of the first layer ($m_2$).

$${\mathrm{m}}_3=\mathrm{f}{\left(\left[\begin{array}{ccccc}0.2244& 0.5309& \cdots & 0.0876& -0.1545\end{array}\right]*\left[\begin{array}{c}0.2698\\ -0.8628\\ \begin{array}{c}⋮\\ \begin{array}{c}1.0000\\ -0.9826\end{array}\end{array}\end{array}\right]\right)}^{’}+\left[0.0331\right]$$

$${\mathrm{m}}_3=\left[0.1192\right]$$

(35)

The output signal emitted by the ANN when using the GLCM method for the characterization of the metallographic image is efficient for the recognition of the intergranular corrosion pattern present in the microstructure of the AISI 304 stainless steel.

3.3. Comparison of Methods Used for Digital Image Processing

To validate the performance of both methods, it is necessary to verify that the characterization of the metallographic image is correct and provides detailed information to the ANN to achieve the efficient classification and recognition of the patterns present in AISI 304 stainless steel. According to [38], the ratio of the true and false predictions specific to each characterization method is determined by the following performance measures: sensitivity, specificity, and accuracy, using Equations (36)–(38), respectively.

$$\mathrm{S}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}=\frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}$$

(36)

$$\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}=\frac{\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{P}}$$

(37)

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}=\frac{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}+\mathrm{T}\mathrm{N}}$$

(38)

where TP (true positive), FP (false positive), TN (true negative), FN (false negative).

The probability of not incurring a type II error, (1-β), is known as the power of the test, equivalent to the sensitivity. The sensitivity is equivalent to the proportion of cases where a certain corrosion pattern is present in the stainless steel and the developed methodology correctly classifies and recognizes this pattern in the microstructure of the metallographic image (true positive rate). The probability of not making a type I error, (1-α), is known as the efficiency of the test, equivalent to the specificity. The specificity is the proportion of events where a certain corrosion pattern is evaluated in the stainless steel and the proposed methodology does not classify a pattern that does not exist in the microstructure of the metallographic image, diagnosing that the corrosion pattern does indeed not exist in that image (true negative rate).

The degree of accuracy of a test is defined as the proportion of cases where the result is correct [39]. The results of the performance of the phase congruence and GLCM methods applied for the characterization of the three types of metallographic patterns present in the microstructure of AISI 304 stainless steel are shown in

Table 9. Performance indicators using the phase congruence method.

	Sensitivity	Specificity	Accuracy
No intergranular corrosion (NIC)	0.86	1.00	0.97
Presence of intergranular corrosion (PCI)	1.00	1.00	1.00
Precipitation of chromium carbides (PCC)	1.00	0.95	0.97

and

Table 10. Performance indicators using the GLCM method.

	Sensitivity	Specificity	Accuracy
No intergranular corrosion (NIC)	0.93	1.00	0.99
Presence of intergranular corrosion (PCI)	1.00	0.96	0.97
Precipitation of chromium carbides (PCC)	0.97	1.00	0.99

.

The results obtained suggest that both ANN topologies developed efficiently perform the task of classification and recognition of intergranular corrosion in stainless steel when using the phase congruency and GLCM characterization methods. However, the architecture using the GLCM characterization method requires more neurons in the hidden layer and iterations to achieve the allowed error. The phase congruency method generates a larger characterization vector; however, the convergence time in its architecture is shorter compared to the ANN topology used in the GLCM method.

Regarding the characterization capacity, it is important to highlight that the GLCM method establishes only an analysis related to the texture in the metallographic image since it focuses on local variations, the probability of occurrence, and the uniformity and closeness of the distribution between pairs of pixels. On the other hand, phase congruency correctly detects features at all angles and is invariant to contrast and illumination. In the application case reviewed, the illumination and position are not noise factors because there is already a standardized process for image capture with the inverted microscope. However, in any other application case where there is variation in the illumination, the sensitivity, specificity, and accuracy results would compromise this because it is a factor in establishing the gray scale in the image.

To compare the results obtained by the multilayer perceptron ANN, two other classification mechanisms were developed. First, support vector machines (SVMs) were built, and as a second step, the Fuzzy ARTMAP ANN was used. For both classifiers, the same training and test sets used in the multilayer perceptron ANN were used; see Table 4. It should be noted that the selection of the SVM and Fuzzy ARTMAP ANN classification models was due to the fact that they work under a supervised training approach, just like multilayer perceptron ANNs.

3.4. Recognition of Intergranular Corrosion Patterns Using SVM

For the development of SVM architectures, it is important to consider that the classification of intergranular corrosion patterns present in metallographic images is of the nonlinear type, so a polynomial kernel function was implemented with the one versus one method, given that a scenario where more than two classes exist was addressed. For the construction of the SVM, it is vital to consider that the hyperparameter cost (C) controls the balance between the bias and variance; it is a concept that allows one to understand the ability of the SVM when faced with data that have not been used in the training phase, that is, its generalization capacity.

To select an optimal cost value for each of the digital image processing methods, different values were evaluated by cross-validation [0.001, 0.01, 0.1, 1, 1, 5, 10, 15, 20, 25]. For the phase congruency image processing method, the cost value resulting in the lowest validation error (0.0380) is five; see Figure 4a. The degree of the generated model is third and the number of support vectors is 173. As for the GLCM method, the cost value resulting in a lower validation error (0.0417) is one; see Figure 4b. The degree of the generated model is third and the number of support vectors is 235.

With the objective of evaluating the performance of each SVM to execute the task of the recognition and classification of the intergranular corrosion patterns present in AISI 304 stainless steel, the indicators of sensitivity, specificity, and accuracy for the digital image processing’s were calculated: phase congruence and GLCM matrix. See

Table 11. Performance indicators using the phase congruence method.

	Sensitivity	Specificity	Accuracy
No intergranular corrosion (NIC)	0.95	0.94	0.96
Presence of intergranular corrosion (PCI)	0.94	0.92	0.95
Precipitation of chromium carbides (PCC)	0.98	0.99	0.98

and

Table 12. Performance indicators using the GLCM method.

	Sensitivity	Specificity	Accuracy
No intergranular corrosion (NIC)	0.90	0.87	0.88
Presence of intergranular corrosion (PCI)	0.92	0.95	0.95
Precipitation of chromium carbides (PCC)	0.94	0.98	0.92

, respectively.

3.5. Recognition of Intergranular Corrosion Patterns Using the Fuzzy ARTMAP ANN

The Fuzzy ARTMAP ANN performs learning that minimizes the predictive error and maximizes generalization. This is achieved by a match-tracking process that increases the surveillance parameter by the minimum amount necessary to correct an error in pattern recognition. The implementation of the Fuzzy ARTMAP ANN starts with a data normalization process since both the training and test patterns must correspond to the interval (0, 1). Subsequently, the vigilance parameters were defined, such as the Base Vigilance (${\rho }_a$), Vigilance (${\rho }_b$), and Rho map (${\rho }_{map}$). Like the training and test sets, the monitoring parameters must be placed in an interval (0.1), so an experimental design is programmed where, for each monitoring parameter, it is increased by 0.1, and the rest are fixed. In this way, the answers are stored, and the architectures found that this minimizes the error in the pattern recognition task.

Another aspect to consider when programming the Fuzzy ARTMAP ANN is the size of the input and output vectors; however, these values were defined depending on the application case and type of processing applied to the input signal. In the case of the recognition of intergranular corrosion patterns from the Fuzzy ARTMAP ANN, an architecture defined for each type of digital processing was implemented in the metallographic images. The selection criterion between the architectures was the minimization of the MSE, and in this way, it achieves the efficient classification of the corrosion patterns present in the microstructures of AISI 304 stainless steel; see

Table 13. Fuzzy ARTMAP artificial neural network architectures.

Parameters	Phase Congruence	GLCM Matrix
Input vector dimension	[30 × 1]	[14 × 1]
Output vector dimension	1	1
Base Vigilance $\left({\rho }_a\right)$	0.1	0.2
Vigilance $\left({\rho }_b\right)$	0.8	0.9
Rho map $\left({\rho }_{map}\right)$.	0.9	0.7

.

With the intention of evaluating the performance of the ARTMAP Fuzzy artificial neural network architectures, the indicators of sensitivity, specificity, and accuracy are calculated. See

Table 14. Performance indicators using the phase congruence method.

	Sensitivity	Specificity	Accuracy
No intergranular corrosion (NIC)	0.93	0.93	0.92
Presence of intergranular corrosion (PCI)	0.91	0.84	0.89
Precipitation of chromium carbides (PCC)	0.95	0.96	0.93

and

Table 15. Performance indicators using the GLCM method.

	Sensitivity	Specificity	Accuracy
No intergranular corrosion (NIC)	1.00	0.96	0.97
Presence of intergranular corrosion (PCI)	1.00	0.91	0.98
Precipitation of chromium carbides (PCC)	0.93	1.00	0.98

.

Table 16. Average accuracy by classification model.

Classification Model	Phase Congruence	GLCM Matrix
Multilayer perceptron ANN	98%	98%
Vector support machine	96%	92%
Fuzzy ARTMAP ANN	91%	98%

shows the average accuracy offered by each of the classification models to recognize the three intergranular corrosion patterns present in AISI 304 stainless steel, based on analyzing the information provided by the digital image processing used in the investigation.

According to the results obtained, the multilayer perceptron ANN presents a greater efficiency using phase congruence image processing. Regarding the GLCM processing method, the Fuzzy ARTMAP ANN managed to match the efficiency achieved by the multilayer perceptron ANN in the task of intergranular corrosion pattern recognition. The SVM achieves its best recognition efficiency when integrated with the phase congruency image processing method.

4. Discussion

The average accuracy indicators obtained by integrating phase congruence image processing with the SVM classification models and the multilayer perceptron ANN are achieved because the processing method generates characterization vectors with greater variation for each corrosion pattern present in steel; in this way, it is easier to draw thresholds that separate the sets of information between the classes. On the other hand, it is important to highlight the average accuracy of 98% achieved by the Fuzzy ARTMAP ANN processing the input information generated by the GLCM method; one answer to this result is the correct coupling of both procedures. The ANN only processes information in the range (0,1) or is normalized, and the vast majority of the indicators of the GLCM method from its origin are in this range, so the transformation is not necessary; this does not mean that the process of normalization is incorrect; however, it is still a transformation of the original nature of the data that represents a state of the steel in the metallographic image. By achieving an average accuracy of 98% with both digital image processing methods, the multilayer perceptron ANN was demonstrated to be a robust classification model for recognizing intergranular corrosion patterns in AISI 304 stainless steel.

Using the multilayer perceptron ANN as a classification model, according to the sensitivity and specificity indicators, the GLCM characterization method shows a minimal improvement compared to the phase congruency method. However, computationally speaking, an important indicator is the convergence time; in this sense, the phase congruency technique presents a shorter duration since an artificial neural network architecture with fewer neurons in the hidden layer is required. The indicator of interest to maximize is the accuracy; both methods provide, on average, a 98% accuracy in the task of the recognition of metallographic patterns present in stainless steel affected by temperature.

The methodology presented recommends the phase congruence method, since, despite characterizing the images with larger vectors compared to the GLCM method, an adequate accuracy for the recognition task is achieved in less time; this is because it provides a greater degree of detail in the description of the microstructure of stainless steel, facilitating the work of the ANN and giving way to the recognition of the intergranular corrosion present in AISI 304 stainless steel by integrating the multilayer perceptron ANN and digital processing of the metallographic images.

An important opportunity to extend the research related to corrosion pattern recognition in stainless steels is to deepen and extend digital image processing techniques using invariant moment characterization or histograms. As for classification tools, experimenting with Bayesian or recurrent artificial neural networks will be the next step to define the recognition phase.

5. Conclusions

The application of the methodology proposed in this research demonstrates that the task of the classification and recognition of the damage generated in stainless steels affected by temperature was achieved efficiently by identifying the states of the material: no intergranular corrosion, no presence of intergranular corrosion, and no precipitation of the chromium carbides. The methodology is composed of the integration of digital metallographic image processing and a multilayer perceptron artificial neural network. The results obtained demonstrate that the methodology could be used for the analysis of metallographic images that need to be examined to verify the state of stainless steel affected by temperature without the need of experts in the area, which will allow for the closer monitoring of the material in operation. The importance of the proposed methodology lies in the generation of a procedure capable of replacing the analysis operation performed by an expert in the thermoelectric plant in an efficient way that identifies any intergranular corrosion patterns in AISI 304 stainless steel through visualizing the microstructure.

It is important to remember that the maintenance plan in a thermoelectric plant involves the supervision of structures and mechanisms involved in the power generation process. With the development of the methodology presented, it is possible to have a diagnosis within reach that is related to the recommendation of the replacement or continuity of the devices used in thermoelectric plants that are made of AISI 304 stainless steel. The results obtained demonstrate the feasibility of a recommendation for the use for each of these devices, which prevents the incursion of unexpected corrective maintenance that generates costs and delays the energy generation process, which translates into higher productivity.

The presented methodology could extend to any industrial situation that requires one to classify some kind of pattern or defect reflected in images, and where it is intended to analyze these images in terms of their texture or contrast, to corroborate and even replace an expert in the area with an artificial intelligence tool.

In this study, in an industrial case, the description of a methodology to process, analyze, and execute the task of the automatic recognition of intergranular corrosion present in stainless steel AISI 304 was demonstrated using the methods of digital image processing phase congruency and a matrix GLCM integrated into a multilayer perceptron artificial neural network with a pattern recognition approach.