Prediction of blast-induced ground vibration using principal component analysis (PCA)-based classification and logarithmic regression technique

Principal component analysis (PCA) is one of the dimension reduction techniques widely used to classify data based on features. Ground vibration is a major hazard arising from rock blasting operations, and accurate prediction of the vibration is necessary for designing controlled blasting parameters. Most of the widely accepted predictors of ground vibration consider the maximum explosive charge weight per delay (MCPD) and distance as the parameters responsible for ground vibration, but mining sites with bigger production targets have varying geometrical parameters to suit the excavator utility. Accordingly, other blast design parameters will also have impacts on ground-vibration intensity. A blast vibration predictor considering all the blast design parameters would be complicated, and some of the parameters will have overlapping contributions to ground-vibration intensity. Data classification using PCA is a feasible solution, and regression analysis may be performed to develop predictors using the classified input data. In this study, PCA was used along with multivariate logarithmic regression to predict ground vibration, and the performance of this technique to predict ground vibration was compared with the performances of various existing empirical predictors. The evaluation suggests that the predictor with logarithmic regression followed by PCA performs better than the existing empirical predictors. Background The intensity of ground vibration at a location is measured by peak particle velocity (PPV) and associated frequency. The accurate and convenient prediction of PPV is of utmost importance for researchers, blast designers and mining engineers. With the advancement in machine learning applications, researchers have used various statistical and soft computing tools to better predict PPV. The selection and classification of input parameters are important while predicting PPV. PCA-based dimension reduction techniques can be useful for the classification of parameters influencing PPV, particularly in identifying linked parameters. The most and least influencing parameters affecting output can also be identified using this technique. This technique along with regression analysis may be helpful for the development of an accurate and less complicated vibration prediction model. Fig. 1 Flowchart of methodology for classification and regression using PCA. Method PCA-based classification and logarithmic regression was used for the prediction of PPV in this study. The purpose of the PCA was to classify the parameters influencing PPV in different sets. To do this, eight input blast design parameters influencing PPV were studied: hole diameter, Φ; number of blast holes, N; burden, B; spacing, S; column length of explosive charge, L; MCPD, Q; total explosive charge in a blasting round, Qt; and distance of blast face from vibration monitoring point, D. The methodology used is shown in Fig. 1. Initially, the optimum number of principal components were selected based on a scree plot to accommodate the maximum information from the data set. Factor scores were extracted along the selected number of principal components. Regression analysis was then performed between the extracted scores and PPV, and the correlation coefficient of the regression analysis was determined. The number of principal components was further increased, and scores were again extracted if the correlation coefficient was less than 0.9. After achieving a correlation coefficient greater than 0.9, the data were classified based on a rotated component matrix. The Kaiser-Varimax rotation was applied to the component matrix of principal components to get the rotated component matrix. The rotation uses a mathematical algorithm that is based on the principle of maximizing the sum of the squares of the loadings. The factor loadings with high and low values are maximized while the factor loading with mid value is minimized under this rotation [1]. Finally, the most dominant parameters along each principal component were classified based on the rotated component matrix. This results in the classification of parameters influencing PPV. Results and discussion Analysis of the experimental data shows that four principal components (PC1, PC2, PC3 and PC4) have variances greater than 95 percent. Scores were extracted for the four principal components. Regression analysis of the four extracted scores and PPV shows a correlation coefficient of 0.931. Hence, the classification of data along the four principal components is accepted. The rotated component matrix with the four principal components is shown in Table 1. The comparison of component scores of each parameter shows that PC1 contains Φ, B and S parameters. The parameters of PC1 can be termed as geometrical parameters. PC2 contains L and Q parameters. PC3 contains N and Qt parameters. The parameters of PC2 and PC3 can be termed as charging parameters. PC4 contains D as the dominant parameter. The scores along all the four principal components were extracted, and logarithmic regression analysis carried out between the extracted scores and PPV. The following relationship among the principal components and PPV was established based on the regression output: Studying the powers of the principal components in this equation reveals that the dependency of PPV on the principal components are in order of PC4 > PC2 > PC1 > PC3. The higher dependency of PPV on PC4 (distance) and PC2 (MCPD and column length of the explosive charge) is in line with the conclusions of other researchers who considered Q and D as the most dominant parameters influencing PPV. Holmberg and Persson [2] also considered column length of explosive charge as a dominant factor influencing PPV. Conclusions Regression analysis followed by PCA-based data classification can be a useful tool to identify parameters and predict PPV. This study used this technique for the classification of eight input parameters influencing PPV. The results show that the principal components consisting of MCPD, distance of blast face from the monitoring point and column length of explosive charge have maximum influence on PPV. The performance of the vibration prediction model using regression analysis followed by PCA was compared with those of existing empirical predictors, and this prediction technique was found to give better predictions than the existing empirical predictors. Hence, the prediction technique can be used for more accurate prediction of PPV at a rock excavation site having large variations in blast design parameters. Selected references Zeller RA (2005) Measurement Error, Issues and Solutions. K.B.T.-E. of S.M.Kempf-Leonard (ed.). Elsevier, pp 665–676 Holmberg R, Persson P (1978) The Swedish approach to contour blasting. Proceedings of 4th Annual Conference on Explosives and Blasting Research, International Society of Explosives Engineers, pp 113–127

Prediction of blast-induced ground vibration using principal component analysis (PCA)-based classification and logarithmic regression technique

Authored by:
Vivek K. Himanshu, A.K. Mishra, M.P. Roy, P.K. Singh, Ashish K. Vishwakarma

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