**GENERAL PAPERS AND TECHNICAL NOTE**

**Peak particle velocity prediction using support vector machines: A surface blasting case study**

**S.R. Dindarloo**

Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, Bella, MO, USA

**SYNOPSIS**

**Keywords**: blast-induced ground vibration, peak particle velocity, support vector machine, surface mining

**Introduction**

Blasting is one of the most economical and energy-efficient methods of rock fragmentation, and is widely used in mining, civil, construction, and environmental projects around the world. However, there are several drawbacks, including (but not limited to) complaints from nearby residents (Kahriman, 2001), damage to residential structures (Singh *et al., *1997; Gad *et al., *2005; Nateghi *etal., *2009), damage to adjacent rock masses and slopes (Villaescusa *et al., *2004; Yi and Lu, 2006; Singh *et al., *2005), damage to existing groundwater conduits, and damage to the ecology of the nearby area (Khandelwal and Singh, 2007). The main cause of these undesirable effects is excessive blast-induced ground vibrations. Thus, predicting the adjacent ground vibrations is essential for safe, environmentally responsible, and sustainable blasting operations. Ground vibrations can be defined and measured in terms of peak particle displacement, velocity, acceleration, and frequency. The peak particle velocity (PPV) has been used by many researchers as a versatile metric for both predicting and controlling the blast-induced ground vibrations. There are three major methods cited in the literature for PPV prediction, including empirical, theoretical, and artificial intelligence techniques.

Conventionally, there are some widely used empirical predictors for estimation of the blast-induced ground vibrations. The US Bureau of Mines proposed the first ground vibration predictor (Duvall *et al., *1959). Subsequently, other empirical predictors were proposed (Langefors and Kihlstrom, 1963; Ambraseys and Hendron, 1968; Ghosh and Daemen; 1983; Pal Roy, 1993). These methods consider two main input parameters -maximum charge used per delay and distance between the blast face and the monitoring points. Despite the simplicity and fast application of these methods, several recent studies have shown their shortcomings in rendering acceptable predictions (Khandelwal and Singh, 2007). More recently, Chen and Huang (2001) conducted a seismic survey to predict blast-induced vibrations and PPV empirically. Ozer *et al. *(2008) examined the results of some 500 blasts in a limestone quarry in Turkey for an experimental analysis of PPV. Ak *et al. *(2009) performed a series of ground vibration tests in a surface mine in Turkey in order to measure PPV. Aldas (2010) proposed an empirical relationship between the explosive charge mass and PPV. Deb and Jha (2010) examined the effects of surface blasting on adjacent underground workings, using PPV measurements. Mesec *et al. *(2010) proposed an empirical relationship between PPV and distance for a series of vibration tests in some sedimentary rock deposits, comprising mainly limestone and dolomite. Nateghi (2011) examined the effects of different rock formations, different detonators, and explosives on ground vibrations induced by blasting at a dam site.

Generally, empirical methods have two major limitations: lack of generalizability and limited number of input variables. Some researchers have proposed theoretical models based on the physics of blasting. For instance, Sambuelli (2009) proposed a theoretical model for prediction of PPV on the basis of some blast design and rock parameters. However, because of the complicated nature of the blasting process and its highly nonlinear interaction with the non-homogeneous and non-isotropic ground, a closed form mathematical model is almost impossible. Recently, following the rapid growth in soft computing methods, including artificial intelligence, several researchers have tried to benefit from these newly emerging techniques. In this category, artificial neural networks (ANNs) might be the most widely used method for prediction of the ground vibrations. ANNs are among the techniques that map input variables into the output(s). The technique is capable of handling extremely nonlinear interactions between different variables through assigning and adjusting proper weights. However, no functional relationship is proposed ('black-box' modelling). Khandelwal and Singh (2006) used ANNs for prediction of PPV in a large mine in India. Iphar *et al. *(2008) employed an adaptive neural-fuzzy inference system (ANFIS) for prediction of PPV in a mine in Turkey. Dehghani and Ataee-pour (2011) employed ANNs for prediction of PPV in a large open pit copper mine. Monjezi *et al. *(2011) used ANNS to predict blast-induced ground vibrations in an underground project. Bakhshandeh *et al. *(2012) used ANNs to adjust burden, spacing, and total weight of explosive used in order to minimize PPV.

The support vector machine (SVM) is a relatively new computational learning method for solving classification and nonlinear function estimation, which is based on statistical learning theory. The SVM has been adopted rapidly by many researchers in different fields of geology, geotechnical, and environmental engineering (Brenning 2005; Yu *et al., *2006; Samui 2008; Mountrakis *et al., *2011; Dindarloo, 2014). Experimental results have revealed the superior performance of SVMs with respect to other techniques. The reasons behind the successful performance of SVMs, compared to other powerful approaches like ANNs, are twofold. Firstly, rather than being based on empirical risk minimization (ERM) as ANNs, which only minimizes the training errors, a SVM makes use of structural risk minimization (SRM), which seeks to minimize an upper bound on the generalization error. Secondly, finding a SVM solution corresponds to dealing with a convex quadratic optimization problem. Thus, the Karush-Kuhn-Tucker (KKT) statements determine the necessary and sufficient conditions for a global optimum (Scholkoff and Smola 2002). For ANNs, however, it is not guaranteed that even a well-selected optimization algorithm will achieve the global minimum in finite computation time (Moura *et al., *2011).

In this study, the SVM was used for analysis of the blast-induced ground vibration by prediction of PPV. A large iron ore mine in Iran was selected as a case study. After obtaining different input variables, a SVM model was constructed and tested.

]]>**Methods**

Developed by Boser, Guyon, and Vapnik (Boser, Guyon, and Vapnik, 1992; Vapnik, 1995, 1998), support vector machine (SVM) is a relatively new computational learning method for solving classification and nonlinear function estimation, which is based on statistical learning theory. SVM is based on Vapnik-Chervonenkis theory (VC theory), which recently emerged as a general mathematical framework for estimating (learning) dependencies from finite samples. This theory combines fundamental concepts and principles related to learning, well-defined formulation, and self-consistent mathematical theory. Moreover, the conceptual framework of VC theory can be used for improved understanding of various learning methods developed in statistics, neural networks, fuzzy systems, signal processing, etc. (Widodo and Yang, 2007).

LIBSVM is a library of SVM algorithms (Chang and Lin, 2011) that was used along with Rapidminer, a data mining (DM) software package (Hofmann and Klinkenberg, 2013). The theory of SVM regression, used in LIBSVM, is presented in the following section.

*Support vector regression*

Consider a set of training points, {(x_{1}, z_{1}), . . . , (x_{L}, z_{L})}, where x_{i}* *Є R^{n} is a feature vector and z_{i} Є R^{L} is the target output. Under given parameters C > 0 and Є > 0, the standard form of the support vector regression (SVR) (Equation [1]) with constraints (Equations [2]-[4]) are as follows (Chang and Lin, 2011):

subject to

The dual problem (Equation [5]) is

]]>subject to constraints (Equations [6]-[7])

where

After solving Equation [5], the approximate function is:

The nomenclature is presented in Table I. For more detailed information about the theory and applications of SVR, see Burges (1998), Müller *et al. *(2001), Hsu and Lin (2002), Chapelle *et al. *(2002), and Smola and Scholkoff (2004).

]]>

**Case study**

Golegohar iron ore mine is located in southern Iran, 50 km from Sirjan, in the southwest of Kerman Province. This iron ore complex includes six known orebodies and is one of the largest producers and exporters of iron concentrate in the country. Mining is by open pit methods, and the measured and indicated reserves of over 1.1 billion tons of ore. The Golegohar deposits are situated in a metamorphic complex of probable Paleozoic age with a northwest-southeast trend, known as the Sanandaj-Sirjan zone, which is parallel to the Zagros thrust belt on the southwest and is bounded on the northeast by the Urmieh-Dukhtar volcanic belt (Moxham and McKee, 1990). The deposits are considered to be of sedimentary or volcano-sedimentary origin, laid down in deltaic or near-shore environments that resulted in abrupt lateral and vertical changes in the sedimentary facies. Subsequent deep burial, folding, metamorphism, and erosion left a group of folded or down-faulted magnetite-rich deposits as elongated remnants of an iron formation that originally had a broader, perhaps more continuous extent. The mine's metamorphic rocks consist mostly of gneiss, mica schist, amphibolite, quartz schist, marble, dolomite, and calcite (Karimi Nasab *et al., *2011). Figure 1 illustrates one of the operating pits. The geometry and slope stability factors of the mine are summarized in Table II.

*Parameter selection*

Rock mass, blast pattern and explosives, and distance from the face are the three major parameters in blast-induced ground vibrations, and hence the measured PPV. The dominant rock types at Golegohar include amphibolite schist, quartz schist, chlorite schist, haematite, and magnetite. Density (t/m^{3}), Young's modulus (Gpa), uniaxial compression strength (Mpa), and tensile strength (Mpa) of representative samples of all the rock types were measured in the rock and soil mechanics laboratory at the mine site (Table III a). The major discontinuities have a significant influence on blast wave propagation in the rock mass. The spacing, dip, and direction of the two major joint sets are presented in Table III b (Dindarloo *et al., *2015). The second group of important parameters is related to the drilling pattern and explosives used. A typical production, buffer, and pre-split pattern are illustrated in Figure 2. The main explosive is ANFO, and a blast delay of 15-75 ms between rows is used. The descriptive statistics of the pattern geometry, including burden, spacing, hole depth to burden ratio, specific charge, and stemming are presented in Table IV. Thus, the 12 input variables include: density, Young's modulus, uniaxial compression strength, tensile strength, joint spacing, burden, spacing, hole depth to burden ratio, specific charge, stemming, delay per row, and distance between the measurement point and the blasting face. Since the main charge for all holes was ANFO, the parameter for type of explosive was omitted, as it was the same for all tests.

**Results and discussions**

One hundred and twenty experiments were conducted at different distances, 15 m to 7500 m, from the blasting faces. The PPV was measured using the procedures described by Dowding (1992). One hundred data-sets, including the 12 input variables and one output (PPV), were used in the SVR model. The results of 20 randomly selected experiments were used for model testing. Figure 3 depicts a scattergram of the predicted SVR *versus *the measured PPVs for the 20 testing data-sets. The coefficient of determination (Equation [10]), root mean squared error (RMSE, Equation [11]), and mean absolute percentage error (MAPE, Equation [12]) were used as the statistical metrics for evaluation of the SVR model (Table V). The obtained R2 value of 0.99 shows a very good correlation between the predicted and measured PPVs. The obtained MAPE value of less than 10% demonstrates the high accuracy and applicability of the method in PPV estimation, using the 12 input variables.

]]>

where

*y _{meas }and y_{pred}* are the observed and predicted values, respectively

*y _{meas} and y*

*and are mean observed and predicted values, respectively.*

_{pred}*Sensitivity analysis*

In order to analyse the effect of each individual variable on the SVM prediction accuracy, a sensitivity analysis was performed.

The optimized SVM parameters were kept the same for twelve sensitivity analysis runs. In each run, one of the input variables was omitted and its effect on prediction accuracy was examined. The results showed that omission of distance, specific charge, delay per row, and joints spacing had the highest negative effects on SVM predictions. Hence the method is more sensitive to these variables. The results of sensitivity analysis for other variables are shown in Figure 4.

]]>

**Comparison with traditional methods**

The partial least-square regression (PLSR) method is mainly used for modelling linear regression between multiple dependent variables and multiple independent variables. An advantage of this method over linear and nonlinear multiple regressions is that PLSR combines the basic functions of regressing models, principal component analysis, and canonical correlation analysis (Zhang *et al., *2009). In addition, PLSR avoids the harmful effect of multi-collinearity and regressing when the number of observations is less than the number of variables. In the context of linear MR, the least-squares solution for Equation [13] is given by Equation [14].

Often, the problem is that *X ^{T}X *is singular, either because the number of variables (columns) in

*X*exceeds the number of objects (rows), or because of collinearities. PLSR circumvents this by decomposing

*X*into orthogonal scores

*(T)*and loadings (

*P*) (Mevik and Wehrens, 2007):

Furthemore, PLSR regresses *Y*, not on *X*, but on the first *α*** **columns of the scores. The goal of PLSR is to incorporate information on both

*X*and

*Y*in the definition of the scores and loadings. The scores and loadings are chosen in such a way to describe as much as possible of the covariance between

*X*and

*Y.*

*(i.e.,*the PLSR can model 94% of the variability in PPV based on the 12 independent variables). Furthermore, both the obtained RMSE and MAPE values in PLSR (see Table VI) were poorer than the SVM (see Table V).

**Conclusions**

**Acknowledgements**

We would like to thank two anonymous reviewers for their critical reviews and constructive comments. Golegohar mine management and staff are acknowledged for their support.

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Received Dec. 2014

Revised paper received March 2015