## 1 Introduction  
One of the primary causes of traffic accidents involving automated vehicles is reduced or lost driver's vigilance [1, 2]. When a vehicle operates in automatic mode, the driver must monitor it for extended periods. This task is usually low-demand, especially when the system runs smoothly with minimal driver intervention. Such monotony often leads to decreased vigilance. Reduced vigilance can lead to diminished responses to unexpected issues, characterized by decreased attention, slower information processing, prolonged reaction times, and impaired operational skills [3]. Therefore, identifying driver's vigilance in automated vehicles is crucial to reducing traffic accidents. Vigilance is a key application of signal detection theory [4]. Driver's vigilance refers to the driver's performance in monitoring the driving task, including their ability to detect and respond to potentially dangerous signals [5]. Many studies have examined changes in driver's vigilance when the allocation or use of cognitive resources are disturbed [6, 7, 8]. According to the multi-resource theory, workload is a crucial indicator of how well task demands align with individual cognitive resources [9, 10]. Workload is defined as the psychological and physical effort required to accomplish a task [9]. This effort is influenced by task duration [11], task demands [12], and participation frequency [13]. Lengthy, demanding, or infrequently performed tasks can lead to a decline in vigilance. Drivers in automated vehicles typically perform monitoring tasks that are long in duration, low in demands, and require infrequent engagement. The measurement of driver's vigilance can be divided into two categories: scale measurement and behavioral measurement. Common scales include the NASA Task Load Index Scale [14] and the Karolinska Sleepiness Scale [15]. A common behavioral measure is the Detection-Response Task (DRT) [16]. Studies have assessed vigilance using driver reaction times [17] or error rates [18] in the DRT. The recognition of driver vigilance in autonomous vehicles primarily depends on the analysis of facial gestures and electrophysiological signals, captured from participants in both real-world [19; 20; 21; 22; 23] and virtual reality (VR) environments [24; 25]. Facial posture-based recognition focuses on physical responses like eye states [19], facial expressions [20], and head movements [21]. For physiological signals, electroencephalograms (EEGs) and electrocardiograms (ECGs) are commonly used. [PERSON] et al. [22] explored the relationship between vigilance and EEG signals, finding significant variations in the power ratios of different EEG bands across vigilance states. [PERSON] et al. [23] detected driver's vigilance by combining heart rate with eye-width ratio. Current driver's vigilance recognition techniques primarily rely on machine learning architectures [26; 27]. [PERSON] et al. [17] developed a manual driving vigilance recognition model based on least-squares support vector machine and particle swarm optimization using fused EEG and driving contexts. [PERSON] et al. [28] proposed a two-layer learning method using EEG data for automated driving modes. However, most existing studies focus on a single driving mode and do not consider scenarios where manual and automated driving coexist within the same vehicle. [PERSON] and [PERSON] [29] and [PERSON] [30] argue from the perspectives of road safety and personal preference, respectively, that manual and automated driving modes will coexist in the same vehicle before fully automated driving is realized. However, significant changes in drivers' physiological signals have been identified between automated and manual driving. [PERSON] et al. [31] observed that drivers' blink frequency and blink duration were higher during automated driving than manual driving. [PERSON] et al. [32] found that the percentage of drivers' safety-relevant AOI gaze was higher during low-speed driving in manual driving and higher in high-speed driving in automated driving.