Geopolymer concrete emerges as a promising avenue for sustainable development and offers an effective solution to environmental problems. Its attributes as a non-toxic, low-carbon, and economical substitute for conventional cement concrete, coupled with its elevated compressive strength and reduced shrinkage properties, position it as a pivotal material for diverse applications spanning from architectural structures to transportation infrastructure. In this context, this study sets out the task of using machine learning (ML) algorithms to increase the accuracy and interpretability of predicting the compressive strength of geopolymer concrete in the civil engineering field. To achieve this goal, a new approach using convolutional neural networks (CNNs) has been adopted. This study focuses on creating a comprehensive dataset consisting of compositional and strength parameters of 162 geopolymer concrete mixes, all containing Class F fly ash. The selection of optimal input parameters is guided by two distinct criteria. The first criterion leverages insights garnered from previous research on the influence of individual features on compressive strength. The second criterion scrutinizes the impact of these features within the model’s predictive framework. Key to enhancing the CNN model’s performance is the meticulous determination of the optimal hyperparameters. Through a systematic trial-and-error process, the study ascertains the ideal number of epochs for data division and the optimal value of k for k-fold cross-validation—a technique vital to the model’s robustness. The model’s predictive prowess is rigorously assessed via a suite of performance metrics and comprehensive score analyses. Furthermore, the model’s adaptability is gauged by integrating a secondary dataset into its predictive framework, facilitating a comparative evaluation against conventional prediction methods. To unravel the intricacies of the CNN model's learning trajectory, a loss plot is deployed to elucidate its learning rate. The study culminates in compelling findings that underscore the CNN model’s accurate prediction of geopolymer concrete compressive strength. To maximize the dataset’s potential, the application of bivariate plots unveils nuanced trends and interactions among variables, fortifying the consistency with earlier research. Evidenced by promising prediction accuracy, the study's outcomes hold significant promise in guiding the development of innovative geopolymer concrete formulations, thereby reinforcing its role as an eco-conscious and robust construction material. The findings prove that the CNN model accurately estimated geopolymer concrete's compressive strength. The results show that the prediction accuracy is promising and can be used for the development of new geopolymer concrete mixes. The outcomes not only underscore the significance of leveraging technology for sustainable construction practices but also pave the way for innovation and efficiency in the field of civil engineering.
Geopolymer concrete provides environmental protection by repurposing industrial by-products such as low-calcium fly ash, blast furnace slag, etc., into efficient construction materials. In geopolymer concrete, a tonne of fly ash or blast furnace slag is comparable in cost to a tonne of Portland cement after subtracting the cost of alkaline solutions. In a study [
Its ability to handle complex nonlinear structural systems under difficult conditions makes machine learning the most successful artificial intelligence subfield. It enhances structural engineering predictability. Machine learning (ML) trains a computer system to make accurate predictions. In order to build any ML model, you must prepare a database, learn, and then evaluate the model. As a computer system learns, it improves. Due to recent advances in ML methods, processing power, and access to large datasets, machine learning is becoming more prevalent in structural engineering. In the study, neural networks were found to be the most used machine learning method for structural engineering, approximately 56 percent of the time, and among neural network methods, artificial neural networks accounted for 84 percent, followed by convolutional neural networks with 8% [
The objectives of the research are outlined as follows:
The primary objective is to create a predictive analytical methodology for forecasting the compressive strength of geopolymer concrete.
The study introduces an optimized deep learning model that utilizes convolutional neural networks (CNNs).
The research involves obtaining a dataset comprising the composition of 162 geopolymer concrete mixes using Class F fly ash and their corresponding 28-day compressive strength values.
The research involves selecting an optimal set of input parameters for the predictive model based on two criteria: the influence of each feature on both the compressive strength and the model's prediction performance.
The use of bivariate plots to explore interactions between various components of geopolymer concrete mix design and compressive strength adds a valuable dimension to the analysis.
Composite geopolymer slump and compressive strength were predicted using a back propagation neural network, and the results were compared to the random forest and k-closest neighbor algorithm models [
This section introduces the proposed convolutional neural network model, describes the model training technique, and discusses the performance metrics used to judge the model's performance.
There are four layers in the CNN model we propose, namely the output layer, the flattened layer, the one-dimension convolutional layer, and the fully connected layers. The architecture of the suggested model is shown in
This layer is primarily in charge of collecting the connections between input parameters using multiple convolutional kernels (the value of which is indicated by p). By utilizing multiple kernels, the model is able to pick up as many trends as feasible and look into further ways to enhance compressive strength forecasting. Each convolutional kernel slides across the entire input feature vectors with a particular stride u for each slide, calculating a weighted sum over all the q components the kernel covers for each slide. The values used for p (no. of convolution layer kernels) and q (dimension of the kernel) are discussed further. The value of u is set to 1 to allow the kernel to discover as many locally existing patterns as feasible, as bigger numbers can result in the kernel losing too much information and slipping through too many features. Within the convolutional kernel, the RELU (rectified linear activation unit) function functions as the activation function. RELU was chosen because the needed compressive strength is a positive real number and RELU can separate negative interim calculation results that influence the outcome.
In
Matrix F is flattened into a 1-d feature vector. Later it passed to the fully connected layers to retrieve further hidden patterns. The flattened layer's corresponding feature vector
Because of the input parameters and compressive strength's extremely nonlinear relationships, only superficial patterns are present in the flattened vector F_{f}, making it impossible to infer compressive strength from it. To solve this issue, A deep latent feature vector is obtained by sending F_{f} across D number of fully connected layers in order to simulate and learn the appropriate non-linear connection. Each fully connected layer's intermediate results are calculated as follows, where d^{th} fully connected layer has
Here, for the i^{th} neuron within d^{th} fully connected layer,
The final compressive strength prediction is carried out by another fully connected layer with a sigmoid activation function.
Here,
A binary cross-entropy loss function was utilized to calculate the loss generated during the prediction process between its real and estimated values. The sigmoid activation function, being the only function compatible with this loss function, was employed. In the following set of formulas, the loss value between real compressive strength values and estimated compressive strength values is determined as shown in the former expression. The latter formula in the set of formulas below is used to compute the overall loss by calculating the mean of individual loss
To improve the model weights based on the above loss, Adaptive Moment Estimation (Adam) is utilized, which is one of the most frequently used optimizers. Adam's ability to asynchronously change learning rates for parameters has been proven to perform successfully in practice with the default configuration. The number of epochs E for learning and Adam’s dynamic rate of learning are two of the many hyperparameters, and optimal values of epochs are investigated and examined in the upcoming sections.
Given that the division of training and testing databases and the arbitrary assignment of trainable weights can affect training and evaluation results, a cross-validation strategy is employed to train and evaluate the model rather than a fixed training-testing split. This method can minimize the impact of randomization and improve the visualization of the model’s predictive accuracy. The technique of k-fold cross-validation is a well-known method for assessing the performance of a machine learning algorithm on a database. The database is divided into k number of non-overlapping folds using the cross-validation technique of k-fold. One of the k-folds is chosen as the held-back test set, whereas the rest are utilized collectively as the training dataset. After fitting and assessing k models on k hold-out test sets, the average performance is provided. The most common choices for the value of ‘k’ are 3, 5, and 10, with 10 being the most frequently used value in many studies to evaluate models. This is because the research was conducted, and k = 10 was discovered to give a suitable trade-off between cheap computing cost and low bias in an assessment of model performance [
The proposed model’s hyperparameters are as follows: kernel dimension; number of neurons in the completely connected layer; number of kernels in the convolution layer; number of fully connected layers; training epochs, learning rate, and the activation function. Because a hyperparameter governs the learning process, its values directly affect other model parameters like biases and weights and thus how well the model works. The convolution layer’s number of kernels was set to 32, the number of fully connected layers was 2, the kernel dimension to 6 the number of neurons in the 1^{st} fully connected layer was 128 and the 2^{nd} was 64, and the learning rate was set to 0.01, and Rectified Linear Unit (RELU) was selected as the activation function for the fully connected layers. These values of hyperparameters were chosen on the basis of previous work which used a similar set of hyperparameters whereas the rest were decided by utilizing a trial-and-error approach. The number of times the learning algorithm will loop through the entire training dataset is determined by the hyperparameter known as the training epoch. Any positive integer between one and infinity can be chosen. The most typical values are 10, 100, 500, and 1000. The training epochs were not chosen based on studies; three empirical values were chosen for them, which were 500, 200, and 5000, and then, utilizing the cross-validation technique, the performance of the model under all possible combinations of training epoch value and k-fold value as mentioned in the previous section was studied. In total, 87 configurations were tested on each dataset, and the combination that produced the least average root mean square error was considered the optimum combination.
Four performance metrics were used to assess how effectively the proposed CNN model functions, which are, the mean absolute error (MAE), mean absolute percentage error (MAPE), correlation coefficient (R), and root mean square error (RMSE). R determines whether the real and estimated compressive strength values have a linear relationship. While Mean Absolute Error takes the square of the errors, RMSE provides an error measure in the target variable’s unit. Instead, it just estimates the absolute value of the errors and then averages them. MAE, like RMSE, does not square the units, making the findings more interpretable. MAPE expresses the percentage of real and estimated values’ differences. By presenting the mistake as a percentage, it provides a better grasp of how far off the forecasts are in relative terms. In general, a larger R-value suggests better model prediction performance, while a lower value indicates better performance for RMSE, MAE, and MAPE. The following is the calculation formulas for the four indicators mentioned above:
In the above-mentioned formulae,
A dataset was acquired from the work of Toufigh et al. [
S. no. | Parameter | Units |
---|---|---|
1 | SiO_{2} in FA (Fly ash) | % |
2 | Na_{2}O in FA | % |
3 | CaO in FA | % |
4 | Al_{2}O_{3} in FA | % |
5 | Fe_{2}O_{3} in FA | % |
6 | Fly ash (FA) | kg/m^{3} |
7 | Percentage of Superplasticizer (SP) | kg/m^{3} |
8 | Sodium hydroxide solution (SH) | kg/m^{3} |
9 | Sodium silicate solution (SS) | kg/m^{3} |
10 | Fine aggregate (Fagg) | kg/m^{3} |
11 | Coarse aggregate (Cagg) | kg/m^{3} |
12 | Extra water (EW) | kg/m^{3} |
13 | Sodium hydroxide concentration (SH concentration) | Molarity |
14 | Percentage of silicon dioxide in sodium silicate | % |
15 | Percentage of silicon dioxide in sodium oxide | % |
16 | Curing time | Hr |
17 | Curing temperature | °C |
By studying the fly ash constituents, it could be deduced that the fly ash used in all these mix designs had a low amount of calcium oxide, which makes it class F fly ash.
Index | Count | Mean | Std | Min | 0.25 | 0.5 | 0.75 | Max |
---|---|---|---|---|---|---|---|---|
SiO_{2} in FA | 162 | 56.49 | 4.59 | 47.8 | 53.36 | 59.7 | 59.7 | 70.3 |
Na_{2}O in FA | 162 | 0.41 | 0.54 | 0 | 0.04 | 0.31 | 0.45 | 2.12 |
CaO in FA | 162 | 1.95 | 1.23 | 0.03 | 1.34 | 2.1 | 2.1 | 5.57 |
Al_{2}O_{3} in FA | 162 | 27.14 | 2.09 | 20.7 | 26.49 | 28.21 | 28.36 | 34.75 |
Fe_{2}O_{3} in FA | 162 | 7.77 | 4.29 | 1.4 | 4.57 | 4.57 | 10.86 | 17.4 |
FA | 162 | 372.68 | 62.81 | 255 | 312.5 | 400 | 420 | 500 |
Cagg | 162 | 1186.12 | 109.03 | 785 | 1170 | 1204 | 1204 | 1591 |
Fagg | 162 | 633.26 | 107.65 | 318 | 623 | 647 | 648 | 1100 |
SH | 162 | 50.63 | 14.46 | 25 | 41 | 49 | 57 | 129 |
SS | 162 | 116.38 | 23.7 | 48 | 103 | 114 | 127.75 | 204 |
EW | 162 | 19.03 | 19.61 | 0 | 0 | 15.5 | 33.75 | 86 |
SP | 162 | 7.09 | 6.14 | 0 | 6 | 6 | 7 | 28 |
SH concentration | 162 | 11.45 | 2.09 | 8 | 10 | 10 | 14 | 16 |
% of SiO_{2} in SS | 162 | 32.46 | 2.9 | 23 | 29.4 | 34.64 | 34.64 | 35.01 |
% of Na_{2}O in SS | 162 | 15.52 | 1.37 | 9.1 | 14.7 | 16.27 | 16.27 | 16.84 |
Curing time | 162 | 26.37 | 8.96 | 24 | 24 | 24 | 24 | 96 |
Curing temperature | 162 | 82.93 | 16.04 | 60 | 70 | 80 | 100 | 100 |
Compressive strength | 162 | 43.14 | 10.57 | 17 | 36 | 42 | 48.89 | 74 |
The data frame was also examined for any null values, and it was determined that no null values existed. While analyzing the data, outliers were discovered in a couple of the features. Although it is said that outliers may cause elevated error rates, no attempt has been made to delete them since some scholars believe that their removal may result in bad outcomes [
Features such as silicon dioxide in fly ash, the content of fly ash, and curing temperature were symmetric negatively. Positively symmetric sodium silicate solution and sodium hydroxide concentration Aluminum dioxide in fly ash, coarse aggregate, and the percentage of silicon dioxide in sodium silicate curing temperature was moderately negatively skewed. Fine aggregate, extra water, and compressive strength were moderately positively skewed. The percentage of silicon dioxide in sodium oxide seemed highly negatively skewed. Sodium oxide in fly ash, calcium oxide in fly ash, iron oxide in fly ash, sodium hydroxide solution, superplasticizer, and curing time were highly positively skewed.
The relationship between each of the possible value pairings is depicted in the matrix. It is an effective tool for analyzing large volumes of data and discovering and visualizing data trends. The correlation matrix is made up of columns and rows, each focusing on a different attribute. The columns and rows are all arranged in the same order. The correlation coefficient is found in each cell of a table. The results confirm that the correlation between the percentage of silicon dioxide in sodium silicate and the percentage of silicon dioxide in sodium oxide was positively and highly related, whereas the correlation between coarse aggregate & fine aggregate and iron oxide in fly ash & silicon dioxide in fly ash was negatively and highly related, and the other correlation was not significant enough.
Some studies claim that using a large dataset formed of key input features to train a model outperforms one trained with fewer input parameters. Some also say that explainable features, i.e., attributes grouped by engineers based on their influence on the development of concrete strength that is already known or potentially discoverable through research, are well-suited for prediction. Input feature groups were created for this study. While some of the input features were engineered from the initial features, others were taken directly from
Group 1: Features with a well-known and significant impact on geopolymer concrete's strength.
Group 2: Features pertaining to fly ash’s composition.
Group 3: Ratios utilized by various researchers to predict geopolymer concrete's strength.
Group 4: The top 12 features from groups 1, 2, and 3 that performed well across three feature-importance methods i.e., Random Forest Regression Feature Importance, CART (Classification and Regression Tree) Regression Feature Importance, and XGBoost Regression Feature Importance. The scores of these methods for every feature can be found in
Group | S. no. | Parameter | Units |
---|---|---|---|
G1 | 1 | FA | kg/m^{3} |
2 | SH | kg/m^{3} | |
3 | SS | kg/m^{3} | |
4 | SH concentration | Molarity | |
5 | % of SP | % | |
6 | Curing time | hr | |
7 | Curing temperature | °C | |
8 | Total H_{2}O | kg/m^{3} | |
9 | Total H_{2}O/FA (mass ratio) | ~ | |
10 | Total H_{2}O/Total solids (mass ratio) | ~ | |
11 | Fine aggregate/Total aggregate (mass ratio) | ~ | |
12 | Coarse aggregate/Total aggregate (mass ratio) | ~ | |
13 | Total solids/Total aggregate (mass ratio) | ~ | |
1 | % of SiO_{2} in FA | % | |
2 | % of Na_{2}O in FA | % | |
3 | % of CaO in FA | % | |
G2 | 4 | % of Al2O_{3} in FA | % |
5 | % of Fe_{2}O_{3} in FA | % | |
6 | % of SiO_{2} in SS | % | |
7 | % of Na_{2}O in SS | % | |
G3 | 1 | AA/FA (mass ratio) | ~ |
2 | SS/SH (mass ratio) | ~ | |
3 | superplasticizer/FA (mass ratio) | ~ | |
4 | Total H_{2}O/Total Na_{2}O (molar ratio) | ~ | |
5 | Total Na_{2}O/SiO_{2} in AA (molar ratio) | ~ | |
6 | Total SiO_{2}/Na_{2}O in AA (molar ratio) | ~ | |
7 | SiO_{2}/Al_{2}O_{3} in FA (molar ratio) | ~ | |
8 | SiO_{2}/Fe_{2}O_{3} in FA (molar ratio) | ~ | |
9 | Na_{2}O/Al_{2}O_{3} in FA (molar ratio) | ~ | |
10 | Al_{2}O_{3} in FA/Na_{2}O in AA (molar ratio) | ~ |
S. No. | Parameter | Units |
---|---|---|
1 | FA | kg/m^{3} |
2 | SH | kg/m^{3} |
3 | SS | kg/m^{3} |
4 | Curing time | hr |
5 | Total H_{2}O | kg/m^{3} |
6 | Total H_{2}O/FA (mass ratio) | ~ |
7 | Total H_{2}O/Total solids (mass ratio) | ~ |
8 | Total solids/Total aggregate (mass ratio) | ~ |
9 | % of CaO in FA | % |
10 | AA/FA (mass ratio) | ~ |
11 | Total H_{2}O/Total Na_{2}O (molar ratio) | ~ |
12 | Total SiO_{2}/Na_{2}O in AA (molar ratio) | ~ |
Combinations | Groups involved | No. of input parameters |
---|---|---|
C-1 | G1+C.S* | 13 |
C-2 | G1+G2+C.S* | 20 |
C-3 | G1+G3+C.S* | 23 |
C-4 | G1+G2+G3+C.S* | 30 |
C-5 | G4+C.S* | 12 |
*C. S –28-day compressive strength |
To examine the adaptability of the CNN model, a secondary dataset was acquired and used in the model. This dataset, generated through the work of I.C. Yeh of the University of California, 1030 compositions and their corresponding concrete strength values for high-strength concrete mixes. Many researchers have used this dataset to study the data in various ways and test out new machine learning techniques.
S. no. | Parameter | Units |
---|---|---|
1 | Coarse aggregate | kg/m^{3} |
2 | Superplasticizer | kg/m^{3} |
3 | Fly ash | kg/m^{3} |
4 | Fine aggregate | kg/m^{3} |
5 | Water | kg/m^{3} |
6 | Blast furnace slag | kg/m^{3} |
7 | Age | day |
8 | Cement | kg/m^{3} |
All the combinations mentioned in
Each epoch value has been represented in each graph by a distinct color.
Also, it was observed that the computational time for combination 4 was the highest since it had the most input parameters as mentioned in
As mentioned in
E | K | Combination | Performance metrics | |||
---|---|---|---|---|---|---|
R | RMSE (MPa) | MAE (MPa) | MAPE (%) | |||
500 | 3 | C-1 | 0.745 | 6.899 | 5.241 | 12.760 |
C-2 | 0.740 | 6.887 | 5.227 | 12.936 | ||
C-3 | 0.734 | 6.902 | 5.259 | 12.921 | ||
C-4 | 0.739 | 6.872 | 5.101 | 12.480 | ||
C-5 | 0.769 | 6.582 | 4.909 | 12.087 | ||
Order of precedence | 5- |
5-4- |
5-4- |
5-4- |
||
2000 | 10 | C-1 | 0.867 | 4.843 | 3.744 | 9.403 |
C-2 | 0.836 | 5.264 | 3.947 | 9.644 | ||
C-3 | 0.818 | 5.452 | 4.266 | 10.759 | ||
C-4 | 0.829 | 5.133 | 3.816 | 9.664 | ||
C-5 | 0.832 | 5.177 | 3.903 | 9.539 | ||
Order of precedence | ||||||
5000 | 28 | C-1 | 0.885 | 3.180 | 2.575 | 6.283 |
C-2 | 0.898 | 3.334 | 2.794 | 7.039 | ||
C-3 | 0.862 | 3.120 | 2.555 | 6.414 | ||
C-4 | 0.865 | 3.364 | 2.708 | 6.607 | ||
C-5 | 0.862 | 3.675 | 2.923 | 7.287 | ||
Order of precedence | 2- |
3- |
3- |
The results convey that combination 1 outperforms the others. The performance metrics of combination 1 improved as the epoch and k-fold values increased. Apart from that, combination 5, which consisted of parameters chosen based on feature importance, performed inconsistently over the range of epoch and k-fold values considered. Its performance was depleted as k-fold and epoch values increased. From studying the performance of each combination in terms of the influence of the number of variables, in agreement with the results of De-Cheng Feng [
A learning curve uses experience to measure changes in learning performance over time. It indicates how well the model learns when plotted against the training dataset and how well it generalizes when plotted against the validation dataset. Models are evaluated and selected based on model performance. B. Accuracy. The optimization curve is calculated according to parameter optimization. B. You incur losses. Loss curve behavior was examined for epoch values of 50, 100, and 200 and k-fold values of 5, 10, and 25. It has been observed that the learning rate improves as the epoch value increases because the loss decreases faster with increasing epoch value. When a higher k-fold value was chosen, the loss value quietly decreased after each epoch.
A comparative study was done where the performance metrics of various traditionally used models were compared to the CNN model for the dataset of combination 1. Other than the CNN model, various models were built, such as the Random Forest regression model, Decision Tree Regression model, Linear Regression model, Ridge Regression model, Gradient Boosting Regression model, AdaBoost Regression model, and an ensemble model (containing the aforementioned models). Except for the CNN model, all the models divided the dataset in a 9:1 ratio, with 90% of the dataset used for training and 10% utilized for testing. This ratio was chosen due to the work of Hamza Imran, who had deduced from his work that the 9:1 ratio as the train-test split ratio would produce the best results [
Models | Performance metrics | |||
---|---|---|---|---|
R | RMSE (MPa) | MAE (MPa) | MAPE (%) | |
CNN (C-1; E = 5000; K = 29) | ||||
Decision Tree Regression | 0.838 | 5.131 | 3.980 | 8.670 |
Random Forest Regression | 0.878 | 4.455 | 3.677 | 8.271 |
Linear Regression | 0.615 | 7.909 | 6.167 | 14.478 |
Ridge Regression | 0.555 | 8.503 | 6.159 | 14.532 |
Gradient Boosting Regression | 0.906 | 3.916 | 3.154 | 7.534 |
AdaBoost Regression | 0.753 | 6.336 | 5.142 | 12.091 |
Ensemble model | 0.819 | 5.429 | 4.151 | 9.656 |
Note: The values in bold correspond to the most effective model.
The gradient-boosting regression model seemed to have performed much like the CNN model. Models such as ridge regression, linear regression, and AdaBoost regression performed the poorest. To check the generality of the CNN model as mentioned in
Model | Performance metrics | |||
---|---|---|---|---|
R | RMSE (MPa) | MAE (MPa) | MAPE (%) | |
CNN (C-1; E = 5000; K = 29) | 9.058 | |||
Decision Tree Regression | 0.788 | 7.665 | 4.389 | 13.816 |
Random Forest Regression | 0.888 | 5.576 | 3.256 | 10.974 |
Linear Regression | 0.603 | 10.474 | 8.477 | 31.506 |
Ridge Regression | 0.603 | 10.474 | 31.506 | |
Gradient Boosting Regression | 0.876 | 5.851 | 3.951 | 11.900 |
AdaBoost Regression | 0.763 | 8.091 | 6.492 | 26.890 |
Ensemble model | 0.814 | 7.168 | 5.315 | 19.222 |
Note: The values in bold correspond to the most effective model.
The gradient-boosting regression model seemed to have performed very similarly to the CNN model. Models such as Linear regression, Ridge regression, and AdaBoost regression performed the poorest.
The technique of score analysis was applied to compare the performance of various models in a simple manner. Using this technique, the model is assigned a score of x. When models are placed in descending order depending on their performance in each metric, x represents the position obtained by each computational model. The maximum value of x would be the total number of computational models used in the performance comparison (maximum value of x is equal to 8 here), which would be assigned to the model with the best performance based on that metric, and the minimum would be 1, for the model with the worst performance in that particular metric. Each computational model would acquire a separate score for its performance for each evaluation metric, i.e., R, RMSE, MAE, and MAPE. Following that, the total score corresponding to each of the models is derived by adding their separate scores [
Model | Performance metrics | Total score | |||
---|---|---|---|---|---|
R | RMSE (MPa) | MAE (MPa) | MAPE (%) | ||
CNN (C-1; E = 5000; K = 29) | 8 | 8 | 8 | 8 | 32 |
Decision Tree Regression | 5 | 5 | 5 | 5 | 20 |
Random Forest Regression | 6 | 6 | 6 | 6 | 24 |
Linear Regression | 2 | 2 | 1 | 2 | 7 |
Ridge Regression | 1 | 1 | 2 | 1 | 5 |
Gradient Boosting Regression | 7 | 7 | 7 | 7 | 28 |
AdaBoost Regression | 3 | 3 | 3 | 3 | 12 |
Ensemble model | 4 | 4 | 4 | 4 | 16 |
The results suggest that the CNN model used in this study gained the best score of 32. Other models whose performance almost matched the performance of the CNN model were the Random Forest Regression model, Gradient Boosting Regression model, and Decision Tree Regression model. The Ridge Regression model performed the least among all, with a score of 5.
To check the generality of the CNN model, the above-mentioned process was repeated with the secondary dataset acquired.
Model | Performance metrics | |||
---|---|---|---|---|
R | RMSE (MPa) | MAE (MPa) | MAPE (%) | |
CNN (C1; E = 5000; K = 29) | 9.058 | |||
Decision Tree Regression | 0.788 | 7.665 | 4.389 | 13.816 |
Random Forest Regression | 0.888 | 5.576 | 3.256 | 10.974 |
Linear Regression | 0.603 | 10.474 | 8.477 | 31.506 |
Ridge Regression | 0.603 | 10.474 | 31.506 | |
Gradient Boosting Regression | 0.876 | 5.851 | 3.951 | 11.900 |
AdaBoost Regression | 0.763 | 8.091 | 6.492 | 26.890 |
Ensemble model | 0.814 | 7.168 | 5.315 | 19.222 |
Note: The values in bold correspond to the best performing model.
To test the predictability of the model, the true values and the predicted values were compared. As shown in
A loss curve was plotted to understand the training process and the way the convolutional neural network learns the data and optimizes itself. The loss (calculated as mentioned in
This section examines the numerous trends and interactions between variables.
This work used an optimized deep learning model utilizing convolutional neural networks to solve the effectiveness and application challenges of current methods for forecasting geopolymer concrete's compressive strength. A dataset comprising the composition of 162 Class F fly ash geopolymer concrete mixes as well as 28-day compressive strength values were obtained. Using prior knowledge of each feature's influence on compressive strength as well as feature importance techniques, an ideal set of input parameters was carefully chosen. The optimal number of epochs (how many groups a certain dataset should be divided into) and the optimal value of k to run the k-fold cross-validation technique (the number of groups into which the data sample should be split) for the model that yielded the best results were determined through a process of trial and error. The performance metrics of this model were compared to different previously existing models for the obtained geopolymer concrete dataset as well as a secondary dataset (the high-performance concrete dataset) to evaluate the model's predictability and adaptability. The following points were made:
In the analyzed geopolymer concrete database, the proposed model's R, RMSE, MAE, and MAPE were 0.939, 3.083%, 2.509 MPa, and 6.222%, respectively, indicating that the prediction error is reasonable and that the model can accurately forecast the compressive strength of geopolymer concrete. Compared to traditional approaches, the proposed model for predicting geopolymer concrete compressive strength has significantly lower error metrics. The difference between the true and anticipated values did not exceed 2,16 MPa, or 4.84%, which indicates the model's predictability is efficient.
It was necessary to adjust hyperparameters for the k-fold cross-validation technique, such as k (the number of groups into which each data sample should be split) and epochs (the number of times the training data was passed through the algorithm). The performance of the model was greatly influenced by the number of passes through the algorithm. In k-fold cross-validation, the optimal value of k was determined to be between 25 and 30 for all dataset combinations. The epoch value of 5000 performed best on all combinations despite the long computational time.
For epoch values of 500, 2000, and 5000 and k values ranging from 2 to 30, the algorithm was executed for five combinations of input parameters that were evaluated and analyzed in the proposed model. Combination 1, which is a collection of essential parameters, outperforms the others. As the epoch and K values increased, so did the performance metrics of combination 1. It was also discovered that as the no. of variables increases, the model's performance depletes, and the computing time increases.
The loss curve behaviour was studied for various epoch values and k-fold values, and it could be concluded that as epoch values increase, the learning rate keeps getting better as the loss decays faster with the increase in epoch values. In the instances where higher k-fold values were chosen, in those the loss value decreased calmly as each epoch was experienced.
A learning curve plotted between the number of epochs and their corresponding loss assisted in visualizing the model's performance and decoding the model's "black box" character. Visualization demonstrated that the suggested model had a high learning rate, indicating that the hyperparameters were set correctly. Furthermore, the model showed no signs of overfitting, which was expected to be avoided due to the limited amount of data utilized.
Bivariate plots are used to study distinct trends and interactions between various components of geopolymer concrete mix design and 28th day compressive strength. Most of the patterns identified were consistent with prior studies' findings. The figures depicting the interaction between the oxides found in fly ash and compressive strength were helpful in understanding their impact on strength.
However, an enhanced data set of geopolymer concrete mixes should be produced for future work, as a larger and more diverse data set could provide opportunities to investigate several more machine-learning techniques. Also, appropriate strategies should be studied and implemented to cut computational time as much as possible so that there is no need to adopt those hyperparameters, which would take less time to train the model and settle for a poorer result.
To summarize, there is a certain novelty value in this study's approach towards predicting strength using machine learning methods. This study provides an AI-based prediction model and method for the compressive strength of geopolymer concrete (made with low-calcium fly ash) by using tuned hyperparameters with a learning rate of 0.01. This would not only allow engineers to use this as the primary design element in geopolymer concrete mix design but also would help to establish the significant material parameters for preliminary design purposes, such as tensile strength, elasticity modulus, and flexural strength.
The authors present their appreciation to King Saud University for funding the publication of this research through Researchers Supporting Program King Saud University, Riyadh, Saudi Arabia.
The research is funded by the Researchers Supporting Program at King Saud University (RSPD2023R809).
Ramujee–Project supervision, project conception, design, validation, writing–review, and editing; Pooja & Madhu–data collection, analysis & interpretation of results, and writing–original draft; Madhu & Sandeep–visualization, and validation; Guojiang–reviewing and editing; Abdulaziz S. Almazyad–funding acquisition and resources; Ali Wagdy–writing, reviewing, and editing. All authors have read and agreed to the published version of the manuscript.
The primary dataset mentioned in
The authors declare that they have no conflicts of interest to report regarding the present study.
S. No. | Parameter | CART regression feature importance | Random forest regression feature importance | XGBoost regression feature importance |
---|---|---|---|---|
1 | FA | 0.086 | 0.020 | 0.027 |
2 | SH | 0.020 | 0.014 | 0.043 |
3 | SS | 0.010 | 0.038 | 0.057 |
4 | SH concentration | 0.000 | 0.009 | 0.013 |
5 | % of SP in FA | 0.000 | 0.008 | 0.009 |
6 | Curing time | 0.003 | 0.004 | 0.007 |
7 | Curing temperature | 0.065 | 0.040 | 0.024 |
8 | Total H_{2}O | 0.017 | 0.042 | 0.039 |
9 | Total H_{2}O/FA (mass ratio) | 0.352 | 0.197 | 0.183 |
10 | Total H_{2}O/Total solids (mass ratio) | 0.028 | 0.224 | 0.085 |
11 | Fine aggregate/Total aggregate (mass ratio) | 0.024 | 0.011 | 0.025 |
12 | Coarse aggregate/Total aggregate (mass ratio) | 0.033 | 0.011 | 0.000 |
13 | Total solids/Total aggregate (mass ratio) | 0.092 | 0.041 | 0.026 |
14 | % of SiO_{2} in FA | 0.000 | 0.007 | 0.019 |
15 | % of Na_{2}O in FA | 0.000 | 0.005 | 0.064 |
16 | % of CaO in FA | 0.061 | 0.041 | 0.081 |
17 | % of Al_{2}O_{3} in FA | 0.000 | 0.010 | 0.048 |
18 | % of Fe_{2}O_{3} in FA | 0.001 | 0.007 | 0.017 |
19 | % of SiO_{2} in SS | 0.000 | 0.008 | 0.047 |
20 | % of Na_{2}O in SS | 0.000 | 0.006 | 0.000 |
21 | AA/FA (mass ratio) | 0.010 | 0.054 | 0.037 |
22 | SS/SH (mass ratio) | 0.001 | 0.014 | 0.010 |
23 | superplasticizer/FA (mass ratio) | 0.006 | 0.008 | 0.000 |
24 | Total H_{2}O/Total Na_{2}O (molar ratio) | 0.168 | 0.098 | 0.048 |
25 | Total Na_{2}O/SiO_{2} in AA (molar ratio) | 0.000 | 0.016 | 0.025 |
26 | Total SiO_{2}/Na_{2}O in AA (molar ratio) | 0.005 | 0.030 | 0.043 |
27 | SiO_{2}/Al_{2}O_{3} in FA (molar ratio) | 0.008 | 0.005 | 0.000 |
28 | SiO_{2}/Fe_{2}O_{3} in FA (molar ratio) | 0.000 | 0.006 | 0.000 |
29 | Na_{2}O/Al_{2}O_{3} in FA (molar ratio) | 0.003 | 0.005 | 0.000 |
30 | Al_{2}O_{3} in FA/Na_{2}O in AA (molar ratio) | 0.006 | 0.023 | 0.024 |