In this study, two types of brain-computer interface devices were used:

1) A product from Open BCI (data sampling rate: 250 Hz).

2) A product from Emotiv (data sampling rate: 128 Hz).

Both companies sell products under $200, which are affordable to regular users, as shown in Figure 1.

In details, the following main materials were used, as shown in Figure 1:

1) Gold-coated electrodes and conductive paste (Open BCI).

2) A data acquisition board (Open BCI).

3) A data wireless receiver (Open BCI).

4) A battery power unity (Open BCI).

5) Integrated electrodes and a data acquisition unit (Emotiv).

6) A data wireless receiver (Emotiv).

7) A bottle of all-purpose saline solution (Emotiv).

The outline of our approach is given in Figure 2(b). First, a brain-computer interface device was used to get the brain wave data of test subjects, as illustrated in Figure 2(a). Then, the data was input into the MATLAB software. In MATLAB, a general-purpose polling algorithm was implemented for computing the depth of drowsiness. Last, the computed depth of drowsiness was compared with the inquired depth of drowsiness and with one of the existing methods [5] .

10 - 20 system is an internationally recognized method to specify the location of scalp electrodes for electroencephalography (EEG) test [15] . In this paper, two ear positions (A1 and A2) were used as a reference and a bias position. Based on the previous studies in sleep science, P3 and C4 (or P7 and F4) were chosen as measurement points for obtaining brain waves of test subjects. Five frequency bands (delta, theta, alpha, beta and gamma) of brain waves are defined by Figure 3(b).

Brain waves contain much random information that is difficult to be analyzed in time domain (Figure 3(b)). Fourier transform was used to convert the waves to frequency domain (Figure 3(c)) by using Equation (1). It is a tool to break a brain wave into a set of sine or cosine functions with different amplitudes and frequencies:

・ is a brain wave (time function)

・ is a frequency, ,

・ is the length of sampling window

・ Euler’s formula:

・ represents the amount of frequency in the breakup

In frequency domain, the norm of different frequency bands (delta, theta, alpha, beta and gamma) is defined as biometric markers for drowsiness:

where is the normalized amplitude of Fourier transform of the brain wave at frequency. The normalization is done by a division from sampling frequency F_s (128 or 250 Hz in this paper). Normalized band norms are defined as

A general-purpose polling formula was designed to predict the human drowsiness:

1) Traditionally, the drowsiness is quantified by a binary variable: Yes or No, which is not accurate enough to describe such a complex process. A real number variable, depth of drowsiness, is proposed to precisely describe the different levels of drowsiness ().

2) In computer graphics [16] , millions of different colors are represented by a linear combination of three basic components: RGB, where R, G, B represent red, green, and blue components, respectively. Inspired by this treatment, the drowsiness is represented by a linear combination of several basic frequency components.

3) In sleep science, different frequency channels are often used to investigate sleep patterns. In signal processing, Fourier transform [17] is an effective tool to convert signals from time domain to frequency domain, and the norm of frequency bands can be used as basic components to quantify human drowsiness. Thus, the norm of frequency bands of brain waves is considered as biometric markers for drowsiness in this paper.

4) Inspired by political voting, a new polling scheme, i.e., judging the drowsiness on the basis of the vote of frequency bands, is designed to express the relation between the depth of drowsiness and the norm of frequency bands:

, , ,

where N_δ, N_θ, N_α, N_β, N_γ are normalized band norms for δ, θ, α, β, and γ channels, respectively., , , are the corresponding weights.

The derivation of the above formula is given in Appendix A.

For calibrating the sampling rate of the hardware, A stopwatch and the data acquisition software of the devices were used. Table 1 shows the test data of stopwatch and acquisition software of Open BCI. The timing data are quite close to each other.

Table 2 is the time acquisition result of Emotiv device in a period of 0.5 second. It indicates that the sampling rate is 128 Hz and sampling time is quite accurate. The absolute value of voltage does not matter in this study because our formula needs only the normalized band norm, which is invariant from voltage amplitude (Appendix B).

A Human Participant Form was approved by a local IRB in 2015 and each participant gave his/her permission before the experiment. Ten human subjects were measured with names replaced by pseudo identification numbers, with four of them tested only in waking states. The main test steps of this study are:

1) Assembling and calibration of the brain-computer interface devices.

2) Design and development of the biometric algorithm (i.e., a polling scheme) as well as the setup of the brain-computer interface device.

3) Collection of brain wave data by wearing a brain-computer interface device. Measurement last for about 6 - 7 seconds at a sampling frequency (F_s = 250 Hz). Drowsy state: a) Test time was chosen around midnight; b) Subjects were asked to click the “Data Collection” button once they felt drowsy. Waking state: a) Test time was chosen during daytime; b) Severe movement was avoided.

4) Inquiry of observed depth of drowsiness from test subjects. Drowsy stage: Extremely sleepy (0.95), Very sleepy (0.8), Moderately sleepy (0.65), Lightly sleepy (0.5).Waking stage: Extremely alert (0.05), Very alert (0.2), Moderately alert (0.35), Lightly alert (0.45).

5) Conversion of brain data to MATLAB data format and execution of the designed polling algorithm for predicting the depth of drowsiness.

6) Analysis and validation of the algorithm.

As shown in Figure 4, plot( ) function in MATLAB was used to draw brain waves in both time and frequency domains. Bar( ) function was used to draw the normalized band norms of five frequency bands (Delta, Theta, Alpha, Beta, and Gamma).

Our biometric markers for drowsiness are roughly invariant between C4 and P3 channels, as illustrated in Figure 5. This is an important feature that eliminates

stringent requirement on the location of electrodes on human scalp. It is difficult to put a sensor at the exact location of a particular channel specified by the 10 - 20 electrode system.

The depth of drowsiness varies more severely in waking stage than in drowsy stage. This may be due to the fact that test subjects are more likely influenced from environment during the waking stage. Even with the variation in the waking stage, there is a clear-cut between the two stages, as shown in Figure 6. This figure plots the drowsiness measured five times on a test subject.

The execution time of the MATLAB code is within 1 millisecond (not including the data acquisition time, which is 1 second for each estimate), as listed in Figure 7. The sum of these two costs supports real-time applications in transportation control.

The computed depth of drowsiness is also generally invariant from ages of test subjects, as illustrated in Figure 8. This avoids the need of a large amount of training data in existing methods.

Figure 9 provides a comparison of our method with one recent study [5] and indicates that our algorithm provides a more accurate clear-cut between drowsy and waking stages. In details, Table 3 shows the results of some tests in this study. The thresholds 0.65 and 0.5 were used to determine the state predictions (w: waking; d: drowsy) in the fourth and sixth columns, respectively. Red color in the table represents the failed cases. Table 4 is a summary of the comparison, indicating 82% and 70% accuracy for our method and the recent method [5] , respectively. Furthermore, the threshold is not sensitive to our method because any value between 0.65 and 0.75 generates a similar accuracy.