Figure 7 Membership functions assigned for the input parameter, W
Related Figures (11)
analysis was carried out by using all data pairs. The determined equation for this site is found to be in accor- dance with the literature and the equation can be used to determine the permissible explosive charge at any distance for a specified scaled distance value by using this equation obtained for this site. In contrast, this equation can enable the operator to determine a compliance or safe value of the distance for a given charge weight of explosive and a specified scaled distance. The equation obtained for the site studied is given below: Table 1 Summary of simple regression analysis It is also possible to graphically determine the permis- sible explosive charge at any distance for a specified scaled distance value. Fig. 2 Peak particle velocity versus scaled distance The adaptive neuro-fuzzy inference system (ANFIS), developed by Jang (1993), is a universal approximator and, as such, is capable of approximating any real continuous function on a compact set to any degree of accuracy (Jang et al. 1997). Thus, in parameter estimation, where the given data are such that the system associates measurable system variables with an internal system parameter, a functional mapping may be constructed by ANFIS that approximates the process of estimation of the internal system parameter. ANFIS is a soft computing technique which incorporates the concept of fuzzy logic into the neural networks, and has been widely used in many applications of engineering science as well as the earth sciences (Grima 2000; Grima et al. 2000; Akbulut et al. 2004; Gokceoglu et al. 2004; Fig. 3 A two-input first-order Sugeno fuzzy model with two rules (Jang et al. 1997) Porwal et al. 2004; Kisi 2005; Singh et al. 2005c; d; Tut- mez et al. 2006). ANFIS can simulate and analyze the mapping relation between the input and output data through a hybrid learning to determine the optimal distri- bution of membership function. It is mainly based on the fuzzy “if-then” rules from the Takagi and Sugeno fuzzy model (Jang et al. 1997) as shown in Fig. 3. It involves a premise part and a consequent part. The equivalent ANFIS architecture is shown in Fig. 4. It comprises five layers in this inference system and each layer involves several nodes, which are described by the node function. Fig. 4 The architecture of ANFIS (Jang et al. 1997) Fig. 5 ANFIS structure used for predicting PPV The membership functions of the inputs were tuned after 27,200 e which co pochs using the hybrid optimization method, nsisted of back-propagation for the parameters associated with the input membership functions and also the least-squares estimation for the parameters associated with the output membership functions. After the RMSE for training data decreased to its minimum value (0.78), the learning procedure of the model was finished. Since the model structure used for ANFIS is fixed, there is a Fig. 6 Membership functions assigned for the input parameter, D The input membership functions of the model after training are given in Figs. 6, 7, and the parameters of these functions are listed in Table 3. The linguistic variables were assigned for “distance” and “charge weight per delay” as very close (VC), close (C), far (F), very far (VF) and very low (VL), low (L), high (H), very high (VH), respectively. The consequent parameters of the output functions for PPV are illustrated in Table 4. Table 4 Values of the consequent parameters for ANFIS-based model Once the network is trained and the antecedent (pre- mise) and consequent parameters are determined (Tables 3, 4), itis an easy task to determine the model prediction for a given set of input parameters. The peak particle velocity (PPV) can either be estimated by using a software in which the ANFIS model was constructed or by manually calcu- lating with the same way described through Eqs. 4-9. A detailed step-by-step sample calculation procedure was illustrated by Habibagahi (2002). Table 3 Values of the antecedent parameters for ANFIS-based model The interpretation of the above-performance indices is as follows: the higher the VAF, the better the model per- forms. For example, a VAF of 100% means that the measured output has been predicted exactly. VAF = 0 means that the model performs as poorly as a predictor using simply the mean value of the data. The lower the RMSE, the better the model performs (Grima and Babuska 1999; Gokceoglu 2002; Gokceoglu and Zorlu 2004; Tut- mez et al. 2007). Contrary to VAF, RMSE also accounts for a bias in the model, i.e. an offset between the measured and predicted data. Fig. 8 Predicted PPV values by ANFIS-based model versus field- recorded values
