## 4 Experiment results  
Two tests cases were conducted in two different days and the acquired data provides sufficient information for the test purpose. To effectively stimulate the fire ants distributed on the tub bottom, the exciting frequency was selected to be 466 Hz according to a previous investigation [16]. The excitation applied in the first case (case #1) resulted in the maximal acceleration amplitude of 0.72 m/s\({}^{2}\) near the tub center, whereas the exciting signal applied in second case (case #2) resulted in the maximal acceleration amplitude of 82.13 m/s\({}^{2}\) at the same position. Therefore, case #1 and case #2 were considered as a weak excitation and a strong excitation, respectively. Since the vibration of the tub bottom surface is perpendicular to the image plane and with limited amplitude, it does not have any obvious influence on the recording of fire ant motion. Figure 7: Individual image tracking results: trail **(a)** and speed **(b)** of a selected ant in 20 seconds. With the described image tracking technique the trail and speed of each active moving ant were determined in a 20-second data acquisition period. As an example, Fig. 7 shows the trail and speed time history of the ant indicated with a white arrow in Fig. 2, which belongs to the ant image recording group in case #2 for a few seconds after the excitation. Fig. 7a shows that the trail of the ant starts at position (0, 0), goes along a \"\(\infty\)\" shape in a region of 90\(\times\)60 mm\({}^{2}\) in the 20-second period. In Fig. 7b the ant speed varies between 0 and 40 mm/s with a very complex distribution on time. The tracking results for a single ant enable study of the individual ant behavior. However, in the present work we concentrated on the overall behavior of the group of 200 ants. Fig. 8 displays the overlapped positions (8a) and speed vectors (8b) of identified 62 active moving ants in 1228 frames, which are evaluation results of the second ant image recording group for case #2. In Fig. 8a the trail of an individual ant can hardly be identified, however, the overlapped ant positions present a distribution of ant appearance probability in the observed area. Fig. 8b shows the corresponding ant moving speed vector at each ant position. Since so many vectors are overlapped, the speed of an individual ant cannot be seen clearly in the figure. In the current test case the constants in Eq. 7 were all set to 1, and those in Eq. 11 were all set to 2. Figure 8: **E**emble image tracking results: overlapped ant positions **(a)** and speed vectors **(b)** in case #2, 2 nd group (view area: 418\(\times\)209 mm\({}^{2}\)). The evaluation results are further processed, so that more useful information can be extracted from the available raw data. At first, the number of the active ants is investigated for the both cases at different delay time in the one-hour test period, and the results are given in Fig. 9. For each case the first symbol on the left represents the active ant number before excitation, and the second symbol, i.e. at \"time delay\"=0, represents data obtained a few seconds after the excitation. The followed eight symbols represent data obtained in the time period of restoration, i.e. 3, 6, 9, 12, 15, 30, 45 and 60 minutes after the excitation. As shown in Fig. 9, test results of both cases indicate that the number of active moving ants reduces after being excited by surface vibration of the tub, and it reaches to the minimum at around 10 minute of the time delay. After 30 minutes, the number of the active moving ants is back to normal, i.e. the number before excitation. After 40 minute the active ant number increases to a little higher than that of before excitation. A probability density function (PDF) of ant moving speed is determined for each ant image recording group with about 36000 speed values as shown in Fig. 8b. The probability density functions (PDFs) of ant speeds determined before excitation, a few seconds after excitation, and 6 minutes after excitation are given in Fig.