Prediction of airblast-overpressure induced by blasting using a hybrid artificial neural network and particle swarm optimization

Applied Acoustics 80 (2014) 57–67

Contents lists available at ScienceDirect

Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust

Prediction of airblast-overpressure induced by blasting using a hybrid artificial neural network and particle swarm optimization M. Hajihassani ⇑, D. Jahed Armaghani, H. Sohaei, E. Tonnizam Mohamad, A. Marto Faculty of Civil Engineering, Department of Geotechnics and Transportation, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia

a r t i c l e

i n f o

Article history: Received 13 May 2013 Received in revised form 28 October 2013 Accepted 14 January 2014 Available online 10 February 2014 Keywords: Quarry blasting Airblast-overpressure Artificial neural networks Particle swarm optimization algorithm

a b s t r a c t Blasting is an inseparable part of the rock fragmentation process in hard rock mining. As an adverse and undesirable effect of blasting on surrounding areas, airblast-overpressure (AOp) is constantly considered by blast designers. AOp may impact the human and structures in adjacent to blasting area. Consequently, many attempts have been made to establish empirical correlations to predict and subsequently control the AOp. However, current correlations only investigate a few influential parameters, whereas there are many parameters in producing AOp. As a powerful function approximations, artificial neural networks (ANNs) can be utilized to simulate AOp. This paper presents a new approach based on hybrid ANN and particle swarm optimization (PSO) algorithm to predict AOp in quarry blasting. For this purpose, AOp and influential parameters were recorded from 62 blast operations in four granite quarry sites in Malaysia. Several models were trained and tested using collected data to determine the optimum model in which each model involved nine inputs, including the most influential parameters on AOp. In addition, two series of site factors were obtained using the power regression analyses. Findings show that presented PSO-based ANN model performs well in predicting the AOp. Hence, to compare the prediction performance of the PSO-based ANN model, the AOp was predicted using the current and proposed formulas. The training correlation coefficient equals to 0.94 suggests that the PSO-based ANN model outperforms the other predictive models. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Blasting is the cheapest and most common way of hard rock fragmentation. Rock is blasted into smaller pieces in surface mining and quarrying operation, or into large blocks for some civil engineering applications [1]. The drilling and blasting cycle consists of drilling one or more rows of blastholes parallel to the free vertical face of the bench. The blastholes are charged with explosives and plugged with crushed rocks or other stemming material. The explosive in each hole is fired and delayed with respect to the others with appropriate initiation systems. The detonation of the explosives breaks and throws the rock mass, so it can be loaded for further processing [2]. In blasting, whenever an explosive is detonated, transient airblast pressure waves are generated and these transitory phenomena last for a few seconds [3]. Only a fraction of explosive energy (20–30%) is used in the actual breakage and displacement of the rock mass. The rest of the energy is wasted causing undesirable effects like ground vibrations, AOp, flyrocks, noises, back breaks and over breaks [4]. AOp is undesirable by ⇑ Corresponding author. Tel.: +60 177625925. E-mail addresses: [email protected] (M. Hajihassani), [email protected] (D. Jahed Armaghani), [email protected] (H. Sohaei), [email protected] (E. Tonnizam Mohamad), [email protected] (A. Marto). 0003-682X/$ - see front matter Ó 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apacoust.2014.01.005

product of blasting that is directly related to some parameters such as blast design, weather and terrain conditions. AOp is produced by a large shock wave from explosion point into the free surface. Consequently, the AOp is a shock wave which is refracted horizontally by density variations in the atmosphere. The atmospheric pressure waves of AOp consist of an audible high frequency and sub-audible low frequency sound. AOp impacts the structures and can be caused damage in quarrying which may result in conflict between the quarry management and those who are affected [5–8]. Based on influential parameters on AOp, many attempts have been done to establish correlations for AOp prediction. Kuzu et al. [9] established a new empirical relationship between AOp and two parameters (distance between blast face and monitoring point and weight of explosive materials) which are the most important variables on AOp. Segarra et al. [10] provided a new AOp predictive equation based on monitoring data in two quarries with 32% accuracy. Their proposed model was validated using five new blasting data with 22.6% accuracy. Numerical models including both free air and rock material properties were programmed and linked to Autodyn2D by Wu and Hao [11] for simulation ground shock and airblast pressures generated from surface explosions. They concluded that numerical results give very good predictions of airblast pressures in the free air. Rodríguez et al. [12]

58

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67

developed semi-empirical model for prediction of the air wave pressure outside a tunnel due to blasting work. Their method was tested with several cases and it was proved that it can be used under different conditions. Rodríguez et al. [13] demonstrated that how natural or artificial barriers can be affected in results of the air wave propagation induced by blasting outside the tunnel. They proposed the phonometric curve and iso-attenuation curves to represent the phenomenon and suggested charge–distance curve for solving the problem. Artificial neural networks (ANNs) are some of the most dynamic areas of research in advanced diversity applications of science and engineering. ANNs are information processing systems that are used for modeling complex relationships between inputs and outputs data. In other words, an ANN is a flexible non-linear function approximation that figures out a relationship between given input and output data. An ANN may consist of an input layer, hidden layers and an output layer. In the input layer, each input parameter is multiplied by a connection weight. Subsequently, the weighted values are come together in the hidden layer and a bias is summed to the weighted values in that particular layer. The obtained value transfer to an activation function and a signal is generated. Using the departing links of hidden nodes, the results are transmitted to the output layer. Many researchers have applied soft computing methods such as ANN, fuzzy inference system, and support vector machine (SVM) to predict AOp. Mohamed [14] predicted the AOp using fuzzy inference system and ANN. He compared the results of these methods with the values obtained by regression analysis and measured field data and concluded that the ANN and fuzzy models have accurate prediction compared to regression analysis. Khandelwal and Kankar [15] predicted AOp due to blasting using 75 datasets by SVM method and compared AOp values with the results of generalized predictor equation. They showed that the predicted values of AOp by SVM were much closer to the actual values as compared to predicted values by predictor equation. Khandelwal and Singh [16] presented an ANN to predict AOp and compared the results with the United States Bureau of Mines (USBM) predictor results and demonstrated ANN yields better prediction compared to USBM predictors. Tonnizam Mohamad et al. [17] used ANN to predict 38 AOp datasets obtained from blasting operations. In their work, hole diameter, hole depth, spacing, burden, stemming, powder factor, and number of rows were considered as input parameters. The results show the applicability of the proposed model to predict AOp. Despite all advantages of ANNs, these methods are associated with some limitations. The slow rate of learning and getting trapped in local minima are known as major disadvantages of ANNs [18–20]. To overcome these problems, the use of powerful optimization algorithms to optimize ANNs is of advantage. Particle swarm optimization (PSO) is a powerful population-based stochastic approach for solving continuous and discrete optimization problems. Since PSO is a robust global search algorithm, it can be used to adjust weights and biases of ANNs in order to increase the performance of ANNs. In this research, a hybrid PSO-based ANN is utilized to predict AOp induced by blasting using actual data obtained from four granite quarry sites in Malaysia.

2. Theory of AOp The explosion is produced by the shock wave of chemical reaction where the pressure reactive gases reach the sonic velocity [21]. The velocity of gas pressure rises rapidly as explosive detonation takes place in the blasthole. The blasthole pressure suddenly loads surrounding rocks which produce a compressive shock pulse and moves quickly away from the blasthole. The pressure in terms

of blasting is mainly indicated with shock and gas mechanisms [1,22]. A large shock wave from explosive into the surface produces AOp. Therefore, the AOp is a shock wave which is refracted horizontally by density variations in the atmosphere. An audible high frequency sound and sub-audible low frequency are two atmospheric pressure waves of AOp [1]. The minimum sound frequency which is detectable by human ear is 20 Hz and below than that is unhearable. However, there is a possibility to get a concussion with the sound more than 20 Hz. According to Kuzu et al. [9], AOp is known in terms of sound which measures with Pascal (Pa) and Decibels (dB). When AOp waves energy exceed the atmospheric pressure (194.1 dB), the surrounding structures may be affected with some damages [23]. The average level and higher spectral frequencies in AOp tend to be higher due to explosions, whilst the amplitude of AOp decreases by 6 dB for every doubling of distance between blast and recipient [24]. Based on the differences between source spectra and propagation conditions, the range of attenuation becomes smaller, 3.1 to 10 dB. An AOp level of the structural damage possibility is 180 dB, glass break is 130–150 dB, and window vibration is 110–130 dB. Therefore, many attempts are made to keep AOp below 110 dB in critical areas where the public is concerned [9,13,25]. In general, AOp waves are produced from four main sources in blasting operations [26–28]:  Air pressure pulse (APP): displacement of the rock at bench face as the blast progresses.  Rock pressure pulse (RPP): induced by ground vibration.  Gas release pulse (GRP): escape of gases through rock fractures.  Stemming release pulse (SRP): escape of gases from the blasthole when the stemming is ejected. There are many influential factors on AOp. The effective parameters of blast induced AOp is directly related to parameters such as maximum charge per delay, detonator accuracy, burden and spacing, stemming, direction of initiation and charge depth. Furthermore, AOp is influenced by other parameters such as atmospheric conditions, overcharging, weak strata and conditions arise from secondary blasting, [1,12,27,29]. However, AOp induced by blasting is not easy to predict as the same blast design can produce different results in different cases. 3. AOp prediction methods Some empirical methods have been suggested by a number of researchers to predict AOp. According to National Association of Australian State [30], AOp from confined blasthole charges can be estimated from following empirical formula:

P¼

qffiffiffiffiffiffi E 140 3 200 d

ð1Þ

in which, P is overpressure in kPa, E is mass of charge in kg, and d is distance from center of blasthole in meter. McKenzine [31] suggested an equation to describe the decay of overpressure as follows:

dB ¼ 165  24 logðD=W 1=3 Þ

ð2Þ

in which, dB is the decibel reading with a linear of flat weighting, D is distance in meter, and W is the maximum charge weight per delay (in kg). In the absence of monitoring, the use of cube-root scaled distance factor (SD) is another method to predict AOp. A relationship between the distance and the explosive charge weight per delay is used through the SD values. SD is formulated as below:

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67

SD ¼ DW 0:33

ð3Þ

where D denotes the distance (m or feet) to the explosive charge and W is the explosive charge weight (kg or lb) and SD is the scaled distance factor (m kg0.33 or ft lb0.33). The establishment of a relationship between AOp and SD values is possible if sufficient data is available. A site-specific AOp attenuation formula can be developed when statistical analysis techniques (i.e. a least squares regression analysis) are applied to the representative AOp data [32–34]. The form of the prediction equation is given as follow:

AOp ¼ HðSDÞb

ð4Þ

in which, AOp is measured in Pa or dB, H and b are the site factors, and SD is the scaled distance factor (m kg0.33 or ft lb0.33) as given in Eq. (3). SD calculated by Eq. (3) is widely used in surface blasting to predict AOp [8,9,27,35]. The Eq. (4) contains site factors, H and b, which their values for different blasting conditions are tabulated in Table 1. According to Table 1, USBM [27] considered the direction of initiation and monitoring location. Kuzu et al. [9] took into account the influence of the rock mass strength on the peak overpressure in quarry blasting. The effect of charge confinement is shown by the dispersion suggested by ISEE [8], and most significantly by the high value reported by Hustrulid [35] from shots of unconfined charges.

4. Case studies A total of 62 blasting operations have been investigated from four granite quarry sites in Malaysia. These sites are located near Johor city, the capital of the Johor State, as shown in Fig. 1. Granite quarry in the mentioned sites are blasted using 75, 89, and 115 mm diameter blastholes and ANFO was used as the main explosive material. Fine gravels were used as the stemming material. Description of the case studies blasting sites are shown in Table 2. The data collection was conducted over six months from June to November (2012). During data collection, blasting parameters such as burden, spacing, stemming length, hole depth, powder factor and Rock Quality Designation (RQD), were measured. AOp was monitored in each blasting operation using a linear L type microphones connected to the AOp channels of recording units manufactured by VibraZEB. This instrument records AOp values ranging from 88 dB (7.25  105 psi or 0.5 Pa) up to 148 dB (0.0725 psi or 500 Pa). The microphones have an operating frequency response from 2 to 250 Hz, which is adequate to measure accurately overpressures in the frequency range critical for structures and human hearing. All AOp measurements have been carried out in front of the quarry bench and approximately perpendicular to it. It should be mentioned that the distance of monitoring point from the blasting face was 300 and 600 m in different sites.

Table 1 Site factors, H and b for different blasting conditions [21]. Source

Description

H

b

USBM [27]

Quarry blasts, behind face Quarry blasts, direction of initiation Quarry blasts, front of face Confined blasts for AOp suppression Blasts with average burial of the charge Detonations in air Quarry blasts in competent rocks Quarry blasts in weak rocks Overburden removal

622 19,010 22,182 1906 19,062 185,000 261.54 1833.8 21,014

0.515 1.12 0.966 1.1 1.1 1.2 0.706 0.981 1.404

ISEE [8] Hustrulid [35] Kuzu et al. [9]

59

5. Hybrid PSO-based ANN model Backpropagation (BP) algorithm is frequently used to train ANNs. However, BP is a local search learning algorithm and therefore the search process of ANNs might fail and return unsatisfied solution [36]. Many attempts have been made to improve the performance and generalization capabilities of ANNs. According to [37], ANNs trained using PSO provide more accurate results than other learning algorithm. Following sections describe the procedure of ANN and PSO algorithm and implementation of hybrid PSO-based ANN models. 5.1. ANNs ANN originally was introduced by McCulloch and Pitts [38] who showed ability of this technique to calculate any arithmetic or logical functions. Processing of the information is performed with the help of many interconnected simple elements known as neurons which are placed in distinct layers of the network. Multi-layer perceptron (MLP), the most well-known type of ANNs, consists of at least three layers: input, output and intermediate or hidden layers. Complexity level of the problem determines the number of the hidden layers and neurons [39]. The neurons are linked from a layer to the next one, but this connection is not within the same layer. Once a series of inputs presents to the network, the input values are transmitted through the links to the second layer. In every link, the transmitted value is multiplied to the weight of the link. The weighted values are come together at a node in the hidden layer and a bias is summed to the weighted values in that particular node. Subsequently, the obtained value transfer to an activation function and a signal is generated. Using the departing links of hidden nodes, the results are transmitted to the output layer. Similar to hidden nodes, the input values of the output nodes are weighted, biased, summed and transferred to the activation function. The generated values of activation functions in output layers are the outputs of the network. Performance of an ANN is dependent on the topology or architecture of the network which is the pattern of the connections existing between the neurons. The network should be trained with enough input–output patterns that are known as the training data [40]. As the error reached specified error goal, training is finished and the optimum model is determined. Then, this trained network can be used to test the model. Various algorithms can be applied for training ANNs. However, the feed-forward BP algorithm has been reported to be the most competent learning procedure for MLP ANN [41]. The BP algorithm is used in layered feed-forward ANNs. This means that the artificial neurons are organized in layers, and send their signals forward, subsequently the errors are propagated backwards. This process is repeated until the error is converged to a level defined by a cost function such as mean square error (MSE) [42,43]. BP algorithm is considered to be the most popular model in the complex conditions and suitable for training MLP networks with supervised learning techniques [44–46]. In this technique, the strengths or weights of the interneuron connections are adjusted according to the difference between the predicted and actual network outputs. 5.2. PSO algorithm PSO algorithm is a stochastic optimization approach based on the simulation of the social behavior of birds within a flock. PSO is a population-based search procedure where the individuals, referred to as particles, are grouped into a swarm. Each particle in the swarm represents a candidate solution to the optimization problem. This algorithm proposed by Kennedy and Eberhart [47] which was further developed by Shi and Eberhart [48]. In PSO

60

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67

Fig. 1. Location of the investigated sites.

Table 2 Description of case studies blasting sites. Site name

Distance from Johor (km)

Latitude

Longitude

RQD (%)

Bench height (m)

Ulu Tiram Pasir Gudang Masai Pengerang

18 35 25 62

1°360 4100 N 1°20 600 N 1.5°290 42.1600 N 1°220 5800 N

103°490 2000 E 103°50 400 E 103°520 27.7900 E 104°70 5800 E

65–88 67–89 60–84 70–91

10–15 13–25 15–20 10–23

algorithm, the particles are scattered throughout a hyper-dimensional search space. The particles positions within the search space are changed based on the social-psychological tendency of individuals to emulate the success of other individuals, according to [37]. Therefore, the movement of each particle in a swarm is inspired by combining some aspect of the history of its own with the knowledge of its neighbors. Based on a few mathematical equations, the particles are moved around the search space area to find the optimum solution. Particles movements are steered by their own best known position, called personal best (pbest) as well as the entire particles best known position, called global best (gbest). The optimization process using PSO algorithm starts with initialization of its parameters. Subsequently, the first swarm of particles is produced. In other word, the particles are flown throughout a multidimensional search space and the initial positions of particles are randomly determined. The velocity of a particle is defined as a vector from its former position to the current position, while the initial velocity of all particles is zero. The new velocity for each particle is determined based on following equation:

!

v new

¼

!

v

! ! ! ! þr 1 C 1  ð pbest  p Þ þ r2 C 2  ð g best  p Þ

ð5Þ

! ! ! in which; v new ; v and p are new velocity, current velocity and current position of particles respectively. C1 and C2 are pre-defined ! coefficients (acceleration coefficients), pbest is personal best position ! of particle and g best is global best position among all particles. r1 and

r2 are random values in the range (0,1) sampled from a uniform distribution. According to Kennedy and Eberhart [47], r1 and r2 added to update scheme of particles to avoid settlement of particles on a united, unchanging direction. The next step is generating new ! position of particles ðpnew Þ, as in Eq. (6). This procedure is continued until termination criterion is met.

! ! ! pnew ¼ p þ v new

ð6Þ

PSO algorithm can be applied for optimization issues in science and engineering purposes. In comparison to the other optimization algorithms, PSO occupies the bigger optimization ability using simple relations and can be completed easily. 5.3. Implementation PSO-based ANN models The main objective in ANN training is to adjust a set of weights and biases that minimized an objective function. Usually, MSE is used as the objective function in ANNs. The PSO and ANNs employ different approaches to minimize an objective function. Typically, there is more probability for convergence at a local minimum by ANNs, whereas, PSO is capable to find a global minimum and continues searching around it. Therefore, a hybrid PSO-based ANN model has the search properties of both PSO and ANN; PSO looks for all the minima in the search space and ANN used them to find the best results.

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67

With the aim of using PSO to train an ANN, a suitable representation function should be determined. Since the main target of ANNs is to obtain the minimum error between actual and predicted values, MSE is defined as representation function. In this case, each particle represents a candidate solution to minimize MSE. Each component of a particles position vector represents one ANN weight or bias. Finally, the optimum weights and biases are introduced to determine the minimum MSE.

6. AOp prediction using hybrid PSO-based ANN To simulate AOp using hybrid PSO-based ANN, all relevant parameters should be determined, due to the fact that ANNs work based on given data and do not have previous knowledge about the subject of prediction. Following sections describe the input and output parameters and simulation of AOp using hybrid PSO-based ANN model.

6.1. Input and output data In PSO-based ANN modeling, any type of input can be used as long as they have effects on output results. However, the selected parameters have to represent the blasting and site conditions, be measurable and easy to obtain simultaneously. The value of AOp in each blasting operation has a direct relationship with the blasting parameters and geological discontinuities. Burden (the distance from the first row of blasthole to the nearest free face), spacing (the distance between adjacent blastholes), hole depth, number of holes, powder factor (the ratio between the total weights of explosive divided by the amount of broken rock), maximum charge per delay (maximum quantity of explosive charge detonated on one delay within a blast) and stemming length are the normal blasting parameters. Improper design of these parameters may increase the AOp intensity. For example, an insufficient burden may cause breakthrough of blasthole charges, resulting in AOp. Moreover, spacing considerably less than the burden tend to cause premature splitting between blastholes and early loosening of the stemming and too close spacing causes crushing between holes. In general, reducing the quantity of powder factor and maximum charge per delay will decrease the AOp

61

generation, but these parameters should remain high enough to sufficiently fracture the rock. Geological discontinuities play a vital role in AOp phenomena. If there is any geological discontinuity, explosive gases escape from the blastholes which lead to high magnitude of AOp. As a degree of jointing or fracturing in a rock mass, RQD can be used to represent the geological discontinuities. RQD is an index of assessing rock quality quantitatively that measured as a percentage of the drill core in lengths of 100 mm or more. In addition to the aforementioned parameters, the distance between the blast face and monitoring point is a significant parameter in measuring the AOp intensity. Undoubtedly the value of AOp decreases with increasing the distance from the blast face. According to Richards [49], the maximum AOp is occurred in perpendicular line to the blast face. Fig. 2 shows the schematic view of the blasting parameters and monitoring point. In order to utilize PSO-based ANN model to predict AOp, four granite quarry sites in Malaysia were investigated. To train and verify the ability and accuracy of the PSO-based ANN model, a total of 62 AOp records from granite quarry sites were used in this research. As already mentioned, the weather condition is an influential parameter on AOp induced by blasting. Since the weather conditions in the case studies blasting sites were approximately similar, this parameter was omitted from the investigated parameters. In total, nine input parameters including hole depth, powder factor, maximum charge per delay, stemming length, burden, spacing, RQD, number of holes and the distance between blast face and monitoring point and one output including the measured AOp were used to predict AOp induced by blasting. Table 3 shows the recorded input and output parameters from the blasting sites. 6.2. Network design In this step, the parameters of the PSO-based ANN model consisted of number of particles in swarm (swarm size), acceleration coefficients (C1 and C2) and network architecture should be determined. To achieve the best results, a series of sensitivity analyses were conducted to find the optimum swarm size and optimum coefficients of velocity equation. Subsequently, optimum network architecture was determined using the trial and error method. To perform the analyses, a MATLAB code was developed and a

Fig. 2. Schematic view of the blasting parameters and monitoring point.

62

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67

Table 3 Investigated parameters to estimate AOp by empirical approaches and proposed PSO-based ANN model. Dataset number

Hole depth (m)

Powder factor (kg/m3)

Maximum charge per delay (kg)

Stemming length (m)

Burden (m)

Spacing (m)

RQD (%)

Number of holes

Distance (m)

AOp (dB)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

15 15 23 25 25 15 15 10 11 10 12 11 13 11 10 12 12 14 12 10 12 13 11 14 12 16 18 11 15 12 19 13 17 19 20 18 15 20 14 13 24 17 16 19 20 22 19 16 19 15 18 15 16 16 11 14 11 16 13 12 10 17

0.43 0.45 0.55 0.46 0.45 0.65 0.62 0.63 0.6 0.61 0.64 0.45 0.61 0.59 0.54 0.66 0.63 0.64 0.56 0.55 0.49 0.65 0.5 0.52 0.48 0.51 0.34 0.69 0.35 0.55 0.5 0.63 0.47 0.56 0.35 0.42 0.55 0.49 0.65 0.63 0.65 0.56 0.65 0.43 0.39 0.39 0.35 0.42 0.51 0.45 0.61 0.65 0.76 0.55 0.43 0.34 0.39 0.35 0.34 0.39 0.45 0.38

93 91 151 171 160 89 90 62 65 60 66 66.5 69 60 60 66 67 71 70 61 66 68 63 78 68 79 95 72 92 67 135 70 81 100 110 101 91 110 76 72 160 100 100 100 121 142 100 92 120 87 93 101 87 93 66 67 71 90 66 68 61 98

1.95 2.1 2 2.4 2.8 1.85 1.95 2.1 2.1 1.9 2 2.4 2.4 2.4 2.5 1.95 2 2.4 2 2.5 1.75 1.8 2 2 1.9 2.1 2.2 2 2.2 1.9 1.9 2.3 1.9 1.85 2 1.75 1.9 2.5 1.95 2.1 2.3 2 2.2 2.4 2.5 3 1.7 2 1.9 1.7 1.8 2.1 1.7 2 1.8 2.1 2 2.2 2.4 1.8 2.1 2

2 2 2.1 2.05 2 1.9 2.2 2 3.1 3.1 2.9 3 3 3 3.1 3.15 2.95 3 2.9 2.1 2.5 2 1.9 2.5 2 2.2 2.8 3 2.8 1.95 2.05 2.1 2 1.95 1.6 2 2.1 1.9 2.2 2 2.1 2.5 3 2.8 2.5 2 2.2 2.8 2.9 3 3.2 2.8 2.8 2.2 1.7 2.05 1.5 1.95 1.6 2 2.1 1.9

2.7 2.7 2.95 2.8 2.7 2.85 3 3 3.7 3.7 3.8 3.6 3.6 3.6 3.7 3.75 3.9 3.6 3.8 2.7 3.2 2.8 2.8 3.3 2.75 3.1 3.6 3.5 3.6 3.7 3.6 3.6 3.7 3.75 3.9 3.6 3.7 3.8 3 3 2.8 2.9 3.3 3.6 3 2.8 2.65 3.2 3.5 3.8 4 3.4 3.6 3.7 3.6 3.7 3.8 2.8 3 2.9 2.8 2.7

75 67 68 87 79 80 75 77 64 61 69 70 68 66 63 63 76 78 81 65 85 86 88 62 86 88 89 89 91 82 84 85 66 81 91 78 77 75 89 80 64 77 88 89 60 91 84 64 77 71 86 84 83 85 91 78 77 70 68 66 63 63

15 39 33 26 43 42 39 43 43 24 42 43 38 24 29 29 41 21 63 56 12 23 47 39 22 26 26 42 39 38 29 21 35 63 37 23 25 55 39 39 56 55 34 54 59 49 55 63 54 51 53 58 48 44 51 39 41 28 31 33 54 49

600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 300 300 300 300 300 300 300 300 300 600 600 600 600 600 300 600 600 600 600 600 600 300 300 300 600 600 600 600 300 600 300 300 600 600 600 600 600 600 600 300 300 300 300 600 600 600 300

100 107 122 121 101 101 100 90.5 97.5 92 91.5 89.7 91 109 105 93.5 91.5 89.1 90 91 95.5 103 96 94 95 100 104 99 104 98 104 97 93 104.9 105.3 106.8 107.8 107.9 108.9 103.2 110.3 110.5 108 114.1 122.6 125.3 113.1 111 122.4 110 107 112.5 109 115.7 112.3 108 110 114.6 111.3 115.7 125.6 126.3

PSO-based ANN model consisting of 1 hidden layer and 10 nodes in hidden layer was utilized as initial model. Each analysis was conducted three times and the best value was selected as the representative value of the model. In each model, data were divided into two groups; 80% to train the models and 20% to test the performance of the models. Training data are presented to the network during training, and the network is adjusted according to its error, whereas testing data have no effect on training and so

provide an independent measure of network performance after training. The first sensitivity analysis was conducted to determine the number of particles in swarm. Large number of particles in swarm covers larger parts of search space in iteration. However, more particles increase the computational complexity and training time. In addition, the optimum swarm size is problem-dependent and should be determined using sensitivity analysis. In order to obtain

63

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67

Fig. 3. Correlation coefficient for models with different swarm size.

Fig. 4. Mean square error for models with different swarm size.

Table 4 The results of sensitivity analyses for acceleration coefficient. Model

1 2 3 4 5 6 7

Relationship

C1 = 0.25 C2 C1 = 0.5 C2 C1 = 0.75 C2 C2 = C1 C2 = 0.25 C1 C2 = 0.5 C1 C2 = 0.75 C1

C1

0.8 1.333 1.714 2 3.2 2.667 2.286

C2

3.2 2.667 2.286 2 0.8 1.333 1.714

Training

Testing

R

MSE

R

MSE

0.97 0.96 0.92 0.93 0.67 0.81 0.88

0.017 0.019 0.046 0.040 0.155 0.090 0.062

0.56 0.76 0.59 0.72 0.69 0.52 0.68

0.346 0.186 0.249 0.122 0.167 0.289 0.172

the optimum swarm size, series of sensitivity analyses were conducted with different number of particles in swarm and correlation

coefficient (R), MSE and consumed training time (elapsed time) were measured in each analysis. In this case, other parameters of the network including acceleration coefficients and network architecture were set constant. Figs. 3 and 4 show the values of R and MSE obtained by the models with different swarm size. The first model was trained with 10 particles, in which R and MSE obtained are 0.52 and 0.31 respectively. According to Figs. 3 and 4, by increasing the number of particles from 10 to 125, R increased sharply and MSE decreased rapidly. A fluctuation in the values of R and MSE can be seen when the number of particles increase from 125 to 400. However, the model with 275 particles yields the highest values of R (0.88) and low value of MSE (0.06). Therefore, swarm size of 275 was selected as the optimum number of particles. The second analysis was conducted to determine optimum values of acceleration coefficients. These coefficients control the stochastic influence of the cognitive and social components on the overall velocity of a particle. Based on the acceleration coefficients suggested by Clerc and Kennedy [50], a series of candidate combinations were utilized to conduct the sensitivity tests. These tests utilized the same initial swarm size of 275 obtained in the previous analysis. The results of analyses are shown in Table 4. As can be seen in the table, the highest value of R for training datasets was obtained when C1 = 0.25 C2, meanwhile R for testing dataset is relatively low for this test. However, the accuracy and applicability of a network has to be determined according to values of R and MSE for testing datasets. According to Table 4, model number 2 yields better results as compared to other models. Therefore, this model was selected as the optimum network in this step and values of 1.333 and 2.667 were selected as optimum values of C1 and C2 respectively. The next analysis was conducted to determine optimum network architecture including the number of hidden layers and the number of nodes in each hidden layer. Therefore, using the trial and error method, 16 models were trained and tested with different architectures in which each model consists of 9 inputs and 1 output. Table 5 shows the Performance of networks with different architectures. According to the table, the highest value of correlation coefficient for training datasets obtained for models number 3 and 16 with R = 0.98, while correlation coefficients of testing datasets in these models are relatively low. However, the values of R and MSE for testing datasets are the criteria for the selection of the proper model. Therefore, the architecture of the model number 2 was selected as the optimum architecture regarding the value of

Table 5 Performance of the networks with different architectures. Model

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Network architecture

Training

Testing

Hidden layers

Nodes in hidden layers

R (Train)

MSE (Train)

R (Test)

MSE (Test)

1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

9 12 15 18 21 24 27 30 9 12 15 18 21 24 27 30

0.96 0.94 0.98 0.95 0.95 0.93 0.96 0.96 0.97 0.95 0.94 0.95 0.97 0.97 0.96 0.98

0.019 0.028 0.009 0.027 0.025 0.035 0.021 0.023 0.016 0.027 0.032 0.029 0.015 0.017 0.022 0.013

0.76 0.91 0.63 0.88 0.72 0.84 0.52 0.51 0.59 0.84 0.33 0.44 0.75 0.61 0.50 0.50

0.186 0.063 0.153 0.065 0.221 0.122 0.248 0.249 0.242 0.088 0.321 0.231 0.232 0.186 0.183 0.277

64

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67

MSE for testing datasets. This model that includes 1 hidden layer and 12 nodes yields highest value of R (0.91) and lowest value of MSE (0.063) for testing datasets. Fig. 5 shows the structure of the selected PSO-based ANN model for simulation AOp induced by blasting. 7. Experimental equation for case studies blasting sites As previously mentioned in Section 3, several empirical relationships have been developed based on the regression analysis. A widely used empirical formula has been presented in the form of Eq. (4) and several site factors have been suggested for different blasting conditions, as in Table 1. In order to obtain appropriate site factors for the case studies blasting sites, a power (log–log) regression analysis was conducted using the 62 measured AOp and SD. Two different site factors were obtained in terms of the distance between monitoring point and blast face. The results are tabulated in Table 6.

using obtained data from four blasting sites in Malaysia to determine the optimum network. Performances of the selected PSO-based ANN model using training and testing datasets are shown in Figs. 6 and 7. As can be seen in these figures, the correlation coefficient for training and testing obtained are 0.94 and 0.91 respectively. The predicted AOp fit the measured AOp almost perfectly for training datasets. Nevertheless, the predicted AOp does not fit perfectly to the measured AOp for testing datasets. This might be caused by a lack of training data in that range. Another cause could be that there are some parameters that have not been taken into account in modeling. In general, it can be said that the proposed PSO-based ANN model is able to predict AOp induced by blasting with high degree of accuracy.

8. Results and discussion In order to increase the accuracy and applicability of ANN for AOp prediction, POS algorithm was used to weighting ANN instead of BP. Several PSO-based ANN models were trained and tested

Fig. 6. Normalized values of measured and predicted AOp for training datasets.

Fig. 5. Structure of the selected PSO-based ANN model to predict AOp induced by blasting.

Table 6 Site factors H and b for case studies blasting sites. Description

H

b

Equation

Granite quarry, front face, D = 300 m Granite quarry, front face, D = 600 m

10,909

1.09

AOp = 10,909(SD)1.091

959.48

0.45

AOp = 959.48(SD)0.45 Fig. 7. Normalized values of measured and predicted AOp for testing datasets.

65

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67 Table 7 AOp predicted by empirical approaches and proposed PSO-based ANN model.

a

Dataset number

Eq. (1)

Eq. (2)

Eq. (4) b = 0.966 H = 22182

Eq. (4) b = 0.706 H = 261.54

Eq. (4) b = 1.1 H = 19062

Eq. (4)a

PSO Based-ANN

Measured AOp (dB)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

139.14 139.08 140.53 140.73 140.70 139.02 139.05 137.98 138.12 137.89 138.16 138.18 138.29 137.89 137.89 144.18 144.22 144.39 144.35 143.96 144.18 144.27 144.05 144.66 138.25 138.68 139.21 138.41 139.11 144.22 140.21 138.33 138.75 139.35 139.63 139.38 145.10 145.65 144.59 138.41 140.70 139.35 139.35 145.37 139.90 146.21 145.37 139.11 139.87 138.95 139.14 139.38 138.95 139.14 144.18 144.22 144.39 145.07 138.16 138.25 137.94 145.31

113.91 113.84 115.58 115.82 115.78 113.76 113.80 112.52 112.68 112.41 112.74 112.76 112.89 112.41 112.41 119.96 120.01 120.21 120.16 119.69 119.96 120.06 119.80 120.53 112.84 113.35 113.99 113.03 113.88 120.01 115.20 112.94 113.44 114.16 114.49 114.20 121.06 121.72 120.45 113.03 115.78 114.16 114.16 121.39 114.82 122.40 121.39 113.88 114.79 113.69 113.91 114.20 113.69 113.91 119.96 120.01 120.21 121.03 112.74 112.84 112.46 121.32

194.90 193.56 227.47 232.62 231.71 192.19 192.88 171.27 173.87 169.49 174.72 175.14 177.21 169.49 169.49 341.30 342.94 349.34 347.76 332.84 341.30 344.56 336.28 359.97 176.39 185.03 196.23 179.63 194.23 342.94 219.49 178.03 186.51 199.46 205.62 200.10 378.10 401.66 357.00 179.63 231.71 199.46 199.46 389.64 211.96 427.74 389.64 194.23 211.40 190.80 194.90 200.10 190.80 194.90 341.30 342.94 349.34 376.77 174.72 176.39 170.39 387.14

8.22 8.18 9.20 9.35 9.33 8.13 8.16 7.48 7.56 7.42 7.59 7.60 7.67 7.42 7.42 12.38 12.42 12.59 12.55 12.15 12.38 12.46 12.24 12.87 7.64 7.91 8.26 7.74 8.20 12.42 8.96 7.69 7.96 8.36 8.55 8.38 13.34 13.94 12.79 7.74 9.33 8.36 8.36 13.63 8.74 14.60 13.63 8.20 8.72 8.09 8.22 8.38 8.09 8.22 12.38 12.42 12.59 13.30 7.59 7.64 7.45 13.57

86.85 86.17 103.55 106.23 105.75 85.47 85.82 74.96 76.26 74.07 76.68 76.89 77.93 74.07 74.07 164.37 165.27 168.79 167.92 159.74 164.37 166.16 161.62 174.65 77.52 81.85 87.52 79.14 86.51 165.27 99.43 78.34 82.60 89.17 92.31 89.49 184.70 197.86 173.01 79.14 105.75 89.17 89.17 191.13 95.55 212.56 191.13 86.51 95.27 84.77 86.85 89.49 84.77 86.85 164.37 165.27 168.79 183.96 76.68 77.52 74.52 189.74

106.37 106.04 113.85 114.94 114.74 105.69 105.87 100.11 100.84 99.61 101.08 101.20 101.77 99.61 99.61 97.84 98.42 100.65 100.10 94.81 97.84 98.99 96.05 104.26 101.54 103.85 106.70 102.42 106.20 98.42 112.12 101.99 104.24 107.49 108.96 107.64 110.18 117.47 103.26 102.42 114.74 107.49 107.49 113.81 110.43 125.05 113.81 106.20 110.30 105.34 106.37 107.64 105.34 106.37 97.84 98.42 100.65 109.76 101.08 101.54 99.86 113.03

101.67 102.43 118.45 116.16 106.11 96.45 102.45 93.89 99.45 88.78 97.74 91.78 88.98 112.34 100.76 90.43 94.23 97.24 86.76 95.19 91.22 105.26 91.2 91.98 98.18 103.86 98.43 102.97 107.56 97.22 97.84 101.33 99.84 106.89 103.08 109.56 99.71 111.43 111.32 100.11 113.59 112.21 105.67 112.95 118.92 128.74 110.34 107.56 126.98 107.88 104.86 116.12 106.87 118.33 108.57 105.56 107.11 111.89 112.41 112.64 131.3 129.24

100 107 122 121 101 101 100 90.5 97.5 92 91.5 89.7 91 109 105 93.5 91.5 89.1 90 91 95.5 103 96 94 95 100 104 99 104 98 104 97 93 104.9 105.3 106.8 107.8 107.9 108.9 103.2 110.3 110.5 108 114.1 122.6 125.3 113.1 111 122.4 110 107 112.5 109 115.7 112.3 108 110 114.6 111.3 115.7 125.6 126.3

Eq. (4) using proposed site factors, as in Table 6. (H = 10909, b = 1.09 for D = 300 m and H = 959.48, b = 0.45 for D = 600 m).

With the aim of evaluating the applicability of the presented model, AOp values were obtained by means of empirical formulas as well as proposed PSO-based ANN model for 62 datasets. The AOp values were calculated using empirical formulas including Eqs. (1), (2), and (4). For Eq. (4), related site factors (H and b) were selected from Table 1. In addition, the obtained site factors for the case studies blasting sites were used to calculate AOp using Eq. (4). Subsequently, a comparison was conducted between the results

obtained by the empirical formulas and PSO-based ANN model. Table 7 shows the AOp values predicted by empirical approaches and proposed PSO-based ANN model. As can be seen in the table, Eqs. (2) and (4) using proposed site factors, and proposed PSO-based ANN model yield better results compared to the other methods. However, in most cases, the values of AOp predicted by PSO-based ANN model are much closer to the measured AOp compared to the empirical formulas. In

66

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67

Fig. 8. Comparison between predicted AOp by PSO-based ANN model, Eq. (4) by proposed site factors, and measured AOp.

addition, in some cases, considerable differences can be seen between the predicted AOp by empirical formulas and measured AOp (e.g. datasets 12, 19, 24). Fig. 8 shows an illustrative comparison between the measured AOp, predicted AOp by PSO-based ANN model, and empirical Eq. (4) using proposed site factors. According to the figure, results of Eq. (4) are in good agreement with the measured AOp values in some cases. However, PSO-based ANN model presents more accurate prediction compared to empirical equation. It is worth mentioning that similar to other kind of ANNs, the range of applicability of the proposed PSO-based ANN model is constrained by the data used in the training step.

9. Conclusion A new approach was developed based on the hybrid PSO-based ANN model to predict AOp induced by blasting. In order to increase the accuracy and applicability of prediction using ANNs, PSO algorithm was used to train ANNs instead of BP. To determine the optimum parameters of the PSO-based ANN and subsequently present an optimum model, a series of sensitivity analyses was conducted and the optimum network architecture was obtained using trial and error method. Finally, a model with 1 hidden layer and 12 hidden nodes was selected. To generate the proposed hybrid PSObased ANN model, a dataset consists of 62 quarry blasting records was used. The hole depth, powder factor, maximum charge per delay, stemming length, burden, spacing, RQD, number of holes, and distance between monitoring point and blast face were used as input parameters. Apart from that, two series of site factors were obtained for two different distances in front of the blast face. To evaluate the accuracy of the presented PSO-based ANN model, AOp values were compared to the results of empirical formula. The results indicate the superiority of the proposed PSO-based ANN model to predict AOp in comparison to other predictive methods. Finally, it can be concluded that presented approach is an applicable tool to predict AOp with high degree of accuracy.

Acknowledgements The authors wish to extend their appreciation to the Ministry of Higher Education of Malaysia for UTM Research University Grant No. 01H88 that makes this research possible. The authors also would like to thank Universiti Teknologi Malaysia to provide required facilities for this research.

References [1] Bhandari S. Engineering rock blasting operations. Netherlands: A.A. Balkema; 1997. [2] Lawrence JD, William HL, Janet SS. Environmentalism and natural aggregate mining. Nat Resour Res 2002;11:19–28. [3] Wharton RK, Formby SA, Merrifield R. Airblast TNT equivalence for a range of commercial blasting explosives. J Hazard Mater 2000;79:31–9. [4] Hagan TN. Rock breakage by explosives. In: Storr ED, editor. Proceedings of the national symposium on rock fragmentation, Adelaide. Australia: Institution of Engineers; 1973. p. 1–17. [5] Mohanty B. Physics of explosions hazards. In: Beveridge A. editors, Forensic investigation of explosions. London; 1998. p. 22–32. [6] Persson PA, Holmberg R, Lee J. Rock blasting and explosives engineering. In: editors, C.R.C. Press; 1994. pp. 375–86, 515. [7] Konya CJ, Walter EJ. Surface blast design. Englewood Cliffs: Prentice Hall; 1990. [8] Hopler RB, editor. Blasters’ handbook. International Society of Explosives Engineers; 1998. [9] Kuzu C, Fisne A, Ercelebi SG. Operational and geological parameters in the assessing blast induced airblast-overpressure in quarries. Appl Acoust 2009;70:404–11. [10] Segarra P, Domingo JF, López LM, Sanchidrián JA, Ortega MF. Prediction of near field overpressure from quarry blasting. Appl Acoust 2010;71:1169–76. [11] Wu C, Hao H. Modelling of simultaneous ground shock and air blast pressure on nearby structures from surface explosions. Int J Impact Eng 2005;31:699–717. [12] Rodríguez R, Toraño J, Menéndez M. Prediction of the airblast wave effects near a tunnel advanced by drilling and blasting. Tunn Undergr Sp Technol 2007;22:241–51. [13] Rodríguez R, Lombardía C, Torno S. Prediction of the air wave due to blasting inside tunnels: approximation to a ‘phonometric curve’. Tunn Undergr Sp Technol 2010;25:483–9. [14] Mohamed MT. Performance of fuzzy logic and artificial neural network in prediction of ground and air vibrations. Int J Rock Mech Min Sci 2011;48:845–51. [15] Khandelwal M, Kankar PK. Prediction of blast-induced air overpressure using support vector machine. Arabian J Geosci 2011;4:427–33. [16] Khandelwal M, Singh TN. Prediction of blast induced air overpressure in opencast mine. Noise Vib Control Worldw 2005;36:7–16. [17] Tonnizam Mohamad E, Hajihassani M, Jahed Armaghani D, Marto A. Simulation of blasting-induced air overpressure by means of artificial neural networks. Int Rev Modell Simulations 2012;5:2501–6. [18] Priddy KL, Keller PE. Artificial neural networks, an introduction. Washington: SPIE-The International Society for Optical Engineering; 2005. [19] Adhikari R, Agrawal RK. Effectiveness of PSO based neural network for seasonal time series forecasting. In: Indian International Conference on Artificial Intelligence (IICAI), Tumkur, India; 2011. p. 232–44. [20] Wang XG, Tang Z, Tamura H, Ishii M, Sun WD. An improved backpropagation algorithm to avoid the local minima problem. Neurocomputing 2004; 56:455–60. [21] Baker WE, Cox PA, Kulesz JJ, Strehlow RA, Westine PS. Explosion hazards and evaluation. Elsevier Science; 1983. [22] Roy PP. Rock blasting effects and operations. India: A.A. Balkema; 2005. [23] Glasstone S, Dolan PJ. The effects of nuclear weapons. Washington (D.C.): US Department of Defense and Energy Research; 1977. [24] Stachura VJ, Siskind DE, Kopp JW. Airheast and ground vibration generation and propagation from contour mine blasting. U.S. Dept. of the Interior, Bureau of Mines; 1984. [25] Griffiths MJ, Oates JAH, Lord P. The propagation of sound from quarry blasting. J Sound Vib 1978;291:358–70.

M. Hajihassani et al. / Applied Acoustics 80 (2014) 57–67 [26] Morhard RC, editor. Explosives and rock blasting. Atlas Powder Company; 1987. [27] Siskind DE, Stachura VJ, Stagg MS, Koop JW. In: Siskind DE, editor. Structure response and damage produced by airblast from surface mining. United States Bureau of Mines; 1980. [28] Wiss JF, Linehan PW. Control of vibration and blast noise from surface coal mining. Northbrook, IL (USA): Wiss, Janney, Elstner and Associates Inc; 1978. [29] Dowding CH. Construction vibrations. In: Dowding, editor; 2000. p. 204–207. [30] National Association of Australian State Road Authorities, Explosives in Roadworks - A Users Guide, NAASRA, Sydney, 1983. [31] McKenzine C. Quarry blast monitoring: technical and environmental perspective. Quarry Manage 1990;17:23–9. [32] White TJ, Farnfield RA. Computers and blasting. Trans Inst Min Metall Sec 1993;102. [33] Rosenthal MF, Morlock GL. Blasting guidance manual, office of surface mining reclamation and enforcement. US Department of the Interior; 1987. [34] Cengiz K. The importance of site-specific characters in prediction models for blast-induced ground vibrations. Soil Dyn Earthquake Eng 2008;28:405–14. [35] Hustrulid WA. Blasting principles for open pit mining: general design concepts. Balkema; 1999. [36] Liou SW, Wang CM, Huang YF. Integrative discovery of multifaceted sequence patterns by frame-relayed search and hybrid PSO-ANN. J Universal Comp Sci 2009;15:742–64. [37] Engelbrecht AP. Computational intelligence: an introduction. 2nd ed. New York: Wiley; 2007. [38] McCulloch WS, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 1943;5:115–33. [39] Simpson PK. Artificial neural system-foundation, paradigm, application and implementations. New York: Pergamon Press; 1990.

67

[40] Meulenkamp F, Grima MA. Application of neural networks for the prediction of the unconfined compressive strength (UCS) from Equotip hardness. Int J Rock Mech Mining Sci 1999;36:29–39. [41] Tawadrous AS, Katsabanis PD. Prediction of surface crown pillar stability using artificial neural networks. Int J Numer Anal Met 2007;31:917–31. [42] Kosko B. Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence. New Delhi: Prentice Hall; 1994. p. 12–7. [43] Dreyfus G. Neural networks: methodology and application. 2nd ed. Berlin Heidelberg (Germany): Springer; 2005. [44] Kalogirou SA. Applications of artificial neural networks for energy systems. Appl Energy 2000;67:7–35. [45] Parker DB. Learning logic. Technical Report TR-47. Center for Computational Research in Economics and Management Science, Massachusetts Institute of Technology, Cambridge (MA); 1985. [46] Neaupanea KM, Krishna M, Shiva H, Achet ASH. Use of backpropagation neural network for landslide monitoring: a case study in the higher Himalaya. Eng Geol 2004;74:213–26. [47] Kennedy J, Eberhart R. Particle swarm optimization, IEEE international conference on neural networks, Perth, Australia; 1995. p. 1942–8. [48] Shi Y, Eberhart RC. A modified particle swarm optimizer. In: Proceedings of the 105 IEEE congress on evolutionary computation; 1998. p. 69–73. [49] Richards AB. Elliptical airblast overpressure model. Mining Technol 2010;119:205–11. [50] Clerc M, Kennedy J. The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evolutionary Comput 2002:58–73.