multivariate regression

Net present value (NPV) index is one of the most important economic parameters in evaluating the mining investment projects. Considering the inherent uncertainty in effective parameters on the NPV in most of the mining projects, its precise estimation is a difficult process and application of the suitable methods is required. In this paper, fuzzy system, neural network and multivariate regression models are used for NPV determination in the Zarshuran gold mine project. In spite of the metal value, the effects of costs and discount rate on the NPV are also considered as an index for evaluation the Zarshuran gold mine project of Takab using the above models. One of the advantages of this research compared to the previous similar studies is the utilization of two new intelligent algorithms i.e., fuzzy system and neural network for modeling the NPV index with higher accuracy. These algorithms are efficient tools to solve the problems having ambiguity and uncertainty such as the mining investment projects and reduce the investment risks. Considering the management challenges in deciding on the economic justification of various projects and the existence of time and resource limitations, the use of these models helps clarify the economic future of a mineral investment project and make the final decision.

In this study, three new models including fuzzy system, neural network and statistical multivariate regression were used to determine the NPV and evaluate the effective parameters on this index in the Zarshuran gold mine investment project of Takab. The obtained results of the above models were compared with each other, with the real data, and with the similar previous studies. Gold price (main element), silver price (byproduct element) and discount rate were considered as input parameters for evaluating the NPV. Application of the fuzzy logic in NPV modeling, which is always accompanied by uncertainty, can lead to more realistic results. Also, the utilization of neural network can be effective due to its high capability in dealing with vague and noisy data that are somehow involved in the evaluation of mining projects.

Using the trial and error method, triangular and trapezoidal membership functions, Mamdani inference motor and center of gravity decentralization function were determined as the optimum parameters of the proposed fuzzy model. Also, a neural network with training function of Levenberg-Marquardt back-propagation type, transfer function of sigmoid logarithm kind, 3-5-10-1 structure and root mean square error of 0.0032 was found as an optimum network. Moreover, a statistical multivariate linear relation was proposed to predict the NPV. According to the performance evaluation indices including determination coefficient, absolute error and relative error, results of the proposed models were compared with each other, with the actual data, and with the previous similar investigations. The above comparison proved that the performance of both fuzzy and neural models in predicting the NPV is acceptable and they have a much better agreement with real data in comparison with the statistical model. However, the performance of fuzzy model is somewhat better than the proposed neural network models in this research and previous studies and its results are more consistent with the actual data. Finally, the sensitivity analysis of the fuzzy model results (due to its greater accuracy) are conducted using the cosine amplitude method (CAM). Accordingly, it was confirmed that the gold price has the highest effect and the discount rate has the least effect on the NPV index.

The present study proved the successful application of two new intelligent-based models including fuzzy logic and neural network algorithms to predict the NPV in the Zarshuran gold mine investment project. Also, a linear multivariate regression relation proposed to forecast the NPV index with a relative acceptable performance. Evaluation the results of proposed models showed that the fuzzy model performance was somewhat better than the proposed neural network models in this study and previous studies and both were much higher than the statistical model in predicting mining projects NPV. Based on the sensitivity analysis of the fuzzy model results (the most accurate proposed model), it was proved that the gold price and discount rate have the highest and lowest effects on the NPV, respectively. Considering the above results, it can be concluded that the proposed intelligent techniques in this research (especially the fuzzy model) can be used with good reliability in the evaluation of mining investment projects in order to cover their involved uncertainty and reduce the investment risk.

Dynamic and static properties of the rocks are very important for designing geotechnical structures and modeling rock foundations. The main purpose of this paper is to present the regional and global relationships between the static and dynamic elasticity modulus with an experimental approach and to estimate the shear wave velocity of limestone by statistical methods and artificial neural network (ANN). For this purpose, petrographic, physical and mechanical experiments were first conducted on 80 limestone cores from the Karun 4 dam site. A database was then created using the literature data and compared with the results of this study. The results of statistical analysis show that the ratio of dynamic to static modulus of elasticity for the studied samples is 2.5. Also, the ratio of dynamic to static Poisson for these rocks was 1.41. The average value of the dynamic modulus obtained from the literature was equal to 19.90 GPa, which is less than the average value of the dynamic modulus of the present study (31.20 GPa). Due to the most accurate fit, the global relationship (R2 = 0.98, RMSE = 7.9, MAPE = 1.67) and the regional relationship (R2 = 0.96, RMSE = 5.24 MAPE = 0.91) were presented with very high accuracy between the dynamic and static modulus of elasticity. The results of artificial neural network and multivariate regression showed that estimation of shear wave velocity (Vs) based on P-wave velocity, water absorption and density is possible with high accuracy. The results showed that the ANN accuracy (R2 = 0.98, RMSE = 0.27) was higher than the multivariate linear regression (R2 = 0.86, RMSE = 0.39). The neural network also acts conservatively in predicting this variable.

The first and most important step in reducing damages and management of gully erosion, which leads to waste of water and soil resources, is the gully erosion susceptibility mapping. In present study, the potential of gully erosion in the Toroud-Najarabad basin were evaluated using the uncertainty of the theory of evidence method and linear multivariate regression as well as the combination of the above-mentioned methods. In view of this the gully erosion inventory map was prepared using various resources, and from 218 identified gullies, 70% (154 gullies) and 30% (64 gullies) were selected randomly for modeling and validation respectively. In the next step, 14 controling factors in the gully occurrence in the study area including topographic, geomorphometric, environmental and hydrologic parameters were determined for modeling. The results of multivariate regression model showed that land use parameters, slope and distance from the road had the greatest impact on gully occurrence. Susceptibility maps classified to five susceptibility classes of very low to very high. The area under curve (AUC) and Seed Cell Area Index (SCAI) were used to validate the susceptibility maps. The results of the validation showed that the combined model has a higher area under the curve (AUC) (0.933) toward the evidence-based (0.914) and multivariate regression (0.890) models, as well as, the SCAI value in the combined model showed that very low susceptibility to a very high susceptibility has a downward trend that indicating a proper separation of susceptibility classes in this model. Considering the excellent precision of the combined method proposed in this research, the results of this research can be used by decision makers and local managers to reduce losses and the methodology presented in this study can be used in similar areas to determine the areas that are susceptible to gully erosion.

Shear strength is one of the most important properties of mudrocks and shales in rock engineering and engineering geology. Because of the difficulty to obtain undisturbed samples of shales as required for determination of shear strength parameters, it is also the most difficult to evaluate. This research investigated properties that can be used to predict the shear strength parameters of Shemshak formation shales. Thirty samples of shales from various depths were collected from boreholes in Shemshak formation in the site of Siahbishe pumped storage powerhouse. Shear strength parameters (c and φ), tensile strength (TS), quartz percent (Qz %), porosity (n) and density (ρ) were determined in lab for each sample. Data were analyzed statistically and with fuzzy inference system to determine the relationships between shear strength parameters with other properties. Results show that cohesion and friction angle of shales can be meaningfully predicted from a few engineering properties by fuzzy inference system. The adjusted R2 values between measured and predicted values for cohesion and friction angle are 0.95 and 0.84 respectively. Also the variation of regression coefficient (R2), performance indices (VAF) and root mean square error (RMSE) with were calculated as for the shear strength parameters, obtained from the multiple regression modeland the fuzzyinference system, revealed that the prediction performance and accuracy of the fuzzy models are high and multiple regression equations not have performance in prediction of shear strength parameters of shales.