Feasibility of particle swarm optimization and multiple

Engineering Computations Feasibility of particle swarm optimization and multiple regression for the prediction of an environmental issue of mine blasting Hajar Eskandar, Elham Heydari, Mahdi Hasanipanah, Mehrshad Jalil Masir, Ali Mahmodi Derakhsh,

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Feasibility of particle swarm optimization and multiple regression for the prediction of an environmental issue of mine blasting Hajar Eskandar

Mine blasting

363 Received 30 January 2017 Revised 4 July 2017 Accepted 26 July 2017

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Department of Construction Engineering and Management, School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

Elham Heydari Naghsh Paydar Consulting Engineers Company, Tehran, Iran

Mahdi Hasanipanah Young Researchers and Elite Club, Qom Branch, Islamic Azad University, Qom, Iran

Mehrshad Jalil Masir Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran, and

Ali Mahmodi Derakhsh Young Researchers and Elite Club, West Tehran Branch, Islamic Azad University,Tehran, Iran

Abstract Purpose – Blasting is an economical method for rock breakage in open-pit mines. Backbreak is an undesirable phenomenon induced by blasting operations and has several unsuitable effects such as equipment instability and decreased performance of the blasting. Therefore, accurate estimation of backbreak is required for minimizing the environmental problems. The primary purpose of this paper is to propose a novel predictive model for estimating the backbreak at Shur River Dam region, Iran, using particle swarm optimization (PSO). Design/methodology/approach – For this work, a total of 84 blasting events were considered and five effective factors on backbreak including spacing, burden, stemming, rock mass rating and specific charge were measured. To evaluate the accuracy of the proposed PSO model, multiple regression (MR) model was also developed, and the results of two predictive models were compared with actual field data. Findings – Based on two statistical metrics [i.e. coefficient of determination (R2) and root mean square error (RMSE)], it was found that the proposed PSO model (with R2 = 0.960 and RMSE = 0.08) can predict backbreak better than MR (with R2 = 0.873 and RMSE = 0.14). Originality/value – The analysis indicated that the specific charge is the most effective parameter on backbreak among all independent parameters used in this study.

Keywords Particle swarm optimization, Multiple regression, Backbreak prediction, Blasting operation Paper type Research paper

Disclosure statement: No potential conflict of interest was reported by the authors.

Engineering Computations Vol. 35 No. 1, 2018 pp. 363-376 © Emerald Publishing Limited 0264-4401 DOI 10.1108/EC-01-2017-0040

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1. Introduction The combination of drilling and blasting is one of the most widely used techniques for rock breakage in surface mines, as well as in tunneling projects. Although the proper rock fragmentation is the main purpose of blasting operations, the other undesirable effects of blasting such as backbreak (BB), flyrock, ground and air vibration are inevitable (Khandelwal and Singh, 2009; Monjezi et al., 2013b; Trivedi et al., 2014; Dindarloo, 2015; Ghiasia et al., 2016; Amiri et al., 2016). These environmental impacts can cause damage to surrounding structures like slopes, roads and railroads (Sharma et al., 2016a; Singh et al., 2017). Among the mentioned effects, BB is one of the most adverse effect which is defined as broken rocks behind the last row of blast-holes (Jimeno et al., 1995). This phenomenon has several undesirable effects such as high dilution, increase in the stripping ratio (decrease in the overall pit slope angle) and poor fragmentation. So, proper estimation of BB is an important task for future blasting operations to minimize the blasting environmental problems. Based on previous related surveys, BB can be affected by various variables such as blast design factors and rock mass properties. Blast design factors can be changed by the blasting engineers (Mohammadnejad et al., 2013; Esmaeili et al., 2014; Ebrahimi et al., 2015). In the other words, the blast design factors such as charge per delay (MC), stemming (ST), blast-hole height (H) spacing (S), burden (B), specific charge (SC) and type of explosive material are all controllable factors. The definitions of the controllable factors are given below:
S is the distance between blast-holes in any given row. As a principle, S = (0.67-1.5) B (Bhandari, 1997; Hustrulid, 1999).
ST is the H minus the length of the explosive column. The fine gravels are mainly used as ST material. As a principle, ST = (0.7-1.3)B (Bhandari, 1997; Hustrulid, 1999).
To control and minimize the undesirable effects of blasting, such as ground vibration, the blast-holes can be blasted in several delay intervals. The range of delay times is between 10-50 ms. MC is the maximum charge weight used in the various mentioned delays. For example, 20 blast-holes should be blasted. These blast-holes can be blasted in the one or more steps. Assuming that holes will be blasted in two steps, in the first step, eight holes are blasted, and the total charge used for these holes is 500 kg. In the second step, after 20 ms, the rest of the blastholes (12 holes) with a total charge of 700 kg will be blasted. Therefore, MC is equal to 700 kg. Note that, the selection of the number of the delays is entrusted to blasting designers.
SC is also defined as the amount of explosive (kg or gr) required to fragment 1 m3 or cm3 of rock (Bhandari, 1997; Hustrulid, 1999). Unlike the controllable factors, rock mass properties such as orientation of discontinuities and dynamic tensile strength are uncontrollable factors and cannot be changed by the blasting engineers (Sari et al., 2014; Monjezi et al., 2013a). In this regard, when the angle of the discontinuities dips toward the bench face, BB considerably increases. Jia et al. (1998) used numerical modeling, and based on their obtained results, joints with a dip angle greater than the friction angle are one of the most important reasons of BB. In the literature, some studies highlighted the efficiency of artificial intelligence (AI) techniques in solving various engineering areas (Khandelwal and Singh, 2005; Sawmliana et al., 2007; Singh et al., 2008; Verma and Singh, 2013; Trivedi et al., 2015; Verma et al., 2016; Sharma et al., 2017a, 2017b). For the BB prediction, different models, e.g. artificial neural network (ANN), adaptive neuro-

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fuzzy inference system (ANFIS), support vector machine (SVM), Monte Carlo simulation and genetic programing (GP) have been proposed. Monjezi et al. (2013a) used ANN and multiple regression (MR) for BB prediction. In their study, ten effective factors on the BB, such as B, MC and SC, were used as the independent factors. Based on their results, ANN can predict BB better than MR. Their results indicated that accuracy of ANN was superior to that of MR model. In another study, Khandelwal and Monjezi (2013) established MR and SVM models for BB prediction. They used blast-hole height, S, B, ST, SC, and selected specific drilling as model inputs. Their results showed significant capability of the SVM model compared to the MR model in predicting BB. A comprehensive research to estimate BB was presented by Esmaeili et al. (2014) using ANN, ANFIS and MR. They revealed that ANFIS can estimate BB better than MR and ANN. Monte Carlo simulation and MR were developed to estimate BB in the research conducted by Sari et al. (2014). Their results showed capability of the Monte Carlo simulation in forecasting BB compared to MR. Shirani Faradonbeh et al. (2015) used non-linear MR and GP for the prediction of BB at Sungun copper mine, Iran. They concluded that GP is more acceptable model for forecasting BB compared to the non-linear MR. In the other study, Sharma et al. (2016b) used MR and ANN for forecasting modulus of elasticity of the soil. They showed the ANN is a powerful tool to indirect estimation of modulus of elasticity of soil. In this paper, a new predictive model is proposed to present an accurate and acceptable model to estimate BB at Shur River Dam, Iran, using particle swarm optimization (PSO). Afterwards, the estimation capability has been compared between PSO and MR, and the obtained results have been compared with the data at hand. 2. Particle swarm optimization PSO is an evolutionary optimization algorithm which was first developed by Kennedy and Eberhart (1995). In the PSO method, an number of particles are put into the search area of the N-dimensional problems. As described by Kennedy and Eberhart (1995), the principle of the PSO is the cognitive system of swarm and social behavior. The PSO has some advantages such as, easy to implement and useful to maintain the diversity of the swarm (Momeni et al., 2015; Ghasemi et al., 2016; Hasanipanah et al., 2016). The PSO consists of a swarm of particles that search for the best position, including the best global (gbest) and personal (pbest) positions, based on its best solution (Abdi and Giveki, 2013; Hajihassani et al., 2014). In other words, during each iteration, each particle moves in the direction of its best pbest and gbest positions. Based on equations (1) and (2), the position and velocity of a particle during its moving process are computed:








Xnew ¼ X þ Vnew

(1)

Vnew ¼ w * V þ C1  r1 ðpbest  X Þ þ C2  r2 ðgbest  X Þ

(2)

X and V denote current position and velocity of particles, respectively. Xnew and Vnew denote new position and velocity of particles, respectively. C1 and C2 denote pre-defined coefficients (positive acceleration coefficients). w denotes the inertial weight. r1 and r2 denote the random numbers in (0, 1).

More descriptions about the PSO algorithm are suggested in few studies (Eberhart and Shi, 2001; Zhang et al., 2007; Yagiz and Karahan, 2011; Gordan et al., 2015).

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PSO, as a powerful optimization algorithm, has been used by a number of researchers. For example, Kalatehjari et al. (2014) developed PSO and conventional methods to estimate slope stability. According to their results, the PSO exhibited higher performance compared to conventional methods. Jahed Armaghani et al. (2015a) developed a hybrid model of ANN and PSO to estimate ultimate bearing capacity (Qu) in the field of rock-socketed piles. Their results confirm the high prediction capability of PSO–ANN model in predicting the Qu. Tonnizam Mohamad et al. (2015) used the PSO–ANN model to estimate the unconfined compressive strength (UCS) of soft rocks. Based on obtained results, the PSO can be introduced as a useful optimization algorithm to design the ANN. Ghasemi et al. (2016) combined the PSO with ANFIS model for predicting ground vibration. Their results showed the PSO–ANFIS model is an acceptable for predicting ground vibration and PSO is a powerful tool for optimizing the ANFIS model. 3. Field investigation The data sets used in the present research were obtained from the Shur River Dam region, which is situated in the south of Iran, between 55°51 0 4700 longitudes and 30°1 0 4800 latitudes. The bed rock at the site is of the tuff and andesite type. This dam is situated in the area with high seismicity, where the maximum design earthquake (MDE) is equal to 0.8 g. To construct the Shur River Dam, two mines, namely, main and second mines, were extracted using bench blasting method. Drilling and blasting are the most important processes in the bench blasting method. Wagon drill machine was used for the drilling process in the main mines and the holes were then blasted. The diameter of the drilled holes was in range of 100-150 mm. In the next step, the blast-holes were stemmed with drill cuttings. It should be mentioned that, in each blasting operation, ammonium nitrate fuel oil (ANFO; specific gravity of 0.85-0.95), was used as the explosive. In each blasting operation, maximum and minimum numbers of rows were six and two, respectively. Moreover, minimum and maximum numbers of blast-holes were 25 and 66, respectively, and the height of benches (HB) ranged from 6 to 9 m. In the investigated blasting events, the delay times were also between 20 and 50 ms. In addition, the maximum measured ST, S and B were 3.3, 5.3 and 4.1 m, respectively, and the SC in these operations ranged between 151 and 213 g/cm3. BB was one of the most undesirable effects induced by blasting operation in this region. This unwanted effect can lead to higher hauling and loading costs, as well as the instability of mine walls. To reduce BB in this site, pre-split blasting with large diameter blast-holes was considered. Also, short delay timing or increasing in stemming were the most important reasons for BB in this site. In addition, an extensive study program was conducted to precisely predict blast-induced BB. To achieve the study aims, 84 blasting operations were considered and the S, B, ST, SC and RMR were measured. Aside from mentioned parameters, the values of the BB for all 84 blasting operations were also measured. To measure S, B and ST, a tape measure was used. To measure SC, a weight charge per blasthole was divided to the blast volume (B  S  HB), as recommended by (Jimeno et al., 1995). The values of BB was also measured using the presented method by Sari et al. (2014). In this method, the horizontal distance between the pre-blast surveyed position of the last row of blast-holes and the crack with the maximum separation (critical crack) was considered as the BB. In this regard, the horizontal distance between the last row of the blast-holes and the critical crack is measured at several points on the crest and then the average of these data is considered as the BB. The mentioned descriptions are illustrated in Figure 1. Tables I and II also summarize the ranges of measured parameters and the relationships between independent variables, respectively. As shown in Table II, B, S and ST are closely related. In addition, Figures 2 to 6 illustrate the plots of the BB versus B, S, ST, SC and RMR. From

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Figure 1. Measurement of BB in the studied case

Parameter

Min

Max

Mean

SD

B S ST SC RMR BB

2.7 3.4 1.8 151 37 3.8

4.1 5.3 3.3 213 55 5.3

3.5 4.4 2.7 182.5 46 4.56

0.34 0.45 0.4 16.16 3.98 0.34

Table I. The range of used Notes: ST: stemming (m), S: spacing (m), B: burden (m), SC: specific charge (g/cm3), RMR: rock mass rating (%), factors for predicting BB BB: backbreak (m)

Parameter B S ST SC RMR

B

S

ST

SC

RMR

1 0.694 0.582 0.462 0.551

– 1 0.411 0.071 0.374

– – 1 0.308 0.401

– – – 1 0.423

– – – – 1

Table II. The correlation coefficients between independent variables

Figure 2. Relationship between burden (m) and BB (m)

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Figure 3. Relationship between spacing (m) and BB (m)

Figure 4. Relationship between stemming (m) and BB (m)

Figure 5. Relationship between specific charge (g/ cm3) and BB (m)

these figures, it can be seen that B, S, ST and SC have a direct relationship with BB, while RMR has an indirect relationship with BB. In the other words, increase in B, S, ST and SC parameters leads to increase BB, while increase in RMR leads to decrease BB. 4. Prediction of backbreak In the present research, the application of PSO and MR models to develop an accurate and acceptable model to estimate blast-induced BB is investigated. To achieve the research aims, five influential factors on BB, including S, B, ST, SC and RMR were set as independent variables of the equations, while BB was set as dependent variable of the equations. The values of independent and dependent variables were measured for 84 blasting events. The used data sets were then categorized into two sets: train and test sets. Training data sets

were used for constructing the PSO and MR models, while testing data sets were used for testing the constructed models. In this research, a ratio of 80-20 per cent was used to train and test sets, as recommended in many studies (Hasanipanah et al., 2015, 2016; Amiri et al., 2016). In the other words, 67 and 17 data sets were used for training and testing. Table III also shows the basic statistics of the train and test sets.

Mine blasting

4.1 BB prediction by multiple regression model The MR is a common method to fit a linear equation between one dependent parameter and one or more independent parameters. This method is widely used to estimate some problems in the fields of geotechnical and mining engineering (Rezaei et al., 2011; Khandelwal and Monjezi, 2013; Liang et al., 2016, Sharma et al., 2017b, Singh et al., 2017). For instance, Esmaeili et al. (2014) established MR in predicting blast-induced BB. Their results revealed the reliability of the MR in BB prediction. The equation that generally describes this model is:

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Y ¼ I0 þ I1 X1 þ    þ In Xn

(3)

where terms Xi(i = 1, . . . ,n) and Y represent independent and dependent factors, respectively. Also, Ii(i = 0,1, . . . ,n) denotes the partial regression coefficients. Considering the established training data sets, equation (4) was constructed by using SPSS version 16:

Figure 6. Relationship between RMR (%) and BB (m)

No. of samples Train set 67

Test set 17

Parameters

Min

Mean

Max

B (m) S (m) ST (m) SC (g/cm3) RMR (%) BB (m)

2.8 3.4 1.8 151 37 3.9

3.5 4.4 2.7 182.1 46 4.6

4.1 5.3 3.4 213 54 5.2

B (m) S (m) ST (m) SC (g/cm3) RMR (%) BB (m)

2.7 3.5 2 153 40 3.8

3.4 4.4 2.9 184.1 45.4 4.6

4.1 5.3 3.4 209 55 5.3

Table III. The basic statistics of the train and test sets

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BB ¼ 0:98 þ ð0:18  BÞ þ ð0:13  SÞ þ ð0:1  ST Þ þ ð0:013  SC Þ  ð RMR  0:01Þ (4) After constructing the equation (4), its performance capacity can be checked using testing data sets. More details regarding accuracy of the developed MR will be given later.

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4.2 Prediction of BB by PSO As mentioned above, the PSO is used to develop an accurate model to estimate BB at Shur River Dam region. Firstly, the data sets including independent and dependent variables, should be normalized, as recommended in many studies (Hasanipanah et al., 2015; Jahed Armaghani et al., 2015b). For this work, the normalized data sets, in range of zero and one, can be calculated using equation (5):

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Xn ¼

X  Xmin Xmax  Xmin

(5)

In equation (5), X, Xmin, Xmax and Xn denote the actual, minimum, maximum and normalized values of the measured parameter, respectively. In the present paper, the quadratic form of the equation was applied in modeling by PSO. A quadratic form can be formulated as follow:
 BBnquadratic ¼ ðx1  BÞ þ ðx2  SÞ þ ðx3  ST Þ þ ðx4  SC Þ þ ðx5  RMRÞ þ x6  B2



 þ x7  S2 þ x8  ST 2 þ x9  SC 2 þ x10  SC 2 þ x11 (6) Where B, ST, S, SC and RMR are independent parameters and BB is the model output. In fact, PSO is used to optimize the indices of the equation (6) (x1 to x9) to construct an accurate model for BB prediction. Afterwards, the PSO searches the best weighting factors in each iteration based on the fitness function. The used fitness function in the presented study is formulated as follow: n X
2 BBmeasured  BBpredicted (7) f ðvÞ ¼ i¼1

In which, BBmeasured and BBpredicted denote the measured and predicted BB. Also, n denotes number of cases. It should be mentioned that if f(v) = 0, the model will be excellent. In PSO coding (where is implemented in MATLAB Software environment), the several parameters, i.e. pre-defined coefficients (C1, C2), inertia weight, number of particles and iterations should be considered/computed. To discover the best values of these parameters, trial and error technique was used. The best values of the PSO parameters are listed in Table IV. It is worth mentioning that the values have been obtained from 30 times of algorithm execution with

Parameter

Table IV. The obtained values of the PSO parameters

Number of iterations Number of particles Pre-defined coefficients (C1, C2) Inertia weight

Value 1000 200 (2, 2) 0.75

different PSO parameters. Based on Table IV, the quadratic form optimized by PSO was developed as follow:

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BBnquadratic ¼ ð0:27  BÞ  ð0:2  SÞ  ð1:04  ST Þ  ð0:017  SC Þ  ð0:03  RMRÞ  ð0:01  B2 Þ þ ð0:02  S2 Þ þ ð0:21  ST 2 Þ þ ð0:00008  SC 2 Þ þ ð0:0002  RMR2 Þ þ 5:89

(8)

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Note that, equation (8) was developed using training data sets. In the next step, the performance of the model can be computed using testing data sets. More details regarding the accuracy of the proposed PSO model in predicting BB will be given in Section 5. 5. Analysis of the results In the presented research work, MR and PSO equations were developed to estimate BB produced by blasting in Shur River Dam. Totally, 67 data sets (80 per cent of whole data) were chosen for the development of the models, while 17 data sets (20 per cent of whole data) were chosen for testing the developed models. To demonstrate the accuracy of the proposed predictors, two statistical metrics, i.e. coefficient of determination (R2) and root mean squared error (RMSE), were used/computed: hXn i hXn i 2 2  x  x x  x ð Þ ð Þ mean p i i i¼1 i¼1 hXn i R2 ¼ (9) 2 x  x ð Þ mean i i¼1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i 1 Xn h 2  x  x RMSE ¼ ð p Þ i i¼1 n

(10)

Where, n is the number of the selected data sets, xp is the predicted BB value and xi is the actual BB value. It should be mentioned that R2 and RMSE equal to 1 and 0, respectively, show the best approximation. Table V presents the results of statistical functions for the developed equations. As shown in this table, when considering the achieved results of the RMSE for the equations, values of 0.08 and 0.13 for PSO and MR equations, respectively, a higher accuracy of PSO equation is revealed. Also, when considering the achieved results of the R2 for the equations, values of 0.943 and 0.849 for PSO and MR equations, respectively, a higher conformity of PSO equation is revealed. Therefore, when considering both RMSE and R2, it is found that the prediction capability of the PSO model is quite remarkable and the values compare well with actual values. Moreover, Figures 7 and 8 present the comparison of the forecasting for the BB by PSO and MR, using training and testing data sets. Observing these figures, it can be seen that the fitting results of the PSO is superior to the prediction results using the MR. In addition, the predicted BBs by the predictive models

Statistical metrics R2

RMSE

Equation

Train

Test

Train

MR PSO

0.865 0.948

0.873 0.960

0.123 0.074

Table V. The obtained 0.140 statistical metrics for the predictors 0.081 Test

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are plotted for testing data, as illustrated in Figure 9. The figure shows that obtained values of PSO equation in predicting BB are closer to the measured BB values versus the obtained values of MR. The obtained R2 in the present research is also compared to other studies, as shown in Table VI. From Table VI, it was demonstrated that the proposed PSO in the present research has better performance to forecast the blast-induced BB than the mentioned studies.

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372 6. Conclusion The aim of this research work is to present an appropriate model to estimate backbreak at Shur River Dam, Iran. For this purpose, PSO and MR were used, using 84 data sets including five input parameters, i.e. S, B, ST, SC and RMR, as well as one output parameter (BB). In modeling, 80 per cent of data sets (67 data sets) have been used for constructing the PSO and MR models, and 20 per cent (17 data sets) for testing the constructed PSO and MR models. In PSO modeling, the values of 2, 2, 0.75, 1000 and 200 were selected for C1, C2, inertia weight, number of iterations and particles, respectively. In the next step, models’ performance was assessed with statistical metrics, i.e. an R2 and RMSE. Based on obtained results, the PSO model with R2 of 0.960 and RMSE of 0.08 for the testing data sets has more suitable performance for predicting the BB than the MR model with an R2 of 0.873 and RMSE of 0.14. The relationships between input parameters and BB were also evaluated. According to obtained results

Figure 7. Prediction result of BB using MR equation

Figure 8. Prediction result of BB using PSO equation

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Figure 9. Prediction results of the BB by MR and PSO equations using testing data sets

Reference

Method

Input parameter

Monjezi et al. (2010) Esmaeili et al. (2014) Mohammadnejad et al. (2013) Sayadi et al. (2013) Ebrahimi et al. (2015) Present research

FIS ANN SVM ANN ANN PSO

S, ST, SD, MC, HD, B, SC N, SC, RD, SR, ST, S/B HD, S, B, SC, ST, SD B, HD, SC, ST, S, SD HD, SC, B, S, ST S, ST, SC, B, RMR

No. of data

R2

115 42 193 103 34 84

0.95 0.92 0.92 0.87 0.77 0.96

Table VI. Comparison between 2 obtained R value in Notes: Rock density (RD), hole-depth (HD); Specific drilling (SD); rock mass rating (RMR); number of rows the present paper and other studies (N); sub-drilling (SD); spacing to burden (S/B); fuzzy interface system (FIS)

from this research, B, S, ST and SC have a direct relationship with BB, while RMR has an indirect relationship with BB. In the other words, increase in B, S, ST and SC parameters leads to increase in BB, while increase in RMR leads to decrease BB. Note that the proposed equations in the paper are site-specific and cannot be direct used in other sites or mines. References Abdi, M.J. and Giveki, D. (2013), “Automatic detection of erythemato-squamous diseases using PSO– SVM based on association rules”, Engineering Applications of Artificial Intelligence, Vol. 26 No. 1, pp. 603-608. Amiri, M., Bakhshandeh Amnieh, H., Hasanipanah, M. and Mohammad Khanli, L. (2016), “A new combination of artificial neural network and K-nearest neighbors models to predict blastinduced ground vibration and air-overpressure”, Engineering with Computers, Vol. 32 No. 4, doi: 10.1007/s00366-016-0442-5. Bhandari, S. (1997), Engineering Rock Blasting Operations, Balkema. Dindarloo, S.R. (2015), “Prediction of blast-induced ground vibrations via genetic programming”, International Journal of Mining Science and Technology, Vol. 25 No. 6, pp. 1011-1015.

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