1. Introduction
A wheel loader is an important piece of construction machinery that is widely used in construction, mining, and transportation activities, performing tasks such as scooping, loading, transporting, and dumping [
1]. The main form of operation is that the wheel loader is inserted into the pile at a certain speed, and then the bucket is turned by the action of the lift arm, the tilt level, and the connecting rod to shovel the pile, and then the lift arm is lifted to transfer the material. During the insertion phase, the resistance of the bucket increases rapidly with the increasing insertion depth. During this process, it will be accompanied by a huge energy consumption [
2]. Therefore, it is important to predict the magnitude and trend of the resistance of the bucket during the insertion phase for the realization of resistance reduction and an energy reduction in wheel loaders.
The study of the insertion resistance of wheel loader buckets has been a typical issue for a long time. In the 1980s, researchers proposed an empirical formula of resistance for insertion resistance, which is the most widely used method at present [
3]. The formula can roughly estimate the magnitude of insertion resistance to a certain extent, but there is a problem of poor accuracy because many empirical coefficients in the formula need to be chosen manually. In response to the shortcomings of the empirical formula, some scholars have analyzed the resistance to the bucket using the method of soil mechanics. Among them, resistance analysis based on Coulomb Theory and Rankine Theory has been widely used [
4,
5,
6]. Compared with the traditional empirical formula, the resistance calculation based on the soil mechanics method is more accurate. The shortcoming of the soil mechanics method is that the calculation process is complicated. In recent years, a bucket-resistance-prediction method based on the agent model has gradually become mainstream, and the advantage of this is that it relies on the establishment of an agent model between the mechanical motion of the wheel loader and the resistance, and then obtains the resistance value through the change in mechanical motion, which largely reduces the error caused by the manual selection of coefficients. Wang et al. [
7] developed a static model of bucket working resistance and a kinematic model of the working trajectory of a wheel loader, from which the key measurement parameters of working resistance were obtained. Based on the static and kinematic models, the corresponding working trajectories and working resistance were fitted based on the indirect measurement parameters. The analysis results showed that the minimum deviation of the resistance was 0.05%, the maximum deviation was 19.59%, and the average deviation was 7.07%. Madau et al. [
8] analyzed the forces during the shoveling operation of the wheel loader, established the dynamics and kinematics equations of the whole wheel-loader system, and then established a dynamic model for bucket resistance estimation and verified that the resistance error was less than 1%.
Although agent models have many advantages, their accuracy depends on dynamic or kinematic models. These models are the result of theoretical analysis, which differs from the actual operating conditions of the bucket and does not reflect the trend of resistance. This problem has been effectively solved by the advent of artificial neural networks (ANN), which are non-parametric models that learn from training data to obtain predicted values of output variables. There have been many successful applications of ANN in predicting insertion resistance. Park et al. [
9] constructed a neural network with parameters such as the diameter of the pile, the insertion depth, the insertion energy, and the soil properties around the pile as the input variables and the insertion resistance as the output variable, and verified the feasibility of using neural networks to predict insertion resistance. Huang et al. [
10] used a BP neural network to predict the resistance to the curved blade and selected the cutting angle, forward turning angle, and cutting speed of the blade as input variables, and the accuracy of the prediction results for the resistance reached 94%. Zhang et al. [
11] constructed a fuzzy neural network to predict the traction resistance of tractor tillage and optimized the structure of the fuzzy neural network through a density-based noise application spatial clustering algorithm, and the average relative error of the predicted resistance was 4.36%. Although the above resistance models achieved good prediction accuracy, they all predicted the special point of insertion depth, ignored the characteristics of resistance change in time sequence, and could not achieve a prediction for the trend of resistance change.
For the characteristics of bucket insertion resistance, which is a timeseries and nonlinear, this study chooses to use the long short-term memory neural network (LSTM) as the basic model. LSTM is a classical method of deep learning [
12,
13], which addresses the problem of gradient disappearance or gradient explosion of recurrent neural networks [
14,
15]. LSTM can ascertain future data changes by historical timeseries data features, and has been widely used in many fields. Meanwhile, the introduction of the dropout layer in LSTM can effectively prevent overfitting in the training process [
16]. However, LSTM is highly sensitive to the number of hidden layer units, the initial learning rate, and the dropout probability, and different parameters will have a large impact on the prediction performance. The best number of hidden layer units, initial learning rate, and dropout probability are not the same for different training sets and samples [
17]. To address the shortcomings of LSTM, this paper combines particle swarm optimization (PSO) to optimize the above parameters. The PSO algorithm has the characteristics of fast searching speed, high efficiency, and easy convergence [
18,
19]. The model, by combining LSTM with PSO, has been applied to many fields. Ji et al. [
20] used a variational modal decomposition method to decompose the propagation loss of electromagnetic waves, and combined PSO and LSTM to achieve the prediction of electromagnetic wave propagation loss in ocean tropospheric ducts. Zhao et al. [
21] used LSTM as the basic model, combined with empirical modal decomposition and PSO, to achieve prediction for electric power fluctuations. The model improved the basis for improving the generator’s fluctuation compensation capability. Ren et al. [
22] developed a PSO-LSTM model to estimate the state-of-charge of lithium-ion batteries, and the error was within 5%. Yang et al. [
23] developed a glacier runoff prediction model by PSO-LSTM, and they used the Muzati River basin as the study object and achieved good prediction accuracy. Peng et al. [
24] analyzed and determined the input layer using the random forest method and the Pearson correlation coefficient method. The PSO-LSTM model was used to predict the ammonia concentration in a piggery and the
R2 achieved 0.9487. Song et al. [
25] constructed a PSO-LSTM model to predict short-term passenger flow in subway stations, and the prediction accuracy of PSO-LSTM is higher compared to LSTM. At the same time, the reasonable selection of characteristic data that can represent the trend of resistance changes assumes a high priority. Liao et al. [
26] proposed a method to calculate the resistance of an excavator by analyzing the relationship between the hydraulic cylinder, excavator bucket, and resistance. The resistance obtained by this method is closer to the actual value and can effectively reflect the dynamic process of the actual resistance during the excavation operation as well as the transient change in the actual resistance and the impact state. This provides a new idea for predicting the insertion resistance of wheel loaders.
In response to the above problems and discoveries, this study proposes a PSO-LSTM model to predict the magnitude and change trend of bucket insertion resistance. Three sets of experiments with different insertion depths of 600 mm, 800 mm, and 1000 mm were conducted in each of two typical piles, gravel and sand. The data relating to cylinder pressure, wheel loader displacement, and resistance were collected by sensors and measurement equipment in the wheel loader. A PSO-LSTM model with cylinder pressure data and insertion depth as the input layer and insertion resistance as the output layer was constructed. Different proportions of data were set as the training set, and good prediction results were achieved.
4. Results and Discussion
4.1. Results and Analysis
The experimental data were obtained from the gravel sample groups and the sand sample groups with insertion depths of 600 mm, 800 mm, and 1000 mm. A total of 50%, 60%, 70%, and 80% of the data were used as the training set, and the remaining 50%, 40%, 30%, and 20% of the data were used as the test set, respectively. To compare the prediction performance of PSO-LSTM, it was chosen to compare it with conventional LSTM, and the relevant parameters of the two model groups were set as shown in
Table 5.
In this paper, the root mean square error (
RMSE), the average relative error (
ARE), and the goodness of fit,
R2, are selected as the indexes to evaluate the prediction performance. The smaller the
RMSE and
ARE, the smaller the deviation between the predicted value and the true value, and the higher the prediction accuracy. The closer the value of
R2 is to 1, the higher the degree of fit and the better the prediction result. Its calculation formula is as follows:
where
yi is the true value,
is the predicted value,
is the average of the true value, and
n is the number of samples.
The prediction results of the LSTM and PSO-LSTM models are shown in
Figure 17,
Figure 18 and
Figure 19, respectively, for the insertion of gravel samples with depths of 600 mm, 800 mm, and 1000 mm.
The prediction performance indexes of LSTM and PSO-LSTM for gravel sample groups with insertion depths of 600 mm, 800 mm, and 1000 mm are shown in
Table 6, and the optimized parameters of PSO-LSTM are shown in
Table 7.
The prediction performance of the LSTM and PSO-LSTM models for inserting sand samples with depths of 600 mm, 800 mm, and 1000 mm are shown in
Figure 20,
Figure 21 and
Figure 22.
The prediction performance indexes of LSTM and PSO-LSTM for sand sample groups with insertion depths of 600 mm, 800 mm, and 1000 mm are shown in
Table 8, and the optimization parameters of PSO-LSTM are shown in
Table 9.
In the LSTM model, when the training samples are fewer, it is easy to create an error accumulation, and the later predicted values of the timeseries show a large deviation from the actual values. This is more obvious in the gravel sample groups, where the AREs of insertion depths of 600 mm, 800 mm, and 1000 mm are greater than 7% when the training set is 50%. In contrast, this value is relatively low in the sand sample groups, but the ARE is as high as 9.9% in the sample with an insertion depth of 1000 mm. The prediction accuracy is further improved with the increase in the number of training samples. When the training set reaches 80%, the ARE is only 2.56% in the sample with 800 mm insertion depth in the gravel experiment groups, but 7.18% in the sample with 600 mm insertion depth. While in the sand experiment groups, only the ARE of the sample with the 800 mm insertion depth reaches 4.06%, and the AREs of the other two groups are below 2.87%. In general, the LSTM model has poor robustness and low stability, which cannot meet the requirements of actual applications.
In the PSO-LSTM model, the prediction accuracy of all samples is improved over some range, even when the training set is sparser. The maximum value of ARE for the three samples in the gravel sample groups is 4.76% when the training set is 50%. When the training set is 80%, the maximum value of ARE is 2.28%. In the sand sample groups, when the training set is 50%, the maximum value of ARE for the three samples is 4.35%. When the training set is 80%, the maximum value of ARE is 1.14% and the minimum value is only 0.60%. Meanwhile, the R2 of both the gravel sample groups and the sand sample groups with different proportions of training sets is greater than 0.9, which indicates that the predicted values fit the actual values better. Moreover, the RMSE values also showed a significant decrease compared with the LSTM model.
Combining the data in
Table 7 and
Table 9, it can be seen that different initial learning rates, the number of hidden layer units, and dropout probability have a large impact on the prediction results. The initial learning rate set in the LSTM model is 0.01, which is a high value, and the reasonable setting interval should be between 0.001 and 0.003, as shown in
Table 7 and
Table 9. For the number of hidden layer units, the prediction performance is better when the setting is above 500. As for the dropout probability, there is no obvious setting method, which is related to the changing trend of the sample data and other parameter settings.
When the proportion of the training set is 80%, the resistance predicted by PSO-LSTM, the resistance calculated by empirical formula, and the true resistance for the gravel sample groups and the sand sample groups are shown in
Figure 23.
Both in the gravel sample groups and in the sand sample groups, it is obvious that there is a large deviation between the resistance calculated by the empirical formula and the true resistance. In particular, the insertion resistance of the wheel loader is unique each time, which makes it difficult to obtain a more accurate resistance by empirical formula. The resistance predicted by PSO-LSTM is closer to the true resistance and can reflect the trend of resistance changes well, which is not available for the empirical formula.
4.2. Discussion
In summary, the PSO-LSTM model developed in this study can predict the magnitude and trend of insertion resistance well, even when the training data are fewer, and considerable prediction results can be obtained. Moreover, the PSO-LSTM model has good stability, robustness, and generalization performance for various piles and insertion depths, which can reflect the change in insertion resistance of wheel loaders. This study provides a basis for subsequent research on the reduction in energy consumption of wheel loaders, energy-efficient operation, reasonable trajectory planning of shoveling, and operation in special operating environments.
The research in this paper also has certain shortcomings. The PSO-LSTM model built in this paper is optimized only for the initial learning rate, the number of hidden layer units, and dropout probability; however, the parameters affecting the prediction performance also include the maximum number of iterations, the number of generations of learning rate attenuation and the learning rate attenuation rate, etc., which can be tried to optimize these parameters. At the same time, increasing the number of LSTM layers can prevent the overfitting situation to a certain extent. In this paper, only a single-layer LSTM model is constructed from the perspective of computational efficiency, and changing the single-layer LSTM into a two-layer LSTM can be considered in the future. Meanwhile, only two typical piles, gravel and sand, are selected for experiments in this paper, and other kinds of piles are not tried, and conducting experiments in other special piles to verify the prediction performance of the model can be considered.