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Abstract
This paper demonstrates an underwater localization system based on an improved phase-sensitive optical time domain reflectometry (φ-OTDR). To localize the underwater acoustic source, 3D-printed materials with relatively high Poisson's ratio and low elastic modulus are wrapped by single-mode optical fibers to serve as an L-shaped planar sensing array, yielding a high-fidelity retrieval of acoustic wave signals. Based on the time difference of arrival (TDOA) algorithm, the time delay of signals detected by multiple sensing elements is used to locate the underwater acoustic source. Consequently, the three-dimensional localization feasibility of the proposed system is experimentally verified, showing a measurement error of about 2% in the localization range. It indicates that the proposed scheme is of great potential for applications in the underwater environment, such as trajectory tracking, oil/gas pipeline security monitoring and coastal defense.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Underwater sound source localization is one of the necessary technologies for ocean exploration, such as trajectory tracking, underwater oil and gas pipeline security monitoring, coastal defense and so on [1]. Up to date, wireless sensor networks with multiplexing of numerous acceleration sensors are widely used to realize underwater acoustic source localization [2]. However, due to the complexity of underwater environment, e.g., serious acoustic attenuation, high requirements for medium uniformity and the existence of multipath characteristics, the inter symbol interference has been always produced, resulting in the degeneration of high-fidelity underwater sound source localization [3]. Moreover, the synchronization of multi node multiplexing in wireless sensor networks is always hard to be achieved, which limits its further improvement of underwater localization accuracy.
F iber optic hydrophones can realize highly sensitive underwater acoustic signal measurement. With assistance of time-division multiplexing (TDM) technology, it is possible to construct arrays for underwater acoustic localization [4–6]. Compared with piezoelectric hydrophones, fiber optic hydrophones have the unique characteristics such as anti-electromagnetic interference, anti-corrosion, and so on. However, the multiplexing technology is challenging in large-scale underwater localization which requires a number of point sensors. To solve this problem, distributed acoustic sensing (DAS) system based on φ-OTDR has been proposed and aroused numerous interests of researches [7,8]. Attentions have been intensively paid on the combination of distribution characteristics and signal processing technology to realize the real-time monitoring of acoustic signals with a high sensitivity [9–11], which is of great significance to practical applications, such as power system, monitoring of trains system and structural health monitoring [12–15]. Recently, the utilization of DAS system for localization has reported that the sound source in the air is located in two-dimensional plane and three-dimensional space [16]. Typically, the φ-OTDR system uses the weak Rayleigh scattering light along the commercial optical fibers for sensing, which limits its sensitivity and imposes the other requirements for high power boost by extra low noise amplifiers. To address this issue, weak Bragg grating arrays or specialty doped fibers are proposed to enhance distributed scattered optical signals [17,18]. More recently, rapid fabrication of sensing element with increased sensitivity by 3D printing technology has been reported [19]. Thanks to its flexible materials, large design space, fast preparation speed and accurate reproducibility, 3D printing technology is widely used in the fields of customized optical sensors, embedded electronic components [20], etc. So far, underwater localization experiments based on distributed optical fiber sensing is rarely reported.
In this paper, 3D-printed materials with relatively high Poisson's ratio and low elastic modulus are wrapped by single-mode optical fibers to serve as an L-shaped planar sensing array, which is interrogated by a φ-OTDR system to detect underwater acoustic source for the first time. Through the time delay of multiple sensing elements in the array, the three-dimensional localization of underwater sound source is realized by using TDOA. The results show that the proposed underwater localization system based on the improved phase sensitive φ-OTDR can achieve high-precision localization in three-dimensional underwater space with an error of 2% in localization range, which paves the way for applications in the underwater environment, such as trajectory tracking, oil/gas pipeline security monitoring and coastal defense.
2. Localization algorithm
Among large numbers of localization algorithms, TDOA is specially used to realize underwater localization [21–23]. Instead of the absolute time signal detected by the sensor, the time synchronization requirement between the acoustic source node and the receiving node is reduced. Therefore, TDOA localization method is less affected by the underwater environment, and has attracted much attention in underwater acoustic localization method based on distance [24].
TDOA algorithm is a localization method by detecting the difference between the time when the signal arriving at the sensor and the reference sensor. This method is actually a hyperbolic localization method. The principle is as following: assuming that the acoustic source propagates linearly to each sensor node, hence the propagation distance difference between the acoustic source and each sensor node can be solved. As illustrated in Fig. 1, a set of hyperbolas focusing on each sensor node pair have an intersection point which is ultimately recognized as the location of the acoustic source node.
As shown in Fig. 1, suppose the location coordinates of the acoustic source are $(x,y,z)$, and $({x_k},{y_k},{z_k})$(k = 1, 2, 3, …, m) is the location of the k-th sensor while $({x_\textrm{0}},{y_\textrm{0}},{z_\textrm{0}})$ is the location of the reference sensor. The distance between the sound source and the k-th sensor, the distance between the sound source and the reference sensor. The difference between the two distances is critical for TDOA localization, which is represented by ${d_k}$, ${\upsilon _\textrm{w}}$ is the velocity of acoustic source propagation underwater and ${t_k}$ is the time delay between the k-th sensor and the reference sensor. The hyperbolic equation of m pairs passing through the acoustic source can be obtained as follows:
When $m \ge 4$, the unique solution of Eq. (1) can be practically obtained, that is, the location estimation of acoustic source.
Since Eq. (1) is difficult to be directly solved and has a large amount of calculation. There are usually two solutions: Taylor series method and Chan algorithm. Taylor series method is an iterative recursive method, but if the initial value is not selected properly, it is easy to fall into the local optimal solution, and the accuracy is difficult to guarantee [25]. On the other hand, Chan algorithm is a non-recursive algorithm, which uses the weighted least square method to resolve the location of acoustic source [26]. In this paper, Chan algorithm is adopted to simplify the calculation.
In addition, TDOA algorithm also has its limitation which requires multiple nodes to locate the target, and the synchronization problem of multiple sensors basically affects the localization accuracy. However, in our scheme, multiple sensors in φ-OTDR system are connected in series in one optical path (i.e. one optical fiber), in which the speed of light is fast enough to guarantee the synchronization among different sensors. Therefore, multiple sensors along adjacent optical fiber positions can naturally be synchronized, benefiting for TDOA algorithm.
3. Simulation of φ-OTDR-based acoustic source localization
φ-OTDR is based on the collection of Rayleigh scattering light in optical fiber, and its whole sensing fiber can be used as sensing unit, which has excellent distributed characteristics. It is also suitable for the array construction of underwater sound source localization system. A preliminary simulation based on φ-OTDR system and TDOA algorithm was made in order to demonstrate the possibility of localization and the principle of array construction, as show in Fig. 2. Here, a section of optical fiber with the length of 3 m was concentrated wound in a 30 mm diameter 3D-printed sensing element as shown in Fig. 2(b) inset. Generally speaking, if the fiber length of sensing element is much less than the spatial resolution, the sensitivity of φ-OTDR signal would be degenerated. On the other hand, although the sensitivity of the sensing element can be improved by increasing the fiber length within it, the sensing element size will become large leading to the loss of flexibility and accuracy of localization. Therefore, according to the 5 m spatial resolution determined by the φ-OTDR system parameters, we set the fiber length of sensing element to 3 m. Pulse width $({\textrm{c}/\textrm{n}} )\cdot ({\tau /2} )$, detector bandwidth $c/({2nw} )$, and data acquisition card $({1/2{f_s}} )\cdot ({\textrm{c}/\textrm{n}} )$ will affect the spatial resolution, where c is the speed of light in vacuum, n is the refractive index of optical fiber, $\tau $ is the pulse width, w is the bandwidth of detector, and ${f_s}$ is the sampling frequency of data acquisition card. The influence of the pulse width on the spatial resolution is typically as meter level, while the influence of the sampling frequency of the data acquisition card and the detector bandwidth on the resolution is about decimeter level [9]. Therefore, the spatial resolution of φ-OTDR system are finally determined by the pulse width. To improve the sensitivity, the sensing element uses materials with high Poisson's ratio and low elastic modulus, which is also more suitable for underwater environment [19]. The relationship between the lateral diameter variation of the sensing element $\Delta D$ and the material parameters (Poisson's ratio $\mu$ and elastic modulus $E$) can be expressed as follows [27]:
where $F$ is the axial pressure, $D$ is the lateral diameter of the sensing element, $S$ is the cross-sectional area of the sensing element.
Fig. 2. Simulation of φ-OTDR-based acoustic source localization: (a) Schematic diagram of sensing element and system device (b) Structure of sensing element array (The inset shows schematic diagram of 3D-printed sensing element) (c) Five sensing elements detect the peak value of the cosine signal in simulation (The inset shows cosine signal detected by five sensing elements)
Because the optical fiber is tightly wound in the sensing element and fixed with glue, the diameter variation of the optical fiber would be the same as that of the sensing element. According to Formula (2), in order to improve the sensing sensitivity, the material with low elastic modulus and high Poisson's ratio should be selected for sensing element. Compared with Acrylonitrile Butadiene Styrene (ABS) and Polylactic Acid (PLA), the Poisson's ratio of flexible material is slightly higher and the elastic modulus is one order of magnitude lower.
The parameters in the simulation are shown in Table 1. An acoustic source with a cosine signal with 300 Hz frequency and 0.3 V peak value is introduced and it generated acoustic wave propagates towards the sensor array consisting of five sensing elements, as depicted in Fig. 2(a). The simulation of underwater signals is mainly based on the time delay of the signal. By calculating the distance difference between the acoustic source signal propagating to the reference sensing element and the ordinary sensing element, the time delay is then obtained. Here, we use the same waveform signals with a certain time delay to conduct the simulation.
Table 1. Parameters of proposed system based on φ-OTDR in simulation
In the simulation, high precision localization can be achieved, when the pulse repetition frequency fp in φ-OTDR system is set as 150 kHz. Figure 2(c) shows the peak value of the demodulated signals detected by the five sensing elements. The Fig. 2(c) inset shows complete demodulated signals. The demodulated signal is obtained by quadrature demodulation (I/Q demodulation) which can extract both amplitude and phase information of backscattered Rayleigh light from beat frequency signals. Quadrature demodulation divides the beat frequency signal into two channels, converting it into I-channel and Q-channel output signals through low-pass filter, and then realizes the phase calculation through arctangent. Appropriate movement was made in the y-axis direction for convenient observation. Then, we get the peak signal time of the five sensing elements by analyzing the waveform from Fig. 2(c) so as to get the time delay. According to the TDOA algorithm mentioned above, the sensing element with the earliest acoustic signal was selected as the reference when calculating, i.e, the sensing element #1. The time delay from sensing element #2 to #5 to the reference (sensing element #1) was 0.113 ms, 0.033 ms, 0.133 ms and 0.267 ms, respectively. The location of acoustic source was calculated as (9.931, 4.359). Compare with the theoretical location of (10, 5), the error of x-axis was −0.069 cm, and that of y-axis was −0.641 cm. In the simulation, it is found that the localization accuracy mainly depends on fp. Consequently, acoustic source localization can be achieved by φ-OTDR incorporating the TDOA algorithm with an optimal accuracy.
In order to determine the sensing array construction, subsequent simulation is conducted based on fp of 150 kHz, which limits the usable optical fiber length up to 666 m. Meanwhile, wp is 50 ns which corresponds to a spatial resolution of 5 m. Therefore, the length of all optical fibers in the array should be in the range of 5-666 m. Theoretically, the fiber length between adjacent sensing elements (l) has little effect on the localization accuracy. When l is set to 50 m, the fiber length between #1 and #5 sensing elements is about 200 m (corresponding to 0.001 ms time delay), the effect on the localization accuracy can be ignored. Due to the influence of the resolution time of φ-OTDR system, the farther the array sensing element spacing (s) is, the larger the detectable distance is. Through simulation, when we set s as 2 m, we can achieve a detection range of 300 m. The 50 m of l enables the array to be used according to the actual scene and situation. The array structure can be arranged flexibly. Due to the limitation of underwater environment, we use l of 50 m, s of 20 cm, five sensing elements array to achieve localization in the follow-up experiment.
4. Experimental setup
As shown in Fig. 3(a), the φ-OTDR system with proposed 3D-printed sensing elements was used to detect underwater acoustic source. The φ-OTDR system used a narrow-linewidth laser (NLL) as the light source. The light output from the light source was divided into two channels by a 90:10 coupler. 90% of the light was modulated into pulse light by an acoustic optical modulator (AOM). After being amplified by an erbium doped fiber amplifier (EDFA), it entered the circulator, and the #2 port of the circulator was connected to the sensing elements. By another 50:50 coupler, the back scattered light and 10% of the local oscillator light beat together for the interference signal which is transformed into electrical signal by a balance photodetector (BPD), then collected by a data acquisition card (DAQ) and processed by a computer. Figure 3(b) is a physical image of the experimental device. We fixed five sensing elements on stainless steel mesh with iron wire to form an L-shaped array, which made the sensing elements array easy to be laid underwater. Meanwhile the sensing element array was flexible, the array structure can be adjusted at any time according to needs. The whole underwater experiment was carried out in a water tank. The water tank is 90 cm in length, 50 cm in width and 50 cm in height. The depth of water in the tank is 30 cm.
Fig. 3. Experimental setup: (a) Schematic diagram of experimental device (b) Physical drawing of experimental device
Then different materials were used to make elastic cylinder of sensing element, which was compared with optical fiber ring to study the influence of structure and material on system sensitivity in the experiment. We made three kinds of elastic cylinder with ABS, PLA and flexible PLA materials. Three kinds of sensing elements were fabricated by winding 3 m long optical fiber on the cylinder. At the same time, the optical fiber of same length of was made into optical fiber ring with the same diameter. The fiber ring was used to compare with the sensing elements of the three materials. Firstly, the sensitivity of the four sensing structures in the air was compared. The four sensing structures were placed on the Lead Zirconate Titanate (PZT) which was driven by a 3 V sinusoidal signal, the frequency ranged from 0.5 kHz to 10 kHz, and the step size was 0.5 kHz. Figure 4(a) shows the peak-to-peak value of phase difference in the air. Meanwhile, we put the four sensing structures in the water tank at the same level as the underwater sound source. They were close enough to be believed that the received underwater signals were consistent. The underwater sound speaker was driven by an electrical continuous sinusoidal signal with 3 V peak-to-peak voltage. The frequency ranged from 0.5 kHz to 10 kHz with 0.5 kHz as a step. The peak-to-peak value of phase difference detected by the four sensing structures changes with the frequency, as shown in Fig. 4(a). And Fig. 4(b) shows the restoration of 1 kHz sinusoidal signal by the four sensing structures. In Fig. 4(a), whether in air or underwater, we can see that the sensitivity of flexible material is about 1.5 times of that of ABS material and PLA material due to its high Poisson's ratio and low elastic modulus, and ABS is slightly better than PLA material. The change trend of sensitivity of the three materials with frequency is roughly the same. Compared with the optical fiber ring without elastomer structure, the sensitivity of the three materials sensing element has a greater improvement. From the reduction of 1 kHz sinusoidal signal in Fig. 4(b), it can be seen that flexible material not only has high sensitivity, but also reduces the signal distortion of sensors with elastomer compared with optical fiber ring. Therefore, in the follow-up experiment, the sensing element array made of flexible material was used to conduct underwater localization experiment. Then as shown in Fig. 3(a), five sensing elements are connected in series to form L-shaped sensing element arrays to study the localization effect combined with the simulation results.
Fig. 4. Comparison of four kinds of sensing structures for detection acoustic waves with different frequencies. (a) Peak-to-peak value of phase difference of three kinds of 3D-printed sensing element and SMF fiber ring in the air and underwater (b) Demodulated phase difference of three kinds of 3D-printed sensing element and SMF fiber ring underwater at 1 kHz
5. Experimental results and discussions
In the whole experimental process of exploring the localization accuracy, we detected the underwater acoustic source signal through different location sensing elements, and realized the localization of acoustic source combining with TDOA algorithm.
Firstly, the influence of fp on the localization accuracy of the system is studied. The structure shown in the simulation is adopted. The acoustic source uses an underwater sound speaker with a burst signal. During the experiment, the location of sound speaker and the sensing elements remained unchanged. fp was changed from 10 kHz to 150 kHz with 10 kHz as a step. The burst signal with a time interval of 80 ms, the cycle of 5, the center frequency of 5 kHz, the peak-to-peak voltage of 1 V was applied to the sound speaker. In the follow-up study of localization accuracy, the burst signal kept consistent.
Through the calculation of the standard deviation of the obtained amplitude at each fiber location, intensity localization can be realized, as shown in Fig. 5(a). There are five obvious localization peaks corresponding to the five sensing elements of the sensing element array. When the distance between sensing element and sound source increases, the peak value decreases. Because the acoustic signal will be attenuated along the propagation, its amplitude will also decrease with the increase of the propagating distance. Therefore, the closer sensing element is to the sound source, the higher the amplitude of the demodulated signal as well as its standard deviation. The ability of sensing element to collect underwater signals is proved. Figure 5(b) shows the underwater acoustic demodulated signals detected by five sensing elements at fp of 150 kHz. The local amplification of the starting location of underwater sound signals are shown in Fig. 5(c). The starting time is obtained by selecting the starting interval and getting peak value corresponding to the time in the starting interval by traversal algorithm. Through traversing, all the amplitudes and corresponding time in the starting interval are stored in the ordered map data structure, and the right boundary value is extracted as the starting time, and the data storage of the starting interval is realized. Appropriate movement is also made in the y-axis direction for convenient observation. It can be seen from Fig. 5(c) that the starting time of demodulated signals detected by sensing elements #1 to #5 was 9.427 ms, 9.540 ms, 9.460 ms, 9.560 ms, 9.693 ms, respectively. The location of acoustic source is (9.933, 4.359) with the error of x-axis is −0.067 cm, and that of y-axis is −0.641 cm.
Fig. 5. Acoustic signal detected by five sensing elements as fp is 150 kHz (a) Intensity localization signal of underwater acoustic source (b) Underwater acoustic signal detected by sensing element (c) Local amplification of the starting location of underwater sound signal.
Taking the actual location of the acoustic source as the benchmark, the offset between the localization results and the actual position in rectangular coordinate, i.e. the offset of x-axis and y-axis, are plotted in Fig. 6(a). Localization error calculated by TDOA algorithm varies with fp in simulation and experiment, as shown in Fig. 6(b). From Fig. 6, we can see that the experimental results are consistent with the simulation, the higher fp is, the shorter the time interval between two adjacent sampling points can be resolved, and the higher the accuracy is. When fp is less than 30 kHz, the localization accuracy is poor because the time interval that can be distinguished is too long. When fp is 30 kHz, the time interval of the minimum distinguishable sampling point is 1/30 ms, which is about 0.033 ms. While the theoretical time interval from the acoustic signal to the #1 sensing element and #3 sensing element is only 0.031 ms, which is less than the minimum resolvable time, so the accuracy has a large deviation compared with other frequencies. Through calculation, when the array structure mentioned in this paper is adopted, and fp is higher than 32 kHz, the localization error can be controlled within an ideal range. This is also verified by simulation and experiment. In Fig. 6(b), on condition that the minimum distinguishable time interval is less than the propagation time difference between the acoustic source and any two sensing elements, the localization error decreases linearly with fp. The experimental results show that the parameters of the φ-OTDR system and array determined by our simulation are correct.
Fig. 6. Localization results of φ-OTDR system with different fp: (a) The offset between the localization results and the actual position in rectangular coordinate (b) Localization error varies with fp in simulation and experiment.
Then, the ability of the proposed structure in three-dimensional localization was explored. In order to explore the accuracy of three-dimensional localization, we introduced z-axis and placed the sound source in different locations. As shown in Fig. 7, the coordinates of sensing elements #1 to #5 are (50, 5, 0), (50, 45, 0), (50, 25, 0), (70, 5, 0), (90, 5, 0), respectively. From (40, 5, 10) to (40, 5, 25), we placed the underwater sound speaker in 18 different locations to explore the localization accuracy of the array in three-dimensional underwater space. The two adjacent underwater sound speaker locations are 15 cm apart in a certain direction of x-axis, y-axis or z-axis, corresponding to the test series #1 to #18.
Fig. 7. Schematic diagram of sound speaker and L-shaped sensing element array in three-dimensional underwater space when localization accuracy is explored
According to the time delay of the signal detected by the sensing element, the localization results can be obtained by the three-dimensional TDOA localization algorithm. Figure 8(a) shows the actual and calculated location of the sound source, and the localization errors of different test series are shown in Fig. 8(b). It can be seen that the single direction maximum error of x-axis, y-axis and z-axis is 2.4945 cm, the minimum error is 0.0164 cm, and the average error is 0.7844 cm from Fig. 8(a). The maximum localization error is 3.4358 cm, the minimum is 0.3338 cm, and the average is 1.6663 cm, as shown in Fig. 8(b). Regarding the localization range, the localization accuracy is estimated at about 2%.
Fig. 8. Sketch diagram of localization results in three-dimensional space by L-shaped array: (a) Actual and calculated location of sound source (b) Localization error of different test series.
In addition, the frequency range of the acoustic signal located by the proposed system was discussed. We fixed the sound source at (10, 5, 10) and changed the frequency of burst signals to implement the experiment. Figure 9(a) shows the offset between the localization position of 3-25 kHz burst signals and the actual position, and Fig. 9(b) shows the localization error varies with the frequency of the sound source signal. When the frequency is less than 3 kHz, it is located near the resonant frequency of the sensing element, which is not suitable for underwater localization. When the frequency is higher than 25 kHz, the signal-to-noise ratio becomes worse due to the serious attenuation of high frequency acoustic signal, resulting in the failure of the localization. It is found that the localization error of the proposed system for 3-25 kHz signal remains about 2% of the localization range. The detectable frequency range basically covers the underwater equipment signals and very low frequency (VLF) band.
Fig. 9. The localization results of burst signals with different frequencies at the same sound source location: (a) The offset between the localization results of different frequencies and the actual position (b) Localization error varies with frequency of sound source signals
In this scheme, the pulse repetition frequency (fp) is critical to the localization performance. To improve the localization performance, one need to increase fp, which, however, would decrease the detectable length of the sensing optical fiber used by φ-OTDR system. The longest available fiber length can be estimated by 108*(1/ fp) in typical φ-OTDR system. Meanwhile, fp will also limit the size of the array, thus affecting the localization range. Therefore, it is suggested to use the minimum size of the array within the detectable range for the reduction of the required fiber length as much as possible, which can benefit an optimal system resolution as well as the highest localization accuracy.
6. Conclusion
In this paper, a φ-OTDR system with a sensing element array for underwater acoustic source localization is demonstrated for the first time. As the sensing element with optimized sensitivity, 3D-printed materials with relatively high Poisson's ratio and low elastic modulus are wrapped by single-mode optical fibers. The sensitivity of optical fiber without any 3D-printed structure between adjacent sensing elements is much lower, thus the detected acoustic signal is relatively weak. Furthermore, the influence of acoustic signal on the optical fiber between adjacent sensing elements can be shielded by using armored fiber cable. By applying the TDOA algorithm to the time delay analysis of the acoustic signal detected by different sensing elements, the proposed system can achieve acoustic source localization with error of centimeter in three-dimensional underwater space. It shows that the proposed underwater localization system has many advantages, such as high localization accuracy, easy deployment, low cost, and excellent synchronization due to the multi-sensing elements within a single long span fiber. With the flexible fabrication of 3D-printed sensing elements and the distributed characteristics of φ-OTDR system, the proposed system can easily multiplex more sensing arrays to meet the expansion of large-scale array. It suggests that the underwater acoustic source localization system based on φ-OTDR can be applied to trajectory tracking, oil/gas pipeline security monitoring and coastal defense.
Funding
National Natural Science Foundation of China (61975108, 61905138, 61735009, 61875118); Science and Technology Commission of Shanghai Municipality (20ZR1420800); Shanghai Professional Technology Platform (19DZ2294000).
Disclosures
The authors declare no conflicts of interest.
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