Detection of Water Changes in Plant Stems In Situ by the Primary Echo of Ultrasound RF with an Improved AIC Algorithm

The detection of water changes in plant stems by non-destructive online methods has become a hot spot in studying the physiological activity of plant water. In this paper, the ultrasonic radio-frequency echo (RFID) technique was used to detect water changes in stems. An algorithm (improved hybrid differential Akaike’s Information Criterion (AIC)) was proposed to automatically compute the position of the primary ultrasonic echo of stems, which is the key parameter of water changes in stems. This method overcame the inaccurate location of the primary echo, which was caused by the anisotropic ultrasound propagation and heterogeneous stems. First of all, the improved algorithm was analyzed and its accuracy was verified by a set of simulated signals. Then, a set of cutting samples from stems were taken for ultrasonic detection in the process of water absorption. The correlation between the moisture content of stems and ultrasonic velocities was computed with the algorithm. It was found that the average correlation coefficient of the two parameters reached about 0.98. Finally, living sunflowers with different soil moistures were subjected to ultrasonic detection from 9:00 to 18:00 in situ. The results showed that the soil moisture and the primary ultrasonic echo position had a positive correlation, especially from 12:00 to 18:00; the average coefficient was 0.92. Meanwhile, our results showed that the ultrasonic detection of sunflower stems with different soil moistures was significantly distinct. Therefore, the improved AIC algorithm provided a method to effectively compute the primary echo position of limbs to help detect water changes in stems in situ.


Introduction
The water content of plant stems is a major index of the physiological activity of plant water, especially in precision agriculture [1][2][3]. Methods for detecting stem water content include drying [4], gamma rays [5], nuclear magnetic resonance (NMR) [6][7][8], X-ray computed tomography [9], resistance [10], time-domain reflectometry (TDR) [11], frequency-domain (FD) capacitance [12][13][14] and infrared detection [15]. Of the above methods, drying constitutes in vitro detection, which cannot detect the dynamic changes in the stem water content. For online detection, the time-domain reflection method and frequency capacitance method could track the changes in stem water content. However, the probes in both methods need to be inserted into the plant stem, which could affect plants' physiological activity [16,17], resulting in detection errors in dynamic changes [18]. It was pointed out that the consistency of the detection of stem water content was influenced by the insertion depth of the probe and the structure of the plant stem [17]. The gamma-ray method and NMR method, two destructive detection methods, had high accuracy but were expensive and difficult to utilize for long-term detection. The infrared method could detect the liquid water and ice content of plant stems in situ, in real time with microdestruction [15]. Recently, non-destructive online detection methods were explored based on the principle of the standing wave rate and frequency-domain capacitance. Both groups

Ultrasonic Detection Principle
The prosperity of the ultrasonic wave is different in various materials. The stem can be studied as a mixture of wood fiber, liquid and ice [38]. The water regulation process of stems is the change in the above mixture components in proportion. The difference between water deficit and filling in stems can be detected using ultrasonic waves [4,29,39]. When the ultrasonic signal propagation forms different ultrasound interface reflection echoes in additional water content, the primary echo positions in stems change. In this paper, the change in water content was studied by determining the position of the ultrasonic primary echo signal of stems.

Ultrasonic Detection of Water Content Changes in Stems
Ultrasonic wave propagation in a solid medium is determined by the density and elastic properties of the medium. Ultrasonic velocity in a solid medium is where v l is the propagation velocity of the ultrasonic wave in the longitudinal direction, E is the modulus of elasticity, ρ is the density of the medium and σ is Poisson's ratio. We hypothesized that when the water content of stems changes, Poisson's ratio and the modulus of elasticity E of the same stem are regarded as constants [4,39]. Therefore, the water content dominates ultrasonic velocity because the water content changes the medium's density ρ [28,29] for the detected stems.
According to Formula (1), the increasing density eventually leads to decreased ultrasonic velocity in stems [39]. On the contrary, the velocity rises when water is deficient, causing the viscosity to fall. Therefore, the water regulation of the plant stem can be obtained by detecting the ultrasonic speed in the plant stem.
In detection, the time of the ultrasonic primary echo position and the distance of the ultrasonic wave propagation are used calculate the ultrasonic velocity: where 2D is the linear distance of the ultrasonic echo in the medium and t is the ultrasonic primary echo position time.

Detection of the Position of Ultrasonic Primary Echo for Stems Based on AIC Algorithm
Because the stem is a non-metallic, heterogeneous, anisotropic material, the path of ultrasonic echo propagation within it is more complex than that in metallic, homogeneous and isotropic materials. Similarly, the energy attenuation of stems is more serious. Therefore, the path and attenuation make it challenging to distinguish the primary echo wave from other multiple ultrasonic echo signals [13,18], affecting the detection of the time of the primary echo.

Detection of Ultrasonic Echo Time Based on AIC
In AIC, the echo signal is assumed to be the local autocorrelation stationary signal alternated with the noise. The AIC for the timely detection of the primary ultrasonic echo is represented as a function of a merging point k.
AIC(k) = k·log(var(s(1, k))) + (N − k + 1)· log(var(s(k + 1, N))) where s(1, k) represents the samples of the ultrasonic echo from the 1st sample to the k-th sample, N is the length of the samples of the ultrasonic echo, and k is the sampling point sequence number from 1 to N. In the function, the following formula expresses the var.
The AIC(k) of stems is calculated using Formula (3) on the ultrasonic echo sampling signal s(l, k). The global minimum AIC(k) is the time of the primary echo. This is when the ultrasonic wave injuncts with the noise. After determining the time of the primary echo, we can calculate the ultrasonic velocity and other parameters of ultrasound echo in the stem, laying the foundation for the effective and accurate construction of ultrasound images of plant stems.

Ultrasonic Detection of Plant Stems Based on AIC Algorithm
The ultrasonic signal of the plant stem is presented in Figure 1. It shows that the ultrasonic wave and the noise alternately appear. The noise, due to the strong attenuation of the plant stem, is the ultrasonic wave drowned by noise. In Figure 1, the position determined by the minimal AIC is not the primary ultrasonic echolocation but the junction of the ultrasound and noise. The position of the primary natural echo is found at the first inflection point convex after the position of the minimal of AIC. Therefore, the classical AIC algorithm cannot accurately detect the position of the ultrasonic echo of the plant stem. where 1, represents the samples of the ultrasonic echo from the 1st sample to the kth sample, is the length of the samples of the ultrasonic echo, and is the sampling point sequence number from 1 to . In the function, the following formula expresses the var.
where ̅ is the mean value of , , , 1, … , , 1, … , . The AIC(k) of stems is calculated using formula (3) on the ultrasonic echo sampling signal , . The global minimum AIC(k) is the time of the primary echo. This is when the ultrasonic wave injuncts with the noise. After determining the time of the primary echo, we can calculate the ultrasonic velocity and other parameters of ultrasound echo in the stem, laying the foundation for the effective and accurate construction of ultrasound images of plant stems.

Ultrasonic Detection of Plant Stems Based on AIC Algorithm
The ultrasonic signal of the plant stem is presented in Figure 1. It shows that the ultrasonic wave and the noise alternately appear. The noise, due to the strong attenuation of the plant stem, is the ultrasonic wave drowned by noise. In Figure 1, the position determined by the minimal AIC is not the primary ultrasonic echolocation but the junction of the ultrasound and noise. The position of the primary natural echo is found at the first inflection point convex after the position of the minimal of AIC. Therefore, the classical AIC algorithm cannot accurately detect the position of the ultrasonic echo of the plant stem.

Hybrid Difference AIC Algorithm
The hybrid difference AIC algorithm highlights the position of the primary echo by the difference mixing with the AIC. The hybrid model used to pick the location of the primary echo comprises the following sequences: 1. Calculate AIC(n) values (AIC(n), n = 1, ..., N); 2. Extract AIC(n) from the sample of the minimal value (AICmin(index)) to the last sample N to form the AICseg(i), i = index, …, N;

Hybrid Difference AIC Algorithm
The hybrid difference AIC algorithm highlights the position of the primary echo by the difference mixing with the AIC. The hybrid model used to pick the location of the primary echo comprises the following sequences:
Extract AIC(n) from the sample of the minimal value (AICmin(index)) to the last sample N to form the AICseg(i), i = index, . . . , N; 3.

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where M is the M order difference.

4.
Compute the envelope of Diff AICseg (i) and normalize it; Because of the phase change of the ultrasonic echo signal, the upper and lower envelopes are retained.
Pick the maximum of the Mixed AIC (i). The time of the maximum is the time of primary echo.

Ultrasonic Detection System
An ultrasound apparatus for detecting the water content of stems was designed, as shown in Figure 2 [5]. It consists of a non-metallic ultrasonic probe of 1 MHz, an ultrasonic pulse transmitting and receiving device (CTS-8077PR), a data acquisition module, and a PC machine. The sampling depth of the detecting system was set to 2000 samples per ultrasonic pulse. The sampling frequency was 10 MHz. The system stores and analyzes the ultrasonic echo signal, as shown in Figure 3. 3. Compute the M order differences of AICseg(i), to obtain DiffAICseg(i); where △M is the M order difference.

Compute the envelope of DiffAICseg(i) and normalize it;
Because of the phase change of the ultrasonic echo signal, the upper and lower envelopes are retained. 5. Multiply Envelope(i) and AICseg(i), 6. Pick the maximum of the MixedAIC(i). The time of the maximum is the time of primary echo.

Ultrasonic Detection System
An ultrasound apparatus for detecting the water content of stems was designed, as shown in Figure 2 [5]. It consists of a non-metallic ultrasonic probe of 1 MHz, an ultrasonic pulse transmitting and receiving device (CTS-8077PR), a data acquisition module, and a PC machine. The sampling depth of the detecting system was set to 2000 samples per ultrasonic pulse. The sampling frequency was 10 MHz. The system stores and analyzes the ultrasonic echo signal, as shown in Figure 3.

Simulation Experiment
Firstly, we evaluated the improved AIC algorithm by applying it to detect the time of primary echo of nine sets of simulated ultrasonic signals in MATLAB 2020a.
Secondly, we applied the algorithm to track the changes in water content in the samples of the stems in the water immersion experiment. Two sets of samples were taken. The first sets are three samples of 2 cm × 4 cm × 10 cm stems with different densities. The thicknesses of ultrasonic detection were all 2 cm. The experiment compared the time of the primary echo and the ultrasonic velocity before and after 24 h immersion. The second sets of samples were cylindrical samples cut from stems. Their sizes were 6 cm × 6 cm, 7 cm × 7 cm and 10 cm × 10 cm. Because the water content changed significantly in the initial immersion, the detection time interval was set to 10 or 20 min and detected six times; in the middle stage of immersion, the detection interval was 3~4 h, detected two times; and the final detection time interval was 24 h. The experiment stopped when the increased amount of water was less than 10 g for 24 h.
Finally, the algorithm was applied to detect the water content changes in stems of living sunflowers in situ with different soil moistures. Two healthy pot-planted sunflowers were selected as samples. The day before the detection, one of the samples was usually watered with 100 mL of water, and the other was not watered. The instrument for measuring soil moisture is ZY-05, and the mechanism for detecting air temperature and humidity is AR837. The ultrasonic probe was placed 6 cm along the stems from the soil's surface. The circumferences of the samples were 4 cm and 6 cm. The detection period was from 9:00 to 19:00. Figure 4b shows the time when the maximum appeared, as found using DiffAICseg. However, it was also found that some interference near 1.10 ns and 1.25 ns of DiffAICseg occurred after the difference operation. Figure 4c shows that the hybrid differential AIC signal, named MixedAIC, can effectively suppress the above interference. The simulated experimental results in Table 1 show that the average error of the primary echo position calculated by the algorithm is 0.1 ns. The hybrid difference AIC can effectively and accurately obtain the primary echo position of the signal.

Simulation Experiment
Firstly, we evaluated the improved AIC algorithm by applying it to detect the time of primary echo of nine sets of simulated ultrasonic signals in MATLAB 2020a.
Secondly, we applied the algorithm to track the changes in water content in the samples of the stems in the water immersion experiment. Two sets of samples were taken. The first sets are three samples of 2 cm × 4 cm × 10 cm stems with different densities. The thicknesses of ultrasonic detection were all 2 cm. The experiment compared the time of the primary echo and the ultrasonic velocity before and after 24 h immersion. The second sets of samples were cylindrical samples cut from stems. Their sizes were 6 cm × 6 cm, 7 cm × 7 cm and 10 cm × 10 cm. Because the water content changed significantly in the initial immersion, the detection time interval was set to 10 or 20 min and detected six times; in the middle stage of immersion, the detection interval was 3~4 h, detected two times; and the final detection time interval was 24 h. The experiment stopped when the increased amount of water was less than 10 g for 24 h.
Finally, the algorithm was applied to detect the water content changes in stems of living sunflowers in situ with different soil moistures. Two healthy pot-planted sunflowers were selected as samples. The day before the detection, one of the samples was usually watered with 100 mL of water, and the other was not watered. The instrument for measuring soil moisture is ZY-05, and the mechanism for detecting air temperature and humidity is AR837. The ultrasonic probe was placed 6 cm along the stems from the soil's surface. The circumferences of the samples were 4 cm and 6 cm. The detection period was from 9:00 to 19:00. Figure 4b shows the time when the maximum appeared, as found using Diff AICseg . However, it was also found that some interference near 1.10 ns and 1.25 ns of Diff AICseg occurred after the difference operation. Figure 4c shows that the hybrid differential AIC signal, named Mixed AIC , can effectively suppress the above interference. The simulated experimental results in Table 1 show that the average error of the primary echo position calculated by the algorithm is 0.1 ns. The hybrid difference AIC can effectively and accurately obtain the primary echo position of the signal.

Simulated Signals The Minimal of AIC (ns) Primary Echo Position (ns)
Observed Hybrid   1  101  153  153  2  101  153  154  3  101  156  159  4  201  253  254  5  201  253  254  6  201  255  258  7  301  351  351  8  301  351  351  9 301 354 359 Figure 5 shows that the hybrid difference AIC algorithm effectively suppresses the interference of the differential AIC. It is easy to detect the position of the primary echo by picking the maximum of the Mixed AIC . The time of the primary echo is 1.31 ns, compared to 1.46 ns after 24 h of immersion.   Hybrid  1  101  153  153  2  101  153  154  3  101  156  159  4  201  253  254  5  201  253  254  6  201  255  258  7  301  351  351  8  301  351  351  9 301 354 359 Figure 5 shows that the hybrid difference AIC algorithm effectively suppresses the interference of the differential AIC. It is easy to detect the position of the primary echo by picking the maximum of the MixedAIC. The time of the primary echo is 1.31 ns, compared to 1.46 ns after 24 h of immersion.   Table 2 shows that the water absorption of truncated stems in the first 1 h after immersing was obvious, especially for the 6 cm diameter of the sample in the first 20 min. The mass increased by nearly 14 g, and the ultrasonic velocity decreased from 4706 m/s to 3859 m/s. The volume of water content increased from zero to 8%. With the increase in soaking time, the water absorption capacity decreases gradually. After 9 days of soaking, the mass of the 6 cm diameter of the sample increases by only 3.8 g, and the final ultrasonic velocity was 1500 m/s. The volume water content of the sample was 42%.

Simulated Signals The Minimal of AIC (ns) Primary Echo Position (ns) Observed
Calculation formula for volume water content: where m A is the mass of the sample after soaking, and m B is the mass of the sample before soaking. β is the density of the water, and V is the volume of the sample. Figure 6 shows that the variation of ultrasonic echo velocity and stem water content of stem samples during water absorption can be effectively fitted by two polynomials. The average correlation coefficient reached about 0.98. Calculation formula for volume water content: where is the mass of the sample after soaking, and is the mass of the sample before soaking. β is the density of the water, and V is the volume of the sample. Figure 6 shows that the variation of ultrasonic echo velocity and stem water content of stem samples during water absorption can be effectively fitted by two polynomials. The average correlation coefficient reached about 0.98.   Figure 7 shows two living sunflowers. From 12:00 to 18:00, the ultrasonic primary echo position and soil moisture have almost the same trends of changes. The average soil moisture value of sample 1 is 64%, the mean value of the ultrasonic primary echo position is 1.40 ns, and the average ultrasonic velocity is 1813 m/s. The average weight of the soil moisture of sample 2 is 61.8%, the mean value of primary ultrasonic echo is 1.65 ns, and the average ultrasonic velocity is 2844 m/s. The ultrasonic rate of the stem with water filling is lower than that of the stem with water shortage. This agrees with the experimental results of the above-water immersion test.

Location Detection of Ultrasonic Echo from the Stem Body of a Living Sunflower
When the sunflower (sample 2) is short of water for a short time, at 12:00, the soil moisture is 70%, the ultrasonic echolocation is 2.07 ns, and the velocity is 2153 m/s. In order to maintain moisture, it shows that the sunflower restricts CO 2 uptake and photosynthesis rate, and the transpiration activity is inhibited. Then, when soil moisture is adequate, the sunflower switch to normal water absorption and transpiration. At 13:00, transpiration activity was the most active all day; stem water decreased rapidly, and soil moisture decreased to 50%. The primary echo position fell to 1.42 ns, and the velocity speed is up to 3138 m/s.
When the sunflower (sample 1) is water-filling, from 11:00 to 14:00, the changes in the primary position are the most active. The velocity changes are moderated compared to the sunflower short of water. moisture value of sample 1 is 64%, the mean value of the ultrasonic primary echo position is 1.40 ns, and the average ultrasonic velocity is 1813 m/s. The average weight of the soil moisture of sample 2 is 61.8%, the mean value of primary ultrasonic echo is 1.65 ns, and the average ultrasonic velocity is 2844 m/s. The ultrasonic rate of the stem with water filling is lower than that of the stem with water shortage. This agrees with the experimental results of the above-water immersion test. When the sunflower (sample 2) is short of water for a short time, at 12:00, the soil moisture is 70%, the ultrasonic echolocation is 2.07 ns, and the velocity is 2153 m/s. In order to maintain moisture, it shows that the sunflower restricts CO2 uptake and photosynthesis rate, and the transpiration activity is inhibited. Then, when soil moisture is adequate, the sunflower switch to normal water absorption and transpiration. At 13:00, transpiration activity was the most active all day; stem water decreased rapidly, and soil moisture decreased to 50%. The primary echo position fell to 1.42 ns, and the velocity speed is up to 3138 m/s.

Discussion and Conclusions
As non-homogeneous anisotropic non-metallic materials, there is a wide range of complex acoustic impedance interfaces within the stem, forming complex ultrasonic echo signals. The hybrid differential AIC algorithm can automatically detect the ultrasonic primary echo position of the plant stem. The experiment shows that using the hybrid difference AIC algorithm can achieve the accurate primary echo positions of stems, which lays the foundation for the ultrasonic detection of the plant stem.
The experiment of measured wood immersion shows that the primary echo position of the ultrasonic wave can effectively track the change in the water content of stems. However, when the ultrasonic attenuation of plant stems is too large, or the plant stems are too thick, the echo signal cannot be obtained even by increasing the ultrasonic emission energy, the method cannot be used.
The dynamic detection of the stem of a living sunflower can be carried out because of the non-destructive testing characteristics of ultrasound. The velocity of the stem when the sunflower is in the filling changes more actively than that in a water shortage. The results may present that the sunflower can regulate the water absorption and transpiration in balance in the filling condition, which ensures the stem has relatively constant water content. On the contrary, the sunflower would compress the absorption and transpiration in a water shortage. So, keeping the relatively regular water content in the stem is hard.
It is assumed that sunflowers have apparent growth regulation for sunflower detection only in the daytime. Therefore, readings were only taken in the daytime, and we did not explore the differences between daytime and nighttime.
Subsequent research can effectively intercept the primary echo signal after obtaining the primary echo's location and analyze the dynamic growth's spectrum characteristics and the change in the stem from the perspective of frequency energy.
To further analyze the characteristics of dynamic physiological changes of plant stems detected by ultrasound, we can design a contrastive analysis between ultrasonic detection and stem structure anatomy to explore features of dynamic physiological changes of the stems with the ultrasonic method.