## 2 Algorithm and Methodology
### Sliding Window Model
However, in a fatigue state [see Figure 8b], the troughs in the \(\eta_{NAE}\) values become more frequent, reflecting the true physiological state of fatigue. As illustrated in Figure 8c, an enlarged view of one \(\eta_{NAE}\) wave indicates that, under normal open-eye conditions, the \(\eta_{NAE}\) values fluctuate randomly within a narrow range of 0.20 to 0.26. However, when the eyes are closed or blinking, the \(\eta_{NAE}\) values sharply drop to around 0.13 but return to the original level once the eyes open. In summary, blink detection can be achieved by calculating the \(\eta_{NAE}\) values. Similarly, the \(\eta_{NAM}\) values indicate the mouth's open or closed state, as shown in Figure 8d. Minor fluctuations around the 0.15 mean line represent a closed mouth state,

Figure 8: Changes in fatigue-related indices and corresponding details over a sliding window of 1800 frames. (**a**) \(\eta_{NAE}\) in the awake state. (**b**) \(\eta_{NAE}\) in the fatigue state and (**c**) the detail of \(\eta_{NAE}\)-Blinking. (**d**) \(\eta_{NAM}\) in the awake state and (**e**) the detail of \(\eta_{NAM}\)-Speaking. (**f**) \(\eta_{NAM}\) in the fatigue state and (**g**) the detail of \(\eta_{NAM}\)-Yawning. (**h**) \(\text{HEA}\alpha\) in the awake state. (**i**) \(\text{HEA}\alpha\) in the fatigue state and (**j**) the detail of \(\text{HEA}\alpha\)-Nodding. while significant jumps in the \(\eta_{NAM}\) values occur during talking and yawning. The duration and amplitude of the value increase reflect the differences between normal open-mouth states (such as speaking) and physiological signs of fatigue. When yawning, the peaks in the \(\eta_{NAM}\) values last longer (over 80 frames) and have greater amplitude. Figure 8e,g detail the changes in \(\eta_{NAM}\) values during talking and yawning, respectively. This demonstrates that the \(\eta_{NAM}\) values differentiate between normal and fatigue states. Generally, when a person is awake, the head posture remains within a limited range of motion angles, whereas involuntary nodding occurs when feeling fatigued. This is well demonstrated in Figure 8h,i, where the HEA\(\alpha\) curves in the fatigued state show more frequent instances of HEA\(\alpha\) exceeding the threshold. Figure 8j captures a segment of the HEA curve during nodding, revealing that the HEA\(\alpha\) values fluctuate within a larger range, with more frequent fluctuations in the fatigued state. ### Fatigue State Changes in Driving Experiments

Figure 9 illustrates the changes in fatigue states among 12 participants from Groups A, B, and C over the course of a 30 min simulated driving experiment. The sessions were conducted during both afternoon and late-night periods. Most participants assigned to the afternoon sessions (Participants \"a, d, e, f, i, l\") were in an alert state at the beginning of the experiment and gradually progressed to mild or moderate fatigue. In contrast, participants tested at late-night (Participants \"b, c, g, h, j, k\") generally exhibited mild or even moderate fatigue from the outset due to reduced physiological alertness. Overall, fatigue levels increased progressively as the experiment proceeded. Several individuals showed distinct fatigue progression patterns. For instance, Participant \"e\" exhibited a rapid transition from an alert state to mild fatigue, eventually progressing to moderate fatigue, indicating a continuous accumulation of fatigue. In contrast, Participant \"j\" showed a temporary decrease in fatigue level during the middle stage of the experiment, which may suggest a brief recovery or self-regulation phase. These observations highlight the influence of the time of day on fatigue development and emphasize the significant inter-individual variability in fatigue progression. To evaluate the system's ability to distinguish between multiple fatigue severity levels, a multi-class classification experiment was conducted based on data from 12 participants across six time points during a 30 min simulated driving task (72 total samples).