1. Introduction
The transmission of a tractor is a complex system. It is one of the components that must have high reliability, as it is the most expensive of the various major components of the tractor [
1,
2]. The conventional tractor design method is reliant on the engine specifications or the weight of the tractor, rather than reflecting actual field load conditions [
3]. Thus, load-sensing under actual agricultural working conditions is required to secure the reliability of the tractor transmission [
4]. The axle torque (AT) of a tractor during agricultural operations is directly related to the transmission torque, which makes it possible to estimate the torque acting on all parts of the transmission by using the AT [
5]. These torque data can be applied to achieve the optimal design of the transmission and can also be used as important data for carrying out various performance and durability tests, such as transmission endurance test [
3]. Therefore, for optimal transmission design, AT data generated during agricultural operations under various conditions are required.
Many researchers have conducted studies on load measurement of the engine [
6,
7], transmission input axle [
6], driving AT [
3,
8], and traction force [
9]. Bai et al. [
6] measured the engine and transmission output shaft torque of a multi-axle vehicle powertrain system, in order to analyze the influence of the main factors on the powertrain load dynamic characteristics and fatigue damage. Kumar et al. [
10] developed a microcontroller based embedded system for measuring dynamic wheel axle torque and drawbar power of agricultural tractor for tillage research. They reported that, a maximum variation of ±320 Nm torque between the theoretically calculated and experimentally measured values under field load conditions. However, the above method has the disadvantage of having to install strain gauges on the transmission and drive axles, as well as having to build expensive telemetry systems, rather than wire-type sensors, as the axle rotates [
5].
Tractor ATs can be estimated using relatively inexpensive sensors and multiple linear regression (MLR)-based models [
11]. MLR-based models have been used to estimate dependent variables in various research fields, where the models are developed based on statistical analysis methods by adopting explanatory variables that are closely related to the prediction targets [
12]. In general, it is important to select variables that have a great influence on the AT of a tractor, in order to develop MLR-based estimation models [
13]. To date, many researchers have analyzed the major tractor parameters affecting the tractor AT. As a result, major parameters such as slip ratio (SR) [
14,
15], travel speed (TS) [
11], and tillage depth (TD) [
10] have been found to have a great influence on the tractor AT. As the driving axle of the tractor during agricultural operations interacts directly with the soil, the axle of the tractor is affected not only by the major tractor parameters, but also by the physical properties of the soil [
16,
17]. Therefore, some researchers have reported that the soil cone index (CI) [
16,
18,
19] and soil moisture content (SMC) [
17,
20] influence the torque of the tractor axle. In conclusion, in order to apply a tractor AT estimation model, it is necessary to select appropriate variables, taking into consideration the ease of measurement and the associated correlation coefficients. However, in order to use such an MLR-based model, there is an associated inconvenience of considering the problem of multicollinearity between various variables and the linearity of variables.
Recently, various machine learning-based research considering techniques such as ANN, which have been shown to be strong in nonlinear analysis cases, has actively been conducted, having also been applied in agricultural research [
9,
21]. Research on engine torque (ET) estimation based on ANNs using data obtained through low-cost sensors as input variables has been reported by several researchers [
22]. Bietresato et al. [
22] proposed an ANN-based model using exhaust gas (EG) and motor oil temperature data as major variables to estimate the ET and brake-specific fuel consumption (BSFC) of a tractor. They reported that the ANN using EG temperature for torque estimation achieved a higher mean coefficient of determination (R
2) than the ANN predicting BSFC in both the training and prediction stages. Rajabi-Vandechali et al. [
23] proposed a tractor ET estimation model based on soft computing using a low-cost sensor. They estimated ET using two models, including a radial basis function (RBF) neural network and an adaptive neuro fuzzy inference system (ANFIS) and, as a result, ET could be estimated using engine speed (ES), fuel mass flow, and exhaust gas temperature. In addition, it was reported that the RBF outperformed ANFIS among the two models. The above studies suggest that the performance of various prediction models using ANNs based on low-cost sensors has been improving. Therefore, we expected such a model to be applicable to tractor AT estimation, as targeted in this study. In particular, the ANN-based model is expected to be expandable to a wider range, as it can also consider soil parameters, which are often non-linear variables, unlike studies that only consider existing tractor variables.
As mentioned above, an ANN can be used to develop estimation models with higher accuracy than conventional approaches. This suggests that this state-of-the-art technology can be applied to model development to estimate tractor AT using a relatively low-cost sensor. Therefore, in this study, we estimated the AT of the tractor as a function of soil physical properties and tractor major parameters using an ANN, comparing its ability to estimate the AT of the tractor with that of a model based on MLR. A simple method using ANN based on a relatively inexpensive sensor that can replace the traditional complex tractor AT measurement method is emphasized. Our approach contributes to the following key points: (1) It provides a simple algorithm for estimating tractor AT that can replace the need for expensive torque sensors, (2) We improve the performance of the model by developing an estimation model that considers not only linear variables but also nonlinear variables, (3) Various applications in agricultural machinery for realization of digital agricultural technologies such as real-time transmission failure diagnosis are possible.
4. Discussion
In this study, tractor AT estimation models based on MLR and ANN were proposed, and the major results (by each of the four input cases) were compared. Overall, the MLR-based models had R
2 values of 0.825–0.851, while the ANN-based models had R
2 of 0.857–0.904. These results were found to be similar to the main results of previous studies using ANNs in agricultural research: Yield prediction of winter rapeseed (R
2 = 0.69) [
30], draft force of a chisel cultivator (R
2 = 0.94) [
9], and constituent properties of Red apples (R
2 = 0.738–0.923) [
21].
As a result of the analysis according to the two modeling methods (i.e., MLR and ANN), the ANN-based model showed better performance. This was considered to be because the ANN is based on multi-layer perceptron and, as it can learn the relationships between measured data using a calibration set, the higher the number of input variables and the higher the dimension, the better the performance. In particular, in Cases 1 and 2, using only the tractor engine and main tractor variables (which are linear variables), the difference in R2 between MLR- and ANN-based methods was 3.9–4.2%. On the other hand, in Cases 3 and 4, using the soil physical properties (i.e., non-linear variables), the difference in R2 was 5.8–6.2%. Thus, it was found that, when a non-linear variable (e.g., SMC and CI, in this study) was used as an input variable, the performance of the ANN-based model was superior to that of the MLR-based model.
In our ANN-based model, the performance of the model on the calibration set was highest in Case 4, which used all variable conditions as input variables. On the other hand, in the validation set, the performance of model in Case 4 was the second highest, while the model in Case 2—which used engine parameters and major tractor parameters as input variables—showed the highest performance. These results are believed to be due to the high input dimensions and high model complexity of the estimation model. This means that the higher the input dimensions can make the model more fit to training data, while the generalization performance is degraded in the same model capacity although the model was trained to avoid overfitting by validation loss check for each case. As a result, the generalization performance of the model was considered to be poor. Nevertheless, it showed high performance in the calibration set, which means that the model capacity was sufficiently fit for the data; thus, it can be seen that the model can be considered to be applicable for tractor AT estimation.
5. Conclusions
In this study, we estimated tractor AT as a function of soil physical properties and major tractor parameters using two different types of modeling approaches. The MLR-based models had R2 values of 0.825–0.851 and the results of the model verification showed a MAPE of 2.58–2.73%. Meanwhile, the ANN-based models had R2 values of 0.857–0.904 and the results of the model verification showed a MAPE of 2.25–2.53%; however, depending on the input variables used, the performance of the model varied greatly. Comparison of the performance of MLR- and ANN-based methods revealed that the most important factor in increasing the R2 in ANN (compared to MLR) was the use of soil physical condition variables. These soil physical variables are non-linear and, thus, the influence of the soil physical properties was greater in ANN-based modeling than in basic MLR-based modeling. The main result of this study was that the ANN-based methods showed a better estimation performance than the MLR-based methods. Therefore, it is possible to estimate tractor AT using ANN.
This study is expected to provide a simple algorithm for estimating tractor AT, which can replace the need for expensive torque sensors and can be applied to the development of an automated system for predicting the fatigue life of a tractor transmission. Although these contribution, this study has several limitations as follows: (1) only general ANN architecture was used without consideration of various topologies like a non-iterative neural-like structure that can train faster [
31], (2) since the variable conditions are very diverse, not all variable conditions affecting tractor AT in this study were considered, and (3) in this study, only 300 soil physical condition and major tractor parameter data measured in specific conditions were used. These issues will be addressed by applying various analysis techniques and collecting data through field experiments under various working conditions in future study.
In addition, the important issues learned through this study are as follows: In order to improve the performance of the tractor AT estimation model, it is necessary to consider even the soil physical properties, which are a nonlinear variable. While this can improve model performance, there is a risk of overfitting, which can lower the generalization performance. Therefore, both the addition of nonlinear variables and the risk of overfitting must be considered.
Finally, in this study, we proposed a method for applying the latest modeling technology to tractor AT estimation; we believe that various applications in this field will be possible in the future, for the realization of potentially various digital agriculture technologies.