## 2 Establishing and Recognizing the Maneuver Intention of HGVs
### Parallel-Stacked LSTM Neural Network  
The LSTM algorithm solves the long-term dependency problem of the traditional RNN algorithm. Furthermore, the gate setting also effectively solves the gradient disappearance and gradient explosion problems. The LSTM algorithm is suitable for learning and memorizing the temporal relationships in long sequence data. To enrich the fitting ability of LSTM, three LSTM network layers are stacked into a multilayer network using multilayer neural networks. A multilayer LSTM network connected in series is called a single-channel LSTM network. The maneuver intention sequences of HGVs have a short-time strong correlation. However, the LSTM learns and remembers all the data input to the network, including the sequence of maneuver intentions for the full time of HGVs. To force the network to focus on the short-term interdependence between data without losing its long-term memory capability, single-channel LSTM networks are connected in parallel using multi-channel neural networks. The network structure of PSLSTM is shown in Figure 2.  
Figure 2: The parallel-stacked LSTM networks for intention recognition. PSLSTM network structure can be described as follows: Sequence data are input through the sequence layer and then connected to the stacked LSTM network, where the number of parallel networks \(P_{n}\) is a variable value. The sequence data are input in different ways for different \(P_{n}\). When \(P_{n}=1\), the network's input is \(Seq_{t}\), and the output is \(R_{t}\). It is the stacked LSTM network. Additionally, when \(P_{n}=2\), the input of the network not only includes \(Seq_{t}\), but \(Seq_{t-1}\) is inputted as the auxiliary data. \(Seq_{t-1}\) and \(Seq_{t}\) are input to the parallel network in turn. These two sequence data are pooled to \(FC_{4}\) after passing through different stacking networks, and the network results \(R_{t}\) are output after \(FC_{4}\) processing. When \(P_{n}=3\), the auxiliary data are \(Seq_{t-2}\) and \(Seq_{t-1}\), latter process is similar to \(P_{n}=2\). The fully connected layer (FC) is represented as:  
\[\iota =\text{FC}(Seq), \tag{9}\] \[=\text{tanh}(wSeq+b),\]  
where \(w\) and \(b\) are trainable parameters and \(Seq\) is the input sequence. The batch normalization layer is used to avoid the gradient disappearance problem and to reduce the probability of the overfitting phenomenon. With such a layer, the recognition network's generalization ability can also be improved. The mathematical description of the batch normalization layer is as follows:  
\[\iota_{bn}=BN(\iota) \tag{10}\] \[=\omega_{bn}\frac{\iota-\iota}{\sqrt{\sigma_{t}^{2}+\epsilon}}+b _{bn},\]  
where \(\iota\) is the input of the batch normalization layer; \(\iota\) and \(\sigma_{t}\) are the mean and standard deviation of \(\iota\), respectively; \(\omega_{bn}\) is the output of the batch normalization layer. Compared with traditional neural networks, in addition to the hidden layer state \(\iota_{n}\), LSTM networks maintain a cell form \(C_{n}\) for storing temporal association relations. The network updates the cytosolic state \(C_{k}\) through the forgetting and input gates. The network updates the cytosolic state \(C_{k}\) through the forgetting and input gates. The cytosolic state \(C_{n}\), the previous hidden layer state \(\iota_{n-1}\), and the current input \(Seq_{n}\) are integrated into the output gate to obtain the network output. With such a cell form, the network output can realize the recent temporal and long-term temporal relationship between memory and inference. In this paper, the LSTM layer is described as:  
\[[\iota_{n},C_{n}]=LS(\iota_{n-1},C_{n-1},Seq_{n}) \tag{11}\]  
where \(\iota_{n-1}\) and \(C_{n}\) are the previous hidden state and the cell state at the last moment, respectively; \(Seq_{n}\) is the current input sequence; and \(\iota_{n}\) and \(C_{n}\) are the hidden state output and the cell state output, respectively. The PSLSTM designed in this section is as follows:  
\[\left\{