Fatigue Estimation Using Peak Features from PPG Signals

: Fatigue is a prevalent subjective sensation, affecting both office workers and a significant global population. In Taiwan alone, over 2.6 million individuals—around 30% of office workers— experience chronic fatigue. However, fatigue transcends workplaces, impacting people worldwide and potentially leading to health issues and accidents. Gaining insight into one’s fatigue status over time empowers effective management and risk reduction associated with other ailments. Utilizing photoplethysmography (PPG) signals brings advantages due to their easy acquisition and physio‑ logical insights. This study crafts a specialized preprocessing and peak detection methodology for PPG signals. A novel fatigue index stems from PPG signals, focusing on the dicrotic peak’s posi‑ tion. This index replaces subjective data from the brief fatigue index (BFI)‑Taiwan questionnaire and heart rate variability (HRV) indices derived from PPG signals for assessing fatigue levels. Correla‑ tion analysis, involving sixteen healthy adults, highlights a robust correlation (R > 0.53) between the new fatigue index and specific BFI questions, gauging subjective fatigue over the last 24 h. Drawing from these insights, the study computes an average of the identified questions to formulate the eval‑ uated fatigue score, utilizing the newfound fatigue index. The implementation of linear regression establishes a robust fatigue assessment system. The results reveal an impressive 91% correlation co‑ efficient between projected fatigue levels and subjective fatigue experiences. This underscores the remarkable accuracy of the proposed fatigue prediction in evaluating subjective fatigue. This study further operationalized the proposed PPG processing, peak detection method, and fatigue index us‑ ing C# in a computer environment alongside a PPG device, thereby offering real‑time fatigue indices to users. Timely reminders are employed to prompt users to take notice when their index exceeds a predefined threshold, fostering greater attention to their physical well‑being.


Introduction
"Fatigue" is a subjective feeling that everyone experiences. Fatigue slows down the brain's ability to respond to stimuli, reduces personal performance, concentration, and judgment, and causes negative emotional reactions. These effects can lead to accidents. In Taiwan, knowledge about fatigue is still limited. According to a report from the Department of Health (Taipei city government), approximately 30% of office workers in Taiwan (more than 2.6 million people) suffer from chronic fatigue. Furthermore, fatigue is not limited to just workers; it can affect everyone. Fatigue can arise from factors such as insufficient sleep and heavy workloads and may even be attributed to conditions like chronic fatigue syndrome or cancer [1]. If people can understand their fatigue condition well over a long period of time, they can not only adjust their fatigue well but also reduce the occurrence of complications from other diseases and accidents.
Heart rate variability (HRV) is a widely utilized method for assessing levels of fatigue [2][3][4]. In order to compute HRV indices, many studies initially employ a specialized device to measure the electrocardiogram (ECG) at three specific points, utilizing conductive glue as the conducting medium. One electrode patch is directly attached to the uncovered chest area, minimizing interference from clothing. The other two measurement sites are confined to the chest and hands. Subsequently, peak detection techniques can be applied to identify intervals between successive heartbeats, enabling the derivation of HRV values [5,6]. The ECG was susceptible to power noise and electromagnetic interference (EMI) during the measurements, thus resulting in an inaccurate analysis of the HRV [7]. Power noise and EMI disrupt the ECG signal, distorting it and introducing unwanted signals. This can obscure R-wave peaks crucial for HRV analysis and complicate interval measurement. Furthermore, HRV assessment was vulnerable to external influences. Changes in breathing patterns, increased parasympathetic nerve activity due to relaxation, or variations in current mood could hinder the clear responsiveness of HRV indices to fatigue [8,9]. Factors such as physical activity [10], caffeine and medications [11], stress and emotional state [12], as well as underlying health conditions [13], all have the potential to affect the precision of HRV measurements.
In recent years, optoelectronic and electronic technologies have advanced, and photoplethysmography (PPG) is a commonly used method to determine the condition of blood vessels. With a combination of an appropriate preprocessing of the PPG signal and an artificial intelligence (AI) algorithm, the variables for calculating physiological parameters can be obtained, including heart rate [14,15], blood pressure [16], blood oxygen saturation levels (SpO 2 ) [17], biometric identification [15], and epileptic seizure detection [18]. Thus, the utilization value of the PPG signal is very high. The measurement of PPG does not require complex algorithms and devices. A PPG signal is convenient to detect, safe, and free of cross-infection. PPG signals provide people with a non-invasive measurement method and are a simple and effective method for monitoring human physiological signals. Although several previous studies adopted PPG to observe the fatigue index [19][20][21], most of them used PPG to calculate the HRV index and then found the relationship between HRV and fatigue. Thus, even after the use of PPG to calculate HRV, certain problems related to HRV descriptions were still encountered [8,9].
When blood circulation is not smooth, metabolic waste accumulates in blood vessels, stimulates nerve endings, and causes fatigue [22,23]. In such a case, PPG can be adopted to observe the temporal intravascular blood volume changes [24] and assess the microcirculation and intravascular fluid volume [25]. The motivation behind this study was to assess and formulate novel fatigue indices utilizing PPG signals, with a specific focus on analyzing fatigue based on the position of the dicrotic peak. The primary objectives included examining the correlation between various fatigue indices (such as HRV indices and the newly proposed fatigue index) and fatigue levels as measured through questionnaires. This analysis aimed to identify the types of indices that are most appropriate for effectively analyzing and evaluating fatigue.
The aim of this study was to substitute the fatigue index using PPG signals for the subjective data obtained from the (BFI)-Taiwan form and the HRV indices obtained from PPG signals to analyze fatigue and develop a fatigue evaluation system. Commercially available instrumentation (COMGO, Giant Power Technology Biomedical Corp, New Taipei City, Taiwan [26]) was adopted to collect the signals considered in this study. The measurement data were transmitted to the computer through the universal serial bus (USB), and the proposed fatigue evaluation system was implemented using C# code executed in a computer environment. Thus, the system could automatically analyze the fatigue value; these results could be used to further prevent fatigue-related problems.

Related Works
Fatigue exerts a profound influence on both physical and mental well-being. Prior research consistently underscores the detrimental implications of fatigue on health [27][28][29].
Recognizing the critical nature of fatigue assessment, if individuals can gain an extensive comprehension of their fatigue levels over an extended period, they can adeptly regulate their fatigue and potentially curtail the likelihood of complications arising from other ailments and accidents. Consequently, a plethora of subjective questionnaires have been devised to facilitate users' direct comprehension of their fatigue status. Nonetheless, concerns often arise regarding the subjectivity of such questionnaires, raising questions about their objectivity and scientific validation. In response, recent times have witnessed the emergence of diverse methodologies that synergize varied physiological signals with AI technology to comprehensively assess fatigue. The subsequent sections expound on the distinct approaches employed for fatigue evaluation.

Subjective Fatigue Questionnaires
Subjective fatigue questionnaires involve assessing fatigue levels across various scenarios and timeframes using a series of questions. Below are several commonly used questionnaires for measuring fatigue, accompanied by brief explanations: A. Brief Fatigue Index (BFI) [30]: A widely employed questionnaire assessing participants' fatigue levels within the previous 24 h; B. Beck Fatigue Inventory (BFI) [31]: Evaluates subjective fatigue sensations and quality of life, suitable for diverse populations; C. Fatigue Severity Scale (FSS) [32]: Quantifies the severity of fatigue and helps discern if fatigue impacts daily activities; D. Multidimensional Fatigue Inventory (MFI) [33]: Assesses fatigue perceptions across various dimensions, including physical, emotional, cognitive, and activityrelated aspects; E. Beijing Fatigue Questionnaire (BFQ) [34]: A Chinese questionnaire gauging the impact of fatigue on quality of life; F.
Fatigue Symptom Inventory (FSI) [35]: Evaluates different fatigue symptoms and impacts, applicable across various medical conditions; G. Amsterdam Fatigue Questionnaire (AFQ) [36]: Designed for cancer patients, this questionnaire measures the frequency and severity of fatigue.
While subjective fatigue questionnaires are advantageous for assessing fatigue levels, they also possess limitations. These questionnaires directly capture participants' subjective perceptions of fatigue, providing insights into individual fatigue during specific timeframes. However, such subjective assessments can be influenced by participants' emotions and subjective biases, potentially introducing errors. Additionally, linguistic and cultural factors may impact the questionnaires' applicability, requiring cross-cultural adaptation and validation for effectiveness. Importantly, these questionnaires extend beyond office workers, finding relevance among diverse global populations. In Taiwan, for instance, around 30% of over 2.6 million office workers experience chronic fatigue. Yet fatigue transcends workplaces, affecting people worldwide and contributing to health issues and accidents. Understanding individuals' fatigue states supports effective fatigue management and mitigates risks associated with other health conditions. While fatigue measurement questionnaires have strengths, they also face limitations. Reliance on participants' reports may introduce subjective errors due to individual perceptions and emotions. Some questionnaires rely on recalling fatigue experiences, subject to memory biases. Furthermore, lifestyle factors like insufficient sleep or high workloads might not be fully considered, impacting fatigue assessment. Language and cultural nuances may affect questionnaires' applicability, necessitating adaptation and validation across diverse cultures.
In conclusion, fatigue measurement questionnaires offer valuable tools but require careful consideration of their limitations. To comprehensively assess fatigue, integrating objective physiological signals may yield more precise results.

Objective Physiological Signals
The evaluation of fatigue using objective physiological signals encompasses a range of methods that provide quantifiable insights into the body's response to fatigue. These approaches offer an invaluable alternative to subjective measures and play a pivotal role in unraveling the intricate interplay between fatigue and physiological changes.
Among these methods, heart rate variability (HRV) stands out as a prominent and widely used approach [2][3][4]. HRV leverages the variations in time intervals between heartbeats to gauge the activity of the autonomic nervous system. As fatigue can exert an influence on autonomic function, HRV serves as a sensitive indicator of fatigue levels and regulatory dynamics.
Skin Conductance [37], another method, involves the measurement of changes in electrical conductivity in response to stress and emotional states. Fatigue-induced alterations in skin conductance provide direct insights into the physiological impact of fatigue on the body's stress response.
Electroencephalogram (EEG) recordings capture the electrical activity of the brain and offer insights into attention, focus, and cognitive states [38,39]. Changes in EEG patterns due to fatigue signify cognitive fatigue and serve as a valuable metric for evaluating mental fatigue. Furthermore, brainwave signal analysis, encompassing various frequencies like alpha, beta, delta, and theta, reveals changes associated with attention, relaxation, and concentration [40]. Brainwave signals furnish an objective measure of cognitive fatigue.
Electromyography (EMG), used to assess muscle fatigue, captures electrical signals generated by muscles during contraction [41]. This method is particularly valuable in studies involving physical tasks and sports-related fatigue, providing objective data on muscle fatigue levels.
Pupillary response analysis involves monitoring changes in pupil size in response to light variations, offering insights into attention and cognitive states [42]. These responses mirror the effects of fatigue on cognitive functioning.
These objective physiological signaling methods transcend the limitations of selfreported questionnaires by providing quantifiable metrics. They bridge the gap between subjective experience and objective assessment, offering a deeper understanding of how fatigue impacts various bodily functions. By decoding these signals, researchers gain crucial insights into the intricate connections between fatigue and physiological responses, facilitating informed interventions and effective management strategies. Among these methods, HRV is extensively utilized in fatigue assessment due to its sensitivity to changes in the autonomic nervous system, which are influenced by fatigue. Fatigue can impact the functionality of the autonomic nervous system, leading to fluctuations in HRV. Consequently, HRV serves as a reliable indicator of an individual's fatigue levels, making it a valuable tool in fatigue evaluation.
HRV can be derived from both ECG [5,6] and PPG signals [43,44]. The ECG measures the electrical activity of the heart, providing precise information about the intervals between consecutive heartbeats. On the other hand, PPG records changes in blood volume and blood flow by analyzing the variations in light absorption or reflection, usually from a fingertip or wrist. Both ECG and PPG can be employed to calculate HRV, which involves analyzing the time intervals between successive heartbeats. HRV is a valuable indicator of the autonomic nervous system's activity and balance, reflecting the dynamic interplay between the sympathetic and parasympathetic branches. By assessing HRV from ECG or PPG signals, researchers gain insights into how the autonomic nervous system responds to various physiological and environmental factors, including fatigue. The choice between ECG and PPG for HRV analysis often depends on the study's objectives, the availability of equipment, and the desired level of accuracy. ECG is considered the gold standard for HRV analysis due to its direct measurement of electrical activity, but PPG offers a more convenient and non-invasive alternative. Both methods contribute significantly to the understanding of fatigue and its physiological implications, enhancing the spectrum of tools available for fatigue assessment and management.
However, the susceptibility of ECG and PPG to power noise and electromagnetic interference (EMI) hampers accurate heart rate variability (HRV) analysis [7,45]. Power noise and EMI disrupt the ECG signal, distorting it and introducing unwanted signals. This can obscure peaks crucial for HRV analysis and complicate interval measurement. EMI further weakens the signal, introduces artifacts, and distorts the ECG and PPG waveforms, undermining HRV calculations. Inaccurate HRV analysis due to these disruptions can misinterpret autonomic nervous system activity, impacting fatigue assessment and physiological insights. The PPG method is relatively easier to implement, as PPG signals can be obtained without the need for electrode patches and typically only require placing a sensor on the skin. This approach is cost-effective and more convenient to execute, making it potentially more straightforward to calculate HRV in certain scenarios. As mentioned above, PPG signals can also be affected by power noise and EMI, leading to signal interference and distortion. To mitigate these interferences and analyze ECG and PPG features, the use of appropriate filters is necessary to ensure that the signals obtained from PPG are stable and accurate.
Even with careful acquisition of ECG or PPG signals and precise HRV calculation, various factors (such as respiration, physical activity, caffeine and medications, stress, and emotional state, as well as underlying health conditions) can influence the accuracy of HRV measurements [8][9][10][11][12][13]. For instance, physical activity introduces variability as movement and exertion can alter heart rate variability, while respiration patterns, particularly during deep or rapid breathing, can impact HRV measurements.
When blood circulation is obstructed or compromised, metabolic waste products can accumulate within blood vessels, stimulating nerve endings. This condition may lead to a sensation of fatigue. This phenomenon is known as lactic acidosis or tissue hypoxia. During this process, metabolic waste products like lactic acid accumulate in tissues, potentially stimulating pain receptors and affecting nerve transmission, thereby resulting in feelings of fatigue or discomfort [22,23]. The status of blood vessel circulation can be observed using PPG technology to monitor changes in blood volume within vessels [24,25]. Charlton et al. conducted a study to evaluate the efficacy of various features within the PPG pulse wave for assessing mental stress [46]. The findings from their study emphasized that the crest time (duration from pulse onset to peak) and diastole duration (duration from dicrotic notch to pulse end) emerged as viable options for stress assessment. Additionally, the analysis suggested that the radial artery was more suitable for stress assessment compared to the brachial or temporal arteries. Enhancing performance might involve combining crest time and diastole duration with other attributes derived from the second derivative of the PPG, which remains unaffected by heart rate variations. PPG has diverse clinical applications, including physiological monitoring (oxygen saturation, heart rate, blood pressure, respiration), vascular assessment (arterial health, compliance, endothelial function, microvascular flow), and autonomic function evaluation (vasomotor activity, blood pressure, heart rate variability). PPG's pulse wave characterization reveals these associations [47]. Therefore, this study departs from using the HRV method and instead examines the position of the dicrotic peak, which appears to vary under different fatigue states. Thus, the position of the dicrotic peak is used to define the fatigue index. Figure 1 shows the overall workflow of this study. In this study, the subjective fatigue scores were derived from the BFI Taiwan questionnaire, while PPG signals were captured using the COMGO measurement device. Subsequently, to address potential noise interference and individual variations inherent in PPG signals during measurements, a preprocessing step was employed to suppress signal noise and standardize the data. Following preprocessing, the signals underwent the peak detection methods introduced in this paper to identify key points-pulse onset, systolic peak, dicrotic notch, and diastolic peak-for each cycle within the PPG signal. Once these four distinctive points were established for each PPG cycle, the systolic peak was utilized to define the HRV index, whereas the diastolic peak and systolic peak were employed to define the proposed fatigue index. Subsequent to this, the relationship between NHF within the HRV index, the proposed fatigue index, and the subjectively assessed fatigue state gleaned from the questionnaire was evaluated using the correlation coefficient. Utilizing the correlation coefficient, this study determined which subjective fatigue items in the questionnaire exhibit strong correlations with the NHF and the proposed fatigue index. Given the questionnaire's multiple fatigue feedback items, this step aimed to identify those most closely aligned with the NHF and the proposed fatigue index. Subsequently, a linear regression analysis was conducted to establish a model wherein the corresponding subjective fatigue state is the output, while NHF and the proposed fatigue index serve as inputs. This model offers flexibility to predict the subjective fatigue state using either the NHF or the proposed fatigue index. Furthermore, the correlation coefficient was employed to assess the relationships between predicting the subjective fatigue state using either the NHF or the proposed fatigue index and the actual subjective fatigue state. This evaluation helps discern which index is better suited for predicting the subjective fatigue state. The resultant linear regression function was then translated into a C# implementation, giving rise to a real-time fatigue analysis system that facilitates on-the-fly assessment of fatigue levels. Subsequent sections of this paper will provide detailed elaborations on each of these methods.

Participants
Sixteen healthy adults (16 males, ages: 22-24) participated in this study. None of the participants had chronic illnesses or sleep disorders. The Institutional Review Board of the National Yang Ming Chiao Tung University approved the experimental protocol (NCTU-REC-109-001F) used in this study. None of the participants were aware of the hy-

Participants
Sixteen healthy adults (16 males, ages: [22][23][24] participated in this study. None of the participants had chronic illnesses or sleep disorders. The Institutional Review Board of the National Yang Ming Chiao Tung University approved the experimental protocol (NCTU-REC-109-001F) used in this study. None of the participants were aware of the hypotheses being tested. All of the participants provided their informed consent prior to any experimentation. The experiment took place in the afternoon (2-3 PM). The tester explained the measurement questionnaires: Brief fatigue index (BFI)-Taiwan form [30]. Once the participants understood the content of these questionnaires, they could fill them out easily. Next, the tester explained the operation mode of the cardiovascular measuring instrument and let the participants understand how to use the instrument to measure the PPG signals in order to avoid the possible termination of the experiment caused by the participants' lack of understanding of how to use it. Before measuring the PPG signals, the participants were asked to rest for 5-10 min until they felt relaxed.
This study was to represent an initial exploration of the relationship between novel fatigue indices derived from PPG signals, with a specific emphasis on assessing fatigue based on the position of the dicrotic peak. In the future, we aim to expand the scope of our research by including a broader range of age groups and gender diversities, thereby enhancing the comprehensiveness of our analysis.

Data Acquisition
Two types of data were considered in this study: behavior data and PPG signals. The behavior data were the subjective data obtained from a brief fatigue index (BFI)-Taiwan questionnaire [30]. The PPG signals were the objective data measured using the COMGO device (Giant Power Technology Biomedical Corp., New Taipei City, Taiwan [26], Taiwan Food and Drug Administration No. 007249) and adopted to develop the objective index for fatigue. Behavior data encompassed subjective assessments of fatigue levels across various situations and time periods through questionnaires. In contrast, PPG signals were employed to capture physiological indices, encompassing HRV indices and a newly proposed fatigue index in this study. The novel fatigue index was defined based on the position of the dicrotic peak. Subsequently, a sequential analysis can be conducted to determine the physiological indices that exhibit correlations with fatigue.

Behavior Data
This study adopted the brief fatigue index (BFI)-Taiwan questionnaire [30] to evaluate the subjective fatigue state. The BFI questionnaire is a simple survey used to assess individuals' fatigue levels in different situations and time periods. Its design aims to rapidly collect participants' subjective fatigue perceptions, allowing for a quick and convenient quantification of their fatigue levels. Additionally, since the participants are all Taiwanese, the questionnaire is more easily understood by them due to its content being tailored to their cultural context. The aim of this study was to determine the type of features that could reflect the fatigue status of the previous day. In the BFI-Taiwan form [30], there were nine questions in all, as shown in Table 1. Each question was assigned a score of 0 to 10 for the subject to choose, and the grading standard is presented in Table 2. The definitions presented in Tables 1 and 2 originate from the BFI-Taiwan form itself [30]. However, considering that the questionnaire is in Chinese, this study has undertaken the task of translating the content into English to facilitate readers' comprehension.  Taiwan Form   1 Current level of fatigue 2

Item Questions in BFI-
Level of general fatigue in the past 24 h 3 Level of most exhaustion in the past 24 h 4 Fatigue affects the level of general activity in the past 24 h 5 Fatigue affects the level of mood in the past 24 h 6 Fatigue affects the level of walking ability in the past 24 h 7 Fatigue affects the level of Daily work (including going out to work and housework) in the past 24 h 8 Fatigue affects the level of social interaction in the past 24 h 9 Fatigue affects the level of enjoyment of life in the past 24 h Moderately tiring and tolerable (tired for about half the time) 7-9 Quite tired (feeling tired most of the time) 10 Very tired (feeling tired all the time)

PPG Signals
In this study, the COMGO device was used to measure the PPG signals for 2 min at a sampling rate of 200 Hz. In the Taiwanese market, wearable devices with comprehensive physiological sensing are rare. The COMGO device stands out by merging smart health bracelet features and offering various functions. Unlike similar products focusing on heart rate alone, COMGO encompasses blood pressure, oxygen levels, body temperature, ECG, and vascular elasticity monitoring. Utilizing simultaneous finger artery measurements for PPG signals, it transmits data via Bluetooth to a smartphone, then to the cloud via a network (4G, 5G, or Wi-Fi). Portable and compact, COMGO enables convenient and rapid PPG measurements, vital for identifying fatigue-related traits.

PPG Preprocessing
When measuring PPG signals, it is possible to encounter various types of noise. These noises can originate from multiple sources, including environmental, physiological, and equipment-related factors, resulting in abnormalities or variations in PPG signals [48,49]. Therefore, during the processing and analysis of PPG signals, appropriate data preprocessing and filtering methods are necessary to mitigate the impact of these noises on the results. In this study, the received PPG signals (Figure 2a) were sequentially processed by using a bandpass filter from 0.5 to 8 Hz in order to remove the DC offset and the PPG drift that occurred when the fingers were shaking ( Figure 2b) and normalized, which set the value of the filtered PPG signal to be in the range of −1 to 1 (Figure 2c) [50]. Figure 2b shows that the filter frequency between 0.5 Hz and 8 Hz could not only eliminate the drift voltage but also maintain the amplitude of the original signal [50]. The signals at other frequencies would have the same obvious attenuation. After filtering the PPG signal, the mean normalization method was employed for subsequent analysis and comparison. This step aimed to confine the amplitude range of each individual's PPG signal between −1 and 1, thereby addressing the significant data gap [51,52] as outlined by Equation (1): where x max indicates the maximum of the filtered PPG signal, and x min represents the minimum of the filtered PPG signal.  Figure 2b shows that the filter frequency between 0.5 Hz and 8 Hz could not only eliminate the drift voltage but also maintain the amplitude of the original signal [50]. The signals at other frequencies would have the same obvious attenuation. After filtering the PPG signal, the mean normalization method was employed for subsequent analysis and comparison. This step aimed to confine the amplitude range of each individual's PPG signal between −1 and 1, thereby addressing the significant data gap [51,52] as outlined by Equation (1): where indicates the maximum of the filtered PPG signal, and represents the minimum of the filtered PPG signal.

Peak Detection Methods
When the preprocessing was completed, the peak of the PPG signal was captured using the proposed peak detection method. The definition of a cycle in the PPG signal was from the beginning of the heart contraction to the next contraction. That is, the time period between two adjacent troughs in each cycle. In order to capture the physiological information from the PPG signal, it was necessary to calculate the positions of the pulse onset, systolic peak, dicrotic notch, and diastolic peak in each cycle.

Systolic Peak
PPG was a continuous and fixed-frequency signal, therefore requiring the definition of how to calculate a computing cycle interval while simultaneously encompassing pulse onset, systolic peak, dicrotic notch, and diastolic peak. The highest peak in a single-cycle PPG signal was the systolic peak. This peak was formed by the direct transmission of the pressure of the cardiac contraction to the end of the measuring device, which resulted in

Peak Detection Methods
When the preprocessing was completed, the peak of the PPG signal was captured using the proposed peak detection method. The definition of a cycle in the PPG signal was from the beginning of the heart contraction to the next contraction. That is, the time period between two adjacent troughs in each cycle. In order to capture the physiological information from the PPG signal, it was necessary to calculate the positions of the pulse onset, systolic peak, dicrotic notch, and diastolic peak in each cycle.

Systolic Peak
PPG was a continuous and fixed-frequency signal, therefore requiring the definition of how to calculate a computing cycle interval while simultaneously encompassing pulse onset, systolic peak, dicrotic notch, and diastolic peak. The highest peak in a single-cycle PPG signal was the systolic peak. This peak was formed by the direct transmission of the pressure of the cardiac contraction to the end of the measuring device, which resulted in the maximum volume and blood flow in the artery. The systolic peak was a representative feature point in the PPG signal. Furthermore, the cycle had to be defined first to obtain the systolic peak. This study adopted the derivative-based approach by identifying the zero crossing points [53,54] to evaluate the computing cycle as follows: 1.
Extract a 10-s normalized PPG signal (Figure 2c) to evaluate the computing cycle; 2.
Define a suitable cycle during the 10-s PPG signal. The default calculation cycle is 10 points; A. Determine the maximum point point(n) within each of the 10 points by using the max function (a MATLAB R2022bfunction). B.
Evaluate the adjacent maximum point to define it slope(n) according to Equations (2) and (3): C.
Use the location of point(n) corresponding to slope(n) = 1 and slope(n + 1) = 0 to find the maximum point from point(n) to point(n) + size of cycle. This maximum point is the temple systolic peak. D.
Calculate the average difference among the adjacent temple systolic peaks and then average the estimates divided by the sample rate (200 Hz); this is the heart rate. E.
If the heart rate is smaller than 0.3 or greater than 1.5 s [55], add 5 points to the cycle and go back to Step A.

3.
Adopt the calculation cycle for the 2-min normalized PPG signal and obtain the highest peak in each cycle. Thus, the systolic peak is obtained.

Pulse Onset
The lowest peak in a single-cycle PPG signal is the pulse onset. The pulse onset is usually located between the previous diastolic peak and the systolic peak of the next cycle. This study adopted the obtained calculation cycle for the 2-min normalized PPG signal and determined the pulse onset by using the min function (a MATLAB function).

Dicrotic Notch and Diastolic Peak
A dicrotic wave, including the dicrotic notch and the diastolic peak, is the critical duration when the systole and the diastole occur ( Figure 3). However, the turning point of the dicrotic wave is not necessarily obvious. The location of the dicrotic wave is affected by many physiological factors and causes the dicrotic wave to be inconspicuous [56], as shown in Figure 3b. In contrast, Figure 3a shows the conspicuous dicrotic wave, and thus, the dicrotic notch and the diastolic peak can be obtained easily.  According to the different conditions of the dicrotic wave, this study proposed two strategies to obtain the dicrotic notch and the diastolic peak as follows: 1. Extract the PPG signal from the cycle of the systolic peak to the cycle of the systolic peak plus half of the time difference between the cycle of the systolic peak and the next cycle of the pulse onset, and calculate the differential signal using the first-order derivatives (Equation (4)): where denotes the first-order derivatives of the normalized PPG signal. Next represents the normalized PPG signal and refers to the time point. If some values of the first-order derivatives are greater than zero, the locations of zero in the first-order derivatives are the dicrotic notch and the diastolic peak. According to the different conditions of the dicrotic wave, this study proposed two strategies to obtain the dicrotic notch and the diastolic peak as follows: 1.
Extract the PPG signal from the cycle of the systolic peak to the cycle of the systolic peak plus half of the time difference between the cycle of the systolic peak and the next cycle of the pulse onset, and calculate the differential signal using the first-order derivatives (Equation (4)): where y[n] denotes the first-order derivatives of the normalized PPG signal. Next x[n] represents the normalized PPG signal and n refers to the time point. If some values of the first-order derivatives are greater than zero, the locations of zero in the first-order derivatives are the dicrotic notch and the diastolic peak.

2.
If no value of the first-order derivatives is greater than zero, the first-order derivatives are adopted to y [n]. That is, this study applied the second-order derivatives to the normalized PPG signal. The maximum and minimum of the second-order derivatives were the dicrotic notch and the diastolic peak ( Figure 4).

HRV Indices
Some previous studies suggested that the HRV indices can respond to fatigue 21]. Thus, this study also evaluated the relationship between HRV indices and fatig HRV indices were calculated using the R-R interval of the ECG signal [57]. The Rval required the tracking of small changes (milliseconds) in the intervals between sive heartbeats (the R peak) in the EEG signal. Furthermore, the R-R interval was to the interval between the adjacent systolic peaks of the PPG signal [58,59]. Thi adopted the PPG signal to obtain the R-R interval and then evaluated the HRV in follows: 1. The R-R interval was calculated according to the interval between the adjac tolic peaks of the PPG signal, as shown in Figure 5. Each R-R interval respo the time point of the previous systolic peak; 2. Furthermore, the R-R interval was resampled in this study.

HRV Indices
Some previous studies suggested that the HRV indices can respond to fatigue [2,3,[19][20][21]. Thus, this study also evaluated the relationship between HRV indices and fatigue. The HRV indices were calculated using the R-R interval of the ECG signal [57]. The R-R interval required the tracking of small changes (milliseconds) in the intervals between successive heartbeats (the R peak) in the EEG signal. Furthermore, the R-R interval was similar to the interval between the adjacent systolic peaks of the PPG signal [58,59]. This study adopted the PPG signal to obtain the R-R interval and then evaluated the HRV indices as follows: 1.
The R-R interval was calculated according to the interval between the adjacent systolic peaks of the PPG signal, as shown in Figure 5. Each R-R interval responded to the time point of the previous systolic peak; 2.
Furthermore, the R-R interval was resampled in this study. The resample function (Signal Processing Toolbox in MATLAB) was used to resample the R-R interval to 250 Hz;

3.
The resampled R-R interval was subjected to the fast Fourier transform with a Hamming window. This study focused on three frequency bands: the VLF (0.003-0.04 Hz), LF (0.04-0.15 Hz), and HF (0.15-0.4 Hz) [60]. The powers of the LF and HF were normalized by the total power minus the power of the VLF, representing the components in normal units (NLF and NHF) as follows: where total power = LF + HF + VLF. The representation in normalized units tended to minimize the effects of the changes in total power on the values of LF and HF [61] and attempted to separate out the influence of the sympathetic and parasympathetic nervous systems on the sympathovagal balance [62]. The sympathovagal balance was calculated by using the ratio of the LF power to the HF power (LF/HF ratio); 4.
Sympathetic and parasympathetic activity were closely linked to emotion [63,64]. The higher sympathetic tone (NLF) responded to the tense, anxious, and excited emotion, and the higher parasympathetic tone (NHF) responded to the tired, calm, and happy emotion [65]. In addition, Jeong et al. suggested that [4] the index of the parasympathetic nerve (NHF) was more obvious than that of the sympathetic nerve (NLF) with respect to the fatigue index. Thus, this study attempted to evaluate the relationship between NHF and fatigue. In addition, the range of values for NHF was from 0 to 100. The range of subjective fatigue and the proposed fatigue index were from 0 to 10. The range of NHF values had been changed to 0 to 10.
where = + + . The representation in normalized units tended to minimize the effects of the changes in total power on the values of LF and HF [61] and attempted to separate out the influence of the sympathetic and parasympathetic nervous systems on the sympathovagal balance [62]. The sympathovagal balance was calculated by using the ratio of the LF power to the HF power (LF/HF ratio); 4. Sympathetic and parasympathetic activity were closely linked to emotion [63,64]. The higher sympathetic tone ( ) responded to the tense, anxious, and excited emotion, and the higher parasympathetic tone ( ) responded to the tired, calm, and happy emotion [65]. In addition, Jeong et al. suggested that [4] the index of the parasympathetic nerve (NHF) was more obvious than that of the sympathetic nerve (NLF) with respect to the fatigue index. Thus, this study attempted to evaluate the relationship between NHF and fatigue. In addition, the range of values for NHF was from 0 to 100. The range of subjective fatigue and the proposed fatigue index were from 0 to 10. The range of NHF values had been changed to 0 to 10.

Fatigue Index
When blood circulation encounters obstruction, there's a potential for metabolic waste products to accumulate within blood vessels, subsequently stimulating nerve endings. This scenario necessitates the heart to exert more effort in processing the accumulated metabolic waste, thereby resulting in fatigue [22,23]. From the perspective of the overall blood circulation, if the heart has to overcome excessive vascular pressure during its contraction, this could impede the propagation of pressure waves during cardiac contractions, consequently leading to a relatively higher position of the dicrotic peak. Therefore, a relatively higher position of the dicrotic peak may suggest alterations associated with fatigue [66]. Consequently, this study employed the position of the dicrotic peak to formulate the fatigue index (as depicted in Figure 6) using the following approach: 1. Obtain the vertical height of the systolic peak as , and define the half of as the zero. Then, the new range is defined from zero to the systolic peak and mapped to 0-10, which corresponds to the score of the brief fatigue index (BFI)-Taiwan form [30]; 2. Calculate the position of the dicrotic peak from the defined range in each cycle. The  Figure 5. The R-R interval is defined as the time interval between adjacent systolic peaks (red *).

Fatigue Index
When blood circulation encounters obstruction, there's a potential for metabolic waste products to accumulate within blood vessels, subsequently stimulating nerve endings. This scenario necessitates the heart to exert more effort in processing the accumulated metabolic waste, thereby resulting in fatigue [22,23]. From the perspective of the overall blood circulation, if the heart has to overcome excessive vascular pressure during its contraction, this could impede the propagation of pressure waves during cardiac contractions, consequently leading to a relatively higher position of the dicrotic peak. Therefore, a relatively higher position of the dicrotic peak may suggest alterations associated with fatigue [66]. Consequently, this study employed the position of the dicrotic peak to formulate the fatigue index (as depicted in Figure 6) using the following approach: 1.
Obtain the vertical height of the systolic peak as x, and define the half of x as the zero. Then, the new range is defined from zero to the systolic peak and mapped to 0-10, which corresponds to the score of the brief fatigue index (BFI)-Taiwan form [30]; 2.
Calculate the position of the dicrotic peak from the defined range in each cycle. The position is one fatigue index in one cycle of the PPG signal; 3.
Calculate all the fatigue indices during the 2-min measurement, and then calculate the average of all of the fatigue indices. Thus, the average fatigue index is defined to represent the objective index of fatigue for the participants.

Linear Regression
A linear regression model is a regression analysis that estimates the relationship between one or more independent variables and dependent variables. The common linear regression is a least-squares fit, which can fit both lines and polynomials, among other linear models [67,68].
This study utilized linear regression to examine the association between the subjective fatigue state assessed using the brief fatigue index (BFI)-Taiwan form [30], the NHF, and the proposed fatigue index. Additionally, linear regression was employed to predict the fatigue state from the BFI-Taiwan form, employing distinct predictors (NHF and the proposed fatigue index). This approach aimed to develop a model that leveraged physiological indices for the prediction of fatigue levels. The regression model could be described as follows: where denotes the subjective fatigue state, while X can be NHF or the proposed fatigue index. The regression coefficients and were determined using the MATLAB function "regress" (Statistics Toolbox), which minimized the sum of the squared residuals of the model.

Correlation Coefficient
The correlation coefficient between two random variables serves as an indicator of their degree of linear interdependence. Pearson's correlation coefficient is a prevalent technique for quantifying a linear correlation [69]. It gauges both the intensity and direction of the relationship between two variables by assigning a numerical value between −1 and 1, as shown in Equation (8): where and denotes the data points of two variables, and each variable has scalar

Linear Regression
A linear regression model is a regression analysis that estimates the relationship between one or more independent variables and dependent variables. The common linear regression is a least-squares fit, which can fit both lines and polynomials, among other linear models [67,68].
This study utilized linear regression to examine the association between the subjective fatigue state assessed using the brief fatigue index (BFI)-Taiwan form [30], the NHF, and the proposed fatigue index. Additionally, linear regression was employed to predict the fatigue state from the BFI-Taiwan form, employing distinct predictors (NHF and the proposed fatigue index). This approach aimed to develop a model that leveraged physiological indices for the prediction of fatigue levels. The regression model could be described as follows: where Y denotes the subjective fatigue state, while X can be NHF or the proposed fatigue index. The regression coefficients a and b were determined using the MATLAB function "regress" (Statistics Toolbox), which minimized the sum of the squared residuals of the model.

Correlation Coefficient
The correlation coefficient between two random variables serves as an indicator of their degree of linear interdependence. Pearson's correlation coefficient is a prevalent technique for quantifying a linear correlation [69]. It gauges both the intensity and direction of the relationship between two variables by assigning a numerical value between −1 and 1, as shown in Equation (8): where X i and Y i denotes the data points of two variables, and each variable has n scalar observations. X and Y represent the mean of two variables. In addition to its application in linear regression within this study, Pearson's correlation coefficient can be effectively employed to measure the relationship between two variables. This encompasses various scenarios, such as comparing the estimated subjective fatigue state obtained through linear regression and the proposed fatigue index with the actual subjective fatigue state, evaluating the connection between NHF and the actual subjective fatigue state, and investigating the correlation between the proposed fatigue index and the real subjective fatigue state.

Fatigue Evaluation System
In this study, the proposed fatigue evaluation system was implemented using C# code that can be executed within a computer environment. Users are required to measure PPG signals using the COMGO device and subsequently transfer the collected data to the system on a computer via USB. Following this, users have the option to input their name in the designated field labeled 'please enter a name' and upload the recorded PPG file by activating the 'Open file and Test' button (as depicted in Figure 7). Subsequently, the system automatically analyzes the fatigue index and displays the corresponding information, including the name and fatigue index, in a table. If the fatigue index, as elaborated in Section 3.6, exceeds a threshold of 6, the system provides a reminder to the participants to take a rest.
Mathematics 2023, 11, x FOR PEER REVIEW 16 of 25 employed to measure the relationship between two variables. This encompasses various scenarios, such as comparing the estimated subjective fatigue state obtained through linear regression and the proposed fatigue index with the actual subjective fatigue state, evaluating the connection between NHF and the actual subjective fatigue state, and investigating the correlation between the proposed fatigue index and the real subjective fatigue state.

Fatigue Evaluation System
In this study, the proposed fatigue evaluation system was implemented using C# code that can be executed within a computer environment. Users are required to measure PPG signals using the COMGO device and subsequently transfer the collected data to the system on a computer via USB. Following this, users have the option to input their name in the designated field labeled please enter a name' and upload the recorded PPG file by activating the Open file and Test' button (as depicted in Figure 7). Subsequently, the system automatically analyzes the fatigue index and displays the corresponding information, including the name and fatigue index, in a table. If the fatigue index, as elaborated in Section 3.6, exceeds a threshold of 6, the system provides a reminder to the participants to take a rest.

Performance of PPG Peak Detection and Proposed Features for Fatigue Index
This study introduced PPG preprocessing and peak detection methods. Figure 8 illustrates the performance of the PPG preprocessing and peak detection techniques employed in this study. The outcomes demonstrate the accurate detection of pulse onset, systolic peak, dicrotic notch, and diastolic peak utilizing the proposed method. This study proposed features for the fatigue index based on the PPG signal. This pattern was observed in our recording data, where the different amplitudes of diastolic peaks responded to different fatigue conditions. The development of the fatigue index was based on the amplitude of diastolic peaks ( Figure 6). Figure 8 shows that the different locations of the diastolic peak could represent the fatigue index.

Performance of PPG Peak Detection and Proposed Features for Fatigue Index
This study introduced PPG preprocessing and peak detection methods. Figure 8 illustrates the performance of the PPG preprocessing and peak detection techniques employed in this study. The outcomes demonstrate the accurate detection of pulse onset, systolic peak, dicrotic notch, and diastolic peak utilizing the proposed method. This study proposed features for the fatigue index based on the PPG signal. This pattern was observed in our recording data, where the different amplitudes of diastolic peaks responded to different fatigue conditions. The development of the fatigue index was based on the amplitude of diastolic peaks ( Figure 6). Figure 8 shows that the different locations of the diastolic peak could represent the fatigue index.

Data Distribution of Subjective Fatigue State, NHF, and Proposed Fatigue Index
In all, 16 healthy adults participated in this study. The data considered in included the subjective fatigue state obtained from the BFI-Taiwan form, th NHF, and the proposed fatigue index estimated from the PPG signals. Figure 9 data distribution of the subjective fatigue state, NHF, and the proposed fatigu 16 healthy adults (histogram function in MATLAB). This study employed the Darling test (adtest function, statistics, and machine learning toolbox in MATL tistical method, to determine if a given dataset is drawn from a normal distrib Anderson-Darling test assesses the fit of the data to a theoretical normal distr considering both the mean and the variance of the data. It provides a quantitativ of how well the observed data aligns with the expected distribution, allowing r to make informed judgments about the normality of the dataset under examin In MATLAB, the "adtest" function was utilized as a means of testing the null that the data within the vector "x" originated from a population characterized b distribution. The result h returned by the adtest function was 1 if the test reject hypothesis and then indicated that x was not from a population with a norma tion. Except for questions (3), (6), (8), and (9) and the proposed fatigue index, m data had a normal distribution (h = 0).

Data Distribution of Subjective Fatigue State, NHF, and Proposed Fatigue Index
In all, 16 healthy adults participated in this study. The data considered in this study included the subjective fatigue state obtained from the BFI-Taiwan form, the objective NHF, and the proposed fatigue index estimated from the PPG signals. Figure 9 shows the data distribution of the subjective fatigue state, NHF, and the proposed fatigue index of 16 healthy adults (histogram function in MATLAB). This study employed the Anderson-Darling test (adtest function, statistics, and machine learning toolbox in MATLAB), a statistical method, to determine if a given dataset is drawn from a normal distribution. The Anderson-Darling test assesses the fit of the data to a theoretical normal distribution by considering both the mean and the variance of the data. It provides a quantitative measure of how well the observed data aligns with the expected distribution, allowing researchers to make informed judgments about the normality of the dataset under examination [70]. In MATLAB, the "adtest" function was utilized as a means of testing the null hypothesis that the data within the vector "x" originated from a population characterized by a normal distribution. The result h returned by the adtest function was 1 if the test rejected the null hypothesis and then indicated that x was not from a population with a normal distribution. Except for questions (3), (6), (8), and (9) and the proposed fatigue index, most of the data had a normal distribution (h = 0).  Figure 10 shows the scatter plot for three datasets: the subjective fatigue state, the NHF, and the proposed fatigue index. Because the aim of this study was to substitute the fatigue index obtained using PPG signals for the subjective data obtained from the (BFI)-Taiwan form and the HRV indices estimated from PPG signals to analyze fatigue, the last two rows of the scatter plot shown in Figure 10 were further explored; they revealed a line relationship between the questions from the BFI-Taiwan form and the proposed fatigue index. Thus, this study adopted Pearson's correlation coefficient to evaluate the relationship among the subjective fatigue state, NHF, and the proposed fatigue index, as shown in Figure 11. The results revealed that only two questions were related to the proposed fatigue index: (2) Level of general fatigue in the past 24 h (r = 0.8743) and (3) Level of being most exhausted in the past 24 h (r = 0.5328).

Relationship among Subjective Fatigue State, NHF, and Proposed Fatigue Index
In contrast, NHF had a low correlation for all nine questions (r = −0.1510~0.4787). The reason why NHF was unable to respond to fatigue was that the participants adjusted their breathing and the parasympathetic nerve effectively deepened, or the influence of the current mood [8,9]. Previous research suggested that irregular respiration can change sympathovagal activities or their balances, as reflected in the HRV indices [71][72][73][74][75]. Lin et  Figure 10 shows the scatter plot for three datasets: the subjective fatigue state, the NHF, and the proposed fatigue index. Because the aim of this study was to substitute the fatigue index obtained using PPG signals for the subjective data obtained from the (BFI)-Taiwan form and the HRV indices estimated from PPG signals to analyze fatigue, the last two rows of the scatter plot shown in Figure 10 were further explored; they revealed a line relationship between the questions from the BFI-Taiwan form and the proposed fatigue index. Thus, this study adopted Pearson's correlation coefficient to evaluate the relationship among the subjective fatigue state, NHF, and the proposed fatigue index, as shown in Figure 11. The results revealed that only two questions were related to the proposed fatigue index: (2) Level of general fatigue in the past 24 h (r = 0.8743) and (3) Level of being most exhausted in the past 24 h (r = 0.5328).

Relationship among Subjective Fatigue State, NHF, and Proposed Fatigue Index
In contrast, NHF had a low correlation for all nine questions ( r = −0.1510 ∼ 0.4787). The reason why NHF was unable to respond to fatigue was that the participants adjusted their breathing and the parasympathetic nerve effectively deepened, or the influence of the current mood [8,9]. Previous research suggested that irregular respiration can change sympathovagal activities or their balances, as reflected in the HRV indices [71][72][73][74][75]. Lin et al. also showed that controlled breathing may be effective in controlling nausea and enhancing autonomic function by decreasing sympathetic activity and increasing parasympathetic activity [9].
The degrees of subjective fatigue in the past 24 h could be represented by two questions (2) and (3) (Figure 11) and related to the proposed fatigue index using the PPG signals. This study attempted to average the scores for questions (2) and (3) in the BFI-Taiwan form to represent the revised subjective fatigue state of the participants. In addition, this study adopted linear regression (the regress function of the statistics toolbox in MATLAB) to estimate the relationship between the revised subjective fatigue state and the proposed fatigue index and NHF using PPG signals ( Figure 12). The results shown in Figure 12 revealed that Pearson's correlation coefficient between the revised subjective fatigue state and the proposed fatigue index was 0.907 and represented a high positive correlation. Therefore, it could be suggested that the proposed fatigue index was positively correlated with the fatigue level felt by the participants. In contrast, the linear regression of NHF relative to the revised subjective fatigue was low (r = 0.14875). This observation corresponds to the trends depicted in Figures 10 and 11, indicating a limited correlation between NHF and the subjective fatigue state. On the other hand, the fatigue index introduced in this study, derived from the position of the dicrotic peak, demonstrates a robust connection with the subjective fatigue state. While earlier literature has suggested a link between NHF and fatigue [2][3][4], it is important to note that numerous studies have underscored the influence of diverse factors (such as respiration, physical activity, caffeine and medications, stress and emotional state, and underlying health conditions) on the accuracy of HRV measurements [8][9][10][11][12][13]. In contrast, the fatigue index proposed in this paper, relying on the PPG dicrotic peak's position, aligns with prior research highlighting the effectiveness of various PPG pulse wave features in assessing mental states [46,47]. Moreover, it resonates with the broad range of physiological monitoring applications encompassing oxygen saturation, heart rate, blood pressure, respiration for pulse wave characterization, arterial health assessment, compliance, endothelial function, and microvascular flow for vascular evaluation, as well as vasomotor activity and heart rate variability for autonomic function assessment. This demonstrates that PPG signals extend beyond their role in HRV or heart rhythm assessment, incorporating a diverse array of implications within their waveform characteristics.  The degrees of subjective fatigue in the past 24 h could be represented by two questions (2) and (3) (Figure 11) and related to the proposed fatigue index using the PPG signals. This study attempted to average the scores for questions (2) and (3) in the BFI-Taiwan form to represent the revised subjective fatigue state of the participants. In addition, this study adopted linear regression (the regress function of the statistics toolbox in MATLAB) to estimate the relationship between the revised subjective fatigue state and the proposed fatigue index and NHF using PPG signals ( Figure 12). The results shown in Figure 12 revealed that Pearson's correlation coefficient between the revised subjective fatigue state and the proposed fatigue index was 0.907 and represented a high positive correlation. Therefore, it could be suggested that the proposed fatigue index was positively correlated with the fatigue level felt by the participants. In contrast, the linear regression of NHF relative to the revised subjective fatigue was low (r = 0.14875). This observation corresponds to the trends depicted in Figures 10 and 11, indicating a limited correlation between NHF and the subjective fatigue state. On the other hand, the fatigue index introduced in this study, derived from the position of the dicrotic peak, demonstrates a robust connection with the subjective fatigue state. While earlier literature has suggested a link between NHF and fatigue [2][3][4], it is important to note that numerous studies have underscored the influence of diverse factors (such as respiration, physical activity, caffeine and medications, stress and emotional state, and underlying health conditions) on the accuracy of HRV measurements [8][9][10][11][12][13]. In contrast, the fatigue index proposed in this paper, relying on the PPG dicrotic peak's position, aligns with prior research highlighting the effectiveness of various PPG pulse wave features in assessing mental states [46,47]. Moreover, it resonates with the broad range of physiological monitoring applications encompassing oxygen saturation, heart rate, blood pressure, respiration for pulse wave characterization, arterial health assessment, compliance, endothelial function, and microvascular flow for vascular evaluation, as well as vasomotor activity and heart rate variability for autonomic function assessment. This demonstrates that PPG signals extend beyond their role in HRV or heart rhythm assessment, incorporating a diverse array of implications within their waveform characteristics.
The results shown in Figure 12 revealed that the subjective fatigue state could be obtained by Equation (9) using the proposed fatigue index using the PPG signals: Subjective fatigue state = 0.6 × fatigue index + 3.1

Fatigue Evaluation System
This study implemented PPG processing, peak detection method, fatigue index, and Equation (9) using C# in a computer environment. The measurement file from COMGO was transmitted and saved to the computer through the USB. The participants could enter their names and upload the measurement file by pressing the button "Open file and Test" (Figure 7). The system then automatically analyzed the fatigue index and reminded the participants to take rest if the fatigue index was greater than 6 ( Figure 13). The results shown in Figure 12 revealed that the subjective fatigue state could be obtained by Equation (9) using the proposed fatigue index using the PPG signals: Subjective fatigue state = 0.6 × fatigue index + 3.1 (9)

Fatigue Evaluation System
This study implemented PPG processing, peak detection method, fatigue index, and Equation (9) using C# in a computer environment. The measurement file from COMGO was transmitted and saved to the computer through the USB. The participants could enter their names and upload the measurement file by pressing the button "Open file and Test" (Figure 7). The system then automatically analyzed the fatigue index and reminded the participants to take rest if the fatigue index was greater than 6 ( Figure 13). This study implemented PPG processing, peak detection method, fatigue index, and Equation (9) using C# in a computer environment. The measurement file from COMGO was transmitted and saved to the computer through the USB. The participants could enter their names and upload the measurement file by pressing the button "Open file and Test" (Figure 7). The system then automatically analyzed the fatigue index and reminded the participants to take rest if the fatigue index was greater than 6 ( Figure 13).

Figure 13.
Fatigue evaluation system in this study. The system reminded the subject to take rest if the fatigue index was greater than 6. The 確認 in the Attention' window indeed means to confirm the content.

Conclusions
This study proposes a novel fatigue index derived from PPG signals, with a specific focus on the position of the dicrotic peak. The proposed fatigue index is utilized to replace subjective data collected through the (BFI)-Taiwan form and the HRV indices obtained from PPG signals in order to evaluate fatigue levels. This research departs from traditional approaches by formulating the fatigue index based on distinct PPG waveform characteristics rather than relying on HRV. Additionally, a comparative analysis is conducted to examine the relationship between the fatigue index derived from PPG waveform characteristics, HRV, and the subjective fatigue assessment in the BFI form. The study also proposes PPG preprocessing and peak detection techniques. The findings demonstrate a robust correlation between the scores of questions in the BFI-Taiwan form and the proposed fatigue index. Of particular significance is the notable correlation observed between two specific questions and the proposed fatigue index: (2) Level of general fatigue in the past 24 h (r = 0.8743) and (3) Level of most exhaustion in the past 24 h (r = 0.5328). However, the correlation with HRV (HF) remains moderate. As a result, this investigation calculates an average of the scores from questions (2) and (3) in the BFI-Taiwan form to represent participants revised subjective fatigue states. Through the application of Equation (9) with the proposed fatigue index derived from PPG signals, a strong correlation (r = 0.907) is established, validating the potential effectiveness of Equation (9). This equation can seamlessly integrate into a C# framework to establish a comprehensive fatigue evaluation system, thereby offering valuable insights for individuals seeking to effectively address fatigue-related concerns. The incorporation of timely reminders serves to alert users when their index surpasses a predefined threshold, thereby cultivating heightened awareness of their physical well-being. Moreover, this study emphasizes that PPG signals surpass their traditional role in HRV, or heart rhythm assessment, encompassing a diverse range of implications within their waveform characteristics.
This study possesses three primary limitations, each offering opportunities for future research enhancement. Firstly, the effect estimates utilized in the adopted approach relied on a relatively modest sample size comprising only 16 healthy adults. To bolster the statistical robustness, expanding participant numbers and encompassing diverse age groups and genders would be advisable. Furthermore, integrating deep learning techniques for estimating fatigue states could introduce advanced analytical capabilities. Secondly, it is plausible that there exist additional factors beyond those addressed in this study that could impact fatigue state prediction. Elements like climatic variations, BMI, age, gender, and others may also exert influence. Consequently, future investigations should consider the inclusion of these variables to foster a more comprehensive grasp of the subject matter. Thirdly, alternate equipment alternatives, such as Doppler ultrasound machines, offer the capacity to visualize specific arteries and their blood flow dynamics through dynamic imaging. By engaging diverse measurement devices, it may be feasible to scrutinize corresponding vascular conditions or capture finer PPG-related features. Delving into the utilization of different measurement tools in forthcoming research would contribute valuable insights, potentially unveiling supplementary features and augmenting the precision of fatigue state prediction within our study.