**2. Background**

#### *2.1. Problem Statement*

The task of wheel loaders is to remove materials, including soil and rock, from a material pile to a nearby dumpsite or an adjacent load receiver in the sophisticated and changing working environment. There are many operation modes for wheel-loaders, including I, V, and T-shaped modes, depending on the route taken by wheel loaders during the loading operation. The difference in operation modes increases the difficulty of data analysis. For wheel-loaders, the V-cycle, which is the most common work cycle, is adopted in this experiment, as illustrated in Figure 1. The single V-cycle is divided into six phases, namely, V1 forward with no load (start and approach the pile), V2 bucket filling (penetrates the pile and load), V3 backward with a full load (retract from the pile), V4 forward and hoisting (approach the dumper), V5 dumping, V6 backward with no load (retract from the dumper), as shown in Table 1.

During the entire working cycle of wheel loaders, the operator needs to constantly modulate the throttle to control the movement of the wheel loaders. The throttle greatly determines the productivity and fuel efficiency during the operation of wheel loaders. When the throttle value is too high, wheel slipping will occur, resulting in a loss of traction as the driving force exceeds the adhesion. Wheel slipping damages tires and results in significant increases in operational cost. While the throttle value is too small, the speed of the vehicle will be lower, resulting in a loss of productivity. For the V-cycle of wheel loaders, the road adhesion coefficient is different for different phases. The quality of the vehicle will vary widely due to loading and dumping, which impacts the throttle value. Therefore, in the process of driving, experienced operators are required to perceive the environment information and select the appropriate throttle value. In this paper, the throttle value of the next moment is predicted.

Lift cylinder pressure, tilt cylinder pressure, engine speed and vehicle velocity are all crucial for wheel loaders. Lift cylinder pressure and tilt cylinder pressure can help to identify the working-cycle stages of wheel loaders. Engine speed and vehicle velocity play an important role in energy management. In this paper, the four parameters are called the state of wheel loaders, and every parameter has a corresponding prediction value. The state prediction is the basis of many control technologies, including model predictive control. The state of wheel loaders is affected by the operator's driving action and the environment, so the state prediction cannot only take their internal dynamics into account. In the operation process, in addition to the current state, operators usually need to consider the past actions and state of wheel loaders. Thus, the throttle value and state prediction of wheel loaders needs to consider the time series characteristics of the working process.

**Figure 1.** V-cycle of wheel loaders.

**Table 1.** V-cycle grouping.


#### *2.2. LSTM Network*

Deep learning models automatically learn multiple levels of representations and abstractions from the data [37], which solves the problem that features need to be manually designed in traditional machine learning. Recurrent neural network (RNN) is a type of neural network specialized for the processing of sequence data. However, in practice, a simple RNN cannot cope with the challenge of long-term dependence.

The most efficient sequence model used in practical applications is called gated RNN, which is based on the idea of creating paths through time that have derivatives that neither vanish nor explode. Long short-term memory (LSTM) [38] is a type of gated RNN and a popular solution for processing sequence data. It has been shown to learn long-term dependencies more easily than simple recurrent architectures through gating

units. Compared to the gated recurrent unit (GRU), a simpler gated RNN, LSTM is more powerful and more flexible, since it has three gates instead of two. Thus, LSTM is applied in this paper.

The LSTM block diagram is illustrated in Figure 2. The most crucial component of LSTM is the cell state, which is the horizontal line running through the top of the figure, making it easy for information to flow without changing. LSTM's ability to remove or add information to the cell state is controlled by the structure called gates. Gates consisting of a sigmoid neural net layer and a pointwise multiplication operation can selectively let information through. The first step of LSTM is to determine which information is discarded from the cell state. This decision is made by the forget gate, which outputs a number between 0 and 1 for each number in the previous cell state. Second, the new information that will be stored in the cell state needs to be determined. The input gate determines which values will be updated and a tanh layer creates a vector of new candidate values that could be used to update the current cell state. Finally, the current cell state and output gate are used to output the hidden state. The process of LSTM can be expressed as follows:

$$\mathbf{i}\_{l} = \text{sigmoid}(\mathcal{W}\_{l} \cdot [\mathbf{x}\_{l}, \mathbf{h}\_{t-1}] + \mathbf{b}\_{l}) \tag{1}$$

$$f\_t = \text{sigmoid}\left(\mathcal{W}\_f \cdot [\mathbf{x}\_t, h\_{t-1}] + b\_f\right) \tag{2}$$

$$\mathbf{g}\_t = \tanh\left(\mathcal{W}\_{\mathcal{K}} \cdot [\mathbf{x}\_t, \mathbf{h}\_{t-1}] + \mathbf{b}\_{\mathcal{K}}\right) \tag{3}$$

$$\rho\_t = \text{sigmoid}(\mathcal{W}\_0 \cdot [\mathbf{x}\_t, h\_{t-1}] + b\_o) \tag{4}$$

$$c\_t = f\_t \* c\_{t-1} + i\_t \* g\_t \tag{5}$$

$$h\_t = o\_t \* 
tanh(c\_t) \tag{6}$$

where *ht*, *ct* and *xt* represent the hidden states, cell state and the input sequence of LSTM at time *t*, respectively. *it*, *ft* and *ot* represent input gate, forget gate and output gate, respectively. *W* and *b* represent the weights and bias , respectively. *ct* and *gt* represent cell state at time *t* and candidate cell state at time *t*. ∗ is the element-wise product.

**Figure 2.** Illustration of Long short-term memory (LSTM).
