Prediction of the Properties of Vibro-Centrifuged Variatropic Concrete in Aggressive Environments Using Machine Learning Methods

Abstract

In recent years, one of the most promising areas in modern concrete science and the technology of reinforced concrete structures is the technology of vibro-centrifugation of concrete, which makes it possible to obtain reinforced concrete elements with a variatropic structure. However, this area is poorly studied and there is a serious deficiency in both scientific and practical terms, expressed in the absence of a systematic knowledge of the life cycle management processes of vibro-centrifuged variatropic concrete. Artificial intelligence methods are seen as one of the most promising methods for improving the process of managing the life cycle of such concrete in reinforced concrete structures. The purpose of the study is to develop and compare machine learning algorithms based on ridge regression, decision tree and extreme gradient boosting (XGBoost) for predicting the compressive strength of vibro-centrifuged variatropic concrete using a database of experimental values obtained under laboratory conditions. As a result of laboratory tests, a dataset of 664 samples was generated, describing the influence of aggressive environmental factors (freezing–thawing, chloride content, sulfate content and number of wetting–drying cycles) on the final strength characteristics of concrete. The use of analytical techniques to extract additional knowledge from data contributed to improving the resulting predictive properties of machine learning models. As a result, the average absolute percentage error (MAPE) for the best XGBoost algorithm was 2.72%, mean absolute error (MAE) = 1.134627, mean squared error (MSE) = 4.801390, root-mean-square error (RMSE) = 2.191208 and R² = 0.93, which allows to conclude that it is possible to use “smart” algorithms to improve the life cycle management process of vibro-centrifuged variatropic concrete, by reducing the time required for the compressive strength assessment of new structures.

1. Introduction

Modern construction requires new approaches to constructive, technological and design solutions in the erection of buildings and structures of different degrees of responsibility. At the same time, a new culture of construction processes comes to the fore, which consists of ensuring high-quality support over the entire life cycle of construction projects. It should be understood that, like many decades ago, the main type of structural element is reinforced concrete structures [1]. At the same time, reinforced concrete structures imply a variety of different solutions in terms of new materials, new technologies and new design solutions. Thus, it is advisable to apply, in construction processes, new knowledge obtained in the course of scientific research, as well as during pilot industrial testing of the most effective technologies, design solutions and materials [2]. Lately, the technology of vibro-centrifugation, specifically of concrete, has emerged as one of the most promising areas in modern concrete science and technology, allowing for reinforced concrete elements with a variatropic structure. Quite a lot of relevant and interesting scientific works are devoted to this issue from the points of view of materials [3,4,5], design solutions [6,7] and forecasting methods [8,9,10]. However, this area is poorly studied and there is a serious deficiency in both scientific and practical terms, which is expressed in the absence of systematic knowledge about the life cycle management processes of vibro-centrifuged variatropic concrete. Artificial intelligence methods seem to be one of the most promising methods for improving the process of managing the life cycle of such concrete in vibro-centrifuged reinforced concrete structures.

When predicting the physical and mechanical properties of concrete, machine learning methods demonstrate a high prediction quality, which is comparable to traditional methods [11,12,13]. Linear machine learning models, characterized by their simplicity and good interpretability, are especially valued when solving practical industrial problems where the cost of error is high [14,15]. Researchers in [16] demonstrated the performance of multiple linear regression (MLR) and polynomial regression (PR) using the Konstanz Information Miner (KNIME) analytical platform. These methods achieved coefficient of determination values R² = 0.589 and 0.745, respectively, on a small dataset (202 observations with 26 attributes). Another study [17] established a linear regression mathematical model to predict the 28-day compressive strength of concrete using accelerated boiling water curing method. The 28-day strength value predicted by the model equation agrees well with the observed 28-day wet concrete strength obtained using the Student’s t-test statistic at the 5% significance level. Other works [18,19] confirmed the feasibility of using linear models when analyzing the strength characteristics of concrete at different ages, taking into account a variety of both external and internal factors. Metric methods, based on the assumption that the properties of an object can be learned by having an idea of its neighbors, have almost no learning phase (lazy learning), but at the same time they have good predictive ability [20,21]. Different works [22,23,24] showed models using one of the most famous metric algorithms—the k-nearest neighbors (KNN) method. The coefficient of determination, R², which is used to evaluate the performance of regression-based machine learning models, in the presented models obtained values from 0.92–0.99. This algorithm is recommended for the design and development of various concretes with improved characteristics [25]. Analysis of the strength characteristics of various concretes in practice often requires engineers to use a lot of time and conduct expensive experiments. Tree structures and boosting are innovative methods that reduce costs and reduce risks. Determining the compressive strength of concrete using ground granulated blast furnace slag is a difficult task because of the complex calculation involved in determining the mixture composition [26]. The results in [27] show that the random forest (RF) algorithm is an excellent forecaster with a root mean square error (RMSE) and mean absolute error of 4.9585 and 3.9423, respectively. Positive experiences in using this class of machine learning methods are a growing trend [28,29,30]. In predicting the strength of concrete, the ensemble regression tree algorithms [31] and extreme gradient boosting (XGBoost) [32] demonstrated high accuracy. Artificial neural networks are capable of capturing hidden nonlinear relationships in data, which is an important property when trying to predict the concrete’s strength [33,34,35]. Deep neural networks also have high prediction accuracy; the correlation coefficient between real and predicted values when used in [36] is 0.9882, and the relative error was up to 1%. Hybrid models are a combination of different approaches and methods for solving problems [37,38], combining the advantages of different models and algorithms to achieve a more efficient and accurate solution to the problem. This class has many potential benefits for the construction industry [39,40]. In their study [41], the researchers used an RF model and a bagging algorithm together to predict concrete’s compressive strength. The article [42] examines the combination of support vector regression (SVR) with an enhanced particle swarm algorithm and genetic algorithm through hybridization testing. The combination of least squares support vector regression (LSSVR) and grey wolf optimization (GWO) in a hybrid AI model effectively predicts foam concrete compression with a correlation coefficient of 0.991 and MAPE of 3.54% [43].

An analysis of the scientific literature suggests the need to expand the theoretical justification and practically confirm, using real experimental data, the feasibility of using machine learning methods to analyze the strength characteristics of concrete that is heterogeneous in cross-section. Consideration of the results of various machine learning methods to improve the process of managing the life cycle of vibro-centrifuged variatropic concrete will allow the selection of the most promising, fast and reliable technologies. In the course of analyzing the scientific literature, we selected the three most well-known models from different classes, which differ in the principle of their operation. One of the tasks of the study was to assess the impact of the feature engineering process on the accuracy of models that are different in nature. Their introduction into the process of assessing the quality of structures and products made from the concrete material in question will reduce the research time. The scientific novelties of the study are as follows:

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The expansion of theoretical knowledge about the applications of machine learning methods in predicting the strength of vibro-centrifuged variatropic (heterogeneous in cross section) concrete, considering the influence of environmental conditions;

-

A description of the possibility of practical use of the developed methods to optimize the production process of vibro-centrifuged variatropic concrete;

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Recommendations for participants in the construction industry on the implementation of intelligent models in order to achieve an economic effect by improving the process of monitoring the physical and mechanical properties of the concrete in question under the influence of aggressive environmental factors.

The main new results of the work are the formation of a dataset during laboratory tests with its subsequent in-depth analysis, as well as increasing the accuracy of the proposed intelligent models using modern approaches.

The purpose of this work is to improve the process of managing the life cycle of vibro-centrifuged variatropic concrete through machine learning methods, namely, predicting compressive strength using the extended linear regression method—ridge regression— and algorithms based on decision tree and XGBoost tree structures. The research plan is as follows:

(1)

Application of existing experience in theoretical analysis and practical implementation of machine learning methods in the life cycle management of vibro-centrifuged variatropic concrete;

(2)

Justification of the need to expand the stack of technologies to determine the physical and mechanical properties of vibro-centrifuged variatropic concrete by creating regression models based on machine learning methods;

(3)

Testing of samples made of vibro-centrifuged variatropic concrete under laboratory conditions, with the subsequent formation of a dataset for the training, optimization and testing of regression models;

(4)

Analysis of the data obtained, identifying the main statistical characteristics and determining dependencies;

(5)

Creating an expanded dataset by adding new features at the feature engineering stage;

(6)

Description and implementation of the ridge regression method on original dataset and feature-engineered dataset;

(7)

Description and implementation of the decision tree and XGBoost method on original dataset and feature-engineered dataset;

(8)

Description and implementation of the XGBoost method on original dataset and feature-engineered dataset;

(9)

Comparative analysis of the results of all models based on the values of the main metrics to assess the quality of the forecast when solving a regression problem;

(10)

Determination of prospects and features of implementation of developed forecasting methods into practice;

(11)

Determining the possibility of “learning transfer” by adapting the results obtained to other types of concrete.

2. Materials and Methods

2.1. Materials

The following materials were utilized for the study:

(1)

Portland cement CEM I 52.5N, produced at the Serebryakovcement enterprise (Mikhailovka, Russia); a compressive strength at 28 days of age of at least 56.0 MPa and a specific surface area of 3400 cm²/g.

(2)

The Kagalnitsky quarry in Kagalnik, Russia provided river sand with a fineness modulus of 1.43 and a bulk density of 1400 kg/m³.

(3)

Crushed sandstone, mined in the Sokolovsky quarry (Novoshakhtinsk, Russia); grain dimensions were from 5 to 20 mm.

2.2. Composition, Manufacturing Parameters and Properties of Vibro-Centrifuged Variatropic Concrete

The concrete mixture was prepared using the following proportions:

-

cement—375 kg/m³;

-

water—185 L/m³;

-

sand—694 kg/m³;

-

crushed stone—1113 kg/m³.

The concrete was molded and compacted in a laboratory centrifuge equipped on the support and drive shafts with steel ribs 5 mm high and 20 mm long, located at a distance of 300 mm from each other, providing high-frequency vibrations when the mold moved. The shafts rotated at a speed of 156 rad/s, and the molding time was 12 min. After molding, the samples were kept in the molds for 24 h, then removed from the molds and hardened under natural conditions until they reached 28 days of age. The manufactured ring-section elements were sawed on a stone-cutting machine into samples of standard sizes and shapes and were exposed to cycles of freezing and thawing, wetting and drying, and chloride and sulfate attacks [44,45,46,47].

The finished concrete had the following characteristics: slump of the fresh concrete cone—from 3 to 4 cm; compressive strength—58.2 ± 3.26 MPa.

2.3. Description and Analysis of the Dataset

Figure 1 provides a visualization of the research process. After data collection, an initial data analysis (EDA) phase was carried out (Figure 1), which involved examining the data to identify anomalies, deviations, missing values and possible relationships between them.

After analyzing the existing data set, an “original dataset” was formed, and it was suggested that conducting an additional, deeper and more complex analysis, including the use of statistical methods and analytical techniques to extract additional knowledge from the data, would help improve the final predictive properties of the models. Thus, using various techniques at the feature engineering stage, an expanded dataset was obtained (hereinafter referred to as “feature-engineered dataset”), which was subsequently adapted for each model using the feature selection method. The next stages of the research are the implementation of machine learning models, subsequent assessment of their quality, and summing up.

As a result of laboratory tests to determine the compressive strength of vibro-centrifuged variatropic concrete, a dataset was generated that describes the impact of aggressive environmental factors on the final characteristics [44,45,46,47].

In a series of experiments, strength measurements (Y, in MPa) were obtained for 664 samples of vibro-centrifuged variatropic concrete while fixing the following characteristics:

• X₁—number of freezing–thawing cycles;
• X₂—chloride content, mg/dm³;
• X₃—sulfate content, mg/dm³;
• X₄—number of moistening–drying cycles.

All of the above factors directly affect the strength of the building material under study [10,48,49]. From the point of view of construction, these parameters are sufficient to assess strength under the influence of an aggressive environment, since the data obtained have undergone mathematical statistical processing and the number of tests performed corresponds to the methods of regulatory and technical documents and, moreover, exceeds the standard quantity. It should be noted here that regulatory methods in construction themselves imply the possibility of projecting the results of a certain sample of tests onto the results of an entire large batch of building products and structures. Reliable and accurate strength predictions for new samples of variatropic concrete under similar operating conditions, without laboratory testing, will speed up construction processes.

3. Results and Discussion

3.1. Creation of Feature-Engineered Dataset and Feature Selection

In this study, the following information technologies and libraries were used for further processing of the resulting dataset: high-level language Python 3.10.11, Sklearn 1.3.2 and Optuna 3.5.0 (Preferred Networks, Inc., Tokyo, Japan) for hyperparameter optimization of intelligent models. A framework for automated search for optimal hyperparameters for machine learning models, Optuna, compared to the traditional GridSearch method, offers a more effective optimization method, due to the speed of operation, in the case of a large search space [50,51].

An important step in preparing data for submission to a regression model is the analysis of all attributes of the dataset, identifying the boundaries of values, and also determining correlations.

Table 1. Data description.

	Number of Freeze–Thaw Cycles	Chloride Content (mg/dm3)	Sulfate Content (mg/dm3)	Number of Wet–Dry Cycles	Compressive Strength (MPa)
Mean	124.38	774.85	621.37	249.98	41.51
Std.	71.92	72.15	80.03	148.64	8.59
Min	1.00	650.00	450.00	1.00	28.50
25%	61.00	715.75	562.75	120.75	33.90
50%	120.00	768.50	626.00	236.50	40.35
75%	188.00	837.25	690.00	377.25	48.53
Max	250.00	900.00	750.00	500.00	63.20

presents the description of the data (Std is standard deviation, Min is minimum value, Max is maximum value).

Figure 2 shows the correlation matrix, wherein we can observe a strong negative correlation between the attack factors (X₁…X₄) and the predicted compressive strength column (Y).

It is also worth noting the presence of multicollinearity. Today, a number of researchers are of the opinion that it is necessary to combat multicollinearity only if it leads to significant problems, for example, to the deliberate inadequacy of the results obtained [52]. Figure 3 allows you to understand how data are distributed within a dataset and identify the main features of their distribution.

The graph shows the dependencies that are actually noted by researchers when working with concrete: with an increase in the degree of exposure to aggressive environmental factors, we observe a decrease in the strength characteristics of the concrete under study. It can also be noted in the figure that, in the “sulfate content” column, the statistical distribution is shifted towards larger values. The “compressive strength” column has more data in the range of 20–40 MPa. This dataset is saved and designated “original dataset” and will subsequently be fed as an input data to the model during machine learning. Points that differ from the total mass in Figure 3 are measured under different conditions and are not outliers.

When conducting a more in-depth analysis of the original dataset (advanced data analysis), the t-SNE (t-distributed Stochastic Neighbor Embedding) dimensionality reduction method was used [53]. Its principle is based on reducing the difference between the data distribution in the original space and the reduced-dimensional space using the Kullback–Leibler distance.

The Kullback–Leibler minimization formula (KL-divergence) works in such a way that the distribution in the low-dimensional space is as close as possible to the distribution in the original space, as follows:

$$KL\left(P‖Q\right)={\displaystyle \sum _{i}P\left(i\right)\log \left(\frac{P\left(i\right)}{Q\left(i\right)}\right)}$$

(1)

where P is the probability distribution in high-dimensional space and Q is the probability distribution in low-dimensional space.

After using the t-SNE algorithm to reduce the dimension of space to two coordinates, clusters were discovered that were characterized by close values of the target variable (Figure 4).

The graph axes (Figure 4) represent a display of the influence of all parameters while preserving metric properties in a new low-dimensional space. Figure 4 shows the distribution of strength versus input parameters. Thanks to the t-SNE algorithm, the conclusion is formulated that the data form a cluster structure; the characteristics of the clusters were subsequently used to generate features.

The elbow method [54] was employed to find the optimal number of clusters. To implement this approach, it is necessary to plot the average intra-cluster distance depending on the number of clusters and select the bend of the curve as the number of clusters used. Figure 5 shows how the average distance according to the Euclidean metric changes for each instance of the dataset to the center of the cluster in which it is located.

The optimal number of clusters is at the inflection of the graph (the red dot indicates the “elbow”), since it minimizes the distance between instances of the cluster and its centers but is not redundant. In this way, the clusters are generalized in the best possible way. Using this graph, it was determined that the optimal number of clusters was seven.

The final visualization of clusters using t-SNE is presented in Figure 6, where the centers of the seven selected clusters are marked with asterisks.

According to the figure, cluster No. 1 contains specimens with maximum strength values, while cluster No. 7 contains specimens with minimal strength.

Next, based on information about the belonging of each object to a specific cluster, various descriptive characteristics (features) were formed, which add information content and detail to the understanding of the essence of the data (

Table 2. Additional features based on knowledge about the cluster.

No	Parameter	Feature	Characteristics
1	X5	Cluster	Cluster number
2	X6	Cluster_mean (Cluster_q50)	Average target value in the cluster
3	X7	Cluster_std	Standard deviation of target in cluster
4	X8	Cluster_q95	95th percentile of target values in the cluster
5	X9	Cluster_q75	75th percentile of target values in the cluster
6	X10	Cluster_q25	25th percentile of target values in the cluster
7	X11	Cluster_q5	5th percentile of target values in the cluster
8	X12	Cluster_median	Median of target values in a cluster
9	X13	Cluster_max	Maximum target value in the cluster
10	X14	Cluster_min	Minimum target value in the cluster
11	X15	Cluster_neighbours	Average of the nearest neighbors to our point in 4th space

).

To select the features that are most significant and can have a significant impact on the process of predicting the final strength value of vibro-centrifuged variatropic concrete, the sequential feature selection algorithm was used.

Initially, all 15 features were taken for analysis (the original X₁–X₄ and the new X₅–X₁₅), and then we removed from the dataset one of the features, the absence of which improves the accuracy of the model in cross-validation. The algorithm converges iteratively when removing a certain number of features and no longer has the effect of improving the forecast. For each machine learning method implemented in this study, feature selection was carried out individually, which made it possible to generate its own set of the most suitable input features—a feature-engineered dataset. Subsequently, when training, validating and testing machine learning models, each of the datasets (both original and feature-engineered datasets) was divided as follows: 65% for training, 15% for validation and 20% for testing.

3.2. Ridge Regression

Ridge regression (RD) is a modification of linear regression. The main difference from linear regression is that, when training the model, it is additionally penalized quadratically for the value of the norm of weights w, and the penalty is weighted by the hyperparameter λ (lambda). This scheme is also called L2-regularization. In this way, it is possible to control the values of the weights, which makes the model more stable and prevents a sharp increase in the weights. The ridge regression loss function is expressed by the following formula:

$$J_{Ride}={‖X_w-y‖}^2+\lambda {‖w‖}^2$$

(2)

Overall, ridge regression is an important machine learning technique, especially in cases where the input data are highly correlated, as seen in our study.

For the ridge regression method, the eight most significant features were selected in the feature-engineered dataset, shown in Table 2. In addition to the main initial feature X1 (number of freeze–thaw cycles), seven artificially obtained parameters had an impact: Cluster, Cluster_mean, Cluster_std, Cluster_q75, Cluster_q25, Cluster_max, Cluster_neighbours (

Table 3. Feature-engineered dataset for ridge regression.

Method	Number of Selected Features	Features
Ridge Regression	8	Number of freeze–thaw cycles Cluster Cluster_mean Cluster_std Cluster_q75 Cluster_q25 Cluster_max Cluster_neighbours

).

Despite the elimination of features X₂–X₄, information about them is stored in artificially created features, the obtaining of which is based on preserving the strength of influence of each of the original features on the cluster membership of each instance of the dataset.

The selection of optimal hyperparameter values for ridge regression for both the original dataset and the feature-engineered dataset, performed using Optuna, is shown in

Table 4. Parameters for RD.

No	Parameter	Definition	Original Dataset	Feature-Engineered Dataset
1	λ	The Power of Regularization	0.042505	0.072677

.

3.3. Decision Tree

To tackle regression problems, decision trees (DT) is an effective non-parametric supervised learning approach. Based on data features, the DT decision tree uses simple decision rules to predict the value of a target variable [55]. Trees can be viewed as a piecewise constant approximation; they cannot extrapolate. This predictive analysis method is especially in demand in commercial and industrial data mining applications [56].

A clear advantage of this method is its ease of understanding and interpretation. Trees can be visualized. Figure 7 shows a visualization of the tree built for this study on the original dataset.

Among the disadvantages, it is worth noting that, during the execution of the algorithm, overly complex over-trained trees can be created.

For the DT method, the 10 most significant features were selected in the feature-engineered dataset, shown in

Table 5. Parameters for DT.

Method	Number of Selected Features	Features
Decision tree	10	Number of freeze–thaw cycles Cluster_mean Cluster_std Cluster_q75 Cluster_q25 Cluster_q5 Cluster_q95 Cluster_q50 Cluster_max Cluster_min

. Features X₂–X₄ turned out to be the least significant for this machine learning method.

To minimize the problem of overfitting for a tree that is prone to this process, hyperparameter optimization is necessary [51].

Table 6. Parameters for the DT model.

No	Parameter	Definition	Original Dataset	Feature-Engineered Dataset
1	Criterion	Criterion that was used to construct each branch	friedman mse	friedman mse
2	Max depth	Max depth of one tree	684	255
3	Min samples split	“Minimum number of objects in a sheet to split it”	7	2
4	Min samples leaf	“Minimum number of objects in a sheet for it to exist”	2	4

presents the final parameter values for the DT model, selected using Optuna for the original and feature-engineered dataset.

As can be seen from the comparison of hyperparameters, the trees became less deep as the model received higher-level features, due to which it became easier to capture patterns (the generalization ability of the model improved). Among the parameters there is “criterion”, a rule by which the most optimal division of a node in the sheet is selected (options “squared_error”, “friedman_mse”, “absolute_error”, “poisson”). “friedman_mse” is selected, which uses mean squared error with Friedman’s improvement score for potential splits.

3.4. XGBoost

XGBoost (XGB) is an optimized distributed gradient boosting library designed to be highly efficient, flexible and portable [57,58]. It is an ensemble learning method that sequentially builds shallow trees that are further ensembled to achieve a more accurate and reliable prediction. XGBoost has proven itself to be a powerful algorithm in the field of machine learning when solving regression problems.

A characteristic feature of the objective function when implementing this algorithm is that it consists of two parts—the learning loss and the regularization term. The regularization inclusion acts as a penalty, reducing model complexity and improving model generalizability and robustness, as follows:

$$obj\left(\theta \right)=L\left(\theta \right)+\mathsf{\Omega }\left(\theta \right)$$

(3)

where L is the learning loss function; Ω is the regularization term; and θ signifies the parameters that the model learns from the provided dataset.

Our model’s ability to predict the training data is measured by the training loss. The mean squared error is often chosen for L. When implementing the XGBoost algorithm, the responses are summed over all trees of the ensemble:

$$F\left(x\right)={\displaystyle \sum _{k=1}^K{f}_k\left(x\right)}$$

(4)

where $f_k$ is the k-e tree of the ensemble.

For the implementation of the XGBoost method, 14 features turned out to be significant, except for Cluster q50.

Table 7. Parameters for XGB.

N	Parameter	Definition	Original Dataset	Feature-Engineered Dataset
1	lambda	L2 regularization	0.425207503	0.0675070558
2	alpha	L1 regularization	0.005520339	0.0053793840
3	Colsample bytree	the proportion of features that will be used to construct each tree	1	0.6
4	subsample	fraction of the training sample that will be used to build each tree	0.8	0.6
5	learning_rate	learning rate	0.014	0.016
6	n estimators	number of trees	1993	841
7	Max depth	maximum tree depth	11	14

presents the summary parameters for the XGBoost model. When moving from the original dataset to the feature-engineered dataset, there was a decrease in the number of trees from 1993 to 841, but at the same time the maximum tree depth has increased by three units.

Figure 8 shows XGBoost training graphs ((a)—original dataset, (b)—feature-engineered dataset). The number of trees is represented on the x-axis, while the loss-function values are shown on the y-axis.

Overtraining is not observed in both cases; learning occurs steadily without sudden jumps. The number of trees along the OX axis in Figure 8b is smaller, since, when working with an extended dataset, the XGBoost algorithm identifies dependencies faster.

Since the algorithm is based on a tree structure, it can be visualized for a more detailed understanding of the logic of the method. Figure 9 shows a visualization corresponding to the logic of the algorithm on the original dataset.

3.5. Assessing the Quality of the Machine Learning Methods Used

The chosen metrics for evaluating and comparing the forecast accuracy of the machine learning models were “mean absolute error” (MAE), “mean squared error” (MSE), “root-mean-square error” (RMSE), “mean absolute percentage error” (MAPE) and the coefficient of determination R². Below are the formulas for calculating (5)–(9), as follows:

$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|y_i-\widehat{y}\right|}$$

(5)

$$MSE=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left(y_i-\widehat{y}\right)}^2}$$

(6)

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left(y_i-\widehat{y}\right)}^2}}$$

(7)

$$MAPE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|\frac{y_i-{\widehat{y}}_i}{{\widehat{y}}_i}\right|\times 100}$$

(8)

$$R^2=1-\frac{{\displaystyle \sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}$$

(9)

where $y_i$ represents the actual value of the compressive strength; ${\widehat{y}}_i$ is the predicted value of compressive strength; and $\overline{y}$ is the average value for $y_i$.

3.6. Results of the Used Machine Learning Methods

The prediction error plots presented in Figure 10 reflect the distribution of actual strength values for samples from the test set, in comparison with the values obtained as a result of prediction using the implemented machine learning algorithms. The red lines show the boundary ∆ = ±5 MPa [10].

The worst fit into a given “tube” of acceptable values, as well as a low value of the coefficient of determination, is observed in the RD model trained on the original dataset. However, when checking the RD algorithm on the feature-engineered dataset, a significant improvement in the predictive properties is observed: an increase in R² to 0.89 and a reduction in the number of emissions outside the specified range ∆ = ±5 MPa, as well as the distribution of points along the blue straight line y = x on the graph. As outliers in Figure 10, when assessing the quality of the model, points are identified that go beyond the boundaries of ±5 MPa. The fight against outliers consisted of using regularization methods at the model training stage.

According to Figure 10, the best fit within the specified boundaries is demonstrated by the XGB algorithm. This is due to the fact that the XGB algorithm itself is a fairly strong model, and a deep analysis of the data made it possible to identify a number of informative features that increased the predictive qualities of the model, reaching a coefficient of determination of R² = 0.93.

Analyzing

Table 8. The obtained metrics values on the test sample.

N	Model	MAE	MSE	RMSE	MAPE, %	R2
1	RD/Original dataset	3.035809	15.601231	3.949839	7.23	0.71
2	RD/Feature-engineered dataset	1.364647	7.061922	2.657428	3.23	0.89
3	DT/Original dataset	1.290714	6.957745	2.637754	3.06	0.90
4	DT/Feature-engineered dataset	1.252009	6.404198	2.530652	2.95	0.90
5	XGB/Original dataset	1.181808	5.413174	2.326623	2.82	0.92
6	XGB/Feature-engineered dataset	1.134627	4.801390	2.191208	2.72	0.93

, which shows the metrics calculated on the test specimens, it can be concluded that the XGBoost gradient boosting algorithm for decision trees is the best among the implemented models for predicting the strength of vibro-centrifuged variatropic concrete when analyzing the influence of aggressive environmental factors. At the same time, for all models there is an improvement in metrics when moving from the original dataset to the feature-engineered dataset.

In Figure 11, for a more visual interpretation and a good understanding of the results, Table 8 is visualized in the form of graphs.

Based on the graphs, we can conclude that, when working with a feature-engineered dataset, the metrics of all models improve: errors are reduced, and the coefficient of determination increases. The changes are especially noticeable when working with the ridge regression algorithm. Thus, the average absolute error in percentage decreased from 7.23 to 3.23%, while the root-mean-square error decreased by 2.2 times.

As a result of this research, several predictive models were created based on ML-algorithms, namely ridge regression, decision tree and XGBoost. The implemented models can be used to improve the process of managing the life cycle of vibro-centrifuged variatropic concrete by reducing the time required to determine the compressive strength of new samples that were subject to similar aggressive influences from external factors. It is assumed that data collected in laboratory conditions are as close as possible to data from field conditions. However, to confirm, test calculations should be carried out, based on which it is possible to track the emergence of data drift or concept drift with further adaptation of the algorithm and taking into account new factors, if any are discovered.

The effectiveness of using the implemented machine learning methods to predict the strength of vibro-centrifuged variatropic concrete is comparable to traditional methods. MAE = 1.134627, MSE = 4.801390, RMSE = 2.191208 and MAPE = 2.72%, as well as R² = 0.93 are not inferior to traditional methods, where these values are usually in the range of 6–7%. Such an error is quite acceptable and adequate for obtaining reinforced concrete products and structures of stable quality. It should be noted that standard calculations in predicting the properties of various reinforced concrete structures differ somewhat depending on the type of these structures. It should be emphasized that, here, we are dealing with vibro-centrifuged concrete; that is, with a rather complex advanced technology. Moreover, the accuracy of predicting such materials with a variatropic structure can reach an error of 10–12%. Here, in our case, we have a significantly lower error; that is, our proposed method is effective, especially for the proposed variatropic vibro-centrifuged concrete. From the point of view of regulatory documents of various countries, the error can reach 13–15%.

Therefore, it is necessary to note the effectiveness of our proposed method and propose it for implementation to manage the life cycle of reinforced concrete structures and products obtained using vibration centrifugation technology, as well as outline prospects for the development of research in the future. They lie in the direction of studying the proposed machine learning methods for reinforced concrete products and structures of other types; for example, with simple structures or variatropic structures of a different nature; for example, obtained not by vibration centrifugation technology, but by other technologies. The practical applicability of the results obtained lies in the direction of introducing these methods at enterprises producing precast reinforced concrete, as well as for specific construction projects that involve the use of particularly high-strength and high-quality vibro-centrifuged elements; for example, columns.

Comparing the results obtained with the results of other researchers who used ML, it can be noted that the performance assessment of the best model is not inferior to the assessment of metric methods in [22,23,24,25], and the root mean square and mean absolute error are lower than in the study that used tree structure model in [27].

To ensure responsible and unbiased use of the machine learning algorithms discussed in this study in actual construction industry practice, as part of the life cycle process of vibro-centrifuged variatropic concrete, the following must be ensured:

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Transparency and interpretability of results with a clear justification of the limits of acceptable errors. Allowable errors must be within generally accepted building codes and regulations. If the permissible errors are exceeded, the forecast model should be modified.

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Data security, in cases of supplementing models with information that is not subject to disclosure.

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Training and regulation. Users of the final product with implemented “smart” algorithms must have clear instructions for their use and intelligently evaluate the decisions made by the system. It is planned to develop a user interface using the Streamlit framework [59].

4. Conclusions

There is a serious deficiency, in both scientific and practical terms, expressed in the lack of a systematic knowledge base, about the life cycle management processes of vibro-centrifuged variatropic concrete using machine learning methods. A comparison was made of the developed machine learning algorithms based on ridge regression, decision tree and XGBoost for predicting the compressive strength of vibro-centrifuged variatropic concrete using a database of 664 samples of experimental values obtained under laboratory conditions. Both theoretical and practical aspects are revealed in the results of the work, as follows:

(1)

A database has been compiled, containing information on vibro-centrifuged concrete strength and its susceptibility to aggressive environmental factors. The collected dataset has been compiled into a database and is planned to be made publicly available to interested researchers.

(2)

A hypothesis was put forward and confirmed about the possibility of dividing data into clusters with the subsequent use of analytical techniques to extract additional knowledge from the dataset, which contributed to improving the final metrics of regression models.

(3)

Machine learning methods have been implemented, optimized and tested; namely, ridge regression, decision tree and XGBoost. The hyperparameters of each model were optimized using the Optuna optimization system.

(4)

The XGBoost model showed the best quality metrics: MAE = 1.134627, MSE = 4.801390, RMSE = 2.191208, MAPE = 2.72% and R² = 0.93.

(5)

Overall, strength prediction of vibro-centrifuged variatropic concrete using ML methods was found to be effective and accurate. In addition, the use of feature engineering and feature selection techniques made it possible to improve the quality of the models.

(6)

The developed models can provide additional information for civil engineers and materials science specialists to make informed decisions regarding the impact of environmental factors on variatropic concrete strength.

(7)

The models implemented in this study were saved with the best parameters and can later be used to analyze new numerical datasets; predictions of compressive strength values for new samples are made by running through the final XGBoost model.

(8)

It is possible to adapt the algorithms for other types of concrete that face challenging environments. To consider a variety of material properties and transitions, it is recommended to employ data drift, concept drift and domain adaptation technologies. This ensures the inclusion of new relationships without compromising quality. It is planned to develop a user interface using the Streamlit framework.

However, this study is limited to the consideration of four characteristics of environmental influence and, therefore, there is scope for further development. In general, improvement in the research lies in the following areas of development: research into the influence of other aggressive factors, the expansion of a number of ML models and the creation of a user interface.