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Sensitivity analysis model The outputs that are shown in Table 1 are the results of the model after running for 500 times. Table 1 indicates meaningful F-values and a great significance (α < 0.0001) for all developed sensitivity analysis models that reject the null hypothesis clearly. Table 1 Analysis of variance for labor energy (LE), fuel energy (FE), total machinery cost (TMC), total machinery energy (TME) Full size table Figure 2 shows the sensitivity analysis for labor energy (LE). In this figure, F1–F7 represent land slope, moisture content, density, soil compressibility factor, embankment volume, Soil Swelling Index, and sand percent, respectively. The results revealed that F3 (density), F4 (soil compressibility factor), and F5 (embankment volume) had the highest sensitivities on LE. Fig. 2 Sensitivity analysis for labor energy (LE), fuel energy (FE), total machinery cost (TMC), total machinery energy (TME) Full size image Sensitivity analysis also showed that three soil parameters including; volume of soil, specific gravity and soil compaction had the greatest impact on the amount of energy required for land leveling. These parameters had direct relation with the required energy. In other words, more density of the soil leads to more required energy for constant volume of the soil. For a soil with higher densities, in addition to its weight, handling it also requires more energy consumption. It is obvious that more working time of the machine leads to higher energy consumptions. In the same manner, the higher the excavation volume, the greater the energy consumption. It can be interpreted in this way that more soil volume needs more time of machine and leads to more fuel consumption. Table 1 shows that soil volume is the most important parameter between all input variables for energy consumption including LE, FE, TMC and TME. It is clear that by increasing cut soil volume, needed time of machinery used increases, and consequently fuel energy increases as well. Furthermore, prolonged working time of machinery increases labor requirement for operation which in turn raises the energy consumption by the labors. On the other hand by decreasing the cut soil volume, required human labor also decreases. Therefore, one of the most important ways for decreasing energy consumption is to reduce soil cut/fill. In addition, in each table, if the F value of a variable is higher than others, it indicates the higher impact of that variable in the final model. This situation has occurred for cut-fill volume as a variable which is the most effective factor and affects all responses of interest. In the same manner, the lower F value of a variable indicates lower impact of that variable on responses. Regression model Since the F-values of all models, that are shown in Table 2, indicated a great significance (α < 0.0001) for all developed regression models, the null hypothesis has rejected. Likewise, all models have significant P values as well. Table 2 Analysis of variance for labor energy (LE), fuel energy (FE), total machinery cost (TMC), total machinery energy (TME) models Full size table Of the seven parameters of soil and land characteristics (moisture, density, soil compressibility factor, land slope, soil type, embankment volume), two factors: embankment volume and soil compressibility have the most significant effect on LE in land leveling. The factors of slope, V and soil type (sand) have significant effects on FE. V, soil compressibility factor and slope have significant effects on TMC in land leveling (Table 2). Moreover, the results show that the effect of the land slope, swelling coefficient and soil type on energy consumption in land leveling is significant. By increasing land slope, volume of excavation and embankment increases and the number of sweep and distance traveled by leveling machines also increases and fuel consumption will increase which is obvious. Increase in soil swelling factor increases the volume of the embankment and increase in volume of the embankment also increases the demand of fuel and energy. The fitted nonlinear equations for the all response of interest including LE, FE, TMC, and TME are represented in Eqs. 19–22, respectively, in which the coefficients are provided in coded units. The coded equation is more easily interpreted. The coefficients in the actual equation compensate for the differences in the ranges of the factors as well as the differences in the effects. Finally, LE, TMC, and TME were affected significantly only by three variables including: land slope, volume of the embankment (V), and soil swelling index (SSI). For FE model, the effect of SSI is not significant; however, soil percent has taken its place and affects the FE significantly. Labor energy consumption in land leveling is a nonlinear function of the soil compressibility factor and slope (Eq. 19). In the same way, fuel energy consumption in land leveling is also a nonlinear function of the soil compressibility factor and slope (Eq. 20). This is true for TMC and TME as well which have been represented in Eqs. 21 and 22, respectively. The value of each coefficient variable in the equation represents the effect of variable on the function. $$\left( {\text{LE}} \right) 0.8 = 34{,}161.36 + 3639.90*{\text{Slope}} + 31{,}173.94*{\text{V}} + 911.96*{\text{SSI}}$$ (19) $$\left( {\text{FE}} \right) 0.8 = 4.148^{5} + 49{,}590.44*{\text{Slope}} + 3.782^{ 5} *{\text{V}} - 10{,}008.33*{\text{Sand}}$$ (20) $$\left( {\text{TMC}} \right) 0.8 = 3.319^{8} + 3.587^{7} *{\text{Slope}} + 3.015^{8} *{\text{V}} + 8.393^{6} *{\text{SSI}}$$ (21) $$\left( {\text{TME}} \right) 0.8 = 2.494^{7} + 2.621^{6} *{\text{Slope}} + 2.277^{7} *{\text{V}} + 6.787^{5} *{\text{SSI}}$$ (22) A relatively flat line shows insensitivity to change in that particular factor. The response trace plot for the LE, FE, TMC and TME was sketched. At this plot, the vertical axis is the predicted values and the horizontal axis is the incremental change made in factors included in the final equation model. The scatter plots of actual values of response of interest vs. predicted values using final models are displayed in Fig. 3a, b. The strong nonlinear effect of cut-fill volume on all the responses of interest is conspicuous (Fig. 3a, b). Figure 4 shows that energy and cost direct relationship with cut-fill volume as the major effect. All responses of interest are moderately affected by slope. Additionally, it is perceived that the increase of the slope led to increased energy and cost. The most appropriate power transformation (lambda) for responses is detected by the Box–Cox diagram that results the minimum residual sum of squares in the transformed model (Fig. 3a). Scatter plots of actual vs. predicted values for regression model are shown in Fig. 4a–d. Fig. 3 a Box–Cox b surface plot of total machines energy versus slope and volume Full size image Fig. 4 Scatter plots of actual vs. predicted using regression models for a labor energy, b fuel energy, c total machines cost, and d total machines energy Full size image Results of ANFIS model prediction In this section, the results of ANFIS models for prediction of LE, FE, TMC, and TME are presented. MATLAB programming language was used for implementing ANFIS simulations. Different ANFIS structures were tried using the programming code and the appropriate representations were determined. Each structure for correspond combination has been evaluated using 100 independent runs and the statistical criteria (R2 and MSE) of the output models have been calculated for responses of interest. In Tables 3 and 4 the minimum, average and maximum values of R2 and MSE for various combinations of developed ANFIS-based models are presented. Additionally, calculated R2 and MSE values of different developed models of labor energy vs. number of clusters are illustrated as well. It is worthwhile to mention that other outputs had similar behaviour. As presented in Table 3, statistical criteria for prediction of LE reveal that FIS model is superior to ANN-back propagation model. Average R2 value in FIS model for prediction of LE was found to be 0.9948 and 0.9944 in Mamdani and Sugeno models, respectively; while in back propagation model, it was calculated as 0.9921. Moreover, as presented in Table 3, statistical criteria for prediction of FE reveal that FIS model are superior to ANN-back propagation model. Average R2 value in FIS model for prediction of fuel energy was found to be 0.9927 and 0.9922 in Mamdani and Sugeno models, respectively. While in back propagation model, R2 value was calculated as 0.9891 and 0.9892, respectively. Table 3 Calculated statistical criteria for prediction of labor energy using/fuel energy different combination of optimization methods and FIS types Full size table Table 4 Calculated statistical criteria for prediction of total machinery cost/energy using different combination of optimization methods and FIS types Full size table As presented in Table 4, statistical criteria for prediction of total machinery cost reveals that FIS model are superior to ANN-back propagation model. Average R2 value in FIS model for prediction of total machinery cost was found to be 0.9921 and 0.9922 in Mamdani and Sugeno models, respectively. While in back propagation model, R2 value was calculated as 0.9894 and 0.9895, respectively. As presented in Table 4, statistical factors for prediction of TMC indicate that FIS model perform better than ANN-back propagation model. Average R2 value in FIS model for prediction of TME was found to be 0.9950 and 0.9952 in Mamdani and Sugeno models, respectively; while in back propagation model, it was calculated as 0.9925 and 0.9926, respectively.