## 3 Definition of the Degradation Signal and Dataset Acquisition  
### Defining the Degradation Signal Based on Driven Current  
The health index signal needs to be defined before the state detection and RUL prediction of an HSV can be applied to the water hydraulic manipulator. The health index signal is a mathematical indicator that represents the condition of the HSV and should be easy to monitor in practice. These requirements exclude the electromagnetic force, the dynamic response time, and spool displacement. In contrast, the drive current can be considered as a fault detection signal since variation of the drive current can be easily monitored using a current sensor. In addition, the current signal curve of the HSV contains some of the information that can be used to determine HSV performance [42], as discussed below. Figure 4 shows the structure of the water hydraulic manipulator and the HSV. The HSV is directly driven by a voice coil motor (VCM). The working state of the HSV is controlled by controlling the state of the VCM. Figure 3: Working flow of ARIMA–LSTM models. Figure 5 shows the schematic diagram of the HSV current change and spool displacement curve. The working process of the HSV consists of four stages: (1) the actuation process; (2) the movement process; (3) the holding process; and (4) the release process. 1. [label=(0)]
2. Actuation process: A change in the control signal from low to high energizes the coil, causing the coil current to rise. However, the self-inductance does not allow the current to instantaneously stabilize. Electromagnetic force at this point is less than the friction force, the valve spool remains stationary, and there is a continuous increase in current. 3. Movement process: An increase in the current in the loop beyond a certain threshold, in combination with sufficient generation of electromagnetic force by the coil to overcome the friction force, allows the spool to start moving. During movement of the spool, the coil generates an induced electromotive force due to the action of the eddy current, and the rate of current increase in the loop gradually declines, and may even gradually decrease until the valve is fully open. As shown in Figure 5, when the current value in the loop reaches point A, the spool starts to move and the current decreases, whereas the spool displacement continues to increase. Maximum opening of the valve spool coincides with no changes in the coil air gap, and the current in the loop once again increases until it reaches stabilization. 4. Maintaining process: The spool is completely open when the current reaches point C, the air gap no longer changes, and the HSV reaches a balanced state while being energized. 5. Release process: The control signal changes from a high to low level when the current is at point D, the coil loses power, and the coil current begins to decrease. However, the spool remains in an open state. When the current in the circuit decreases to point E, the valve spool starts to move until the valve port is closed. An analysis of the relationship between the current of the HSV and the movement of the spool implied that the change in current in the loop during the operation of the HSV was different among the different stages. Moreover, degradation of the performance of the HSV was accompanied by a change in driving the current waveform. Therefore, the degradation of the HSV can be assessed by the characteristics of current change during each stage. The present study defined the distortion of the driving current curve as the  
Figure 4: Three-dimensional model. (**a**) Water hydraulic manipulator. (**b**) Water hydraulic HSV. Figure 5: Current variation and spool displacement curves. health index of the HSV. A template current waveform represented by \(I_{temp}\) was defined when the HSV started to work. \[I_{temp}=[i_{1}\ i_{2}\ i_{3}\ i_{4}\ \dots\ i_{n}] \tag{18}\]  
where \(i_{n}\) is the \(n\)th sample point of the template current waveform.