Unsupervised machine learning for automatic corrosion staging using optical microscope images

Calculation of local porosity

The method for calculating local porosity is divided into three parts: (i) pore detection, (ii) local porosity estimation, and (iii) pore characterization. The process of characterizing the porosity of the overall thickness of the boiler deposit is shown in Figure 8.

k-means³⁶ is an unsupervised clustering algorithm in which cluster (or group) data points are used for pore detection depending on the similarity score (often square error). In contrast to other machine learning methods, unsupervised learning reduces dependency on labeled data, which is extremely rare in corrosion datasets. In certain images, a random cluster of centrosomes is first selected and the cluster centroids are refined in multiple iterations until the convergence criteria are met. As shown in Figure 9a, there are three clusters. (i) waterfront areas, (ii) sediments, and (iii) metal pipes that can group data points. Each pixel (data point) has three intensity values ​​corresponding to the red, green, and blue (RGB) color model. A detailed breakdown of pore detection from optical microscope (OM) images is shown in Figure 9.

Consider an OM image made up of each pixel (each pixel) (each pixel)x₁,. . . x_n) is represented by vector 3×1. The goal was to divide the data into three clusters to minimize the distance within each cluster and maximize the distance between each cluster. For a specific data point x_n and Centroid μ_k Binary variables for KTH clusters g_nk ∈ 0, 1 indicates whether x_n It belongs to cluster k. In other words, the case x_n It is assigned to group K. g_nk Gets the value of 1. Otherwise, a value of 0 is required. The clustering process is intended to minimize:

The algorithm starts by assigning a random value to each cluster centroid. μ_k. The first is the objective function j Minimizes with regard to equation (1) g_nk Maintaining μ_k Repaired. after that, j It is minimized regarding μ_k While maintaining the value of g_nk Repaired. This two-stage process is repeated until convergence is achieved. After that, blob removed³⁷ Runned to fill small black/white areas of segmented images s(r, c) (Figure 9b) Acquire tube deposition images t(r, c) (Figure 9c). here, (r, c) corresponds to r^th Line and c^th A row of OM images. This is followed by logic and operations³⁷ To obtain tube deposits in pores t_p(r, c)(eq. (2)) As shown in Figure 9d,

Finally, pores p(r, c) Extracted using the XOR operation t(r, c) (Figure 9c) and t_p(r, c) (Figure 9d): (3). Equation (3) produces an output consisting of pores present in the deposition region, as shown in Figure 9E.

Local porosity estimation processes first generate local porosity maps by aggregating the porosity values ​​within the defined neighborhood for each pore. To calculate the porosity within this neighborhood, m All entries were set to 1 and adopted with a size of 55×55. This corresponds to a physical area of ​​5μm x 5μm. This matrix m Next, it is convolved with a pore image p(r, c) and tube deposit image t(r, c), as shown in the formula. (4), and equation (5), respectively.

Edge of p and t There's a proper zero pad. but, \({v}_{v}^{local}(r,c)\) and \({v}_{t}^{local}(r,c)\) Trimmed to maintain the same size p. This step is performed using MATLAB's CONV2D function³². Samples of accumulated pores (\({v}_{v}^{local}(r,c)\)and accumulated tube deposits (\({v}_{t}^{local}(r,c)\)) considered local neighborhoods are shown in Figures 10a, b, respectively. The local porosity map/image (Fig. 10c) is then calculated as

Finally, the averaged local porosity is calculated as the average of the local porosity map given to the equation. (6). Ref. ³³. Similarly, local torture was calculated using the same empirical relationship for torture, but porosity was replaced by mean local porosity.

Characterizes local porosity along the thickness ϕ^th(r) of deposits, ϕ^local(r, c) Equation (6) Averaged on each row r Local porous images,

where n_c The number of pores of rthrow. The thickest part of the deposits in each sample image is identified, and the sediment width at that location is

where n_p Number of pixels and resolutIon The length of pixels expressed in μm. In this case, the pixel resolution is 0.11μm.

Criteria for corrosion stage classification

This study further evaluated the importance of calculated sediment thickness and local porosity. ³³. Classification was performed based on porosity. Porosity was initially calculated as the percentage of total pores of total pores. By analyzing experimental studies reported by Abitha et al.³³,Each OM image is assigned a UDC stage based on the porosity values ​​listed in Table 1. The same criteria based on porosity values ​​were used for averaged local porosity-based classification. In thickness-based classification, UDC stages are assigned according to the thickness values ​​reported in Table 1.³³. Secondly, for the voting method, if the two criteria mentioned above agree, a corresponding stage is assigned to the OM image. If not agreed with each other, a thickness-based standard was used.

The four boilers operating in a total volatile processing (AVT) implementation produced 12 coil pieces each measuring about 1 m long. The OM images used in this study were all obtained from a group of boilers that suffer from UDC and theoretically identically behaved. Typically, boilers have a helical coil design^38,39 There is boiling water on the outside and hot process gas inside. For more information on image acquisition and characterization of corrosion stages of UDCs, see Abitha et al.³³.