Convolutional Neural Network and Support Vector Machine for Prediction of Damage Intensity to Multi-Storey Prefabricated RC Buildings

Abstract

This paper presents the results of a comparative analysis of Convolutional Neural Network (CNN) and Support Vector Machine (SVM) models created for the prediction of the extent and intensity of damage caused to multi-storey reinforced concrete (RC) buildings. The research was conducted on a group of residential buildings, which were subjected to mining impacts in the form of surface deformations and rock mass tremors during their technical life cycle. Damage to buildings poses a significant threat to the safety of the structure and the serviceability of the buildings. They are often the cause of breaks in thermal insulation, which leads to excessive consumption of thermal energy used for space heating, which in turn contributes to over-emissions of CO₂ into the atmosphere. Therefore, this problem is important, not only from a technical dimension, but also includes social, economic, and environmental aspects, which allows it to be classified as an issue of sustainable development in the building industry. As a result of the conducted analysis, among the CNN models, the highest level of classification accuracy was the model obtained using the ADAM (derived from adaptive moment estimation) algorithm, which was also characterized by a very high level of generalization, obtaining 80.35% correctly classified patterns for the training set and 80.52% for the test set. However, its accuracy level was slightly lower than that of the SVM model (85.15% for the training set and 84.42% for the test set), in which Bayesian optimization was used to determine the parameters. The analysis confirmed the effectiveness of the adopted methodology for predicting the extent and intensity of damage. The developed tool can support the optimization of building maintenance management, resulting in reduced economic and environmental expenditures for renovations.

1. Introduction

From the technical and social points of view, multi-storey reinforced concrete (RC) residential buildings are a particularly important group of buildings. In the literature, damage to these type of buildings is analyzed mainly in terms of safety [1,2]; however, damage often also causes the deterioration of thermal insulation properties, raising heating costs. In addition, damages contribute to the formation of thermal bridges, but they can also be the cause of disruption of the waterproof layers, leading to the penetration of moisture into the building. This lowers the thermal and humidity properties of the building, generating an increase in the energy expenditure needed to heat or dry the walls [3]. Therefore, it is very important to predict the extent of potential damage to buildings and to adapt renovation management to this damage.

The causes of damage to RC buildings may include prefabrication defects, assembly errors, improper methods of exploitation, aging of the materials, improper repair management, environmental impacts, and anthropogenic factors such as mining activity [3]. Therefore, each time damage is detected, the cause of the damage must be identified. Due to the potentially large number of buildings, the multiplicity of the factors involved, and the diversity of damage, it is usually not possible to perform this assessment using the Finite Element Method (FEM). Such an assessment is performed by structural engineers, who should pay particular attention to the extent and intensity of the damage in the context of determining the causes of the damage, as well as the means of repair, taking into account a number of factors such as those mentioned above [4,5]. This is very important, as this assessment is the basis of further actions to restore the appropriate functional and energetic properties of buildings, as well as planning modernization activities.

In Europe, efforts have been made recently to integrate energy and seismic retrofitting of buildings [6], including multi-storey RC buildings [7]. By contrast, in Poland, many of these buildings are located in mining areas and have been subjected to the damaging impacts of the industrial environment throughout their entire life cycle. Underground mining interferes with the rock mass, inside which stresses and deformations are generated. Then, as a result of the release of elastic potential energy, they are transmitted to the ground surface. These impacts most often manifest as continuous deformations [8] and mining tremors [9] and less often as discontinuous deformations [10]. These impacts induce kinematic loads transmitted through the ground to buildings, and this in turn can have a negative effect on buildings [9,11,12,13] and initiate the damage process.

An additional motivation for this research topic was the situation observed in recent years in the building market in Poland. Rising prices of building materials and their dwindling supply generate the need to save natural resources. Therefore, in recent years, more and more attention has been paid to the renovation of existing structures, thus extending their service life [14]. These trends are also prescribed by European Union regulations [15], which stipulate requirements for the sustainable consumption of natural resources, stating that construction works must be designed to ensure the reuse of existing structures or the materials recovered from dismantling them, the durability of construction works, and the use of eco-friendly materials.

With environmental protection in mind, it is important to mention here that the building and construction sector accounts for almost one-third of the world’s energy consumption and almost 15% of direct CO₂ emissions [16]. Therefore, a change is needed to reduce the energy demand of newly constructed buildings, as well as the use of systems powered by RES. Unfortunately, the building stocks (including housing) in the European Union member states are aging. This was confirmed by the European Commission report, which states that 75% of the buildings in the European Union were built before 1990 [17] with a renovation rate of 1.2% [18,19]. Thus, it can be concluded that buildings have a large impact on the level of energy consumption. This is especially true for older buildings that were built before 1990, which represent the majority of the European building stock Therefore, the European Commission in 2019 made the recommendations [20], which also take into account older buildings, showing a greater need for their renovation, which will contribute to reducing CO₂ emissions. However, it is important to remember that any renovation has not only economic but also environmental costs. The production of construction materials, the related work of machines and people, transportation of the materials to the renovation site, and finally the repair or replacement of worn-out or damaged elements of the building lead to increased CO₂ emissions as well as consumption of natural resources, which are limited. Therefore, the widely understood Maintenance Management [21], which aims to determine the optimal time of repair, due to changes in the reliability level of the structure associated with the damage intensity function, has recently become an important factor [22].

Analyses of the extent and intensity of damage caused to multi-storey RC buildings in conjunction with the considered socio-economic and environmental aspects fit well with the idea of sustainable development. The basic assumption of this doctrine is to achieve social sustainability by increasing the economic and environmental efficiency of construction projects [23,24,25], increasingly using Artificial Intelligence and Machine Learning [26,27]. All of this creates a need to use more accurate tools for predicting building damage and to implement ML methods in research that have not been previously used for such issues.

With this in mind and employing the experience gained from previous studies that used Machine Learning methods [28,29,30], the following was defined the subject of the study: to create a tool that can accurately predict the extent of damage to buildings, based on their degree of technical wear and the value of predicted deformation and indicators of mining tremors. To accomplish this task, classifiers from the area (family) of Machine Learning—Support Vector Machine (SVM) and Deep Learning—Convolutional Neural Network (CNN) were used. In the case of the CNN, it should be mentioned that it has not been used in such research before and required the processing of numerical data into a quasi-image. Therefore, an additional objective of this research was to evaluate the utility of CNNs in this type of task.

In this paper, the applied methodology will allow predicting the extent of damage to multi-storey RC buildings. It will contribute to more effective decision-making related to Maintenance Management, so that buildings maintain the best possible energy properties throughout their technical life cycle. It will increase opportunities related to the proper use of building materials and the determination of optimal repair dates for buildings located in mining areas. All of this can support sustainability in the construction industry and can have a positive impact on renovation costs and the environment, as well as natural resources.

2. Methods

The main objective of the study was to create a tool that will effectively predict the extent and intensity of damage caused to buildings threatened by industrial environmental impacts. An additional objective was to evaluate the usefulness of a CNN to classify the intensity of building damage based on numerical data on the degree of technical wear of the building and on mining indicators, recorded in the form of quasi-images. To assess the usefulness of the CNN method, similar analyses were performed on numerical data using the SVM method. The analyses were performed in the MATLAB program [31]. A framework of the study is shown in Figure 1.

2.1. Convolutional Neural Network

Among the deep learning methods, CNNs deserves special attention, as these are the most widely used methods in computer vision tasks since 2012 when the ImageNet Large Scale Visual Recognition Competition (ILSVRC) published astonishing results of image recognition research [32,33,34]. Most of the contemporary research on building damage and its intensity is conducted by using conventional machine learning classifiers such as Support Vector Machines, Probabilistic Neural Networks or Random Forests [28,35,36]. Recently, Bayesian Belief Networks have also become very popular [3,37].

CNNs are commonly used for the analysis of images/photographs, which consist of pixels. In issues related to building construction, CNNs are used, for example, to identify objects damaged by earthquakes on satellite/UAV images [38,39], to detect and classify buildings and other structures in issues of modeling and to monitor changes in urban spaces [40], or to detect surface scratches on architectural glass panels [41]. All of these studies use various types of imagery created in the field, which means that these data were originally saved as images. In the present study, numerical data were transformed into an image and were classified in terms of the percentage of the building damage intensity index wu [42]. To date, the literature on the subject does not contain cases where data were similarly used for CNN-based analysis to classify building damage intensity based on the value of technical wear and mining indicators.

The architecture of deep neural networks should be configured to handle particular types of data as well as possible. A general diagram of a CNN is shown in Figure 2. The start of the network is the Input layer, where the images are loaded. The end of the network is the output (Final layer), while inside the network (in hidden layers), there are three main types of layers: Convolutional, Pooling, and Fully connected layers [43].

The Convolutional layer is the foundation of a CNN. Its parameters are centered around the use of learned filters (kernels), which are able to extract features that distinguish images from each other. Spatial filters (kernels) are usually selected for a small area (e.g., 3 × 3 px) to “ move” along the dimension of the input data. Subsequently, through a convolution layer, these filters are converted to form a two-dimensional activation map [33,43]. This means that the user can specify the values of hyperparameters such as the kernel size, number of filters (neurons in the layer), padding, or strides, while the values in the filters are selected and optimized during network training and are chosen to minimize the network error when solving the problem.

In input images, pixels that lie in close proximity tend to have similar values, which tends to generate similar values for neighboring pixels in the outputs, which in turn makes much of the information contained in the output data “so-called noise” and redundant. The Pooling layer uses a down-sampling operation that reduces the dimensions of the feature maps in the plane in order to reduce the amount of learning data. This layer has no learning parameters. In pooling operations—as with the Convolutional layer—kernel size, padding, and strides are hyperparameters. The most popular operations performed on two-dimensional filters of a given size are max, min, or average pooling [33,44].

After the features are extracted with the Convolutional layers and are downsampled by the Pooling layer, they are mapped by the Fully connected layer to the final output of the network, such as the probabilities for each class in the classification tasks. The final Fully connected layer has the same number of output nodes as the number of classes [33,45].

In addition to these layers, nonlinear activation functions play an important role in the architecture and proper operation of the network. They are necessary to produce nonlinear decision boundaries so that the result cannot be written as a linear combination of inputs [44]. In addition to the architecture, the learning algorithm plays a key role in the proper performance of the network. In this study, the learning algorithm is used for multiclass classification.

2.2. Support Vector Machine

To verify the correctness of the results obtained through CNN analyses, the SVM classifier was used, which can distinguish data points belonging to two (binary classifier) or more classes (multiclass classifier) of the decision variable. In an SVM, data are represented by n-dimensional vectors, each of which belongs to one of the classes. The data (depending on the class) are separated by a hyperplane. Multiple hyperplanes can be fitted between groups of data to properly separate them. The SVM selects the hyperplane that has the largest margin in order to maximize data separation between classes, as shown in Figure 3. Such a hyperplane will generalize better, meaning that it correctly classifies “unseen” or test data [46].

In an SVM, different types of kernel functions (linear, polynomial, radial, and sigmoidal) can be used. With their help, classification tasks can be performed for both continuous and categorized variables [47]. However, using a linear description of the separating hyperplane is often inefficient and applies to cases where the data are indeed linearly separable. To increase the chances of separating x-patterns, Cover’s theorem is applied [48]. It involves projecting the original patterns x onto a higher dimensional feature space. Assuming that the projection of the original patterns x onto the feature space is done by some transformation φ(x), a separation hyperplane with the following form is obtained:

$$\mathrm{y}\left(x\right)=w^{\mathrm{T}}\mathsf{\phi }\left(x\right)+\mathrm{b}=0$$

(1)

where

$\mathbf{x}\in {\mathrm{R}}^{\mathrm{n}}$ is the vector of the input data in the n-dimensional space;

${\mathsf{\phi }: \mathrm{R}}^{\mathrm{n}}\to {\mathrm{R}}^{{\mathrm{n}}_{\mathrm{h}}}$ is a certain transformation converting raw input data into the so-called feature space;

w^T is the vector of the weights.

The mapping ${\mathsf{\phi }: \mathrm{R}}^{\mathrm{n}}\to {\mathrm{R}}^{{\mathrm{n}}_{\mathrm{h}}}$ is given in an implicit way and results from the application of a specific type of kernel function. The final description of the SVM classifier, according to [49], can be written as follows:

$$\mathrm{y}\left(x\right)={\displaystyle \sum }_{\mathrm{k}=1}^{{\mathrm{N}}_{\mathrm{sv}}}{\alpha }_{\mathrm{k}}{\mathrm{d}}_{\mathrm{k}}\mathrm{K}\left(x,x_{\mathrm{k}}\right)+\mathrm{b}$$

(2)

The factor K(·) in Equation (2) is the kernel of the system, which is predetermined explicitly and it is the result of merging the implicit functions $\mathsf{\phi }$ as follows:

$$\mathrm{K}\left(x_{\mathrm{k}},x_{\mathrm{j}}\right)=\phi \left(x_{\mathrm{k}}\right)\phi \left(x_{\mathrm{j}}\right)$$

(3)

The form of the kernel is selected arbitrarily from all functions that meet the assumptions of Mercer’s Theorem [50].

The main problem that is associated with the construction of the SVM classifier is determining the optimum values of the parameters C and γ. The parameter C is a regularization constant present in the formulation of the so-called loss function, which determines the learning process. On the other hand, the parameter γ determines the width of the adopted kernel functions (4).

$$\mathrm{K}\left(x_{\mathrm{k}},x_{\mathrm{j}}\right)=\exp \left(-\frac{{\left(x_{\mathrm{k}}-x_{\mathrm{j}}\right)}^2}{{\gamma }^2}\right)=\exp \left(-\sigma {\left(x_{\mathrm{k}}-x_{\mathrm{j}}\right)}^2\right)$$

(4)

The optimal values of these parameters are determined in MATLAB using Bayesian optimisation [51].

3. Materials (Preparation of a Testing Ground)

The research relied on a database containing information on 306 prefabricated RC buildings located in the mining area of Legnica-Głogów Copper District (LGCD). These are residential buildings built in the large-panel or large-block technology, which, in recent years, have been the subject of a comprehensive architectural and construction inventory and damage. The collected data included information on age, geometry, structural solutions, technical condition, and intensity of damage to individual building elements. Additionally, on the basis of mining exploitation data, maximum values of mining indices were determined for each building and were included in the database.

Based on the damage intensity indices of particular building elements (w_ui) and the formulas determined in the published paper [25], the values of the damage intensity index (w_u) for buildings were determined. This formula has the general form

$$w_u={\displaystyle \sum }_i{a}_i{w}_{ui}$$

(5)

where

$a_i$—Directional coefficients of the linear combination of components occurring at individual damage indices determined by the PLSR method [25],

$w_{ui}$—The value of indicators of damage intensity of individual building elements.

The subject of the study was to obtain a tool that could be used to predict damage; therefore, the whole damage intensity index (w_u) was chosen as the decision variable.

Due to the high similarity in both structural and geometric terms of the buildings under study, the following indicators were selected as predictive variables in the analysis:

• The degree of technical wear (s_z), which was determined for individual buildings using the weighted average method, taking into account individual structural and technological solutions.
• Extreme horizontal ground deformation (ε_max), one of the indicators of the risk of continuous deformation of the ground surface, which takes into account the maximum deformation that occurred from the date of construction to the date of the building inventory.
• Maximum horizontal component of the vibration acceleration (a_Hmax), which is the maximum ground vibration acceleration induced by a tremor that occurred during the lifetime of the building.
• Tremor intensity index (a_sg), which is a measure of the impact of mining tremors on the technical wear of buildings [52].
• Number of tremors (n), which indicates the number of tremors with a maximum vibration acceleration value higher than the threshold value a_p ≥ 0.12 m/s² [52] that has occurred during the lifetime of a building.

CNNs are most often used to analyze images in which neighboring pixels are often correlated. In this case, the data adopted for analysis are for five indicators that do not correlate with each other. Therefore, even before the CNN, it was suspected that filters moving only within a single row (1 px high) might be the most suitable, and this was confirmed in later tests.

Preparation of Quasi-Images Displaying Data for CNN Analysis

Before proceeding, the values of each predictor had to be qualified by dividing them into the appropriate number of intervals so that they could be saved as an quasi-image. According to the distribution of values for each variable, it was determined that the optimal image size would be 5 × 18 pixels, where 5 represents the number of predictor variables and 18 represents the maximum number of equal intervals into which each predictor variable was divided. The first interval for each variable started at “0”. The division of the predictor variables is presented in Figure 4. The decision variable was divided into four equal intervals with boundary values w_u of 3.2%; 6.4%; 9.6%; and 12.8%.

According to the partitioning described above, the data were converted into monochrome images with a grayscale of 256 shades, where 0 represents black and 255 represents white. Examples of the data images are shown in Figure 5.

Each horizontal portion of the image with a height of one pixel presents a different predictor variable. Depending on the value obtained (see Figure 4), a white pixel appears in the drawing. The drawings created in this way were used in further analyses.

4. Results

One of the intentions of the research presented in this paper was to test the feasibility of using CNNs in building damage intensity studies. Not without reason, an SVM was used to evaluate this method because it performs well in this type of task, which has been confirmed by many publications [28,35,53,54,55]. To be able to compare the two methods, the analyses had to be performed on the same datasets. The data were first divided into a training set and a test set in a 75% to 25% ratio. Then, the CNN and SVM analyses were conducted on exactly the same sets.

To evaluate the correctness of the classification and to compare the results of the two methods, a confusion matrix was used. The general form of the confusion matrix for binary classification is shown in

Table 1. Confusion matrix for a binary classification.

	Actual Positive	Actual Negative
Predicted positive	True positives TP	False positives FP
Predicted negative	False negatives FN	True negatives TN

.

The overall quality classification level (accuracy) is the essential comparative parameter [56]:

$$\mathrm{Qc}=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{FP}+\mathrm{FN}+\mathrm{TN}}$$

(6)

In addition, the following parameters were assumed for evaluation [56]:

• Precision:

$$\mathrm{PPV}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}$$

(7)

• Recall:

$$\mathrm{TPR}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$$

(8)

A very important factor in the evaluation of the obtained models is the generalization [57]. To verify this, the relative difference in classification accuracy for the training and test set (ΔQc) was calculated.

4.1. Results for the Convolutional Neural Network

Even though CNNs provide opportunities to create a nested network architecture [58], in this case, attempts to implement more complex networks yielded poorer results due to the low complexity of the input data. It was sufficient to create a simple network, whose operation scheme is shown in Figure 6.

Figure 6 presents a schematic of the optimal network created for the defined task. Besides the layout itself, the choice of parameters in each layer was also important. The first layer (Image input), as the name suggests, was used as an input layer for data in the form of images, the generation of which is discussed in chapter three. Next, a Convolutional 2D layer (Convolution) was used. For this, the optimal filter dimensions turned out to be 1 × 3 pixels with 12 filters (neurons) per layer. After the Convolutional layer, the Normalization layer (Batch norm) was applied. Rectified Linear Activation (Relu) was used to obtain the necessary nonlinearity. Downsampling was done using the Pooling layer (Max pooling). It should be noted here that the optimal filter dimensions at this stage, as in the Convolutional layer, turned out to be 1 × 3 pixels. Another important step was the use of the Fully connected layer (Fully connected), which created connections inside the network along with assigning appropriate weights. The so-called network output step was the use of Softmax and Class output (Classification layer). After going through the first one, each class now corresponded to a certain probability.

In addition to the proper selection of the network architecture, an important step was the selection of an appropriate learning algorithm for the assigned task and the identification of training options. In our task, the best accuracy was demonstrated by the ADAM (derived from adaptive moment estimation) [59] and SGDM (stochastic gradient descent with momentum) algorithms. The other algorithms proved to be much less accurate, achieving accuracy levels of less than 74% for both training and test data sets. The results of the analyses using the ADAM and SGDM algorithms are shown in

Table 2. CNN quality classification levels.

Algorithm	Data Set	Quality Classification Level Qc [%]
ADAM	training set	80.35
	test set	80.52
SGDM	training set	78.60
	test set	80.52

.

It can be concluded from the results in Table 2 that for the CNN, both the ADAM and SGDM algorithms achieved a high level of correct classification. Using the ADAM algorithm yielded less than 2% better classification accuracy for the training set. Nevertheless, both algorithms achieved the same classification accuracy on the test set. The ADAM algorithm maintained a higher level of generalization, as evidenced by similar quality classification levels (Qc) for the training and test sets, so it was used in the following study. More detailed test results for the ADAM algorithm are presented in

Table 3. Confusion matrix for the CNN classifier—quality of classification, average precision, and average recall for training and test sets.

Training Set Containing 229 Cases
Damage intensity	Value (up to)	3.2%	6.4%	9.6%	12.8%	Σ	Precision PPV
	Category	1	2	3	4
Predicted	1	0	7	2	0	9	0.00%
	2	0	51	11	0	62	82.26%
	3	0	5	120	4	129	93.02%
	4	0	1	15	13	29	44.83%
Σ		0	64	148	17	229	avg. PPV
							55.03%
Recall TPR		0.00%	79.69%	81.08%	76.47%	avg. TPR	Qc
						59.31%	80.35%
Test set containing 77 cases
Damage intensity	Value (up to)	3.2%	6.4%	9.6%	12.8%	Σ	Precision PPV
	Category	1	2	3	4
Predicted	1	0	3	0	0	3	0.00%
	2	0	13	8	0	21	61.90%
	3	0	0	43	0	43	100.00%
	4	0	0	4	6	10	60.00%
Σ		0	16	55	6	77	avg. PPV
							55.48%
Recall TPR		0.00%	81.25%	78.18%	100.00%	avg. TPR	Qc
						64.86%	80.52%

.

The created CNN classifier showed good classification quality (accuracy) for both training and test sets of more than 80%. Based on the classification accuracy results, the generalization ability of the model was evaluated as very good (ΔQc = 0.17%). Figure 7 shows the learning process of the CNN model.

Figure 7 presents a line plot of the classification results during the training and testing processes of the created network. The continuous line indicates the results for the training set, while the dashed line represents those of the test set. In the initial phase of learning, the classification accuracy for the training set was 12%, increasing with subsequent iterations, and reaching an accuracy of 80% after eight iterations. This value remained similar until the last (30th) iteration. The classification accuracy for the test set initially reached a value of 62%, increasing to more than 80% after the learning process.

4.2. Results of the Support Vector Machine

According to the adopted course of analysis, the construction of the model began with the determination of the optimal hyperparameters C and γ. For this task, the Bayesian optimization method was used with cross-validation. Radial basis functions (RBF) were adopted as the kernel function of the model. The results are presented in

Table 4. SVM hyperparameters.

Optimization Method	Parameters
	C	γ	Kernel Function
Bayesian optimization	1.048	0.98	RBF

.

The SVM classifier, created for the extracted optimal values of hyperparameters C and γ, was characterized by the number of support vectors equal to 150. The number of support vectors with respect to all patterns used during learning was thus 65.50% of the training set size. This indicates an average complexity of the model, which should not significantly translate into a reduction of its generalization properties.

Table 5. Confusion matrix for the SVM classifier—quality of classification, average precision, and average recall for training and test sets.

Training set containing 229 cases
Damage intensity	Value (up to)	3.2%	6.4%	9.6%	12.8%	Σ	Precision PPV
	Category	1	2	3	4
Predicted	1	1	6	2	0	9	11.11%
	2	0	53	9	0	62	85.48%
	3	0	2	125	2	129	96.90%
	4	0	1	13	15	29	51.72%
Σ		1	62	149	17	229	avg. PPV
							61.30%
Recall TPR		100.00%	85.48%	83.89%	88.24%	avg. TPR	Qc
						89.40%	84.72%
Test set containing 77 cases
Damage intensity	Value (up to)	3.2%	6.4%	9.6%	12.8%	Σ	Precision PPV
	Category	1	2	3	4
Predicted	1	0	3	0	0	3	0.00%
	2	0	15	6	0	21	71.43%
	3	0	1	42	0	43	97.67%
	4	0	0	2	8	10	80.00%
Σ		0	19	50	8	77	avg. PPV
							62.28%
Recall TPR		0.00%	78.95%	84.00%	100.00%	avg. TPR	Qc
						65.74%	84.42%

shows the results.

According to the results in Table 5, it can be concluded that the SVM network obtained by optimally selecting hyperparameters with Bayesian optimization, for both the training and test sets, provided a high result (less than 85%) of correct classification while maintaining a very high level of generalization, as evidenced by similar Qc values for the training and test sets (ΔQc = 0.30%). For this reason, this model was qualified for further analysis and was used for comparison with the CNN model.

4.3. Comparison of the CNN and SVM

The final step of the study was to compare the results from the selected CNN model and the control SVM model. These results are presented in

Table 6. Comparison of classification parameters for the CNN and SVM classifiers.

Method	Training Set			Test Set
	Qc	avg. PPV	avg. TPR	Qc	avg. PPV	avg. TPR
CNN	80.35	55.03	59.31	80.52	55.48	64.86
SVM	84.72	61.30	89.40	84.42	62.28	65.74

. The comparative parameters are the Qc classification accuracy and the average values of PPV precision and TPR sensitivity.

The results, in Table 6, confirm that the CNN exhibited classification agreement with the SVM control model, yielding classification results that were a few percentage points lower. The difference here was quite subtle and placed both methods at a good level in terms of classification correctness. The results for PPV precision and TPR sensitivity were slightly worse, mainly due to the small amount of data for the first and fourth damage intensity categories. In the case of the CNN network, despite the worse result, it retained better generalization properties as evidenced by the small difference between the quality of the classification level (Qc) for the training and test sets.

It would also be appropriate to refer here to Table 3 and Table 5, which show how the two methods behave in the following categories. The biggest differences can be seen in small datasets, where CNN performed much worse than SVM. For larger datasets (3rd category of damage intensity) in the test set, the CNN classifier achieved 100% precision.

4.4. Critical Analysis and Discussion

In damage classification and prediction problems, SVM models perform well, as demonstrated in many works, e.g., [60]. The main shortcoming of this method is generally the relatively large accuracy difference between the training set and the test set, e.g., [28,57]. In the present study, an SVM model was created that maintained a high level of generalization (∆Qc = 0.30%). The CNN model performed even better in this respect, where the difference in the classification accuracy between the training and test sets was only ∆Qc = 0.17%. On the other hand, parameters such as PPV precision and TPR sensitivity, mainly due to the small number of data points, performed unfavorably compared to other studies. In this case, out of the two methods compared, the SVM performed better with fewer data than the CNN. In contrast, as the amount of data in each category increased, the CNN became stronger, reaching an accuracy for the third category of 100% for the test set. This state of affairs creates a need to expand the dataset and continue the present research.

When analyzing the results in terms of the applied methodology, one should also pay attention to the structure of the models being compared. A CNN model is created for image classification, while an SVM model operates on numerical data. In the SVM model, by definition, all input variables are independent and simultaneously influence the value of the output variable. In order to maximize the quality classification level, only the weights between the value of the activated kernel function and the output variable are adjusted. Admittedly, in the CNN model, the correlation between variables (image rows) is not examined, but filters are applied, which can somehow exclude values contained in neighboring pixels. The input to the CNN was stored as images, which were treated as an inseparable whole from the moment they were converted into images. This provided some opportunities to apply larger filters that were able to generalize the values contained in neighboring pixels. However, it was ultimately found that filters operating on only one row at a time were best. This may indicate a low correlation between the values of the variables recorded in adjacent rows. The input data to the model, namely, the degree of technical wear (s_z), extreme horizontal ground deformation (ε_max), maximum horizontal component of the vibration acceleration (a_Hmax), tremor intensity index (a_sg), and number of tremors (n), proved to be good predictors in the prediction of damage caused to multi-storey prefabricated RC buildings. Based on these data, it is possible to estimate the level of damage intensity to the buildings with a classification accuracy of more than 80%.

5. Conclusions

The main objective of the research was to develop a model for the prediction of the extent and intensity of damage caused to multi-storey prefabricated RC buildings located in mining areas. An additional task of the research was to assess the usefulness of Convolutional Neural Networks in problems of this type, which until now have been used only for image detection/differentiation and classification. In this case, numerical data containing information about the degree of technical wear of buildings but also mining indicators were used for the research and converted into an image.

In this research, multiple analyses were performed using different optimization criteria. Among the CNNs, the network using the ADAM algorithm (derived from adaptive moment estimation) proved to be the best, achieving a classification accuracy of 80.52% for the test set. Similar accuracy was also achieved for the training set, indicating a high level of generalization of the resulting network. The SVM model was used for comparison. Bayesian optimization was used to select the model parameters. Radial basis functions (RBFs) were used as the kernel function of the model. The resulting model had a higher classification accuracy, at 84.42% (for the test set), and a slightly lower generalization level, though nevertheless still very high. Therefore, the SVM model proved to be better for solving the task at hand. However, it should be pointed out here that the CNN model also performed quite well and can be used in further studies of this type. The main shortcoming of the analysis was the small dataset, which primarily influenced the inferior performance of the CNN’s analysis. Therefore, it is planned to develop this research in the future using a larger dataset containing information on more buildings and a damage intensity index wu with a wider range of values. It is important to mention that the CNN analyses are more automated, which will be very helpful with a growing dataset. This may allow the build-up of a real-time system, which seems to be essential in the case of mining tremors. As the main limitation in using the proposed CNN method, there is a need to use a very good graphics processing unit (GPU) as well as a large amount of storage space.

Practically speaking, the resulting models can be used to predict the intensity of damage caused to buildings at a stage when we only have information about the degree of technical wear of the building and a prediction of future mining impacts.

Moreover, considering that these damages cause disruption of thermal and waterproofing layers, accurate prediction of these damages can contribute to the development of maintenance management. More efficient property management, including repairs, can lead to a reduction in the energy demand of buildings and to savings in building materials in the long term. Taking into account the large number of such buildings located in mining areas, this can lead to significant energy, economic, and environmental savings, as well as increased quality of life of users and the sustainable development of buildings.

In the case of buildings exposed to high-intensity damage, these predictions can support preventive building protection work, effectively reducing the future extent of damage. It should be noted that the methodology adopted in this research can also be applied to buildings of other construction as well as other structures.