## 1 Introduction  
In mining and civil engineering projects, a common technique to remove rock mass is to blast the rock mass. This results in a problem of wasted blasting energy, which occurs for different reasons, and brings about a number of environmental issues, like ground vibrations, backbreak, dust and fumes, air overpressure and flyrock [1; 2; 3; 4; 5]. One of the most adversative effects is ground vibration (GV) which may cause damage to neighbouring structures [6; 7]. In the literature, GV is defined generally as a wave motion that can be extended from the blast point to adjacent zones [8]. Thus, blast-induced GV needs to be predicted, and its risks should be analysed and assessed in a way to enable making the best decisions about the design of blasting operations and minimize associated environmental issues. Different controllable or uncontrollable factors affect the blast-induced GV level. Controllable factors include the blast geometry, stemming, burden, spacing and the type and volume of explosive material, while the uncontrollable ones include meteorological conditions and rock mass parameters [9]. The controllable parameters can typically be changed by the designers, while uncontrollable factors cannot be changed, and are almost constant [10; 11; 12; 13]. The GV can be evaluated in terms of the four following indicators: (a) frequency, (b) peak particle velocity (PPV), (c) peak particle acceleration, and (d) peak particle displacement [14; 15]. Among these parameters, PPV is the preferable and most frequently-used parameter mentioned in almost all standards [16; 17]. All methods proposed in the literature for predicting the PPV value are classified into three groups: empirical, statistical, and soft computing. The empirical methods are developed mainly on the basis of two parameters: distance from the blast face and maximum charge per delay [18; 19; 20; 21]. Empirical equations commonly fail to deliver appropriate results, due to the fact that they consider a limited number of predictors (only two mentioned parameters). Scholars have also used statistical approaches for the purpose of developing an appropriate formula for estimating the PPV values [7; 22]. According to several published reports, these methods have also shown inefficiency in giving accurate values [7; 22; 23]. To fill this gap, many researchers have applied various soft computing (SC) and artificial intelligence (AI) techniques to various fields of engineering and science [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], particularly to obtain more accurate PPV values. For example, [PERSON] et al. [60] developed a model based on an artificial neural network (ANN) with two hidden layers for predicting PPV for a dam in Iran. The PPV predictions of their ANN model were compared with empirical and multilinear regression (MLR) models. They demonstrated that the proposed ANN model was the most dominant model in predicting PPV, with a determination coefficient (R\({}^{2}\)) of 0.949. In two other studies, [PERSON] et al. [61] and [PERSON] et al. [62] developed two hybrid ANN-based models--namely, particle swarm optimization ((PSO)-ANN) and imperialism competitive algorithm ((ICA)-ANN)--for predicting PPV, and interpreted that the PSO and ICA algorithms played a big role in the optimization of the ANN model in terms of receiving higher performance prediction. [PERSON] et al. [63] proposed a hybrid intelligent technique for predicting PPV using the adaptive neuro-fuzzy inference system (ANFIS), called PSO-ANFIS. A superior result was obtained in their study by the PSO-ANFIS model compared with a pre-developed ANFIS model. [PERSON] et al. [64] combined the K-nearest neighbours (KNN) algorithm with ANN, resulting in ANN-KNN. A single ANN model and two empirical techniques were also used to estimate PPV and compare these with the ANN-KNN model. In their results, the proposed ANN-KNN model was the best model at predicting blast-induced PPV.