Intelligent modeling of blast-induced rock movement prediction using dimensional analysis and optimized artificial neural network technique

https://doi.org/10.1016/j.ijrmms.2021.104794Get rights and content

Abstract

For maximum metal recovery, considering the movement of ore and waste during the blasting process in loading design is meaningful for reducing ore loss and ore dilution in an open-pit mine. The blast-induced rock movement (BIRM) can be directly measured; nevertheless, it is time-consuming and relative expensive. To solve this problem, a novel intelligent prediction model was proposed by using dimensional analysis and optimized artificial neural network technique in this paper based on the BIRM monitoring test in Husab Uranium Mine, Namibia and Phoenix Mine, USA. After using dimensional analysis, five input variables and one output variable were determined with both considering the dimension and physical meaning of each dimensionless variable. Then, artificial neural network technique (ANN) technique was utilized to develop an accurate prediction model, and a metaheuristic algorithm namely the Equilibrium Optimizer (EO) algorithm was applied to search the optimal hyper-parameter combination. For comparison aims, a linear model and a non-linear regression model were also performed, and the comparison results show that the provided hybrid ANN-based model can yield better prediction performance. As a result, it can be concluded that the developed intelligent model in this article has the potential to predict BIRM during bench blasting, and the analysis method and modeling process in this paper can provide a reference for solving other engineering problems.

Introduction

To meet the mineral requirements for societal development, humans try to make the best possible efforts to extract the ore in the most economical way using surface or underground mining methods. Meanwhile, drilling and blasting, a method of using explosive energy to fragment the rock mass, has been the most commonly used method for both surface mining and underground mining in the past and future decades. During the mining process, ore boundary details which can be used to design an efficient drilling plan prior to the blast and guide shovel loading after the blast play an important role. When explosive detonating, strong impact energy is released, causing the movement of ore and waste and leading to the difference of pre-blast and post-blast ore boundary (see Fig. 1). In view of that the determination of the post-blast ore boundary is a complex issue while considering the movement of ore during the whole blasting process. Number of mines simply use the pre-blast ore boundary to design the loading plan and guide the shovel, which usually leads to serious ore loss and dilution.

In recent years, a series of devices listed in Table 1 have been invented by researchers1, 2, 3, 4, 5, 6, 7, 8, 9, 10 to monitor blast-induced rock movement (BIRM) for determining the post-blast ore boundary. Among these BIRM monitoring devices, it was found that the Blast-induced movement monitoring system (BMM) is the most accurate device compared with others, and the effectiveness of BMM has been demonstrated in many published studies. As an example, the research of Eshun and Dzigbordi1 shows that the use of this monitoring system can significantly improve the economic benefits of the mine.

Besides the direct BIRM monitoring, some works have also been done using numerical simulation4,11,12 and theoretical calculations,13, 14, 15 but they are too far from determining the post-blast ore boundary for an actual opencast blast.

Additionally, benefited from the rapid development of artificial intelligence (AI) technology, machine learning (ML) method, an important part of artificial intelligence technology, was successfully used in obtaining BIRM recently. In this area, the feasibility of using the optimized support vector machine (SVM) and optimized random forest (RF) algorithm to predict BIRM were studied by Yu et al.,16,17 and several prediction models with nice prediction performance were proposed based on the collected BIRM database. Compared with the blast-induced rock movement monitoring, numerical simulation, and theoretical calculations, machine learning method has the characteristics of easy-to-use and high-precision, such features can significantly help to determine solutions of higher reliability and accuracy for many problems especially the nonlinear problems that arise in the engineering field. Hence, the study of how to better apply the machine learning technique in analyzing the blast-induced rock movement phenomenon is meaningful. After reviewing the study of using machine learning methods to predict the BIRM in previous articles, some limitations were found: First, these models were developed based on various variables, but the physical meaning of these variables was not considered and the calculation complexity is high. Then, it is impossible to find an algorithm for solving all classes of problems, because if an algorithm is tuned for a class of problems, it must be offset by another class of problems. So the trying of new algorithms in the specified engineering problem is beneficial for providing a better solution.

The first limitation can be overcome by using the Dimensional analysis (DA) and considering the physical meaning of variables in DA before model development as the feature selection process. DA is usually used to analyze the relationship among various parameters for complex engineering problems.18 For example, Dehghani and Shafaghi19 utilized DA and developed a flyrock prediction equation with high predictive precision based on a flyrock database. Khandelwal and Saadat20 applied DA to study blast-induced ground vibration and suggested a new prediction equation for this hazard. In the DA method, some dimensional variables are selected first and then used to construct the dimensionless π-terms for prediction model development, which can provide variables with physical meaning for the establishment of an artificial intelligence model.

For the second limitation, as far as the authors knew that the proposal and application of novel hybrid predictive models on the basis of the concept of an ANN model is missing in this field. ANN, first introduced by McCulloch and Pitts,21 is a powerful machine learning algorithm based on neural network theory and has been widely used and proven effective in many engineering problems. For example, Nguyen et al.22 applied ANN in predicting the blast-induced ground vibration, and the comparison results of model performance show that the ANN model is more accurate than SVM, CART (Classification and Regression Trees), and KNN (K-Nearest Neighbors) models. Koopialipoor et al.23 proposed a novel hybrid ANN-based model namely ABC-ANN (Artificial Bee Colony- Artificial Neural network), and the ABC-ANN model receives a high level of accuracy when predicting the overbreak in Gardaneh Rokn Tunnel. Armaghani et al.24 combined the Particle Swarm Optimization (PSO) algorithm and ANN, and that technique was found to be more successful than the conventional ANN regarding predicting the ultimate bearing capacity of rock-socketed piles. Given the lack of the ANN-based model in this area, the proposal and application of a hybrid ANN-based model in analyzing blast-induced rock movement are meaningful.

Based on the above discussion, the author of this study decided to illustrate the capability of the ANN technique in blast-induced rock movement prediction. During that process, Dimensional analysis (DA) will provide help for feature selection. Meanwhile, the determination and search of the hyperparameter combination are also worthy of attention, so a newly proposed meta-heuristics algorithm namely Equilibrium Optimizer (EO) algorithm is used here. It should be noted that this is innovative work due to the fact that hybrid ANN-based models have not been proposed and applied in BIRM prediction and no study about BIRM was investigated in the manner described in the present paper.

Section snippets

Dimensional analysis

The development of dimensional analysis is based on the work of Maxwell that he used some symbols such as [F], [M], [L] to respectively indicate the force, mass, and length. Number of complex engineering problems can be simplified and analyzed by dimensional analysis and this has been confirmed by many scholars, such as Einstein, Reynolds, etc.18 Using dimensional analysis, a model composed of some dimensionless parts can be developed, and the change of variable size does not affect the model.

Artificial neural network (ANN)

ANN algorithm was inspired by the neural structure in the human brain, it can learn the knowledge from the provided training datasets and develop a nonlinear relationship between the input variables and the output variables.28,29 Verifying by many successful cases in civil, mining, economic fields,30, 31, 32 ANN was found to have great potential for solving nonlinear problems. It is therefore that the ANN model was selected here for developing the prediction model of blast-induced rock

Discussion and conclusions

The BIRM phenomenon is normal and has an obvious effect on the metal recovery in a surface mine. Therefore, it is a need to develop a simple, easy to use and reliable method to predict BIRM. A dimensional analysis with the physical meaning of reach dimensionless variables was carried out. The relationship between each dimensionless variable was determined by the soft computing method (Optimized Artificial neural network model based on an Equilibrium Optimizer (EO) algorithm) and conventional

Declaration of competing interest

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.

Acknowledgments

The financial support from the National Natural Science Foundation Project of China (Grant Nos. 41807259, 72088101 and 51874350), the National Key R&D Program of China (2017YFC0602902), the Fundamental Research Funds for the Central Universities of Central South University (2018zzts217), and the Innovation-Driven Project of Central South University (2020CX040), are gratefully acknowledged.

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