# Perspective on the Application of Machine Learning Algorithms for Flow Parameter Estimation in Recycled Concrete Aggregate

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}and for loosely packed samples. Differences in the structures of the test results are presented for both materials. The lowest prediction errors were obtained for the k-NN model. This algorithm obtained for the training sample a coefficient of determination (R

^{2}) equal to 0.947 and for the test sample an R

^{2}equal to 0.980. In the case of ANN, the coefficient of determination was in the range of 0.877–0.936. An important part of the study was the interpretation with SHAP of the obtained models, allowing insight into which parameters influenced the predictions. That is significant and novel, considering the heterogeneity of the materials studied, and provides a rationale for further research in this area.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials and Filtration Study Method

^{3}]), grain size (particle sizes d5, d10, d20, d30, d60, and d90 [mm]), dry density, specific density, porosity, and void ratio. The average values of these parameters are presented in Table 1.

#### 2.2. Data Preparation and Overall Methodology for the Applied Machine Learning Algorithms

#### 2.3. Artificial Neural Networks

#### 2.4. k-Nearest Neighbors

#### 2.5. Error Analysis

- Mean square error (MSE) represents the mean squared difference between the raw and predicted values in a data set. It measures the variance of the residuals.

- Root mean square error (RMSE) is the square root of the mean squared error. It measures the standard deviation of the residuals.

- Mean absolute error (MAE) represents the average absolute difference between the observed and predicted values in a data set. It measures the average of the residuals in a data set.

- Coefficient of determination (R
^{2}) represents the portion of the variance of the dependent variable that is explained by the linear regression model. This is a scale-free result, i.e., whether the values are small or large, the R^{2}value will be less than one.

## 3. Results and Discussion

^{3}were applied.

^{2}result similar to that for linear regression was obtained, 0.877 and 0.829, respectively.

^{2}of 0.936.

^{3}. Since the predictive results for the linear regression canceled each other out, better final R

^{2}(overall) results were obtained than the data analysis based on the compaction energies allows. The partial results for this algorithm were as follows: for samples without additional compaction energy, r = 0.84; with the compaction energy of 0.17 J/cm

^{3}, r was −0.34; and with 0.59 J/cm

^{3}, r was 0.33. The resultant r was 0.92.

^{2}was observed for parameters both strongly and weakly correlated with the permeability coefficient, which may indicate the high robustness of the model to outliers, for example, dry density correlation of −0.9 and specific density of 0.1.

## 4. Conclusions

- The results of the study suggest that the methods of machine learning algorithms may be applicable for the prediction of the coefficient of permeability and, more broadly, geotechnical parameters.
- To ensure the quality and reliability of the estimated model, a sufficiently large database should be provided and continuously developed. Also important is the proper preparation of the database for analysis, which is the basis for the determination of reliable models.
- The results of the post-prediction error analysis obtained for the k-NN algorithm may indicate the correct choice of the model for estimating the coefficient of permeability for recycled anthropogenic aggregates. Error analysis for the training sample showed an RMSE error of 0.004, while the MAE was 0.002. The coefficients of determination for both the training and test sets were accordingly 0.947 and 0.980. However, taking into consideration the analysis of significant characteristics impacting the explanation of the model (Figure 8 and Figure 9), one should take into account the lower resistance of the model to changes in the characteristics of materials.
- Given the above conclusions, the neural network model should also be considered. Admittedly, the model performs worse when analyzing errors (RMSE: 0.005–0.006 and MAE: 0.003–0.004) and R
^{2}(0.877 for the trial set and 0.936 for the test set) than the model based on the k-NN algorithm, but it takes into account more features that affect the prediction of the model. As a result, it can affect lower errors when estimating the coefficient of permeability for other materials. - According to Darcy’s law, the dependence of gradient and filtration velocity is linear, and most of the empirical equations formed based on this relation are linear regression. The research presented in this article proves that this model is not suitable for generalizing predictions based on the features and parameters of anthropogenic materials and allowing at the same time the consideration that machine learning algorithms are better suited to these prediction tasks.
- The analysis should be repeated for other anthropogenic and post-industrial materials used in civil engineering to validate the usefulness of the analyzed algorithms.
- The use of interpretive methods such as SHAP allows for better insight into the performance of the model and provides valuable information about parameters that have an important impact on the final model and are a significant part of the study. We suggest using interpretive machine learning methods to support decision criteria in civil engineering applications.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**The relationship of the permeability coefficient results to compaction energy in the context of the tested material.

**Figure 7.**Regression plot of the prediction results of each algorithm to the test results: (

**a**) k-NN algorithm. (

**b**) Neural network algorithm. (

**c**) Linear regression.

**Figure 8.**The results of the significance of the various features of the models: (

**a**) k-NN. (

**b**) Neural network. (

**c**) Linear regression.

**Figure 9.**The structure feature values at the impact on the model in different algorithms: (

**a**) kNN. (

**b**) Neural network. (

**c**) Linear regression.

**Figure 10.**The figure of influential observations in different algorithms: k-NN: Trial set (

**a**), Test set (

**b**). Neural network: Trial set (

**c**), Test set (

**d**). Linear regression: Trial set (

**e**), Test set (

**f**).

Description | Mean Value |
---|---|

Particle size d5 [mm] | 0.27 |

Particle size d10 [mm] | 0.60 |

Particle size d20 [mm] | 1.78 |

Particle size d30 [mm] | 3.38 |

Particle size d60 [mm] | 11.06 |

Particle size d90 [mm] | 23.38 |

Dry density [g/cm^{3}] | 1.35 |

Porosity [-] | 0.465 |

Void ratio [-] | 0.902 |

**Table 2.**Performance results of using the various algorithms to predict the permeability coefficient.

Trial Set | ||||
---|---|---|---|---|

Model | MSE | RMSE | MAE | R^{2} |

kNN | 0.000 | 0.004 | 0.002 | 0.947 |

Neural network | 0.000 | 0.006 | 0.004 | 0.877 |

Linear regresion | 0.000 | 0.007 | 0.005 | 0.829 |

**Table 3.**Performance results of using the various algorithms to predict the permeability coefficient.

Test Set | ||||
---|---|---|---|---|

Model | MSE | RMSE | MAE | R^{2} |

kNN | 0.000 | 0.003 | 0.002 | 0.980 |

Neural network | 0.000 | 0.005 | 0.003 | 0.936 |

Linear regresion | 0.000 | 0.007 | 0.006 | 0.844 |

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**MDPI and ACS Style**

Dzięcioł, J.; Sas, W.
Perspective on the Application of Machine Learning Algorithms for Flow Parameter Estimation in Recycled Concrete Aggregate. *Materials* **2023**, *16*, 1500.
https://doi.org/10.3390/ma16041500

**AMA Style**

Dzięcioł J, Sas W.
Perspective on the Application of Machine Learning Algorithms for Flow Parameter Estimation in Recycled Concrete Aggregate. *Materials*. 2023; 16(4):1500.
https://doi.org/10.3390/ma16041500

**Chicago/Turabian Style**

Dzięcioł, Justyna, and Wojciech Sas.
2023. "Perspective on the Application of Machine Learning Algorithms for Flow Parameter Estimation in Recycled Concrete Aggregate" *Materials* 16, no. 4: 1500.
https://doi.org/10.3390/ma16041500