*4.1. Yield Stress Output from NN's Model*

The relation between the experimental result and the result obtained from the ANN model for YS showed better accuracy, as indicated by the R<sup>2</sup> value of 0.89, which can be seen in Figure 3. The distribution of the variation between the actual result and ANN's model output can be seen in Figure 4. This difference gave the maximum and minimum values as 59.85 Pa and 1.35 Pa, respectively. However, it was noted that 25.95% of the variation's data lied between the minimum value and 30 Pa, and 27.77% of the data were reported between 30 Pa and 50 Pa. However, 42.59% of these data were reported above 50 Pa.

**Figure 3.** Yield stress relationship for the actual and predicted result of ANN model.

**Figure 4.** Error distribution of NN model for yield stress.

#### *4.2. Yield Stress Output from R-F Model*

R-F model showed strong relation when a comparison was made for the result of YS with the experimental result. R-F gives the R2 value equal to 0.96, indicating a much high precision level in terms of predicting the YS of the fresh concrete as opposed to the NN model, as shown in Figure 5. The result of the data representing the difference between the real and forecasted values can be seen in Figure 6. This data showed the maximum, minimum, and average values to be 59.85 Pa, 1.35 Pa, and 30.36 Pa, respectively. It was also noted that 50% of these data were lying between a minimum value of 30 Pa, and 40.74% of the data were reported between 30 Pa to 50 Pa. However, only 9.25% of the aforementioned data were noted above 50 Pa.

**Figure 5.** Yield stress relationship for the actual and predicted result of R-F model.

**Figure 6.** Error distribution of R-F model for yield stress.

#### *4.3. Plastic Viscosity Outcome from NN's Model*

When comparing the ANN's model output for the PV of fresh concrete with the experimental result, the precision level in predicting the required result was better. This is indicated by the R2 value equal to 0.87, as shown in Figure 7. However, the distribution of the difference values between the experimental and predicted ANN models is depicted in Figure 8. This distribution gives the highest, minimum, and average values as 7.72 Pa·s, 0.11 Pa·s, and 3.52 Pa·s. Moreover, it was noted that 33.33% of these data lie between its minimum value and 2 Pa·s, 35.08% of the data lie between 2 Pa·s and 5 Pa·s, and 31.5% of the difference data were reported above 5 Pa·s.

**Figure 7.** Plastic viscosity relationship for the actual and predicted result of the NN model.

**Figure 8.** Error distribution of NN model for plastic viscosity.

#### *4.4. Plastic Viscosity Outcome from R-F Model*

The relationship for the PV of fresh concrete between the actual and forecasted results of the R-F model showed high accuracy as opposed to the ANN model. This confirmation was made by examining the coefficient of determination (R2) value equal to 0.96 for the R-F model, the reflection of which can be seen in Figure 9. However, the error distribution for the result of PV of fresh concrete between the experimental and predicted outcome is shown in Figure 10. The distribution gives the highest, minimum, and average values equal to 12.18 Pa·s, 0.589 Pa·s, and 3.59 Pa·s, respectively. In addition, 22.80% of these data were reported between the minimum value (0.589 Pa·s) and 2 Pa·s, 52.63% of the data were between 2 Pa·s and 5 Pa·s, while 24.56% of these data were noted above the 5 Pa·s.

**Figure 9.** Plastic viscosity relationship for the actual and predicted result of R-F model.

**Figure 10.** Error distribution of R-F model for plastic viscosity.

#### **5. Result of K-Fold Cross Validation (C-V)**

C-V is a statistical method for judging or speculating how well machine learning models really work. Because it is important to know how well the chosen models work, users need a validation method to figure out how accurate the model's data are. For the k-fold validation test, the data set needs to be mixed up randomly and separated into k classes. In this study, experimental sample data were split into 10 subsets. It utilized nine of the ten subgroups, but only one of them was used to test the model. The same part of this process was then performed 10 times to get an average of how accurate these 10 times were. It was clear that the 10-fold cross-validation method gave a good picture of the model's performance and accuracy.

C-V could be used to confirm bias and decrease deviation for the data set. Figures 11–14 show how a correlation coefficient (R2), a mean absolute error (MAE), and a root mean square error (RMSE) were used for both plastic viscosity (PV) and yield stress (YS) to quantify the impact of cross validation. The ANN model's K-fold C-V for PV gave the highest values for MAE, RMSE, and R2 as 255.75 Pa·s, 288.47 Pa·s, and 0.95, respectively, as depicted in Figure 11. A steady increase in MAE in the graph was reported until the k-fold value of 4, while an abrupt decrease was reported at values 5 and 7. Similarly, in the case of R2, after a second k-fold value, the minimum result was reported, which seemed to normally increase until the 10th k-fold value. The maximum values of the same parameters for the R-F model to analyze plastic viscosity are 188.48 Pa·s, 147.38 Pa·s, and 0.97, respectively, as shown in Figure 12. In this case, MAE showed a fluctuation in the result until the end point of the graph, while a decrease in the R2 result was noted with some variations. Similarly, the maximum values of the ANN's model for MAE, RMSE, and R2 of YS were noted as 28.36 Pa, 32.42 Pa, and 0.98, respectively, as shown in Figure 13. An abrupt increase in MAE was reported at the initial phase, but it showed a sharp decrease at the stage of the 3rd k-fold. Moreover, R<sup>2</sup> showed a steady decrease until the 6th k-fold and a dramatic increase was reported to reach the maximum value. However, the maximum values for YS of the R-F's model for the same parameters give 25.1 Pa, 29.39 Pa, and 0.96, respectively, as shown in Figure 14. A steady decrease in MAE was noted in this case until the 4th k-fold value and then fluctuated in the MAE result until the last k-fold. However, the R<sup>2</sup> result also showed a declining curve until the 4th k-fold value, and then random changes were noted. In contrast, the statistical checks for the YS and PV of concrete for both the models are listed in Tables 2 and 3, respectively.

**Figure 11.** K-fold result of plastic viscosity from ANN model.

**Figure 12.** K-fold result of plastic viscosity from R-F model.

**Figure 13.** K-fold result of yield stress from NN model.

**Figure 14.** K-fold result of yield stress from R-F model.


**Table 2.** Statistical outcomes of yield stress for employed models.

**Table 3.** Statistical outcomes of plastic viscosity for employed models.


**6. Sensitivity Analysis (S-A) Outcome**

The S-A was introduced to examine the influence and the impact of each input parameter used to determine the predictive outcome for both plastic viscosity (PV) and yield stress (YS). This analysis revealed that the stronger influence on the prediction of rheological parameters was cement, which showed a 32.74% contribution, and superplasticizers with 24.61%. However, other variables contributed less towards the anticipation of rheological parameters of fresh concrete. Contributions made by other variables in descending order were small gravel (14.37%), medium gravel (11.07%), fine aggregate (9.73), and water (7.48%), as shown in Figure 15.

**Figure 15.** Influence of input parameters on the targeted outcome.

#### **7. Discussion**

This study examines the use of machine learning techniques to predict the rheological characteristics of fresh concrete. The selection of ANN and R-F models was based on their classification from different types of ML techniques. ANN belongs to the individual ML approach category, while R-F refers to the ensemble ML algorithm. ANN model uses the connection system of neurons and executes the process accordingly for the required output. However, in addition to its basic execution process, twenty R-F sub-models were trained on data and optimized to get the highest R2 value. Moreover, the data were also validated by means of K-fold C-V using R2, MAE, and RMSE. The input parameters played a vital role in the accuracy level of the employed model. The variation in the result may occur from both increasing or decreasing the total number of input parameters. However, the confirmation, such as statistical checks, sensitivity analysis, and validation for the models, was validated to achieve the precision level.

#### **8. Conclusions**

This paper proposed a comparison of predictive machine learning (PML) models for the rheological parameters of fresh concrete. The plastic viscosity (PV) and yield stress (YS) properties of the concrete at the initial stage were predicted using artificial neural network

(ANN) and random forest (R-F) models. The following conclusions can be drawn from the study:


The data set can be enhanced with the experimental approach to check the performance level of the models with a large data set. The input parameters can be increased with the addition of the chemicals in concrete, the effect of temperature, the water to cement ratio, and the cement to aggregate ratio. Other ML approaches, such as SVM, Adaboost, XGboost, and deep learning methods, can also be introduced to investigate these properties.

**Author Contributions:** M.N.A.: Conceptualization, Funding acquisition, Resources, Project administration, Supervision, Writing-Reviewing and Editing. A.A.: Conceptualization, Data curation, Software, Methodology, Investigation, Validation, Writing-original draft. K.K.: Methodology, Investigation, Writing—Reviewing and Editing. W.A.: Resources, Visualization, Writing-Reviewing and Editing. S.E.: Visulization, Writing—Reviewing and Editing. A.A.A.: Visualization, Funding acquisition. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia [Project No. GRANT347]. The APC was funded by the same "Project No. GRANT347".

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used in this research have been properly cited and reported in the main text.

**Acknowledgments:** The authors acknowledge the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia [Project No. GRANT347]. The authors extend their appreciation for the financial support that has made this study possible.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

