Introduction
Soil compaction is a significant component that has a detrimental impact on soil structure, inhibits plant development, lowers water penetration rate, diminishes crop production, and raises machine (e.g., tractors, cultivators, etc.) usage costs. In general, compaction is the result of applied pressure that results in a rise in bulk density or decrease in soil porosity. One of the most used indices for the investigation and evaluation of soil compaction is based on penetration resistance (PR) of the soil. However, identifying soil compaction by the records of soil penetrometer equipment in the field is time-consuming, expensive, and may produce unreliable results due to instrumental errors; thus, it is useful to apply different intelligent models to predict PR through easily accessible and low-cost soil parameters. The aim of this study was to compare the performance of three intelligent models, namely neuro-fuzzy (NF), gene expression programming (GEP), and random forest (RF), in estimating PR from readily available soil variables.

Materials and methods
Disturbed and undisturbed soil samples (n=105) were collected from 0-10 cm depth of agricultural lands in Ardabil plain, Iran. The values of sand, silt, clay, CaCO₃, bulk (BD) and particle (PD) density, organic carbon (OC), field water content (FWC) and saturated water content were measured in the soil samples in the laboratory according to the standard methods. Mean geometric diameter (d_g) and geometric standard deviation (σ_g) of soil particles were calculated from sand, silt and clay percentages. Total porosity (n) was computed using BD and PD data. The penetration resistance (PR) of the soil was obtained in the field using cone penetrometer (analog model) with 5 replicates. Data were randomly divided in to two sets: 78 data points for training and 27 for testing the models. Fifteen different combinations of readily available soil variables were selected as inputs for the neuro-fuzzy (NF), gene expression programming (GEP), and random forest (RF) models to estimate PR. The triangular, sigmoid, trapezoid, gaussian and bell shape membership functions in the input layer and constant membership function in the output layer, were applied in the neuro-fuzzy (NF) modeling using MATLAB software through a trial-and-error method. A set of optimal parameters was chosen before developing a best GEP model in the Gene Xpro Tools 4.0 software. The number of chromosomes and genes, head size and linking function were selected by the trial and error method, and they are 30, 3, 8, and +, respectively. The rates of genetic operators were chosen according to the literature studies. Weka software was used for planning random forest (RF) models. The accuracy of NF, GEP and RF models in estimating PR was evaluated by coefficient of determination (R²), normalized root mean square error (NRMSE), mean error (ME) and Nash-Sutcliffe coefficient (NS) statistics.

Results and discussion
The values of sand (26.26 to 87.43%), silt (5.99 to 67.18%), clay (3.99 to 17.34%), OC (0.30 to 2.41%), FWC (4.56 to 33.18%), BD (1.02 to 1.63 g cm^-3) and PR (1.10 to 6.60 MPa) indicated good variations in the soils of the studied area. Significant correlations were found between PR and FWC (r = - 0.57^**), sand (r = - 0.21^*), OC (r = - 0.47^**) and BD (r = 0.66^**). Previous researchers also reported a negative and significant correlation between PR and FWC and a positive and significant correlation between PR and BD. The results of NF, GEP and RF models showed that the most suitable variables to predict PR were field water content (FWC), sand, bulk density (BD), total porosity and mean geometric diameter (d_g) of soil particles. Values of coefficient of determination (R²), normalized root mean square error (NRMSE), mean error (ME), and Nash-Sutcliffe coefficient (NS) were calculated for the best models based on the test data as follows: 0.50, 0.19, 0.03 MPa, 0.51 for NF; 0.51, 0.20, 0.13 MPa, 0.48 for GEP; and 0.58, 0.20, 0.31 MPa, 0.50 for RF.

Conclusion
The results showed that according to the lowest values of normalized root mean square error (NRMSE) and the highest values of Nash-Sutcliffe coefficient (NS), the accuracy of the neuro-fuzzy (NF) model to estimate soil PR was higher than that of the gene expression programming (GEP) and random forest (RF) models in this study; The input variables of the best NF model in estimating soil penetration resistance (PR) were field water content (FWC), sand and bulk density (BD).