After the excavation of the roadway, the original stress balance is destroyed, resulting in the redistribution of stress and the formation of an excavation damaged zone (EDZ) around the roadway. The thickness of EDZ is the key basis for roadway stability discrimination and support structure design, and it is of great engineering significance to accurately predict the thickness of EDZ. Considering the advantages of machine learning (ML) in dealing with high-dimensional, nonlinear problems, a hybrid prediction model based on the random forest (RF) algorithm is developed in this paper. The model used the dragonfly algorithm (DA) to optimize two hyperparameters in RF, namely _{try} and _{tree}, and used mean absolute error (MAE), root mean square error (RMSE), determination coefficient (R^{2}), and variance accounted for (VAF) to evaluate model prediction performance. A database containing 217 sets of data was collected, with embedding depth (^{2} = 0.9577, VAF = 94.2645; test set: MAE = 0.1115, RMSE = 0.1417, R^{2} = 0.9423, VAF = 94.0836). The results of the sensitivity analysis showed that the relative importance of each input variable was

After the excavation of the roadway, the original stress equilibrium state of the surrounding rock is broken, resulting in stress redistribution. On the one hand, the radial stress decreases and the tangential stress increases; on the other hand, the stress state of the surrounding rock changes from a three-dimensional stress state to an approximately two-dimensional stress state. Therefore, the surrounding rock will appear strength reduction and stress concentration phenomenon. When the induced stress in the surrounding rock exceeds the strength of the rock mass, the rock mass will be broken, and a ring-shaped broken rock zone (BRZ) will be formed within a certain range around the roadway, which is called the excavation damaged zone (EDZ) or loose circle [

At present, there are several methods for predicting EDZ thickness, including the empirical formula method, on-site measurement method, numerical simulation, and machine learning (ML). Based on onsite tests and theoretical analysis, various empirical formulas for calculating EDZ thickness have been proposed [

Due to the advantages of ML methods in dealing with nonlinear problems, ML has been widely used to solve complex problems in the engineering field [

Random forest (RF), as an efficient machine learning (ML) technique, has been applied in many engineering practices and has shown good predictive ability [_{try}) and the number of trees (_{tree}), to enhance its predictive power. In addition, the DA-RF hybrid model is compared with three classical models to evaluate its predictive performance. Finally, the degree of influence of each output parameter on the prediction of EDZ thickness was determined by sensitivity analysis.

The dragonfly algorithm (DA) is a metaheuristic algorithm proposed by Mirjalili [

Separation refers to the behavior of dragonflies to separate from the population in order to avoid static collisions with neighbors during flight, its mathematical model is as follows:

_{j} is the position of the

Alignment refers to the speed at which a dragonfly individual maintains the same speed as its neighbors when flying, and its mathematical model is as follows:

_{j} denotes the flight speed of the

Cohesion refers to the behavior that dragonfly individuals tend to gather toward the center of neighboring individuals, and its mathematical model is as follows:

Foraging is the behavior of a dragonfly that is attracted to food and flies towards it, and its mathematical model is as follows:

^{+} is the location of the food source.

Avoiding the enemy refers to distracting the enemy's attention and escaping from the natural enemy, and its mathematical model is as follows:

^{−} represents the position of the enemy.

The position of the food source is the current optimal position of the algorithm, and the fitness value is the best, and the position of the enemy is the current worst position, and the fitness value is the worst. DA is developed based on the particle swarm algorithm, and to imitate the flight direction of the dragonfly in space as well as the step length, a step vector

_{t+1} is the next population location update step.

The position vector represents the position of the individual dragonfly movement. When the former individual has neighboring dragonflies (i.e., there are other dragonflies within his radius (

When there is no neighboring dragonfly, to improve the randomness of dragonfly searching, the Lévy flight method is used to fly around the search space to update the position of the dragonfly. The mathematical model is as follows:

_{1} and _{2} are random numbers in [0,1], and

To adjust the search performance of the DA algorithm, the parameter values (

Random Forest (RF) algorithm is a machine learning model based on the decision tree proposed by Breiman [

First, the bagging method is used to repeatedly randomly select

To construct a DA-RF hybrid model for predicting EDZ thickness, we built a database by referring to previous literature [

Parameter | Unit | Min | Max | Mean | Standard deviation |
---|---|---|---|---|---|

m | 97 | 1159 | 501.82 | 240.70 | |

m | 2.4 | 10 | 3.73 | 1.13 | |

MPa | 7.5 | 147.89 | 29.14 | 27.71 | |

– | 1 | 5 | 2.95 | 1.19 | |

m | 0.3 | 3.45 | 1.57 | 0.62 |

In order to verify and evaluate the prediction performance of the DA-RF hybrid model and ensure that the model can reliably predict the thickness of the EDZ around the roadway, four evaluation indicators were selected in this study, namely mean absolute error (MAE) and root mean square error (RMSE), determination coefficient (R^{2}), and variance accounted for (VAF) [^{2} is to 1, and the closer the VAF value is to 100, indicating that the prediction quality of the model is higher. The formulas of the evaluation indexes are as follows [

In this paper, the RF algorithm is used to predict the thickness of the EDZ around the roadway, and DA is used to optimize the two hyperparameters _{try} and _{tree} in RF to improve the prediction performance of the RF model. From this, a DA-RF hybrid prediction model is constructed. To more intuitively illustrate the architecture of the proposed hybrid prediction model, the construction process of DA-RF model development and evaluation is shown in _{try} and _{tree} in RF through DA, and the RMSE was used as the fitness value to determine whether the termination condition was satisfied and if so, the best RF model was determined. Finally, the prediction performance of the proposed hybrid models was evaluated by calculating the evaluation indicators (R^{2}, VAF, RMSE, MAE) for the training and test sets.

The correlation between the predicted and actual values of the training and test sets of the DA-RF model is shown in ^{2} of 0.1246,0.1636, and 0.9277, respectively, during the test phase. Yu et al [^{2}, and VAF of 0.1591, 0.9153, and 89.2192, respectively, during the testing phase. The MAE, RMSE, R^{2}, and VAF of the DA-RF model constructed in this paper were 0.1115, 0.1417, 0.9423, and 94.0836, respectively, in the testing phase, which was significantly better than the above two models and possessed higher prediction performance.

Several classical models and risk assessment procedures have been applied to high-risk operations and projects such as blasting and quarrying [

Model | MAE | Score | RMSE | Score | R^{2} |
Score | VAF | Score | Final score |
---|---|---|---|---|---|---|---|---|---|

Training | |||||||||

BPNN | 0.2170 | 2 | 0.2984 | 2 | 0.7844 | 2 | 78.3876 | 2 | 8 |

ELM | 0.2145 | 3 | 0.2916 | 3 | 0.7872 | 3 | 78.7218 | 3 | 12 |

RBF | 0.2243 | 1 | 0.2993 | 1 | 0.7758 | 1 | 77.5804 | 1 | 4 |

RF | 0.1653 | 4 | 0.2214 | 4 | 0.9268 | 4 | 87.7347 | 4 | 16 |

DA-RF | 0.1036 | 5 | 0.1514 | 5 | 0.9577 | 5 | 94.2645 | 5 | 20 |

Testing | |||||||||

BPNN | 0.1954 | 3 | 0.2628 | 3 | 0.7769 | 2 | 76.6210 | 3 | 11 |

ELM | 0.2287 | 1 | 0.2811 | 1 | 0.7618 | 1 | 74.1459 | 1 | 4 |

RBF | 0.2131 | 2 | 0.2647 | 2 | 0.8163 | 3 | 76.2808 | 2 | 9 |

RF | 0.1436 | 4 | 0.1893 | 4 | 0.9081 | 4 | 88.1133 | 4 | 16 |

DA-RF | 0.1115 | 5 | 0.1417 | 5 | 0.9423 | 5 | 94.0836 | 5 | 20 |

The prediction results of the test set of DA-RF and classic models are shown in

As can be seen from

The prediction of the thickness of the EDZ around the roadway is related to the roadway excavation and the design of the support structure, which plays an important role in ensuring the stability of the roadway. To accurately predict the EDZ thickness, the influence of various factors must be comprehensively considered. It is known that the four input parameters selected in this paper have a certain influence on the prediction of the thickness of the EDZ, but the extent of their influence is not clear. Therefore, sensitivity analysis is needed to judge the importance of each input variable in the DA-RF model to the output EDZ thickness.

The RF algorithm has built-in feature importance to calculate the sensitivity of the input parameters [

The thickness of the excavation damaged zone (EDZ) is an important basis for determining and controlling the stability of roadway engineering construction, and it is of great significance to accurately predict the thickness of the EDZ in engineering practice. Therefore, in this paper, a hybrid RF-based prediction model is developed to accurately predict the thickness of the EDZ around the roadway. The model utilized the dragonfly algorithm (DA) to optimize two hyperparameters in RF, namely _{try} and _{tree}. We established a database containing 217 sets of data, of which 174 sets were used as the training set and the remaining 43 sets as the test set. The embedding depth (^{2} = 0.9577, VAF = 94.2645; test set: MAE = 0.1115, RMSE = 0.1417, R^{2} = 0.9423, VAF = 94.0836), so it is recommended to predict the thickness of the EDZ around the roadway. Finally, the relative importance of each input variable was determined by sensitivity analysis, and the order from low to high was

This research was funded by the

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.