Porosity Analysis and Thermal Conductivity Prediction of Non-Autoclaved Aerated Concrete Using Convolutional Neural Network and Numerical Modeling

Abstract

Currently, the visual study of the structure of building materials and products is gradually supplemented by intelligent algorithms based on computer vision technologies. These algorithms are powerful tools for the visual diagnostic analysis of materials and are of great importance in analyzing the quality of production processes and predicting their mechanical properties. This paper considers the process of analyzing the visual structure of non-autoclaved aerated concrete products, namely their porosity, using the YOLOv11 convolutional neural network, with a subsequent prediction of one of the most important properties—thermal conductivity. The object of this study is a database of images of aerated concrete samples obtained under laboratory conditions and under the same photography conditions, supplemented by using the author’s augmentation algorithm (up to 100 photographs). The results of the porosity analysis, obtained in the form of a log-normal distribution of pore sizes, show that the developed computer vision model has a high accuracy of analyzing the porous structure of the material under study: Precision = 0.86 and Recall = 0.88 for detection; precision = 0.86 and recall = 0.91 for segmentation. The Hellinger and Kolmogorov–Smirnov statistical criteria, for determining the belonging of the real distribution and the one obtained using the intelligent algorithm to the same general population show high significance. Subsequent modeling of the material using the ANSYS 2024 R2 Material Designer module, taking into account the stochastic nature of the pore size, allowed us to predict the main characteristics—thermal conductivity and density. Comparison of the predicted results with real data showed an error less than 7%.

1. Introduction

Currently, the construction industry continues to be the most conservative in terms of its introduction of innovative methods compared to other industries, a conservatism explained by a number of factors [1,2]. Specialists in this industry try to minimize errors by giving preference to proven design and calculation methods, as well as choosing proven construction materials and technologies. The occurrence of errors can lead to serious consequences, including threats to human safety and lives [3,4,5]. Another reason for the slow adoption of new technologies is the scale of construction projects, which are often accompanied by large volumes of investment and the presence of various risks. The wrong choice of innovative tool, the wrong method for its implementation, and certain specialists accompanying this integration can lead to the halting of the entire process [6,7]. Also, throughout the entire life cycle of a construction project, in the event of the introduction of a previously unused technology, a number of approvals and integrations are required, entailing increased coordination among all stakeholders. State regulatory restrictions, such as laws, standards, rules, and other regulatory instruments, do not always keep up with the rapid pace of development of innovative technologies, which also results in a delay in their implementation in construction processes [8,9]. Despite the slow pace of automation and digitalization of the construction industry, companies have also noted positive changes from the implementation of innovative methods, including intelligent methods [10]. Artificial intelligence (AI) algorithms, when they are properly implemented and operated, have become reliable and effective tools in the following processes: forecasting the mechanical characteristics of various construction materials [11,12,13,14], ensuring safety at construction sites [15,16,17], design and planning [18,19], maintenance and operation of buildings [20,21], monitoring the quality of construction materials, and compliance with the requirements of standards for products and structures [22,23,24,25]. Intelligent tools provide a means of verifying the practical applications of modern building materials that promote energy efficiency and mitigate greenhouse gas emissions [26,27]. Comparative analysis of four machine learning models—Long Short-Term Memory (LSTM), Least-Squares Boosting (LSBoost), Support Vector Machines (SVMs), and Multiple Linear Regression (MLR)—for predicting the compressive strength of sustainable geopolymer concrete yielded accuracies of 99.23%, 98.08%, 78.57%, and 88.03%, respectively [28].

Let us consider the set of problems associated with the use of intelligent techniques for monitoring the quality of construction materials, products, and structures. Such techniques are based on computer vision algorithms that perform visual diagnostic analysis in automatic mode [29,30,31,32,33,34]. Convolutional neural networks (CNNs) most often perform the functions of detection, segmentation, and classification of damage, defects, and structural features [35,36,37,38]. CNN systems are built into cameras locally in production, are built into robotic inspection systems, and are also built into unmanned aerial vehicle (UAV) systems [39]. It is known that increasing the volume of objects monitored in an automated mode through the use of robotic intelligent systems will improve labor productivity [40]. A method for corrosion detection using intelligent recognition of UAV images has already been demonstrated [41]. The subject of the study is the detection of corroded areas on large cranes and other large steel structures in open air using a six-rotor UAV. The convolutional neural network of the Visual Geometry Group (VGG16 model) was used as a deep learning algorithm. In the final test images, most of the corrosion zones were localized and marked correctly. There were almost no gaps or incorrect markings [41]. Studying structure is one of the forms of quality control for building materials. Searching for structural and microstructural defects in concrete specimens from various structures is possible using U-Net, LinkNet, and Pyramid Scheme Parsing Network (PSPNet) architectures. The best accuracy (Precision = 0.91, Accuracy = 0.90) was achieved by the U-Net architecture, which was expanded using a cellular automaton algorithm [42]. A specific set of researchers demonstrated their methods for analyzing a concrete structure for cracks using CNN Inceptionv3. The accuracy of this model was 88.5% [43]. The analysis of constituents of the mix, such as aggregates, anhydrous cement, hydrated cement, and pores, was possible using a combination of scanning electron microscopy images and deep learning methods (CNN U-Net). The accuracy of the automated approach to the analysis of the properties of the sample microstructure was up to 94.43% [44,45,46,47]. The literature search for studies on the application of intelligent technologies, particularly computer vision, showed that approaches using neural networks (both alone and in combination with other methods) demonstrated high accuracy in some cases. As a result, using computer vision for detecting structural anomalies and defects has gained immense popularity in studies related to monitoring the quality of construction materials and compliance with standards for products and structures [48,49,50,51,52]. Detection of structural changes in various kinds in specimens of building materials will improve production quality by changing technical and technological factors, and avoiding the release and distribution of defective products [53,54,55,56]. The growing relevance of computer vision applications in the construction industry encourages researchers, including us, to apply this technology to analyze the structural features of various building materials of particular interest [57,58].

Based on the above review, it is clear that the successful application of machine learning algorithms in assessing the properties of cement composites can be as equally successfully directed to different types of such composites such as cellular concrete. This paper substantiates the case for the use of the YOLOv11 convolutional neural network for analyzing the structure of aerated concrete products. This study’s scientific novelty lies in our development of an algorithm for determining the porosity of aerated concrete products based on an intelligent model which has not previously been used for building materials, followed by extended statistical analysis and visualization. The objectives of this study include the following:

→

Collecting an experimental database of pictures of aerated concrete products and marking them;

→

Conducting the process of augmentation to expand the set of representative data;

→

Justification of the selected method for localizing the pores of aerated concrete products;

→

Building the optimal algorithm of the CNN YOLOv11 to implement a method for the determination of pore characteristics;

→

Comparison of two empirical distributions using Hellinger distance and Kolmogorov–Smirnov criteria;

→

Creation of a “heat map” of porosity based on the conclusions of the intelligent model.

This research makes a technological contribution by demonstrating the potential of computer vision technologies for analyzing the structural properties of porous building materials and associated products.

2. Materials and Methods

The algorithm developed for intelligent image analysis is practical, exhibiting universality, cross-platform compatibility, and scalability, particularly for analyzing cellular materials. The research algorithm is presented in the form of a block diagram in Figure 1.

This algorithm is innovative in analyzing the structure of this type of building material; as the literature analysis shows, such a study using this CNN in combination with the ANSYS 2024 R2 Material Designer module has not been conducted before and can be divided into several intellectual steps.

2.1. Composition, Properties and Structure of the Studied Aerated Concrete Samples

Non-autoclaved cellular concrete was chosen as the material for the analysis of the geometric characteristics of the porous structure. Experimental samples of cellular concrete were manufactured under laboratory conditions. The properties of the main raw materials used to manufacture experimental prototypes of cellular concrete are presented in

Table 1. Properties of raw materials.

Raw Materials	Property	Value
Portland cement grade CEM I 42.5N JSC “CEMROS” (Voronezh, Russia)	Setting times (min) -Start -End	190 240
	Standard consistency of cement paste (%)	26.0
	Compressive strength at 28 days (MPa)	52.8
	Bending strength at 28 days (MPa)	6.0
Quartz sand (Don Resource, Kagalnik, Russia)	Bulk density (kg/m3)	1335
	Apparent density (kg/m3)	2587
	The content of dust and clay particles (%)	0.03
	Content of clay in lumps (%)	0
Aluminum powder PAP-1 OOO “SKIF” (Saint Petersburg, Russia)	Bulk density of powder (g/cm3)	0.3
	Content of active aluminum (%)	92
Gypsum molding produced by Magma LLC (Moscow, Russia)	Bulk density (kg/m3)	650
	Fineness of grinding, residue on a sieve with a clear cell size of 0.2 mm (%)	0.8
	Ultimate compressive strength of prism samples 2 h (MPa)	7.3
	Ultimate flexural strength of prism samples at 2 h (MPa)	4.1
Lime produced by Roskhimprom LLC (Rostov-on-Don, Russia)	Content of active CaO and MgO (%)	94.5
	Slaking rate (min)	17
	Content of hydrated water (%)	2.1

.

Table 2. Composition of the raw mix for aerated concrete (as a percentage of the total mass).

Component Name	Content (wt.%)
Portland cement	26
Quartz sand	32
Aluminum powder	0.1
Lime	4.3
Molding gypsum	2.5
Water	35.1

provides a summary of the raw material composition for the production of non-autoclaved aerated concrete.

The aerated concrete composite for each batch of samples was prepared under the same mixing conditions. All components, except aluminum powder and water, were mixed for 60 s in a laboratory concrete mixer, BL-10 (ZZBO, Zlatoust, Russia). Then, water was poured in the following amounts and for the following durations: 50% with mixing for 90 s; another 50% while mixing with aluminum powder and holding the mixture for 60 s; and then mixing until a homogeneous consistency was achieved. Then, the mixture was poured in one layer into molds, compacted with a steel rod, packed in film and held for 24 h. After removing them from the molds, the samples hardened in natural conditions. The curing conditions were as follows: temperature—24 ± 2 °C; relative air humidity—90 ± 10%.

The resulting cellular composite had an average density of 610 kg/m³, compressive strength of 4.5 MPa, and thermal conductivity of 0.162 W/m·K. These characteristics were taken from the specifications provided by the product manufacturer. Figure 2 shows an image of the aerated concrete; the size of the presented sample is 110 mm × 110 mm.

In the upper part of the aerated concrete sample, there is an area with pores that can be seen with the naked eye, the sizes of which stand out against the background of the main mass (this area is highlighted in blue in the image). Large pores can also be observed, distinguishable against the general background (highlighted in green).

It should be noted that the nature of the pore structure is critical for cellular concrete and directly affects its properties. Cellular concrete with a uniform pore structure has better thermal insulation properties and higher compressive strength than concrete with a non-uniform pore structure. The uniform pore structure of the cellular composite can be characterized as follows. Most of the pores are of similar sizes and have clearly defined inter-pore partitions. The coefficient of variation of the pore size varies up to 10%. With a non-uniform pore structure (the coefficient of variation of the pore size is greater than 20%), the sizes of most pores vary greatly, the interpore partitions are thin and poorly defined in places, and there are also zones where gas bubbles collapse during the formation of the cellular structure and large pore cavities (shells) [59]. Intermediate values of the coefficient of variation indicate an average degree of variability and characterize both the homogeneity and heterogeneity of the porous structure. Aerated concrete’s porous structure results from gas volume release, which is formed on the surface of aluminum powder particles that interact with the alkaline binder component Ca(OH)₂: 2Al + 3Ca(OH)₂ + 6H₂O = 2CaOAl₂O₃ 6H₂O + 3H₂↑ + Q [60,61]. In the mass production of products from aerated concrete, timely detection of products with a non-uniform pore structure will reduce the number of defects and generally improve the production technology. However, analyzing the porous structure of mass-produced aerated concrete is difficult due to the large production volumes. The quality of human analysis of the structure of the product may be reduced due to increasing fatigue and the difficulty in perceiving the product’s texture. Consequently, the application of artificial intelligence methodologies to the porosity analysis of aerated concrete products constitutes a significant and promising area of research.

2.2. Data Annotation and Augmentation

AI-based analysis of the structure of a building material should include the detection of critical changes in the sample that make it unsuitable for use, and the identification of non-critical defects permitted by the manufacturer’s standards. As a rule, non-critical defects include the presence of cavities on the surface of a product or structure made of cellular concrete, and chipping on corners and edges to an extent that does not exceed the limits set by the manufacturer. Critical defects include the presence of cracks, cavities, and chipping on corners and edges to degrees that exceed the limits set by the manufacturer.

To create an intelligent algorithm capable of high-quality visual monitoring, a sufficient number of representative photographs is required [62,63]. Initial dataset quality directly impacts the neural network’s ability to accurately identify structural anomalies. In essence, the system requires simulation of the work of an experienced, qualified materials scientist. In total, 60 photographs of aerated concrete sections, taken under uniform laboratory conditions, constituted the initial dataset for this study. Photographic recording was carried out using a CANON EOS 650D camera (CANON Inc., Tokyo, Japan). Image labeling (Figure 3) was carried out using a comprehensive platform for simplifying the process of creating, training and deploying computer vision models with Roboflow (Roboflow, Inc., San Francisco, CA, USA) (https://app.roboflow.com/) (accessed on 8 July 2025).

The process was carried out using the “polygon annotation” method, in which a set of coordinates is drawn around the object of interest. The created coordinates tightly surrounded each pore, avoiding the capture of unnecessary information. Annotating each pore in an image with polygons is a labor-intensive process, one much more difficult than isolating them in bounding boxes. In the case of overlapping pores during marking, they were highlighted as a single object.

After annotating such images, data augmentation should start. The process of creating new data based on the existing material eliminates the need for additional photographic recording and labeling (which is especially difficult given the complex texture of the object). At the same time, expanding the dataset via various modifications to the original images increases the model’s stability in response to various noises during processing. This allows it to be used in changing the photographic conditions (for example, changing low-light conditions or the shooting angle).

The following modifications were made in the augmentation process (

Table 3. Image modifications.

№	Modifications	Example
1	Merging
2	Vertical and horizontal mapping
3	Shifting the image along the Ox and Oy axes in a random order
4	Rotation of the picture by 90°, 180°, and 270°
5	Brightness, contrast and saturation changes

).

Brightness and contrast parameters were adjusted using the author’s BrightnessBooster algorithm, an algorithm based on a two-parameter family of absolutely continuous distributions used for correction. This ensured more natural and high-quality results without going beyond the boundary values of the Red, Green, Blue (RGB) color model [64].

We observed that, during the augmentation, the system automatically recalculated the limiting coordinates for the modified photograph. In total, the dataset was expanded to 100 images.

Augmentation had a positive effect on the quality of the model. It was noted that, by introducing various types of modifications during the augmentation process, the detection accuracy increased and the training time increased. The optimal number of augmented images was selected.

Expanding the database by adding “original images” requires significant labor costs and, accordingly, financial expenses. In addition, such data must be collected under various conditions regarding lighting, phone models, the cameras used to shoot, etc. All of this complicates the collection of the required number of examples for training the sample. On the other hand, the results of training the system on such data can be used to judge its effectiveness in real conditions. Expanding the database by augmentation significantly improves the performance of the recognition system. Original images were used in our study for validation. They can be used to assess the most common types of errors, and more images can be added with the corresponding distortions to the training base. This method of creating training examples does not require high material costs and allows researchers to create a large number of examples needed to train the sample. Difficulties can be caused by the careful selection of parameters for expanding the training sample from the “original images”. On the one hand, the number of examples must be sufficient for the neural network to learn to recognize even noisy examples; on the other hand, it is necessary that the quality does not decrease for other types of complex images. Thus, both strategies have their advantages and disadvantages. The higher quality accorded by the addition of “original images” may be offset by the higher resource costs associated with this. It is necessary to choose wisely between these strategies depending on the required task.

It is worth noting that the study examines the presented type of aerated concrete described above in Section 2.1, and the sample is representative of it. In this study, a specific type of aerated concrete with a specific porous structure was selected. The amount of data was representative of it, and the data described the variability in pore sizes and the various shooting conditions. We plan to develop intelligent models capable of dealing with the variability in the pore structures of aerated concrete depending on the various production conditions, material compositions and hardening processes by collecting additional data, changing the augmentation parameters and further training the CNN.

2.3. Implementation of the YOLOv11 CNN

This study employed a YOLOv11 convolutional neural network-based computer vision algorithm implemented using Python 3.12 (Python Software Foundation, Dover, DE, USA) [65]. The architecture of this network is the latest iteration in the You Only Look Once (YOLO) series.

YOLO11 uses an improved “spine” and “neck” architecture, which enhances feature extraction capabilities, enabling more accurate object detection while using fewer parameters through advanced design and optimization methods. Thus, it is worth noting the replacement of the C2f block with C3k2, which is a computationally more efficient implementation of the Cross Stage Partial (CSP) Bottleneck.

The main characteristics of the implemented convolutional neural network are presented in

Table 4. Parameters for training the YOLOv4 convolutional neural network.

№	Characteristics	Value
1	Number of images in the training set	70
2	Number of images in the validation set	20
3	Number of images in the test set	10
4	MiniBatchSize	5
5	Number of epochs	100
6	Learning rate	0.001
7	Solver	Adam solver

. The dataset was divided to achieve a 70/20/10 ratio of training, validation, and test samples.

After training the neural network and testing it on the test sample, it was necessary to evaluate not only the quality metrics of the network itself, but also the correspondence between the real distribution of pore sizes in the aerated concrete sample and the distribution produced by the intelligent algorithm. To assess the degree of correspondence, a statistical measure, the Hellinger distance, was chosen. In the context of analyzing the porosity of a building material, this metric allows researchers to visually assess the degree of correspondence between two distributions. It also helps to avoid ambiguity when interpreting the results.

2.4. Experimental Determination of the Aerated Concrete’s Thermal Conductivity

Experimental determination of the thermal conductivity of aerated concrete samples was carried out using the Thermal Conductivity Meter ITP-MG4 (Stroypribor, Chlyabinsk, Russian Federation). A general overview of the ITP-MG4 device is shown in Figure 4.

Thermal conductivity measurements were carried out in accordance with GOST 7076 [66] and ASTM C518 [67]. The samples were prepared in the form of rectangular parallelepipeds with dimensions of 100 × 100 × 21 mm. The samples were placed in the device, followed by monitoring of the heat flow, which was then carried out automatically. The timer on the bottom line of the display counted down the observation time, after which the thermal conductivity values were automatically calculated.

Table 5. Aerated concrete specimens’ characteristics.

Number	Sizes, cm	Volume, cm3	Mass, g	Density, kg/m3	Porosity	Thermal Conductivity, W/(m·K)
1	10 × 10 × 2.1	210	117.0	557.1 ± 11.1	0.786	0.109 ± 0.006
2			115.0	547.6 ± 10.9	0.789	0.114 ± 0.007
3			109.5	521.4 ± 10.4	0.799	0.111 ± 0.006

shows the characteristics of aerated concrete.

The standard deviations for average density values were no more than 2%, and for thermal conductivity, they were no more than 6%.

The characteristics presented in Table 4 were further used to model the porous structure of the material.

3. Results and Discussion

3.1. Training CNN YOLOv11

The implemented CNN allowed for the detection of objects of interest by selecting them in the bounding box (bbox), as well as segmenting each pore. Figure 5 displays the model training graph. The OY axis represents error values for detection (train/box_loss, val/box_loss) and segmentation (train/seg_loss, val/seg_loss) during training and validation. The OX axis denotes the number of epochs.

During the CNN training process, it is important to monitor both the training and validation curves to understand them and optimize a particular model parameter. As can be seen from Figure 5, at the beginning of training, the model parameters were still far from optimal values, so significant jumps in the loss function values can be observed for both samples. As training progresses, a decrease in the amplitude of the jumps was observed as the loss function values stabilized. The risk of overfitting was excluded in this case, given the use of standard control techniques on the validation dataset, with the use of data augmentation and the use of the model on a specific type of building material.

Figure 6a,b show the increases in the precision and recall metrics for pore detection and segmentation, respectively, that were achieved by the model during the training process.

The formulas remain the same as for regular object detection [68].

Let us denote precision and recall during detection as Precision_det and Recall_det. Then,

$$Precisio{n}_{\det }={\displaystyle \frac{T{P}_{\det }}{T{P}_{\det }+F{P}_{\det }}}$$

(1)

$$Recal{l}_{\det }={\displaystyle \frac{T{P}_{\det }}{T{P}_{\det }+F{N}_{\det }}}$$

(2)

Here, $T{P}_{\det }$ (true positives) are correctly predicted bounding boxes with an IoU (intersection over union) greater than the threshold of 0.5;

$F{P}_{\det }$ (false positives) are predicted bounding boxes that either do not overlap with the true object or overlap with it incorrectly;

$F{N}_{\det }$ (false negatives) are missed objects for which no suitable bounding box are predicted.

In turn, we denote the precision and recall of segmentation as $Precisio{n}_{seg}$ and $Recal{l}_{seg}$; as a result,

$$Precisio{n}_{seg}={\displaystyle \frac{T{P}_{seg}}{T{P}_{seg}+F{P}_{seg}}}$$

(3)

$$Recal{l}_{seg}={\displaystyle \frac{T{P}_{seg}}{T{P}_{seg}+F{N}_{seg}}}$$

(4)

where $T{P}_{seg}$ is the number of correctly predicted pixels belonging to the pore;

$F{P}_{seg}$ is the number of predicted pixels that do not actually belong to the pore;

$F{N}_{seg}$ is the number of pixels belonging to the pore but missed by the model.

The following results were achieved on the test sample: Precision = 0.86 and Recall = 0.88 for detection; Precision = 0.86 and Recall = 0.91 when selecting polygons (segmentation).

The obtained values satisfy the needs of the pore detection task on aerated concrete samples and have practical application value. In this case, the F1-score metric was not used, since when detecting a large number of small objects, the model can accurately detect boundaries with high precision (e.g., 0.99), but cannot find all objects with low recall (e.g., 0.61). In this case, the F1-score is 0.75, which is difficult to interpret the implications of. Therefore, precision and recall were analyzed separately, without combining them into one metric. Figure 7 shows a section of the product that passed through the intelligent algorithm.

According to Figure 7, the pores were detected with high accuracy: the bounding boxes clearly highlight the pores.

The size (diameter) of the pores can be determined by analyzing the bounding boxes generated by the neural network, as well as by analyzing the obtained polygons. In this study, we chose to determine the pore diameter based on the bbox dimensions. The diameter was calculated as the average of the two sides of the bbox.

3.2. Comparison of Two Distributions Using Hellinger Distance and Kolmogorov–Smirnov Criteria

Figure 8a,b show a visual comparison of the real distribution reflecting the pore size in the image (obtained during manual marking) and the distribution obtained by processing the results of the computer vision algorithm. The OX axis represents the pore size in mm, and the OY axis depicts the relative number of pores from the total number. To compare the two distributions, this study uses the Hellinger distance as a statistical measure, as it is intuitive for comparison.

The Hellinger distance, H(P,Q), between two discrete probability distributions, P and Q, is formulated as [69] follows:

$$H\left(P,\hspace{0.17em}Q\right)={\displaystyle \frac{1}{\sqrt{2}}}\sqrt{{\displaystyle \sum _{i=1}^n{\left[\sqrt{P\left(i\right)}-\sqrt{Q\left(i\right)}\right]}^2}}$$

(5)

Here, P(i) and Q(i) are the probability values for event i in distributions P and Q, respectively.

The difference in relative frequencies at a pore size of 0.4 mm is due to the rather small size of the pores and the quality of the original photographs. Such pores are more difficult to detect for the algorithm.

The Hellinger distance formula allows us to compare the differences between columns of two distributions. Its main advantage is that the value is always in the range from 0 to 1, which makes this metric convenient for assessing the degree of deviation. If the value is 0, the distributions are completely identical; if it is 1, the distributions are maximally different. H(P,Q) = 0.15 for the compared distributions, which indicates a relatively high degree of correspondence.

The hypothesis that the two samples, P and Q, belong to the same distribution law was also tested using the Kolmogorov–Smirnov goodness of fit criterion. The formula determining the Kolmogorov–Smirnov statistics is as follows [69]:

$$D_n=\underset{x\in R}{\sup }\left|P\left(i\right)-Q\left(i\right)\right|,$$

(6)

For this case, $D_n=0.218\hspace{0.17em}<0.36=K_{\alpha }$; here, $K_{\alpha }$ is ultimate value.

3.3. Obtaining a Porosity Map

Figure 9 shows the porosity map obtained for an aerated concrete product (from Figure 2) based on the sizes of the pores; this map was segmented by the algorithm.

Using computer vision, the unevenness of the pores was recorded on the porosity map, allowing us to analyze the pore structure of the material.

The figure shows pores ranging in size from 1 to 5 mm, corresponding to the real scenario. Large pores stand out from the general mass (highlighted in yellow) and are observed along the upper edge of the product.

This porosity map acts as a visual representation of the pore sizes of the cellular building material. Such a map can be an important tool for the subsequent analysis of a cellular building material’s properties. By analyzing the distribution of pores, conclusions can be drawn regarding the strength characteristics of the material, as well as its properties of water absorption and frost resistance. In the production stage, using such maps can be helpful for tracking, particularly when adjusting the steps in the process and changing the production technology used.

3.4. Thermal Conductivity Prediction

Among the most important characteristics of cellular concrete are the thermal engineering characteristics, including the thermal conductivity coefficient. The thermal conductivity of cellular concrete can be used as an indicator of how comfortable buildings are as a result of their porous structure. The pores in cellular concrete are filled with air, allowing the material to retain heat in the best possible way.

The low thermal conductivity coefficient of cellular concrete allows individuals to save the costs imposed by the heating system and the electricity used to maintain a comfortable temperature in the room. The walls of a house made of aerated concrete help maintain a pleasant microclimate, retaining heat in winter and creating a pleasant coolness during hot summers due to the fact that they do not let heat from outside in.

In addition, with equal thermal parameters, walls made of cellular concrete are several times lighter than those made of traditional materials, significantly reducing the load on the foundation.

The empirical distribution function of the predicted pore values, shown in Figure 8a,b, is satisfactorily approximated by a log-normal distribution law, with probability density [70]:

$$f_X(x)={\displaystyle \frac{1}{x\sqrt{2\pi }\sigma }}{e}^{-{\displaystyle \frac{{\left(\ln x-\mu \right)}^2}{2{\sigma }^2}}},$$

(7)

where $\mu ,\hspace{0.17em}\sigma$ represents the parameters of log-normal distribution.

Statistical estimation of the distribution parameters using the maximum likelihood method yields $\mu$ = 0.4540 and $\sigma$ = 0.4113.

Thus, the mathematical expression of the pore size (mm) is [70] as follows:

$$d_p=\mathrm{E}\left(X\right)=e^{\left(\mu +{\displaystyle \frac{{\sigma }^2}{2}}\right)}=1.714$$

(8)

That for dispersion is as follows [70]:

$${\sigma }_p^2=\mathrm{D}\left(X\right)=\left(e^{{\sigma }^2}-1\right)\hspace{0.17em}{e}^{2\mu +{\sigma }^2}=0.541,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\sigma }_p=0.735$$

(9)

To simulate the behavior of a porous material under thermal influences, the module ANSYS 2024 R2 Material Designer was used. This module, used for designing functional properties of composite materials, allows for the calculation of physical and mechanical properties (strength, thermal conductivity, and density).

Figure 10 shows the geometric model of the RVE, which includes a continuous matrix and pores with sizes randomly generated from a log-normal distribution with mean (8) and variance (9).

To construct the finite element model (Figure 11), a conformal mesh generation algorithm was used. To evaluate the thermal conductivity of the aerated concrete and to obtain predictions before production in accordance with the requirements of the standards, a combination of ANSYS 2024 R2 Workbench and ANSYS 2024 R2 Material Designer was used. The geometry of the model was a concrete matrix with included air spheres. The matrix was discretized with 382,626 tetrahedral elements. Each sphere was discretized depending on the diameter from 642 to 52,000 elements. The diameter of the spheres was randomly generated according to the log-normal law (7) and parameters (8) and (9). To ensure the convergence of the numerical solution, a convergence analysis was performed with a gradual increase in the number of elements and while checking the pore distribution.

The configuration of the representative volume of the composite material under study and the setting of the matrix and filler parameters were carried out based on the air pore sizes, taking into account the probabilistic nature of these. The length of the edge of the cubic volume was determined based on the principle that at least five pores should be placed on the length of the edge (Figure 10). Taking into account the probabilistic nature of the pore size, 178 pores of different sizes were presented in the simulated volume, ensuring a fairly representative sample.

The problem was solved under the following initial and boundary conditions. The origin was located at the bottom of the cube at the point $x=y=z=0$ (Figure 10 and Figure 11). On the boundary of the body, on surface S at x = a, for each node A_i, a constant temperature T was specified, $T(x=a,\hspace{0.17em}0\le y\le a,\hspace{0.17em}0\le z\le a,\hspace{0.17em}\tau =0)=const,\hspace{0.17em}{A}_i\in S$, where τ represents time, and a is the length of the cube side. The temperature, T, was measured on the opposite side. The convection exchange with the environment was excluded.

A comparison of the experimentally measured data with predicted results for aerated concrete is presented in

Table 6. Comparison of experimentally measured and predicted values of the density and thermal conductivity of porous concrete.

Porosity	Experimental Density, kg/m3	Predicted Density, kg/m3	Experimental Thermal Conductivity,W/(m·K)	Predicted Thermal Conductivity, W/(m·K)
0.786	542.0	555.7	0.111	0.114

.

Table 5 shows that the proposed method for determining porosity using the CNN allows one to determine the thermal conductivity of aerated concrete quite accurately.

3.5. Discussion

When comparing the experimental results with the results obtained from in previous works, it is worth noting not only studies based on artificial intelligence methods but also those featuring various methods and techniques for determining the porous structure of cellular materials. Thus, using X-ray computed microtomography (XCT) to study the role of the critical degree of saturation (DOS) and the air void system in the propagation of cracks in Portland cement mortar subjected to freeze–thaw cycles requires special equipment and safety measures due to the ionizing radiation involved [71]. In turn, the use of intelligent algorithms requires the use of a computer or smartphone, as well as clear rules for interpreting the results obtained. Ease of use and cross-platform compatibility make computer vision technology increasingly interesting and significant. In Ref. [72], the researchers note that the cost of X-ray computed tomography should be taken into account, and technologies for highlighting areas of interest using intelligent algorithms may be a better alternative in terms of time and money. Porosity is a property that must be taken into account, since it is directly related to the performance characteristics of cellular concrete [73]. Working with different samples of aerated concrete made of Portland cement, the researchers pre-processed the images, applied edge detection methods, and, based on the obtained boundaries, performed segmentation of pores. A comparison was made by detecting the number of real pores using the operator against the number of real pores determined by manual counting. The best result was demonstrated by the morphological operator Tiansi, which detected about 98% of the total number of pores. The algorithm proposed in our study demonstrates high accuracy in both detection and segmentation on more porous material, highlighting its ability to compete with existing methods, particularly in scenarios involving complex structures.

In Ref. [74], high-resolution micro-computed tomography in combination with 3D image analysis is presented as a promising approach for studying porosity and pore systems in bricks. Future research should focus on creating 3D models of building material samples.

The task of analyzing the porous structure of cellular concrete requires significant cognitive efforts [75]. The algorithm for analyzing the porosity of a composite material developed in this study is the least labor-intensive compared to other methods for analyzing the porosity of composites, a conclusion reached based on the amount of time required and the availability of specialized high-tech and expensive research equipment [76]. For example, one of the methods for analyzing the pore structure is mercury intrusion porosimetry (MIP). The principle of MIP is based on the properties of liquid mercury, which has high surface tension and non-wetting characteristics. The process of analyzing the porosity of a material using MIP includes pumping air out of the pores of the material under study, after which mercury enters the pores under pressure and sequentially fills the larger pores first; then, as the pressure increases, it fills the smallest pores. The volume of mercury and the pore size distribution curves corresponding to higher and lower pressures make it possible to estimate pore sizes from nanometers to micrometers and the nature of the pore distribution [77,78,79]. The nitrogen adsorption–desorption (NAD) method is also used to analyze the porosity of composites. The principle of the NAD method is based on the ability of nitrogen to penetrate into pores with a lower density. This method requires very careful sample preparation. First, all samples are processed to obtain the cleanest possible surface, and all vapors and gases that could be adsorbed on the surface of the experimental sample are removed. After cleaning and vacuum treatment, the apparatus is filled with gaseous nitrogen and the adsorption process begins. Then, isotherms and the volume of nitrogen adsorbed under pressure are measured and analyzed, giving us insights into the pore structure, the size of pores and their distribution pattern [80,81]. It is expected that the developed algorithm, when implemented both in laboratory conditions at composition development stage and directly on the production line, will be able to perform analysis with an accuracy comparable to that of specialists. Products with a disrupted ratio of cellular structures can be identified at the earliest stages. AI-based detection of defective structures in complex industries will facilitate the smooth identification of critical product defects, rendering them unsuitable for use, as well as of non-critical defects permissible for us by construction industry standards. The developed algorithm can be distinguished from other methods because it provides reliable results (confirmed by the quality metrics of the test sample) and is an easily adaptable tool for the implementation of projects related to the introduction of intelligent algorithms for monitoring the quality of building materials. The CNN architecture chosen in this study belongs among the state-of-the-art technologies and exhibits an excellent combination of speed, accuracy and efficiency. YOLOv11 is aimed at improving the detection of small objects and increasing accuracy while maintaining inference speed in real time, which will be useful when applying this algorithm in practice. To prevent the model’s performance from deteriorating over time, it is necessary to take into account that the structure of the building material can be affected by various external and internal factors, for example the impact of previously unaccounted climatic conditions (including aggressive environments) and the use of new technologies in production, which entails changes in defect characteristics. Monitoring data drift will make it possible to identify changes in the distribution of data and promptly update training datasets, thus allowing researchers to track the current state of the analyzed process. In turn, changes in our understanding of the associated concepts will allow for the standards or quality norms in the field of construction material production to be updated. Defects that were previously considered significant may become insignificant due to the economic feasibility of using a given material in less critical structures, as well as due to changes in operating requirements brought about by the progress made in construction technologies. Despite the slow pace of digitalization, the construction industry is increasingly beginning to adopt intelligent innovations to improve the quality, speed and safety of construction materials.

The developed forecast model will be most in demand when constructing enclosing structures from low-density, heat-insulating highly porous cellular concrete. For modern construction, taking into account the requirements of norms and rules, an important aspect is the energy efficiency of objects. This parameter directly depends on thermal conductivity, but instrumental determination of thermal conductivity is not always possible and is often difficult. Thus, we propose using the presented forecast model in such complex cases. This will simplify and speed up the process.

As a short-term course of action for the developed algorithm’s practical implementation, we plan to obtain a patent for the specified method. As a long-term course of action for its practical implementation, industrial implementation in an enterprise producing aerated concrete products is envisaged. We plan to continue this line of research by applying new models to further improve the quality of forecasting.

4. Conclusions

During the implementation of the YOLOv11 convolutional neural network for analyzing the porosity of aerated concrete products, the following results were achieved:

(1) To expand the sample, an augmentation algorithm was used that can recalculate the bounding box and segmentation area.

(2) Experimental results showed that the developed model has high accuracy in identifying areas of interest: Precision = 0.86 and Recall = 0.88 for detection; Precision = 0.86 and Recall = 0.91 when identifying polygons (segmentation).

(3) A comparison of two distributions—real and predicted—was carried out using the Hellinger distance. H(P,Q) = 0.15, and Kolmogorov–Smirnov $D_n=0.218$, which indicates a high degree of significance.

(4) The conducted SNN and statistical analysis allowed us to model a porous material using ANSYS 2024 R2 Material Designer and predict its thermal conductivity with an error of less than 7%.

(5) Prospects for improving the model include the following:

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Applying the developed algorithm to other building materials with a cellular structure;

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Expanding the number of predicted mechanical characteristics of the material, such as its elastic modulus, strength, acoustic properties, and others;

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Implementing the developed model in a modern computer vision application for the quality control of building materials, products, and structures at various stages of their life cycle.