# Application of Bayesian Neural Network (BNN) for the Prediction of Blast-Induced Ground Vibration
## 1 Introduction
However, due to the accuracy of the predicting model, measuring the complexity of the rock mass conditions and input data parameters, and other criteria, prediction and estimation of the blasting vibration becomes a more challenging and time-consuming process. Hence, conventional empirical models are insufficient, due to the limitations of the empirical formulas. \[\text{[PERSON] and Fogleson (USBM)}\qquad\text{PPV} =K\left(\frac{D}{Q^{1/2}}\right)^{-b} \tag{1}\] \[\text{Ambraseys and Hendron}\qquad\qquad\qquad\text{PPV} =K\left(\frac{D}{Q^{1/3}}\right)^{-b}\] (2) \[\text{[PERSON] and Kihlstrom}\qquad\qquad\text{PPV} =K\left(\frac{D^{1/2}}{Q^{3/4}}\right)^{b}\] (3) \[\text{Indian standards}\qquad\qquad\qquad\text{PPV} =K\left(\frac{D}{Q^{2/3}}\right)^{b} \tag{4}\]  
where \(D\) is the distance from the blasting face to the monitoring station (m), PPV is the peak particle velocity (mm/sec), and \(Q\) is the maximum instantaneous charge (Kg), whereas \(k\) and \(b\) are the site constants; each site has its own site constants (\(K\) and \(b\)). To address the limitations of the conventional empirical equations, researchers over the years have used different advanced soft computing analytics to describe complicated real-world occurrences, by interrelating the characteristics that have been determined to cause such limitations. [PERSON] et al. [8], [PERSON] [9], and [PERSON] et al. [10] predicted blast-induced ground vibration using artificial intelligence techniques, mainly artificial neural networks (ANNs). Based on the number of parameters employed to generate an ANN, their proposed models are divided into two (i.e., training and test) categories. In addition to the ANN technique, different researchers have developed a variety of artificial intelligence methods, such as the fuzzy model [11; 12], linear regression, decision tree [13],random forest [14], and deep learning, to predict and estimate blast-induced vibrations. The review study by [PERSON] et al. [15] revealed an excessive number of ML approaches being used to predict the PPV, with artificial neural network (ANN), support vector machine (SVM), and the adaptive neuro-fuzzy inference system (ANFIS) being the most frequently used algorithms (ANFIS). The interaction between the algorithms and the variables determines the efficiency of the models. Combining two or more machine learning (ML) algorithms has led to the creation of hybrid models, which improve the accuracy of stand-alone ML approaches. Nevertheless, these hybrid models provide impractical mathematical formulations, which are difficult to interpret. Table 1 summarizes the relevant research on blast-induced vibration prediction using artificial intelligence (AI) approaches in tabular form. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  
Therefore, in this study, a total of 100 datasets, from Mikurahana quarry in Japan, have been examined to develop a Bayesian neural network (BNN) prediction model and four machine learning regression techniques. Each dataset consists of different parameters such as monitoring the distance from the blasting face (D), maximum instantaneous charge (MIC), scaled distance (SD), elevation (E), blast longitudinal, blast latitude, measured longitudinal, and measured latitude. The Bayesian neural network (BNN) model, and the four machine learning techniques, are evaluated using different evaluation metrics, such as R, RMSE, and MSE. In consideration of the number of factors and assessment criteria, it was found, via the evaluation of these metrics, that they are remarkably accurate. The findings indicate that the four machine learning relationships have weak PPV estimation capabilities. However, due to its nonlinear structure, great flexibility, and low error, the BNN is much more capable of estimating the PPV compared to the other models. The major contribution of this study is as follows: first, the study introduces a new prediction methodology using the Bayesian neural network (BNN).