Comparison of machine learning models predicting the pull-off strength of modified epoxy resin floors

Epoxy resin coatings are a common solution for floors in industrial facilities. This coating, as the top layer of the floor, is exposed to many destructive factors (Fig. 1). A special requirement of such a coating is its pull-off strength from the substrate layer specified as 1.5 MPa [1]. To improve these properties as in concrete or mortar, all kinds of modifications are used. One method is to interfere with the composition of the material by adding ingredients such as mineral powders or fibers in different amounts, which affects the parameters of the target element. A repellent glass powder [2] is added to improve the adhesive properties of resin coatings. Graphene oxide can exhibit self-healing properties in resins, while carbon fibers embedded in epoxy resin can increase its fire resistance and strengthen the material itself [3]. Montmorillonite [4] makes it possible to achieve enhanced thermal shock resistance in resin coatings. The problem is to determine if the coating made meets the requirement without destroying it [5]. Repairing the areas where the tests were performed is time-consuming, generates costs, and results in discontinuity of the floor, which is often a key requirement in warehouses, for example. One of the alternatives used to eliminate destructive testing from the process of determining strength parameters is the use of nondestructive testing [6][7]. Among other things, nondestructive methods work well for determining the compressive strength of existing structures [8] or to assist in assessing the reactivity of alkali aggregates [9]. However, in some cases, there is necessity to improve the accuracy of those methods. The popularity of using artificial intelligence and machine learning to solve engineering problems continues to grow [10]. It provides tools that can realistically support the determination of strength parameters of construction materials by eliminating or significantly reducing the need for destructive methods.

The application of machine learning to modified cementitious composites when determining pull-off strength by examining the ultrasonic pulse velocity (UPV) achieves very good results [11]. In particular, in the aforementioned research, it should be noted that the very good results were obtained for the random forest model (RF) when analyzed on data outside the database used for learning. Various machine learning techniques were presented using a database of fly ash-doped cementitious composites as an example [12]. The most important parameter studied was compressive strength. This study involved collecting data from experimental work and applying machine learning techniques. The chemical and physical properties of all materials used in this study were evaluated. The machine learning systems used were gene expression programing (GEP) algorithm, artificial neural network (ANN), and decision tree (DT). These were tested to predict compressive strength. Concrete samples with different compositions were cast and tested at different maturation times to obtain the data required to create the models.

Artificial neural network (ANN) models show high accuracy based on material composition information of the composite when determining the subsurface pull-off strength [13] and also used to predict the residual compressive strength of concrete exposed to elevated temperatures [14].

Prediction of flexural and compressive strength with machine learning models in epoxy resin stones [15] shows the potential of these algorithms in working with different materials. Neural networks can also be used in the prediction of slip resistance of such floors [16].

It should be noted that the application of artificial intelligence in construction is much more developed in the case of the most popular material concrete. Analysis of AI capabilities in epoxy resins is much more limited, which indicates a research gap. Figure 2 is prepared from keyword search results on Science Direct and Google Scholar. The potential for developing research on the application of artificial intelligence to epoxy resins is noticeable.

In this study, the authors attempted to determine the pull-off strength of epoxy resin coating modified with granite powder and linen fibers using artificial intelligence. Machine learning models were compared in terms of efficiency and accuracy of model prediction based on material composition information of modified resins. The aspect of the influence of material modifications on the properties of the composite was discussed in more detail in an earlier paper [17].

2

Materials and methods

2.1

Preparation of the concrete substrate

The first stage of the present study was the preparation of the concrete substrate. It was made of concrete of class C25/30, which is the minimum class required by resin coating manufacturers. This layer was made from a dry concrete mix available on the market. From its manufacturer’s recipe, it appears that an aggregate size of up to 4 mm was used and the thickness of the coating is a minimum of 20 mm. In this study, 80 mm was used so that the thickness of the substrate would not affect the pull-off strength of the resin coatings. The concrete slab was 1200 × 800 mm, which, divided into individual 200 × 200 mm test fields, allowed 24 test fields to be created, thus testing as many material combinations as possible. All the necessary concrete mixes were prepared in one go in the proportions recommended by the manufacturer. The mixture was placed in the mold, compacted, and the surface leveled. The concrete was cured under normal conditions for a further 28 days.

2.2

Granite powder

The granite powder used in this study came from a Polish mine (Strzeblowskie Koplanie Surowców Mineralnych Sp. z o. o.). It is sold under the designation MS063D-01. The chemical composition declared by the manufacturer is SiO₂ (74.00–78.00%), Al₂O₃ (12.50–14.00%), Fe₂O₃ (0.20–0.40%), TiO₂ (max. 0.05%), K₂O + Na₂O (7.50–8.50%), MgO (max. 0.50%), and CaO (max. 0.50%). 63 μm is the maximum grain size. Figure 3 shows a view of the granite powder used.

2.3

Linen fibers

The linen fibers used in the study were derived from the processing of linen stalks. This material does not absorb water, is odorless, and can operate at temperatures up to 130°C. The density is 1.5 g/cm³. The length of the fibers varied between 10 and 12 mm. Figure 4 shows the prepared fibers for testing.

2.4

Epoxy resin

The epoxy resin used in this study is Meteor Primer. It is used to prime concrete surfaces. It was this layer that was modified in this study. At the same time, it was the top layer—no topcoats were used, as is the case with a typical epoxy floor. This was chosen to find out the pull-off strength value of the resin/concrete interface. Furthermore, the bond between one layer of resin and another is stronger than with another material (in this case concrete). The resin is formed by the reaction of bisphenol A with epichlorohydrin (epoxy resin, average molecular weight ≤700). The values of the basic parameters of the resin are as follows: reaction to fire, Bfl-s1; release of corrosive substances, SR; abrasion resistance ≤ AR1; impact resistance ≥ IR4; pull-off adhesion ≥ B1.5; density, 1.0–1.2 g/cm³; viscosity, 400–600 MPa*s; shelf life (at 20°C), 20–30 min; and full curing after 24 hours. Components A and B were mixed at a ratio of 100:45.

2.5

Preparation of the epoxy coating

Preparation of the coating started with sanding the concrete substrate. Afterward, the treatment removed any remaining cementitious milky residue from the surface of the slab. After this, the whole thing was washed using a pressure washer. The result was a clean flat surface. After drying the slab under natural conditions, the surface was degreased using acetone and individual test fields of 200 x 200mm were separated. A total of 24 fields were obtained.

The resin was modified with granite powder at 0%, 10%, 20%, 30%, 40%, 50%, and 60% of the total resin weight and linen fibers at 0%, 0.5%, 1.0%, and 1.5% of the total resin weight. The reference test was defined as a coating in which no additives were added. The preparation of the resin mixture started with a measured amount of component A, to which a measured amount of granite powder was added. Once the contents were mixed, a measured amount of fiber was added. These caused difficulties in mixing the contents. The fibers were dry, causing the liquid to thicken considerably, which was strongly noticeable with more fibers. After combining the three components, about one hour was waited and component B was added and mixed again. The prepared mixture was poured over the respective test fields, obtaining a coating thickness of 3 m. The coating was vented and thickened using a hard bristle brush. With more additives, there were difficulties in leveling the coating surface.

2.6

Pull-off strength test

Once the resin coating had set, the pull-off strength test was prepared. The resin surface was sanded with fine sandpaper to smooth out any irregularities and to increase the adhesion of the adhesive to the coating. In the next step, holes were drilled, using a diamond borer, 50 mm in diameter into each of the coatings to a depth of 5 mm. Four such boreholes were drilled in each of the test fields. During the initial drilling phase, the borehole was stabilized using a special rack. Each borehole was divided into several stages in order not to increase the temperature of the coating (not to overheat it). After the holes were drilled, the surface was cleaned of dust generated during drilling and degreased using acetone. The surface of the discs was also degreased. The disc was glued to the resin using epoxy resin. Once the glue had fully cured, the pull-off strength proceeded. A screw connector was screwed into the steel disc at the end of which was a round head, which provided an articulated connection between the disc and the jaw of the device. For each test, the device was positioned horizontally and the test was performed (Fig. 5). Each test lasted up to 100 seconds, and the load increment was 0.05 MPa/s. A Proceq Dy-216 device was used, and the entire test was performed with ASTM D4541 [18]. According to it, the minimum number of tests is three, but in this study, four were performed each due to the larger amount of data that could be used in subsequent stages of the test.

2.7

Soft computing techniques

For modeling, the following four algorithms were used: linear regression (LR), random forest (RF), decision tree (DT), and artificial neural networks with Levenberg–Marquardt (LM) learning algorithm. Algorithm adjustment was done as follows: –

In linear regression, the use of no regularization, L2 regularization, L1 and L2 regularization, and no regularization were tested.

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In artificial neural networks, the predictive capabilities of the models were analyzed depending on the number of hidden layer neurons in the range of 1–35 and pitch in increments of 1.

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For decision trees, the variable was the depth of the tree in the range of 1–20 and with a pitch in increments of 1 similarly to random forest. In addition, for RF, the number of trees in the forest was still changed in the range of 20–200 and a pitch of 20 (Table 1).

Table 1:

Elements of the decision tree and random forest algorithm.

Number of input categories	Depth of trees	Number of trees (only for RF)	Minimum subset to be divided	Minimum number of categories in the leaf
5	1–20	20–200	5	2

All models were taught and valenced using 10-fold cross-validation.

3

Statistical analyses of collected data

The main objective was to analyze and select the most predistinct model for predicting the pull-off strength of modified resin coatings. The database needed to teach the artificial intelligence models was created from a compilation of pull-off strength test results and material composition information [17]. To enable a more universal application of the machine learning model, it was decided to base further work on the percentages of components specified for the entire composition of the finished coating. The material information was as follows: the amount of component A [%], amount of component B [%], amount of granite powder [%], amount of linen fibers [%], and density [g/cm³]. The database consists of 140 data sets. The database was analyzed using descriptive statistics (Table 2) to better understand the relationship between the input parameters and the fb output variable. The database can be made available upon request. Figure 6 shows violin plots of the input parameters.

Table 2:

Descriptive statistics of the input and output parameters.

	Min.	Max.	St.dev.	Mean	Range
Amount of Component A [%]	0,455	0,752	0,077	0,560	0,297
Amount of Component B [%]	0,155	0,310	0,035	0,252	0,105
Amount of granite powder [%]	0,000	0,375	0,112	0,182	0,375
Amount of linen fibers [%]	0,000	0,015	0,005	0,006	0,015
Density [g/cm³]	1,100	1,306	0,060	1,196	0,206
fb [MPa]	1,950	3,520	0,223	2,546	1,570

Pearson correlations of input and output parameters were calculated and presented on the heat map (Fig. 7). It can be seen that the value of pull-off strength is affected to the highest degree by the amount of Component B. The amount of Component A is strongly dependent on the amount of Component B, which is understandable given the manufacturer’s requirements for a constant ratio between these components. The density depends on all other components at a similar level, which is also obvious from the scheme of density calculations. After this analysis, the researchers performed the Shapiro–Wilk on the formula (1). The test statistic is compared with the critical value, which is determined by the sample size and the significance level. If the test statistic is less than the critical value, the sample is considered to be from a normal distribution. The calculated indices are included in the violin charts (Fig. 6). Green color is used to record the results of parameters whose significance level α was set at 0.01; therefore, the probability level W should be a minimum of 0.955 to treat the distribution of a parameter as normal, while those that do not have a normal distribution are marked in red. According to the calculations, the parameters fb and amount of component B: (1) $W = \frac{\sum_{k = 1}^{n} {(w_{k} a_{k})}^{2}}{\sum_{k = 1}^{n} {(a_{k} - \bar{a})}^{2}}$ W = {{\sum\nolimits_{k = 1}^n {{{\left( {{w_k}{a_k}} \right)}^2}} } \over {\sum\nolimits_{k = 1}^n {{{\left( {{a_k} - \bar a} \right)}^2}} }}

4

Pull-off strength of resin coatings machine learning analyses

4.1

Evaluating the effectiveness of the models

Each model was then evaluated by analyzing the results predicted by the models juxtaposed with experimental results. The evaluation was done using the following statistical metrics: (2) R (correlation coefficient), (3) RMSE (root mean squared error), (4) MAPE (mean percent error of prediction), and (5) RE (relative error). Using the rank method, the models with the highest pull-off strength fb prediction efficiency of the epoxy resin coating modified with granite powder and linen fibers were selected. (2) $R = \frac{\sum_{i = 1}^{n} (e x_{i} - \bar{e} x_{i}) (m o_{i} - \bar{m} o_{i})}{\sqrt{\sum_{i = 1}^{n} {(e x_{i} - \bar{e} x_{i})}^{2}} \sum_{i = 1}^{n} {(m o_{i} - \bar{m} o_{i})}^{2}}$ R = {{\sum\nolimits_{i = 1}^n {\left( {e{x_i} - \bar e{x_i}} \right)\left( {m{o_i} - \bar m{o_i}} \right)} } \over {\sqrt {\sum\nolimits_{i = 1}^n {{{\left( {e{x_i} - \bar e{x_i}} \right)}^2}} } \sum\nolimits_{i = 1}^n {{{\left( {m{o_i} - \bar m{o_i}} \right)}^2}} }} (3) $RMSE = \sqrt{\sum_{i = 1}^{n} {(e x_{i} - \bar{m} o_{i})}^{2}}$ RMSE = \sqrt {\sum\nolimits_{i = 1}^n {{{\left( {e{x_i} - \bar m{o_i}} \right)}^2}} } (4) $MAPE = \frac{100}{n} \sum_{i = 1}^{n} |\frac{e x_{i}}{\bar{m} o_{i}}|$ MAPE = {{100} \over n}\sum\nolimits_{i = 1}^n {\left| {{{e{x_i}} \over {\bar m{o_i}}}} \right|} (5) $RE = \frac{|m o_{i} - e x_{i}|}{|e x_{i}|} * 100 %$ RE = {{\left| {m{o_i} - e{x_i}} \right|} \over {\left| {e{x_i}} \right|}}*100\% where ex_i is the experimental value, ēx_i is the mean experimental value, mo_i is the predicted value, m̅o_i is the mean predicted value, and n is the number of samples.

Selection of the most effective models for predicting pull-off strength for resin coatings was based on rank analysis of the obtained results of statistical metrics for each model. The models have metrics as close as possible to the ideal ones.

The best-fit network was obtained for: –

Linear regression with no regularization.

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Artificial neural networks on the Levenberg–Marquardt learning algorithm’s basis and the number of hidden neurons equal to 15.

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Decision tree algorithm had a tree depth of 9.

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Random forest performed best with 160 trees with a depth of 10. Note the difference between the algorithms.

5

Results

5.1

Pull-off strength

The modified resin layers proved to be very strong in the near-surface layer. In all samples, the concrete substrate (cohesive type) was found to be overgrown. Also, with a higher fiber and powder content, there was no viscosity problem despite the apparent thickening of the mixture. The cohesive type was also present in these samples. This means that the mixture adequately filled the pores in the concrete.

Figure 8 shows a graph of the dependence of the pull-off strength of the modified epoxy resin coating as a function of the amount of granite powder added in the linen fiber. Nine of the twenty-three modified samples scored higher than the reference coating, whose strength was 2.63 MPa. 3.09 MPa (σ = 0.17 MPa) was the highest strength obtained in the entire test. It was found after the addition of 1.5% linen fibers and 30% granite powder. This is 17.5% higher than the reference test. An equally high strength was obtained when only 20% granite powder was added—3.02 MPa. The other samples did not exceed a strength of 3 MPa. The results show that the addition of between 20% and 40% granite powder allows an increase in strength, regardless of the number of fibers. Their presence, however, has no direct effect on the strength. This can be seen especially in the first part of the graph, where no powder was added, and the results are among the lowest in the entire test. With the addition of 10% powder, the results were also lower than the reference in every case.

5.2

Machine learning models

The accuracy of linear regression depends on the regularization method used. For the linear regression-based machine learning with no regularization, graphs of the predicted pull-off strength values of modified epoxy resins compared to experimental values are shown in Figure 9a. The green solid line indicates a perfect match, while the green dashed lines indicate an error area of ± 10%. The cross-validation yielded, respectively, the value of the coefficient of correlation R = 0.6277; RMSE = 0.2299 MPa; absolute percentage error MAPE = 7,4244%.

It can be seen that artificial neural network learning algorithms perform better when the procedure receives a sufficient number of neurons in the hidden layer. For a machine learning model based on artificial neural networks with the Levenberg–Marquardt machine learning algorithm with 15 hidden layer neurons, their ability to predict pull-off strength results was visualized in comparison with experimentally obtained results (Fig. 9b). The following network fit evaluation rates were obtained: R = 0.8744, RMSE = 0.1312 MPa, and MAPE = 3,8098%.

For the Decision Tree algorithm, the tree depth of 9 was adjusted. The following network fit evaluation rates were obtained: R = 0.8310, RMSE = 0.1643 MPa, and MAPE = 4,0814% (Fig. 9c).

For the Random Forest algorithm, the best model included 160 trees. The tree depth of 10 was adjusted. The following network fit evaluation rates were obtained: R = 0.8848, RMSE = 0.1376 MPa, and MAPE= 3,7156% (Fig. 9d).

6

Discussion

Table 3 summarizes the correlation coefficient R, RMSE, and the mean percentage forecast errors MAPE. The R-values for random forest, artificial neural networks, and decision tree were very similar although they were the highest with the former method. Significantly, they were in the range of 0,7 ≤ R < 0,9, meaning that the correlation was very high (except linear regression) [19]. As before, the best parameters were obtained with random forest.

Table 3:

Summary of correlation coefficients R, RMSE, and average percentage forecast errors MAPE for selected models.

AI Model	Statistical metrics
AI Model	R [-]	RMSE [MPa]	MAPE [%]
Linear regression	0,6277	0,2299	7,4244
Decision tree	0,8310	0,1643	4,0814
Random forest	0,8848	0,1376	3,7156
Artificial neural networks	0,8744	0,1312	3,8098

Figure 10 shows a graph of relative errors (RE) for each data set in each of the methods used (linear regression, decision tree, random forest, and artificial neural networks). A significant portion of the results are within the 10% limit. Two strong outliers can be observed. Interestingly, all methods failed to deal with these particular sets. In contrast, artificial neural networks and random forest performed best with the data. They had the smallest error values in most sets.

Figure 11 shows histograms of absolute error values for all the methods used. The histograms are divided into 8 parts, each with a range of 4%. The range of the entire graph is from −12% to +12%. Importantly, if the histogram resembles a normal distribution, this is a good sign (a large amount of data had a low error percentage). In the case of the decision tree method, random forest, and artificial neural networks, such a relationship can be seen, where errors of ± 8% occurred in at most a few data. In the case of linear regression, the distribution of prediction errors deviates significantly from the normal distribution, which suggests poor fit and low efficiency confirmed by the values of statistical metrics (Table 3).

6.1

Sensitivity analysis of the models

The sensitivity analysis of the model mainly uses the SHapley Additive exPlanations (SHAP) method. SHAP is commonly used to interpret machine learning models and provides an understanding of how individual features contribute to the model’s predictions [20]. The main objective of SHAP analysis is to clarify why a model makes certain predictions by examining specific input features. It does this by calculating SHAP values for each feature, which indicate the impact of that feature on the model’s prediction for a particular instance. These SHAP values are additive, so the total of all SHAP values for an instance matches the difference between the model’s prediction and the baseline value (usually the dataset’s mean). Figure 12 illustrates SHAP sensitivity analysis for the best machine learning model, which is a random forest.

The main parameter affecting the pull-off value of the modified resin coating in the RF model is the amount of granite powder in the formulation. The density and amount of linen fibers are not particularly important for our model and have a low impact on the predicted value. The reported analysis does not reflect the results obtained from the Pearson correlation test.

7

Conclusions

The above analyses have shown that the application of artificial intelligence in modeling the tensile strength of epoxy floors yields appropriate results. Tested algorithms include linear regression, decision tree, random forest, and artificial neural networks. In each of them, the following parameters were determined: correlation coefficient R, RMSE, and mean percentage prediction errors MAPE.

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The best efficiency was obtained for random forest algorithm at depths of 10 and 160 trees. The statistical metrics were R = 0,8848, RMSE = 0,1376, MAPE = 3,7156%. RMSE was almost the lowest (larger by only 0.0065 MPa relative to artificial neural networks).

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Analyzed material solutions using various machine learning methods allow to develop much less destructive strength test results on the used floor.

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Linear regression as a basic heuristic tool is capable of providing information about the pull-off strength of resin coatings modified with granite powder and linen fibers at a decent level, and it should not be completely discarded.

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Correlational indications of input parameters to output parameter are not a sufficient indicator for assessing which parameters should be excluded or included in the database for machine learning.

In the future, it would be worthwhile to expand the database with new filler materials to develop more universal models for predicting the pull-off strength of modified resin coatings. Also, it would be worthwhile to develop models that could support the evaluation of tensile strength of finished floors based on information other than formulation composition.

Using machine learning to identify the thermal shock resistance of modified resin coatings [21] could be of interest. The use of nondestructive methods or chemical composition analysis would eliminate destructive methods from the process of evaluating the properties of resin floors.

Language:: English

Publication timeframe:: 4 times per year
Journal Subjects:: Geosciences, Geosciences, other, Materials Sciences, Composites, Porous Materials, Physics, Mechanics and Fluid Dynamics

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Comparison of machine learning models predicting the pull-off strength of modified epoxy resin floors

Mateusz Moj

Łukasz Kampa

Sławomir Czarnecki

Article Category: Original Study

Published Online: Nov 10, 2024

Page range: 377 - 388

Received: Jul 07, 2024

Accepted: Sep 18, 2024

DOI: https://doi.org/10.2478/sgem-2024-0024

Keywordsresin coatings, granite powder, machine learning, linen fibers

© 2024 Mateusz Moj et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
resin coatings, granite powder, machine learning, linen fibers