Using synthetic data to develop machine learning models to predict the performance of fiber- reinforced concrete

doi:10.21203/rs.3.rs-4974170/v1

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Using synthetic data to develop machine learning models to predict the performance of fiber- reinforced concrete

https://doi.org/10.21203/rs.3.rs-4974170/v1

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Concrete is a widely used construction material due to its high compressive strength. However, its durability is often compromised by the development of cracks caused by tensile stress within structures. These cracks can occur during the drying process, leading to water infiltration and corrosion of the concrete reinforcement, which subsequently require repair. As a result, innovative technologies, such as self-repairing concrete and crack control, have become crucial in reducing the costs associated with structural repairs. Given this context, this study investigated novel crack control technologies in concrete structures using a machine learning model that can accurately predict the performance of a specific fiber in fiber-reinforced concrete using a comprehensive dataset. The dataset was compiled from 18 studies and further augmented using synthetic data generation techniques. It encompassed 13 different fiber types and a total of 1953 fiber-reinforced concrete formulations. The computational model was then implemented in Python, and multiple linear regression (MLR), support vector regression (SVR), Random Forest and GradientBootsting techniques were employed to develop the prediction model. The results showed that Random Forest (R² = 0.887 and RMSE = 0.110), GradientBoosting (R² = 0.868 and RMSE = 0.368) and SVR models (R² = 0.856 and RMSE = 0.376) outperformed its MLR counterpart (R² = 0.587 and RMSE = 0.637). Moreover, Random Forest shows a lower RMSE, making it more suitable to accurately predict the performance of the performance of fiber-reinforced concrete.

Machine learning

fiber-reinforced concrete

crack control

Concrete is the most widely used man-made construction material due to its affordability, durability, and widespread availability of its components[1] and a staggering 25 billion tons of concrete are produced each year [2]. The extensive utilization of concrete can be attributed to its advantageous properties, including its water resistance and plasticity [3].

Despite its high compressive strength, concrete has low tensile strength [4]. As a result, cracks can form in the tensile regions of structural elements, requiring the incorporation of materials with higher tensile strength into the concrete. Cracking can occur even before loads are applied to the structure, such as during the fresh state of concrete due to plastic shrinkage or settlement or during the hardened state due to drying-induced shrinkage or restricted thermal movements of the structural elements, making reinforced structures more susceptible to water infiltration and corrosion. As a result, structural interventions and repairs are often required and sometimes even unavoidable. Despite the affordable nature of concrete structures, their restoration costs can be substantial. In fact, repairing structures affected solely by reinforcement corrosion can range from 1.5–3.50% of the gross national product of both developed and developing countries [5].

In light of these challenges, there has been a growing interest in developing technologies that can enhance the durability of concrete structures. Research on the use of nanotechnology in concrete has also gained particular relevance, with a substantial increase in published studies observed in recent years [6, 7]. Among these technologies, the addition of fibers in concrete, as well as in other cementitious materials, improves their mechanical properties [8–12]. These improvements include increased resistance to tension after cracking and enhanced flexural toughness. The fibers mainly function in cracked areas, acting as “bridges” between the cracks, which helps transfer stress and enables the materials to absorb energy. Studies on the performance of fiber-reinforced concrete have utilized various types of fibers, including synthetic fibers such as steel [12–15], polypropylene fibers [15, 16], and natural fibers (e.g., bamboo and hemp) [17]. Therefore, expanding the diversity of fibers tested as reinforcement materials for crack control is crucial. Given that using fibers as concrete reinforcement to control cracking involves various processes (e.g., mixing fibers with fresh concrete, molding test specimens, and conducting mechanical property tests), computational models as tools for preselecting fibers can be highly advantageous and reduce time and material use by identifying inefficient fibers. Thus, machine learning (ML) models have been applied to assist the development of fiber-reinforced concrete [7, 18, 19]. ML uses computational methods and learning algorithms to make predictions of material properties based on available datasets and has been shown as a valuable tool to minimize time requirements or simplify complex processes in creating new materials. By employing these models, researchers and engineers can effectively preselect materials that are better suited and more efficient for their study or application, among other potential benefits.

Despite the benefits of ML, the creation of a good and trustable ML model often requires a large amount of data, and many data sources may contain errors, missing values, or incomplete information, which can negatively impact the performance of machine learning models. Moreover, depending on the field of study or knowledge domain, collecting a large and diverse dataset may be impractical or expensive, limiting the development of robust models. A small and non-diverse dataset can also lead to the data imbalance problem, that is, some datasets may have an uneven distribution of samples, leading the model to be biased towards the majority samples and perform poorly on minority samples. Hence, techniques such as data augmentation[20, 21] and synthetic data generation[22, 23] have been used to improve data quality and to obtain adequate and representative training data for ML. Synthetic data are statistically generated from sample real data to produce higher data volume for ML models training and development. Civil engineering has been using synthetic data to develop ML models when the availability of real data is limited [24, 25], including predicting concrete properties and formulations [26, 27].

Therefore, due to limited data available regarding toughness in concrete incorporated with synthetic fibers, this work aimed to generate synthetic data and develop a ML models designed explicitly to assist in choosing fibers to be tested as reinforcement for cracking control and to select the best model or ML algorithm to predict the toughness factor of fiber-reinforced concrete elements.

All the necessary code was written in Python 3 using the following packages: Pandas (v. 1.4.2), NumPy (v. 1.22.4), Scikit-Learn (v. 1.1.2), Matplotlib (v. 3.5.1), Seaborn (v. 0.11.2), SciPy (v. 1.7.3), Synthetic Data Vault (version 1.2.0), SDMetrics (version 0.10.1), and Imbalanced Learning Regression (version 0.0.1).

2.1 Dataset preparation

Concrete toughness was chosen as the target property. We specifically selected data obtained from the same test method to ensure data standardization (JSCE-SF-4) [28]. For this, data was compiled from 14 research papers [8–13, 15, 16, 29–34]. From the papers selected, we extracted data on the addition of 13 different types of fibers and specimens without the addition of fibers (reference or control concrete), resulting in 14 types of concrete: 13 types of fiber-reinforced concrete and the control (concrete without fiber). The fibers selected for training the ML model and their concentrations are listed in Table 1.

Table 1

Types of fibers and concentrations of the studies found in the literature.
Types of fiber	Concentrations (%)
Steel fiber	0.19, 0.25, 0.32, 0.375, 0.45, 0.50, 1.00, 2.00, 2.50
Polypropylene fiber	0.20, 0.25, 0.33, 0.40, 0.50, 0.63, 0.67, 0.70, 0.75, 0.90, 1.00, 1.10, 1.30, 2.00
Polypropylene microfiber	0.50, 1.00, 1.50, 2.00
High modulus polyethylene (HMPE)	1.00
Polyethylene terephthalate (PET)	0.50, 1.00, 1.50
Basalt microfiber	0.22, 0.50, 1.00, 1.50
Polyvinyl alcohol (PVA)	0.50, 1.00
Polypropylene	0.22, 0.25, 0.33, 0.50, 0.66, 0.82, 1.00
Polyamide fiber	0.25, 0.50, 0.75, 1.00
Polyamide microfiber	0.25, 0.50, 0.75
Polyacrylonitrile	0.50, 1.00, 1.50
Modified olefin	0.20, 0.40
Polyester	0.50

To train the ML model, we utilized fiber concentration as a percentage of the total volume to ensure that the specific mass of the fibers, which is also a factor in the model composition, does not interfere with the correlation between fiber concentration and toughness factor. The data were compiled into a spreadsheet, which included the following columns: water/cement ratio, fiber type, fiber concentration (%), fiber specific mass (g/cm³), fiber length (mm), aspect ratio, modulus of elasticity (GPa), fiber tensile strength (MPa), flexural tensile strength (MPa), toughness (N.m), toughness factor (MPa), span (m), width of the specimen section (m), and height of the specimen section (m).

Despite being composed of data extracted from various papers and a diverse range of data samples (n = 140), the dataset still had a limited number of data lines available for each type of fiber. To overcome this limitation, improve data diversity, and enhance the model’s accuracy, we employed synthetic data generation techniques to increase the size of the dataset and provide more data for model training.

2.2 Data Processing

We processed the data and removed any missing values by analyzing the dataset and removing columns that solely consisted of missing values, followed by removing rows that only contained missing values. However, even after these steps, three columns remained with missing values: fiber length, fiber aspect ratio, and flexural tensile strength of the specimen. Two columns represented commercial characteristics of the fibers used (length and aspect ratio) and one represented test results obtained from the studies (flexural tensile strength). Considering that replacing these missing values with estimated values was inappropriate, we also discarded these columns. Lastly, a new analysis was conducted, and all missing values had been successfully removed from the dataset.

Then, four columns were eliminated to refine the dataset and eliminate unnecessary data that could hinder or be redundant for the model: span, width of the specimen, height of the specimen, and toughness. These columns could be removed because the toughness factor already represented the relationship between these parameters, which was obtained precisely from these four variables.

2.3 Synthetic Data Generation

Synthetic data generation involves a range of techniques that can be employed to address datasets with limited information, and this approach has been gaining popularity in ML. For this study, the Synthetic Data Vault package was used to generate synthetic data [35]. The first stage of synthetic data generation consisted of establishing the minimum and maximum range of values the generated synthetic toughness factor data should adhere to, which were defined as 0 and 11 MPa, respectively. Next, the conditions the model should adhere to during synthetic data generation were established; they specified that certain values related to fiber characteristics must remain constant, such as the fiber type, specific mass, modulus of elasticity, and tensile strength. Subsequently, to create a dataset that is ten times larger than the original set, 100 lines of data were generated for each of the 14 types of concrete in the dataset, resulting in a dataset containing 1400 rows of data. Although the data distribution had improved, a significant concentration of values remained within a specific range, which required data balancing.

To ensure that the evaluation of the synthetic data was not affected by data misbalancing, it was necessary to assess the generated data's quality. Therefore, the Imbalanced Learning Regression package was used to balance the synthetic data. For data balancing, oversampling was performed via Imbalanced Learning Regression, which involves augmenting data for columns with a lower frequency of occurrence and resulted in a balanced dataset consisting of 1953 data lines. This improvement is characterized by a more uniform distribution in the occurrences of each toughness factor value. Lastly, the final dataset was exported to a new spreadsheet, facilitating its utilization in developing the prediction model.

2.4 Development of the Machine Learning Models

The data was normalized using the StandardScaler estimator, which is available in the Scikit-Learn package. This estimator removes the mean and scales the values to have a unit variance. Its purpose is to mitigate the influence of values with significantly higher orders of magnitude on the algorithm’s learning process, ensuring that it can effectively learn from the other provided data. Lastly, two methods were selected to develop the prediction model: multiple linear regression (MLR), support vector regression (SVR), Random Forest and GradientBoosting.

2.4.1 Multiple linear regression

The MLR model was employed to obtain prediction values that could be used as a reference to assess SVR performance. As independent variables, we utilized water/cement ratio, fiber concentration, fiber specific mass, modulus of elasticity, and fiber tensile strength. The correlations between these variables and the dependent variable (toughness factor) are illustrated in Fig. 1.

The toughness factor (with modulus values above 0.50) exhibited more significant correlations with concentration (0.539), fiber specific mass (0.664), and fiber tensile strength (0.522). The correlation between the toughness factor and modulus of elasticity yielded − 0.138, which was different from what was expected due to the relationship between this mechanical property and the stiffness and deformation of the materials. Additionally, the dataset was divided into two parts in an 8:2 ratio, with one part used for training the model and the other for testing. Once the MLR model was established, the separated data mass assigned to test the prediction model was employed to calculate the coefficient of determination (R²) and root mean square error (RMSE).

2.4.2 Support vector regression

This model is an extension of support vector machine (SVM) algorithms. Unlike SVM, which provides a binary output (e.g., determining whether an object belongs to a specific class), SVR estimates a real-valued function and is better suited for solving regression problems. In contrast, SVM is more appropriate for addressing classification problems and work by generating a hyperplane separating the dataset and nonlinearly remapping data into a higher-dimensional space to achieve linear correlation [36].

In order to utilize the SVR techniques, it was first necessary to establish the required parameters for the calculations. Hence, the following parameters and their functions were defined as described in the literature: kernel, which is a mathematical function responsible for data transformations in SVR techniques; C (regularization parameter), which controls the trade-off between maximizing the hyperplane margin and minimizing the training error term; epsilon (regression precision), which establishes the maximum acceptable error; gamma, which improves classification accuracy and reduces regression errors for training data; and degree, which controls the complexity of the transformed space [37]. In addition, the coef0, defined by the parameter that reflects the extent of influence of higher polynomial degrees on the model, and the max_iter, which defines the maximum number of iterations performed during the calculations, also required configuration. Hence, this study used tools that could assess the impact of different values assigned to these parameters on the model’s performance. We then selected the values that improved performance using GridSearchCV method. The tested values for each of the necessary parameters are presented in Table 2.

Table 2

Tested values for the support vector regression (SVR) parameters.
Parameters	Values
Kernel	Polynomial; RBF
C	1; 5; 10; 100
Degree	1; 2; 3
Coef0	0; 0.1; 0.5; 1.0
Gamma	0.01; 0.05; 0.1; 0.5; 1.0
Max_iter	10000
Note: RBF = Radial Basis Function kernel.

The dataset was then divided into two datasets: one to train the data model and the other to test it. The GridSearchCV tool was used to determine the optimal values for the required parameters. This tool operates through an iterative process, where each iteration defines a combination of parameter values and calculates a score. The tool ultimately identifies the combination with the highest score as the best one. Once the values that yielded the highest score were determined, the model was trained using those values. Subsequently, the necessary metrics were calculated to evaluate the accuracy and performance of the prediction model.

2.4.3 Random Forest regression

Random forest regression is an ensemble machine learning technique that combines decision trees to predict the value of a target response [38]. Random forest algorithms use bootstrap sampling to generate sets of random samples for training each model base tree, which means that instead of training all observations, each tree of RF is trained on a subset of the observations. The predictive ability and range of random forest models can be tuned by adjusting some parameters. In this study, four parameters were used, as will be discussed below. The first parameter is "n_estimators", which represents the number of trees in the forest. In this work, the final value n_estimators = 100 wa selecteds. The second parameter is "random_state", which controls the bootstrap randomness. To ensure reproductivity, an integer value equal to 0 was adopted in this work. The third parameter is "criterion", which control how the algorithm will measure the quality of the training and test. Hence, in this work, the criterion was set as “mean_absolute_error” to ensure comparison with multiple linear regression and support vector machine results. Finally, the parameter “oob_score”, which controls how the model will score its performance, was set to “True”.

2.4.4 Gradient Boosting

Gradient Boosting is another ensemble ML method that trains a set of weak estimators to produce a final stronger estimator that often outperforms other ML algorithms. In this work we trained Gradient Boosting models using the implementation present in scikit-learn. In this study, some parameters were tuned to adjust the training of gradient boosting. The first parameter is the “loss”, which was set to 'squared_error' and control how the error during training will be handled. The second parameter is the “learning_rate”, which controls the rate of correction of training weights and was set to 0.01; the third parameter is “n_estimators”, which was set to 500 and control the maximum number of weak estimators that will be trained.

3.1 Synthetic data quality analysis

An overall quality score of 83.35% was achieved, with the analysis of column pair trends yielding 89.95%. Column pair trends measure the correlation between synthetic and real data, with a higher percentage indicating a higher quality of generated data. Another significant analysis focuses on adherence to boundaries, resulting in a value of 1.0 (the maximum possible) and indicating that all generated data remained within the specified limits. Furthermore, a final data analysis was conducted to assess the coverage of the synthetic data and determine whether new data or copies of real data had been generated. The results were satisfactory in both analyses, with the synthetic data covering over 90% of the range of possible values and over 90% of the synthetic data comprising new data, thereby avoiding the duplication of real data.

3.2 Machine Learning Models

3.2.1 Multiple linear regression

The results showed that the MLR model achieved R² = 0.587 and RMSE = 0.6378. It is important to note that while the RMSE value is relatively low, indicating a small standard deviation between the predicted and test values, the MLR model falls short in terms of R². This suggests that the regression line does not adequately fit the data (Fig. 2). As a result, this model is not suitable for accurately predicting the toughness factor due to its low precision.

The final form of the regression line equation obtained for the MLR model is presented below (Eq. 1):

$$\:Y=-0.681\cdot\:A+0.262\cdot\:B+0.216\cdot\:C-0.00011\cdot\:D+0.00026\cdot\:E-0.638$$

where Y is the toughness factor, A is the water/cement ratio, B is the fiber concentration, C is the fiber specific mass, D is the modulus of elasticity, and E is the tensile strength.

Despite the low precision of Eq. 1 in predicting the toughness factor, it is evident that the fiber concentration and specific mass of fibers significantly affect the resulting value of the toughness factor. This observation corroborates the findings presented in the correlation matrix in Fig. 1. Furthermore, a negative correlation was identified between the water/cement ratio and modulus of elasticity, while a positive correlation was observed for the fiber concentration, fiber specific mass, and fiber tensile strength, which also corroborate the trends in Fig. 1.

3.2.2 Support vector regression

For the SVR-based prediction model, the parameters required for the model were initially evaluated to determine the ideal values. The results of this evaluation, including the ideal values, are presented in Table 3.

Table 3

Ideal values obtained for the support vector regression (SVR) parameters.
Parameters	Values
Kernel	RBF
C	5
Degree	1
Coef0	0
Gamma	1.0
Max_iter	10000
Note: RBF = Radial Basis Function kernel.

A score of R² = 0.874 and RMSE = 0.125 during training and of R² = 0.856 and RMSE = 0.142 during test. These values are considered satisfactory although still not optimal, for the prediction model. Hence, the SVR model is more suitable than MLR for predicting the toughness factor in terms of the model’s fit to the data and the standard deviation between predicted and test values (Fig. 3). In fact, the predictions generated by the SVR model exhibited higher accuracy than those produced by MLR.

The superiority of SVR techniques over MLR in predicting values was not surprising due to their efficiency in handling regression problems, particularly in situations involving nonlinear relationships, as reported elsewhere [18]. Analyzing the correlation matrix between the variables (Fig. 1), it is evident that the elastic modulus does not significantly correlate with the toughness factor, which contradicts expectations and suggests that this mechanical property has minimal influence on the effectiveness of fibers as reinforcing material against cracking in fiber-reinforced concrete. Furthermore, Fig. 1 also reveals that the impact of fibers on toughness factor values is not solely attributed to a single mechanical property of the reinforcement material, as initially hypothesized. Instead, it results from a combination of characteristics and mechanical properties, including tensile strength, specific mass, and fiber concentration used as reinforcement against cracking.

3.2.3 Random forest regression

The random forest regressor performed as follows: R² = 0.981 and RMSE = 0.018 during training and R² = 0.899 and RMSE = 0.098 during testing (Fig. 4), outperforming multiple linear regression and support vector regression models.

The RMSE values for the random forest regressor show that there is no significant deviation between the training and test sets, thus indicating that the model is reliable and does not suffer from under- or overfitting. Moreover, out-of-bag-scores (0. 885) shows that the prediction deviation is low for this model.

3.2.4 Gradient Boosting

Gradient Boosting performed as follows: R² = 0.988 and RMSE = 0.012 during training and R² = 0.897 and RMSE = 0.102 during testing (Fig. 5), outperforming multiple linear regression and support vector regression models and having performance similar to random forest.

The RMSE values for the gradient boosting show that there is significant deviation between the training and test sets, but not as large as the deviation found for SVR and MLR models, indicating that the model is reliable and still precise.

3.3 Comparison of the prediction ability of all ML models

Comparing the results of all predictive models (Table 4), the worst predictive model is the MLR regressor, while the best predictive model is the random forest closely followed by gradient boosting model. Indeed, for a practical application, random forest and gradient boosting show the same performance. The performance of SVM models depends upon the kernel choice and hyperparameter tuning. RBF kernel outperformed the other SVM kernels with a low RMSE in the test set. The SVR has reliable performance, but not as high as the performance shown by the random forest and gradient boosting models, which have higher accuracy.

Table 4

Performance Comparison of ML models
ML model	R²		RMSE
	Train	Test	Train	Test
MLR	0.612	0.587	0.568	0.637
SVM	0.874	0.856	0.125	0.142
Random Forest	0.981	0.899	0.018	0.098
Gradient Boosting	0.988	0.897	0.012	0.102

Ensemble models such as random forest and gradient boosting are both the optimal models for predicting the toughness factor, since their validation metrics (R² and RMSE) are better than the same metrics for all other models. Ensemble models outperformed SVM, which is known for having satisfactory performance for small and mid-size datasets [39]. This result is similar to other results found in the literature, where the ensemble methods are better than other ML techniques to predict properties of concrete [7, 40]. As ensemble methods that represents a set of weak learners, it can generate and balance weak learners to be more generalizable, boosting the final performance [41, 42], explaining the reason for the highest performance for the ensemble models in this study. Furthermore, SVM and MLR algorithms are single learning algorithms, while ensemble algorithms such as RF and others such as gradient boosting integrate several learners that are weighted, and those with higher weight are integrated in the final model [42, 43].

3.4 Influence of independent variable sensitivity

ML algorithms are often referred to as black boxes, that is, it is not possible to infer the relationship between the input (independent) and the output (dependent) variables, unlike often done in statistical modeling. However, it is a myth that the relationships between variables and how ML models work cannot be explained [44].

Hence, to determine the influence of each concrete component (variable) in the toughness factor, we used the permutation_importance function available at the sklearn.inspection package. Details on the methodology are described elsewhere[45]. A graph with the importance of each variable (Fig. 6) shows that the specific mass, concentration, and tensile strength of fibers have a direct influence on toughness factor. Thus, this analysis corroborates the previous observation in MLR that the fiber concentration and specific mass of fibers significantly affect toughness factor. Moreover, previous studies involving toughness factor of concrete, machine learning as well as experimental assays found the same influence of concentration and specific mass of fibers in toughness factor [18, 31].

Our findings led us to conclude that the influence of multiple factors on the performance of fibers as reinforcement against cracking makes using simplified methods and techniques, such as multiple linear regression, unsuitable for the regression problems addressed herein. Therefore, using more sophisticated techniques, such as support vector regression and ensemble methods, is more appropriate for the regression problems addressed in this study. Moreover, synthetic data generation techniques proved to be an important tool for overcoming the initial challenges posed by the limited data availability in bibliographic databases. These techniques were particularly helpful in mitigating problems that could arise during model training due to the limited availability of data [22, 24]. The results demonstrate that in cases where large quantities of data are not available, synthetic data can be employed to train enhance the performance and accuracy of prediction models.

Thus, using synthetic data can lead to the development of accurate ML models that can boost and aid the formulation of improved cementitious materials, even when limited by dataset size, helping the practitioners of civil construction to save time and valuable resources.

Data Availability Statement

All Data and Jupyter Notebook can be found at: https://github.com/vhperes/FiberML.git.

Acknowledgments

This study was supported by the Coordination for the Improvement of Higher Education Personnel (CAPES; grant no. 001)

Conflicts of Interest

We declare none.

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Using synthetic data to develop machine learning models to predict the performance of fiber- reinforced concrete

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Abstract

Figures

1. Introduction

2. Materials and Methods

2.1 Dataset preparation

2.2 Data Processing

2.3 Synthetic Data Generation

2.4 Development of the Machine Learning Models

2.4.1 Multiple linear regression

2.4.2 Support vector regression

2.4.3 Random Forest regression

2.4.4 Gradient Boosting

3. Results and Discussion

3.1 Synthetic data quality analysis

3.2 Machine Learning Models

3.2.1 Multiple linear regression

3.2.2 Support vector regression

3.2.3 Random forest regression

3.2.4 Gradient Boosting

3.3 Comparison of the prediction ability of all ML models

3.4 Influence of independent variable sensitivity

Conclusions

Declarations

References

Additional Declarations

Status:

Version 1