A Bio-Inspired MEMS Wake Detector for AUV Tracking and Coordinated Formation

: AUV (Autonomous Underwater Vehicle) coordinated formation can expand the detection range, improve detection efﬁciency, and complete complex tasks, which requires each AUV to have the ability to track and locate. A wake detector provides a new technical approach for AUV cooperative formation warfare. Now, most of the existing artiﬁcial lateral line detectors are for one-dimensional ﬂow ﬁeld applications, which are difﬁcult to use for wake detection of AUVs. Therefore, based on the pressure gradient sensing mechanism of the canal neuromasts, we apply Micro-Electro-Mechanical System (MEMS) technology to develop a lateral line-inspired MEMS wake detector. The sensing mechanism, design, and fabrication are demonstrated in detail. Experimental results show the detector’s sensitivity is 147 mV · (m/s) − 1 , and the detection threshold is 0.3 m/s. In addition, the vector test results verify it has vector-detecting capacity. This wake detector can serve AUVs wake detection and tracking technology, which will be promising in AUV positioning and coordinated formation.


Introduction
With the advancement and maturation of AUV technology, the difficulty and complexity of the tasks it undertakes are also greatly increased. These tasks include large-scale ocean mapping, shipwreck search, seabed exploration, and underwater target detection and identification. AUV collaborative formation technology can effectively expand the detection range, improve detection efficiency, and even complete complex tasks that are difficult to complete with a single AUV [1]. To achieve AUV cooperative formation for combat tasks, each AUV needs to possess sensing, positioning, and tracking of other AUVs.
AUV remote sensing detection technology currently encompasses acoustic, optical, and electromagnetic detection techniques [2]. Acoustic detection has traditionally been the primary method for AUV sensing and positioning. However, sonar detection is greatly influenced by marine ambient noise, and sound waves experience refraction in the ocean's transition layer, which can adversely affect the performance of active sonar detection. With advancements in AUV silent technology, the role of passive acoustic detection based on hydrophones is becoming increasingly difficult. Optical detectors employ optical imaging technology to detect the underwater environment and sense targets. Nevertheless, the refraction and the dim underwater visual environment seriously impact the sensing and positioning functions of AUVs. Additionally, electromagnetic wave attenuation in the ocean is also severe [3,4]. Consequently, AUV sensing and detection in complex marine environments pose significant challenges.
When the hull is sailing, because of the propulsion system, the wake zone, bubble wake, and turbulent wake generated by the propulsion system exhibit distinct characteristics compared to the surrounding seawater [5]. The two different wake zones can be used as we propose a wake detector with a bionic package structure for AUVs. This packaging design not only protects the detector from being washed out by high-velocity currents bu also avoids underwater foreign objects (silt, etc.) impact. By equipping AUVs with wake detectors, they can navigate in formation and transmit a wider range of detection infor mation to ships and satellites, which is important for ocean exploration, as shown in Fig  ure 1. The red dashed circle is the locally enlarged content and the white arrow indicate the wake signal in the Figure 1.

Bionic Principle
In the lateral line system of fish, the canal neuromasts in the fish's lateral line play a crucial role. When the fish interacts with the surrounding water flow, the flow velocity and water pressure cause the mucus in the lateral line canal to flow, resulting in the tilting of the cilia. Consequently, the sensory nerves beneath the cilia generate nerve signals tha open ion channels in the cell membranes, altering the potential difference between the inside and outside of the cell. This process converts the fluid mechanical information into neural electrical signals, as depicted in Figure 2a [23]. Based on this principle, we have designed a bionic diversion shell and ciliated cross-beam sensitive unit, as shown in Fig  ure 2b,c. The red arrow means imitation, e.g., cilia mimics kinocilium. The bionic MEMS wake detector comprises two main components. The first component is the detector's core sensitive unit, which emulates the canal neuromasts in the fish's lateral line system. The second component is the bionic diversion cap, which mimics the structure of the latera line canal.
The bionic principle of the bionic diversion cap is the pressure gradient sensing mechanism of the fish lateral canal. When water flows through the canal, it creates a pres sure difference between the two small holes, resulting in the liquid flow from high to low

Bionic Principle
In the lateral line system of fish, the canal neuromasts in the fish's lateral line play a crucial role. When the fish interacts with the surrounding water flow, the flow velocity and water pressure cause the mucus in the lateral line canal to flow, resulting in the tilting of the cilia. Consequently, the sensory nerves beneath the cilia generate nerve signals that open ion channels in the cell membranes, altering the potential difference between the inside and outside of the cell. This process converts the fluid mechanical information into neural electrical signals, as depicted in Figure 2a [23]. Based on this principle, we have designed a bionic diversion shell and ciliated cross-beam sensitive unit, as shown in Figure 2b,c. The red arrow means imitation, e.g., cilia mimics kinocilium. The bionic MEMS wake detector comprises two main components. The first component is the detector's core sensitive unit, which emulates the canal neuromasts in the fish's lateral line system. The second component is the bionic diversion cap, which mimics the structure of the lateral line canal.
The bionic principle of the bionic diversion cap is the pressure gradient sensing mechanism of the fish lateral canal. When water flows through the canal, it creates a pressure difference between the two small holes, resulting in the liquid flow from high to low pressure within the canal. Figure 2d depicts the simulation of the pressure gradient principle simulation in the bionic diversion cap. As water flows over the top of the detector, the pressure at point 1 is 1190 Pa, and the pressure at point 2 is 875 Pa. The difference between the two points is 315 Pa. The fluid in the encapsulation cap flows from point 1 to point 2, leading to the deflection of the cilia. pressure within the canal. Figure 2d depicts the simulation of the pressure gradient principle simulation in the bionic diversion cap. As water flows over the top of the detector, the pressure at point 1 is 1190 Pa, and the pressure at point 2 is 875 Pa. The difference between the two points is 315 Pa. The fluid in the encapsulation cap flows from point 1 to point 2, leading to the deflection of the cilia. The core of the wake detector primarily consists of cilia and a high-precision fourbeam structure, as shown in Figure 2b. The cilia receive wake disturbance signals, and eight varistors are placed on the crossbeam to form the Wheatstone bridge. When water flows, the pressure difference generated by the small holes on both sides causes the liquid within the lateral line encapsulation cap to flow, resulting in the swinging of the cilia. This motion drives the mass block at the bottom of the cilia to deflect, thus driving the deformation of the crossbeam. Consequently, the resistance value of the varistor positioned on the crossbeam changes, causing an imbalance in the Wheatstone bridge, generating the output voltage and thus completing the transition from the wake signal to the electrical signal. The detectors can receive signals in both directions as the two Wheatstone Bridges are vertically aligned.

Signal Conversion Circuit
Eight varistors, R1-R8, are fixed on the crossbeam forming two Wheatstone fullbridge circuits, as illustrated in Figure 3b. When the cilium is subjected to the force generated by water movement, it oscillates to one side, driving the mass block at the bottom of the cilium to deflect. At this time, the mass block drives the crossbeam to produce bending. According to the piezoresistive effect, the varistors at each end of the cantilever feel compressive and tensile forces, respectively, so that the two varistors produce opposite changes, a resistance becomes larger, a resistance becomes smaller. The original equilibrium of the Wheatstone bridge is then broken, and the output voltage is generated. By converting the resistance variation of the piezoresistor into a corresponding voltage The core of the wake detector primarily consists of cilia and a high-precision four-beam structure, as shown in Figure 2b. The cilia receive wake disturbance signals, and eight varistors are placed on the crossbeam to form the Wheatstone bridge. When water flows, the pressure difference generated by the small holes on both sides causes the liquid within the lateral line encapsulation cap to flow, resulting in the swinging of the cilia. This motion drives the mass block at the bottom of the cilia to deflect, thus driving the deformation of the crossbeam. Consequently, the resistance value of the varistor positioned on the crossbeam changes, causing an imbalance in the Wheatstone bridge, generating the output voltage and thus completing the transition from the wake signal to the electrical signal. The detectors can receive signals in both directions as the two Wheatstone Bridges are vertically aligned.

Signal Conversion Circuit
Eight varistors, R1-R8, are fixed on the crossbeam forming two Wheatstone full-bridge circuits, as illustrated in Figure 3b. When the cilium is subjected to the force generated by water movement, it oscillates to one side, driving the mass block at the bottom of the cilium to deflect. At this time, the mass block drives the crossbeam to produce bending. According to the piezoresistive effect, the varistors at each end of the cantilever feel compressive and tensile forces, respectively, so that the two varistors produce opposite changes, a resistance becomes larger, a resistance becomes smaller. The original equilibrium of the Wheatstone bridge is then broken, and the output voltage is generated. By converting the resistance variation of the piezoresistor into a corresponding voltage change across the bridge, the detector converts the wake signal into the output voltage signal.  Due to the identical principles of the two channels, we can take the X channel as an example to analyze the detector's output. In the absence of a wake signal, the Wheatstone bridge circuit is in balance, and the bridge output is 0. When the wake flows through the cilia, the cilia swing and the Wheatstone bridge loses balance. The output voltage of the X channel, denoted as , can be expressed as follows: In Equation (1), is the input voltage, and since in the bridge and the cilia is at the center of the crossbeam, ∆ ∆ ∆ ∆ , so the above formula can be simplified as follows: Similarly, Y channel operates based on the same principle. According to the piezoresistive effect, the piezoresistive change is related to the stress on the beam in the following manner: ∆ where is the longitudinal piezoresistive coefficient and is the longitudinal stress of the piezoresistive. From the above equation, it can be seen that the output signal amplitude of the detector is proportional to the stress on the beam. By positioning the piezoresistor in the region of maximum stress on the beam, the sensitivity of the detector can be effectively enhanced.

Theoretical Analysis of the Detector's Mechanical Structure
The main properties of the detector include sensitivity and characteristic frequency, and our goal is to enhance the detector's sensitivity while ensuring it maintains sufficient bandwidth. It is well known that the working bandwidth of the detector is related to the resonant frequency of the detector's sensitive microstructure. According to previous related studies [24], it can be seen from Equation (4) that the eigenfrequency of the detector microstructure is influenced by the mass m and the elasticity coefficient k. Due to the identical principles of the two channels, we can take the X channel as an example to analyze the detector's output. In the absence of a wake signal, the Wheatstone bridge circuit is in balance, and the bridge output is 0. When the wake flows through the cilia, the cilia swing and the Wheatstone bridge loses balance. The output voltage of the X channel, denoted as V out−X , can be expressed as follows: In Equation (1), V in is the input voltage, and since R 1 = R 2 = R 3 = R 4 in the bridge and the cilia is at the center of the crossbeam, ∆R 1 = ∆R 2 = ∆R 3 = ∆R 4 , so the above formula can be simplified as follows: Similarly, Y channel operates based on the same principle. According to the piezoresistive effect, the piezoresistive change is related to the stress on the beam in the following manner: where θ l is the longitudinal piezoresistive coefficient and σ l is the longitudinal stress of the piezoresistive. From the above equation, it can be seen that the output signal amplitude of the detector is proportional to the stress on the beam. By positioning the piezoresistor in the region of maximum stress on the beam, the sensitivity of the detector can be effectively enhanced.

Theoretical Analysis of the Detector's Mechanical Structure
The main properties of the detector include sensitivity and characteristic frequency, and our goal is to enhance the detector's sensitivity while ensuring it maintains sufficient bandwidth. It is well known that the working bandwidth of the detector is related to the resonant frequency of the detector's sensitive microstructure. According to previous related studies [24], it can be seen from Equation (4) that the eigenfrequency of the detector microstructure is influenced by the mass m and the elasticity coefficient k.
Based on the aforementioned equation, we observe that the resonant frequency of the detector is negatively correlated with the mass and positively correlated with the elasticity coefficient. It can be seen from Equation (3) that the sensitivity characterization of the detector is closely related to the stress on the varistor on the cantilever. As shown in Figure 4, the external pressure signal is transmitted to the crossbeam through the cilium and the central mass block. Then, the moment M at the center of the crossbeam can be calculated through the following formula [25]: emote Sens. 2023, 15, x FOR PEER REVIEW Based on the aforementioned equation, we observe that the resonant fr detector is negatively correlated with the mass and positively correlated wit coefficient. It can be seen from Equation (3) that the sensitivity characteriza tector is closely related to the stress on the varistor on the cantilever. As sh 4, the external pressure signal is transmitted to the crossbeam through the central mass block. Then, the moment M at the center of the crossbeam can through the following formula [25]: The equation of stress on the cantilever beam is as follows [22]: In Equations (5) and (6), M is the moment at the central junction of can H is the height of cilium, r is the ciliary radius, p is the pressure on the cilia. from each point on the beam to the center of the beam, and S is the area of th received by the cilium. The names of other parameters are presented in Ta seen from Equation (6) that the sensitivity of the detector is positively corre height and radius of the cilia.

Description
Parameter Half-length of center block's side a Width of the cantilever beam b Length of the cantilever beam L Thickness of the cantilever beam t Based on the analysis provided in Section 2.2, it is established that the the detector is directly proportional to the stress applied to the beam. Refe tions (5) and (6), it becomes evident that the stress on the crossbeam exhi correlation with the parameters of the cilia. However, it is worth noting th The equation of stress on the cantilever beam is as follows [22]: In Equations (5) and (6), M is the moment at the central junction of cantilever beams, H is the height of cilium, r is the ciliary radius, p is the pressure on the cilia. X is the length from each point on the beam to the center of the beam, and S is the area of the wake signal received by the cilium. The names of other parameters are presented in Table 1. It can be seen from Equation (6) that the sensitivity of the detector is positively correlated with the height and radius of the cilia. Table 1. Description of microstructure parameter.

Description Parameter
Half-length of center block's side a Width of the cantilever beam b Length of the cantilever beam L Thickness of the cantilever beam t Based on the analysis provided in Section 2.2, it is established that the sensitivity of the detector is directly proportional to the stress applied to the beam. Referring to Equations (5) and (6), it becomes evident that the stress on the crossbeam exhibits a positive correlation with the parameters of the cilia. However, it is worth noting that larger cilia parameters result in increased cilia mass. Equation (4) further highlights that a larger mass leads to a smaller resonant frequency. Consequently, based on the above analysis, we observe that the resonant frequency and sensitivity of the detector are contradictory and cannot be simultaneously improved. Therefore, it is necessary to find a suitable parameter to ensure the performance of the detector. In order to address this, we will establish a mathematical model and conduct a parametric scan of the relevant parameters. The cilia material is photosensitive resin, whose density is similar to that of water, which can better pick up the wake vibration signal. In addition, the high Young's modulus of photosensitive resin can bring higher resonant frequency to the detector and ensure the working bandwidth of the detector.

Parameterization of Detector's Sensitive Microstructure
COMSOL is a numerical simulation software. It can optimize detector parameters and find crucial parameters among all of them. COMSOL was used to analyze the stress simulation and modal resonant frequency of the wake detector. In addition, COMSOL was used to simulate the actual application environment of the wake detector and analyze the detector's performance in the wake environment.
The above analysis makes it easy to find that the sensitivity and resonant frequency of the detector are mainly influenced by the structural dimensions of the cantilever beam and cilia. To obtain the inherent frequencies of the detector microstructure and the maximum stress on the crossbeam, we used the controlled variable method to scan the parameters with COMSOL. The results of the parameter scanning are depicted in Figure 5. material is photosensitive resin, whose density is similar to that of water, which can better pick up the wake vibration signal. In addition, the high Young's modulus of photosensitive resin can bring higher resonant frequency to the detector and ensure the working bandwidth of the detector.

Parameterization of Detector's Sensitive Microstructure
COMSOL is a numerical simulation software. It can optimize detector parameters and find crucial parameters among all of them. COMSOL was used to analyze the stress simulation and modal resonant frequency of the wake detector. In addition, COMSOL was used to simulate the actual application environment of the wake detector and analyze the detector's performance in the wake environment.
The above analysis makes it easy to find that the sensitivity and resonant frequency of the detector are mainly influenced by the structural dimensions of the cantilever beam and cilia. To obtain the inherent frequencies of the detector microstructure and the maximum stress on the crossbeam, we used the controlled variable method to scan the parameters with COMSOL. The results of the parameter scanning are depicted in Figure 5. Upon observing the scanning results, it becomes apparent that the sensitivity of the detector is positively correlated with the cilium height h, negatively correlated with the cilium radius r, and also negatively correlated with both the cantilever beam thickness t and width b. The resonant frequency of the detector is negatively correlated with the cilia height and positively correlated with the cilium radius; it is positively correlated with the thickness and width of the cantilever beam. These simulation results agree with the previous theoretical analysis. We can also find that the sensitivity and resonant frequency are Upon observing the scanning results, it becomes apparent that the sensitivity of the detector is positively correlated with the cilium height h, negatively correlated with the cilium radius r, and also negatively correlated with both the cantilever beam thickness t and width b. The resonant frequency of the detector is negatively correlated with the cilia height and positively correlated with the cilium radius; it is positively correlated with the thickness and width of the cantilever beam. These simulation results agree with the previous theoretical analysis. We can also find that the sensitivity and resonant frequency are much more influenced by the cilium height and cantilever beam thickness than by the cilium radius and cantilever beam width.
Based on the correlation analysis mentioned above, appropriate structural parameters are selected to enhance the detector sensitivity while ensuring the working bandwidth of the detector. Considering the process fabrication difficulty, we select the following parameters: L = 700 µm, t = 50 µm, b = 120µm, h = 8 mm, and r = 175 µm. Next, we performed eigenfrequency and steady-state simulations for the sensitive microstructures with determined structural parameters.
The simulation results are shown in Figures 6 and 7. Figure 6 is the stress distribution diagram in the X direction on the crossbeam. We can see that the largest stress is distributed at both ends of the cantilever. The piezoresistor is arranged in this area to maximize the piezoresistor force and thus improve the sensitivity of the detector. In the resonant frequency simulation, the resonant frequency of the detector microstructure is 1110.2 Hz. Then it was placed in water for wet mode simulation, and the first-order resonant frequency was 798.43 Hz, as shown in Figure 7. The upper bandwidth limit of the wake signal is less than 2/3 of the resonant frequency of the microstructure, which meets the needs of wake detection within 500 Hz [26]. much more influenced by the cilium height and cantilever beam th cilium radius and cantilever beam width.
Based on the correlation analysis mentioned above, appropriate ters are selected to enhance the detector sensitivity while ensuring the of the detector. Considering the process fabrication difficulty, we sele rameters: L = 700 µm, t = 50 µm, b = 120µm, h = 8 mm, and r = 175 µm. eigenfrequency and steady-state simulations for the sensitive microst mined structural parameters.
The simulation results are shown in Figures 6 and 7. Figure 6 is th diagram in the X direction on the crossbeam. We can see that the larg uted at both ends of the cantilever. The piezoresistor is arranged in th the piezoresistor force and thus improve the sensitivity of the detec frequency simulation, the resonant frequency of the detector microstr Then it was placed in water for wet mode simulation, and the first quency was 798.43 Hz, as shown in Figure 7. The upper bandwidth lim is less than 2/3 of the resonant frequency of the microstructure, which wake detection within 500 Hz [26].

Detector Package Design
According to the pressure difference principle of the fish lateral line canal, the bionic diversion cap is designed, as shown in Figure 8. The cap features four diversion holes that are aligned with the crossbeam and arranged orthogonally. This design enables the enhancement of one-dimensional flow field detection to two-dimensional flow field detection. Furthermore, the presence of this bionic diversion cap can protect the sensitive microstructure from the impact and collision of the current and sediment. In addition, the packaging structure effectively filters out low-frequency marine environmental noise and the low-frequency noise generated by the carrier's movement [27][28][29].

Detector Package Design
According to the pressure difference principle of the fish lateral line canal, the bionic diversion cap is designed, as shown in Figure 8. The cap features four diversion holes that are aligned with the crossbeam and arranged orthogonally. This design enables the enhancement of one-dimensional flow field detection to two-dimensional flow field detection. Furthermore, the presence of this bionic diversion cap can protect the sensitive microstructure from the impact and collision of the current and sediment. In addition, the packaging structure effectively filters out low-frequency marine environmental noise and the low-frequency noise generated by the carrier's movement [27][28][29].

Detector Package Design
According to the pressure difference principle of the fish lateral line canal, the diversion cap is designed, as shown in Figure 8. The cap features four diversion hol are aligned with the crossbeam and arranged orthogonally. This design enables t hancement of one-dimensional flow field detection to two-dimensional flow field tion. Furthermore, the presence of this bionic diversion cap can protect the sensiti crostructure from the impact and collision of the current and sediment. In additi packaging structure effectively filters out low-frequency marine environmental noi the low-frequency noise generated by the carrier's movement [27][28][29].  To obtain the optimal size, it is necessary to use the fluid-solid coupling module of COMSOL to construct the corresponding finite element models and conduct a parametric scan of the key parameters that affect the detector's performance. The primary parameters include the distance s from the diversion hole to the center of the top surface of the hat, the radius n of the diversion hole, and the height m of the diversion hole. Subsequently, the wake detector model is put into the wake environment model with an inlet flow velocity of 0.8 m/s, as shown in Figure 9. In this environment, these parameters are subjected to a parametric scan, and the obtained scanning results are presented below. To obtain the optimal size, it is necessary to use the fluid-solid coupling module of COMSOL to construct the corresponding finite element models and conduct a parametric scan of the key parameters that affect the detector's performance. The primary parameters include the distance s from the diversion hole to the center of the top surface of the hat, the radius n of the diversion hole, and the height m of the diversion hole. Subsequently, the wake detector model is put into the wake environment model with an inlet flow velocity of 0.8 m/s, as shown in Figure 9. In this environment, these parameters are subjected to a parametric scan, and the obtained scanning results are presented below. According to the scanning results, as shown in Figure 10, the diversion pore in the bionic diversion cap is also the main factor affecting the detector's sensitivity. A larger radius of the hole corresponds to higher sensitivity. However, it is crucial to consider the impact of sediment present in seawater, as a larger pore radius does not function better. Here, we choose the radius of the diversion pore as 900 µm. The height of the hole is negatively correlated with the sensitivity of the detector, but the effect is not significant. Considering the accuracy of 3D printing and the hardness of the resin material, we choose m = 500 µm. The distance between the diversion hole and the center is generally positively correlated with sensitivity. Here, we choose the point of maximum stress, s = 5200 µm. Thus, the main parameters of the detector have been determined. We performed finite element simulation analysis in COMSOL and placed the sensitive microstructure in the bionic diversion cap to form the detector model. The material According to the scanning results, as shown in Figure 10, the diversion pore in the bionic diversion cap is also the main factor affecting the detector's sensitivity. A larger radius of the hole corresponds to higher sensitivity. However, it is crucial to consider the impact of sediment present in seawater, as a larger pore radius does not function better. Here, we choose the radius of the diversion pore as 900 µm. The height of the hole is negatively correlated with the sensitivity of the detector, but the effect is not significant. Considering the accuracy of 3D printing and the hardness of the resin material, we choose m = 500 µm. The distance between the diversion hole and the center is generally positively correlated with sensitivity. Here, we choose the point of maximum stress, s = 5200 µm. Thus, the main parameters of the detector have been determined. To obtain the optimal size, it is necessary to use the fluid-solid coupling module of COMSOL to construct the corresponding finite element models and conduct a parametric scan of the key parameters that affect the detector's performance. The primary parameters include the distance s from the diversion hole to the center of the top surface of the hat, the radius n of the diversion hole, and the height m of the diversion hole. Subsequently, the wake detector model is put into the wake environment model with an inlet flow velocity of 0.8 m/s, as shown in Figure 9. In this environment, these parameters are subjected to a parametric scan, and the obtained scanning results are presented below. According to the scanning results, as shown in Figure 10, the diversion pore in the bionic diversion cap is also the main factor affecting the detector's sensitivity. A larger radius of the hole corresponds to higher sensitivity. However, it is crucial to consider the impact of sediment present in seawater, as a larger pore radius does not function better. Here, we choose the radius of the diversion pore as 900 µm. The height of the hole is negatively correlated with the sensitivity of the detector, but the effect is not significant. Considering the accuracy of 3D printing and the hardness of the resin material, we choose m = 500 µm. The distance between the diversion hole and the center is generally positively correlated with sensitivity. Here, we choose the point of maximum stress, s = 5200 µm. Thus, the main parameters of the detector have been determined. We performed finite element simulation analysis in COMSOL and placed the sensitive microstructure in the bionic diversion cap to form the detector model. The material We performed finite element simulation analysis in COMSOL and placed the sensitive microstructure in the bionic diversion cap to form the detector model. The material pa-rameters used in the simulation model are the actual values in the detector manufacturing process. Then, the constructed detector model was placed within the wake simulation environment for further analysis. This enabled us to obtain the flow field distribution around and inside the detector, as well as the displacement stress distribution of the crossbeam.
The wake detector's axis aligns parallel to the axis of the AUV carrier. When the AUV moves forward straightly, or the wake comes straight along the axis of the AUV, there is neither a pressure difference between the diversion pore of the wake detector nor obvious flow in the chamber. As a result, the output voltage of the detector is approximately zero, as shown in Figure 11a. However, when the wake comes along the direction deviated from the axis of the wake detector, the cilium would vibrate, and there would be a corresponding output signal, as shown in Figure 11b. In addition, the bionic diversion cap mimicking the lateral line canal can also filter out the low-frequency marine environmental noise and the noise generated by the movement of the carrier [12]. Figure 11c shows the stress distribution on crossbeams at different flow rates, and Figure 11d demonstrates the displacement curve on the crossbeams corresponding to Figure 11b. parameters used in the simulation model are the actual values in the detector manufacturing process. Then, the constructed detector model was placed within the wake simulation environment for further analysis. This enabled us to obtain the flow field distribution around and inside the detector, as well as the displacement stress distribution of the crossbeam.
The wake detector's axis aligns parallel to the axis of the AUV carrier. When the AUV moves forward straightly, or the wake comes straight along the axis of the AUV, there is neither a pressure difference between the diversion pore of the wake detector nor obvious flow in the chamber. As a result, the output voltage of the detector is approximately zero, as shown in Figure 11a. However, when the wake comes along the direction deviated from the axis of the wake detector, the cilium would vibrate, and there would be a corresponding output signal, as shown in Figure 11b. In addition, the bionic diversion cap mimicking the lateral line canal can also filter out the low-frequency marine environmental noise and the noise generated by the movement of the carrier [12]. Figure 11c shows the stress distribution on crossbeams at different flow rates, and Figure 11d demonstrates the displacement curve on the crossbeams corresponding to Figure 11b. After all parameters are determined, the output voltage of the detector is simulated. According to the simulation calculation of Formulas (2) and (3), the output sensitivity curve of the detector after 300 times amplification is shown in Figure 12. The sensitivity of the wake detector obtained by simulation is 300 mV·(m/s) −1 . After all parameters are determined, the output voltage of the detector is simulated. According to the simulation calculation of Formulas (2) and (3), the output sensitivity curve of the detector after 300 times amplification is shown in Figure 12. The sensitivity of the wake detector obtained by simulation is 300 mV·(m/s) −1 . Remote Sens. 2023, 15, x FOR PEER REVIEW 12 of 19 Figure 12. Simulation curve of wake detector output sensitivity after 300 times magnification.

Process Preparation
The first step was to form piezoresistive and heavily doped regions, as shown in Figure 13a. The prepared SOI sheets were standard cleaned, and the wafers were pretreated with (HMDS) to enhance the adhesion between SOI and photoresist. The silicon wafer was coated with a photoresist and exposed by a lithographer to form a piezoresistive mask. The piezoresistive region was then subjected to ion implantation (boron ions) to form a varistor, which was then de-gelled. After lithography, a heavily doped region mask was formed to expose the silicon at both ends of the piezoresistive region. Finally, both ends of the silicon were injected with concentrated boron ions. The second step was to sputter and graphic the metal leads as shown in Figure 13b. Firstly, a layer of 300 nm aluminum metal was sputtered on the surface of the device layer by a magnetron sputtering machine. Then the lead mask was formed by photoresist lithography on the aluminum film. The photolithographic wafer was corroded in an

Process Preparation
The first step was to form piezoresistive and heavily doped regions, as shown in Figure 13a. The prepared SOI sheets were standard cleaned, and the wafers were pretreated with (HMDS) to enhance the adhesion between SOI and photoresist. The silicon wafer was coated with a photoresist and exposed by a lithographer to form a piezoresistive mask. The piezoresistive region was then subjected to ion implantation (boron ions) to form a varistor, which was then de-gelled. After lithography, a heavily doped region mask was formed to expose the silicon at both ends of the piezoresistive region. Finally, both ends of the silicon were injected with concentrated boron ions.  Figure 12. Simulation curve of wake detector output sensitivity after 300 times magnification.

Process Preparation
The first step was to form piezoresistive and heavily doped regions, as shown in Figure 13a. The prepared SOI sheets were standard cleaned, and the wafers were pretreated with (HMDS) to enhance the adhesion between SOI and photoresist. The silicon wafer was coated with a photoresist and exposed by a lithographer to form a piezoresistive mask. The piezoresistive region was then subjected to ion implantation (boron ions) to form a varistor, which was then de-gelled. After lithography, a heavily doped region mask was formed to expose the silicon at both ends of the piezoresistive region. Finally, both ends of the silicon were injected with concentrated boron ions. The second step was to sputter and graphic the metal leads as shown in Figure 13b. Firstly, a layer of 300 nm aluminum metal was sputtered on the surface of the device layer by a magnetron sputtering machine. Then the lead mask was formed by photoresist lithography on the aluminum film. The photolithographic wafer was corroded in an The second step was to sputter and graphic the metal leads as shown in Figure 13b. Firstly, a layer of 300 nm aluminum metal was sputtered on the surface of the device layer by a magnetron sputtering machine. Then the lead mask was formed by photoresist lithography on the aluminum film. The photolithographic wafer was corroded in an aluminum etching solution to form metal leads. After corrosion and complete annealing in a vacuum annealing furnace, an ohmic contact is formed.
The third step was reactive ion etching (RIE) to form a crossbeam as shown in Figure 13c. The photoresist was used to create a crossbeam pattern. Then RIE machine was used to etch the device layer and the buried oxygen layer, forming a crossbeam structure.
The final step was back-deep silicon etching (DRIE) as shown in Figure 13a. The photoresist was used on the back of the wafer for lithography and formation of the back cavity pattern. A deep silicon etching machine was used to etch the silicon on the substrate to release the crossbeam structure.

Detector Integration and Packaging
We glued the detector chip prepared by the process to the receiving circuit board and bonded the two with gold wire. The 3D-printed columnar cilia were then glued to the center of the crossbeam using UV glue. They were then fed into the chemical vapor deposition system to deposit a layer of 6µm thick parylene, thus achieving an insulation and waterproofing effect [30]. In addition, it can strengthen the bond between the chip and the cilia. Figure 14 shows the packaging process and structure of the detector. Since the wake detector produces a weak signal, we have incorporated a pre-amplification circuit that amplifies the output by a factor of 300. At the same time, the circuit can filter out noise signals above 500 Hz. aluminum etching solution to form metal leads. After corrosion and complete annealing in a vacuum annealing furnace, an ohmic contact is formed. The third step was reactive ion etching (RIE) to form a crossbeam as shown in Figure  13c. The photoresist was used to create a crossbeam pattern. Then RIE machine was used to etch the device layer and the buried oxygen layer, forming a crossbeam structure.
The final step was back-deep silicon etching (DRIE) as shown in Figure 13a. The photoresist was used on the back of the wafer for lithography and formation of the back cavity pattern. A deep silicon etching machine was used to etch the silicon on the substrate to release the crossbeam structure.

Detector Integration and Packaging
We glued the detector chip prepared by the process to the receiving circuit board and bonded the two with gold wire. The 3D-printed columnar cilia were then glued to the center of the crossbeam using UV glue. They were then fed into the chemical vapor deposition system to deposit a layer of 6µm thick parylene, thus achieving an insulation and waterproofing effect [30]. In addition, it can strengthen the bond between the chip and the cilia. Figure 14 shows the packaging process and structure of the detector. Since the wake detector produces a weak signal, we have incorporated a pre-amplification circuit that amplifies the output by a factor of 300. At the same time, the circuit can filter out noise signals above 500 Hz.

Detector Sensitivity Test
To determine the most critical performance of detector sensitivity, we have designed a calibration system for detector sensitivity measurement. The measuring system mainly includes a water tank, flow pump, Vectrino Profiler, NI acquisition card, fixed steel frame, upper computer, power supply, and so on. Figure 15 shows the platform photo.

Detector Sensitivity Test
To determine the most critical performance of detector sensitivity, we have designed a calibration system for detector sensitivity measurement. The measuring system mainly includes a water tank, flow pump, Vectrino Profiler, NI acquisition card, fixed steel frame, upper computer, power supply, and so on. Figure 15 shows the platform photo. In the experiment, we used the flow generator pump to generate the wake flow and used the Vectrino Profiler to measure the different flow rates at the fixed point (where the detector is located). The position of the detector and the flow-generating pump is shown in Figure 16. Firstly, the output of the X channel was measured, and then the output of the Y channel was measured by rotating the detector 90°. The detector probe was situated 5 cm away from the pump. The NI acquisition card was used to collect the output voltage signal of the detector. We repeated the test at different flow rates and calculated the rootmean-square value of the collected data. The fitting curve was obtained, as shown in Figure 17. It can be seen from Figure 17 that the output voltage of the detector has a linear relation with the flow velocity. The sensitivity of the two channels is highly consistent, with a sensitivity of 147 mV·(m/s) −1 and a detection threshold of 0.3 m/s. Due to the test equipment and packaging, the actual sensitivity of the detector is only half of the simulated result.  In the experiment, we used the flow generator pump to generate the wake flow and used the Vectrino Profiler to measure the different flow rates at the fixed point (where the detector is located). The position of the detector and the flow-generating pump is shown in Figure 16. Firstly, the output of the X channel was measured, and then the output of the Y channel was measured by rotating the detector 90 • . The detector probe was situated 5 cm away from the pump. The NI acquisition card was used to collect the output voltage signal of the detector. We repeated the test at different flow rates and calculated the root-meansquare value of the collected data. The fitting curve was obtained, as shown in Figure 17. It can be seen from Figure 17 that the output voltage of the detector has a linear relation with the flow velocity. The sensitivity of the two channels is highly consistent, with a sensitivity of 147 mV·(m/s) −1 and a detection threshold of 0.3 m/s. Due to the test equipment and packaging, the actual sensitivity of the detector is only half of the simulated result.

Detector Sensitivity Test
To determine the most critical performance of detector sensitivity, we have designed a calibration system for detector sensitivity measurement. The measuring system mainly includes a water tank, flow pump, Vectrino Profiler, NI acquisition card, fixed steel frame, upper computer, power supply, and so on. Figure 15 shows the platform photo. In the experiment, we used the flow generator pump to generate the wake flow and used the Vectrino Profiler to measure the different flow rates at the fixed point (where the detector is located). The position of the detector and the flow-generating pump is shown in Figure 16. Firstly, the output of the X channel was measured, and then the output of the Y channel was measured by rotating the detector 90°. The detector probe was situated 5 cm away from the pump. The NI acquisition card was used to collect the output voltage signal of the detector. We repeated the test at different flow rates and calculated the rootmean-square value of the collected data. The fitting curve was obtained, as shown in Fig  In order to showcase the superiority of the wake detector, we conducted tests using the same experimental method to evaluate the PNS and turbulence sensors. The results of these tests are presented in Table 2. Comparing the wake detector with PNS and artificial lateral flow sensors, the wake detector has superior sensitivity and 2D vector properties. Because the cilia of the turbulence sensor are directly exposed to water and directly disturbed by water flow, its sensitivity is higher than that of the wake detector. However, the disadvantage of the turbulence sensor is that it cannot be directly loaded on the AUV. Additionally, in order to show the working efficiency of the detector, we tested the effective value of the output voltage of the detector without external excitation is 2 mV. The effective value of the output voltage of the detector at the minimum flow velocity is 32 mV. The SNR (signal-noise-ratio) of the detector is calculated as: 20 24 .

Experiment for Vector Property of Detector
The vector test process is the same as the sensitivity test process. In this process, the detector is first placed in the position shown in Figure 16b, and the two output voltage signals of the detector at different flow rates are collected. From the principle of differential pressure detection, the output of the X-way of the detector should be larger than the output of the Y-way when placed in this way. The previous experiment was repeated by rotating the wake detector by 90°. Figure 18a,b show the results of the root-mean-square calculation of the experimental data. The histograms compare the output of the X-way and Y-way of the wake detection, visually showing the difference in the horizontal and vertical wake signals. Figure 18c,d show the voltage distribution points of the wake signal collected by the wake detector in the two experiments, respectively. These points represent the actual trajectory of the cilia. In Figure 18a, the strength of the wake flow received In order to showcase the superiority of the wake detector, we conducted tests using the same experimental method to evaluate the PNS and turbulence sensors. The results of these tests are presented in Table 2. Comparing the wake detector with PNS and artificial lateral flow sensors, the wake detector has superior sensitivity and 2D vector properties. Because the cilia of the turbulence sensor are directly exposed to water and directly disturbed by water flow, its sensitivity is higher than that of the wake detector. However, the disadvantage of the turbulence sensor is that it cannot be directly loaded on the AUV. Additionally, in order to show the working efficiency of the detector, we tested the effective value of the output voltage of the detector without external excitation is 2 mV. The effective value of the output voltage of the detector at the minimum flow velocity is 32 mV. The SNR (signal-noise-ratio) of the detector is calculated as: 20lg V s V n = 24 dB.

Experiment for Vector Property of Detector
The vector test process is the same as the sensitivity test process. In this process, the detector is first placed in the position shown in Figure 16b, and the two output voltage signals of the detector at different flow rates are collected. From the principle of differential pressure detection, the output of the X-way of the detector should be larger than the output of the Y-way when placed in this way. The previous experiment was repeated by rotating the wake detector by 90 • . Figure 18a,b show the results of the root-mean-square calculation of the experimental data. The histograms compare the output of the X-way and Y-way of the wake detection, visually showing the difference in the horizontal and vertical wake signals. Figure 18c,d show the voltage distribution points of the wake signal collected by the wake detector in the two experiments, respectively. These points represent the actual trajectory of the cilia. In Figure 18a, the strength of the wake flow received by the cilium in the lateral direction is greater than that received in the vertical direction. When the detector is rotated by 90 • , we can see that the voltage point map in Figure 18d is also rotated by 90 • compared to Figure 18c. This result further verifies the vector performance of the wake detector and its feasibility for wake detection. by the cilium in the lateral direction is greater than that received in the vertical direction. When the detector is rotated by 90°, we can see that the voltage point map in Figure 18d is also rotated by 90° compared to Figure 18c. This result further verifies the vector performance of the wake detector and its feasibility for wake detection.

Detection Range Experiment
We designed two AUV models with the wake detector installed on AUV-2. Before commencing the experiment, we measured the specific speed of the nine-speed gears of AUV-1. At the beginning of the experiment, the AUV-1 was fixed at the position shown in Figure 19. The AUV-1 was set to the first gear, and then the head of AUV-2 was placed at the end of the wake area to collect the wake signal using an acquisition card. If the signal was successfully collected, AUV-2 was moved back by 1 cm until the wake signal could not be collected. In this case, the previous position was considered as the detectable range of the AUV wake signal. If the wake signal cannot be collected, AUV-2 was moved forward by 1 cm until the wake signal was successfully collected. This position was then identified as the detectable range of the AUV wake signal. Then, the gear of AUV-1 was adjusted to the second gear. Based on the detection range of the AUV wake signal at the first gear speed, the detectable range of the AUV wake signal at the second gear speed was measured. Finally, the detectable range of the AUV wake signal at the remaining seven gear speeds was repeatedly tested. Figure 20 shows the scatter diagram of the wake signal detection range of the AUV at different speeds.

Detection Range Experiment
We designed two AUV models with the wake detector installed on AUV-2. Before commencing the experiment, we measured the specific speed of the nine-speed gears of AUV-1. At the beginning of the experiment, the AUV-1 was fixed at the position shown in Figure 19. The AUV-1 was set to the first gear, and then the head of AUV-2 was placed at the end of the wake area to collect the wake signal using an acquisition card. If the signal was successfully collected, AUV-2 was moved back by 1 cm until the wake signal could not be collected. In this case, the previous position was considered as the detectable range of the AUV wake signal. If the wake signal cannot be collected, AUV-2 was moved forward by 1 cm until the wake signal was successfully collected. This position was then identified as the detectable range of the AUV wake signal. Then, the gear of AUV-1 was adjusted to the second gear. Based on the detection range of the AUV wake signal at the first gear speed, the detectable range of the AUV wake signal at the second gear speed was measured. Finally, the detectable range of the AUV wake signal at the remaining seven gear speeds was repeatedly tested. Figure 20 shows the scatter diagram of the wake signal detection range of the AUV at different speeds.

Discussion
In the discussion, several key points are addressed. Firstly, it is noted that the axis of the wake detector and the AUV carrier are parallel. When the AUV moves straight ahead or when the wake flows directly along the AUV axis, there is no pressure difference between the diversion pores of the wake detector, resulting in an output voltage close to zero (Figure 11a). Secondly, when the wake flows in a direction deviating from the axis of the wake detector, the cilium vibrates, generating a corresponding output signal (Figure 11b). This case can be further divided into two scenarios. When the wake detector is aligned along the X direction of the wake, with the AUVs propeller as the axis (Figure 16b), the output voltage of the wake detector is shown in Figure 18c. Similarly, when the wake detector is aligned along the Y direction of the wake, the ground output voltage of the wake detector is shown in Figure 18d.
Finally, it should be pointed out that the wake detector is a novel concept introduced for the first time, and its stability, sensitivity, and threshold need further improvement. Future work will focus on enhancing the overall performance of the detector by refining the packaging and experimental methods. The emergence of a wake detector provides a new solution for AUV collaborative detection technology, which holds strategic and military significance for ocean exploration and operations.

Discussion
In the discussion, several key points are addressed. Firstly, it is noted that the axis of the wake detector and the AUV carrier are parallel. When the AUV moves straight ahead or when the wake flows directly along the AUV axis, there is no pressure difference between the diversion pores of the wake detector, resulting in an output voltage close to zero (Figure 11a). Secondly, when the wake flows in a direction deviating from the axis of the wake detector, the cilium vibrates, generating a corresponding output signal (Figure 11b). This case can be further divided into two scenarios. When the wake detector is aligned along the X direction of the wake, with the AUVs propeller as the axis (Figure 16b), the output voltage of the wake detector is shown in Figure 18c. Similarly, when the wake detector is aligned along the Y direction of the wake, the ground output voltage of the wake detector is shown in Figure 18d.
Finally, it should be pointed out that the wake detector is a novel concept introduced for the first time, and its stability, sensitivity, and threshold need further improvement. Future work will focus on enhancing the overall performance of the detector by refining the packaging and experimental methods. The emergence of a wake detector provides a new solution for AUV collaborative detection technology, which holds strategic and military significance for ocean exploration and operations.

Discussion
In the discussion, several key points are addressed. Firstly, it is noted that the axis of the wake detector and the AUV carrier are parallel. When the AUV moves straight ahead or when the wake flows directly along the AUV axis, there is no pressure difference between the diversion pores of the wake detector, resulting in an output voltage close to zero (Figure 11a). Secondly, when the wake flows in a direction deviating from the axis of the wake detector, the cilium vibrates, generating a corresponding output signal (Figure 11b). This case can be further divided into two scenarios. When the wake detector is aligned along the X direction of the wake, with the AUVs propeller as the axis (Figure 16b), the output voltage of the wake detector is shown in Figure 18c. Similarly, when the wake detector is aligned along the Y direction of the wake, the ground output voltage of the wake detector is shown in Figure 18d.
Finally, it should be pointed out that the wake detector is a novel concept introduced for the first time, and its stability, sensitivity, and threshold need further improvement. Future work will focus on enhancing the overall performance of the detector by refining the packaging and experimental methods. The emergence of a wake detector provides a new solution for AUV collaborative detection technology, which holds strategic and military significance for ocean exploration and operations.

Conclusions
In conclusion, this study draws inspiration from the fish lateral line system and combines it with a turbulence sensor to design the MEMS wake detector. This paper introduces the wake detector's principle, design, simulation, manufacturing process, and experimental characterization results. The lateral line structure of the wake detector not only maintains the vector performance of the turbulence sensor but also enables wake detection during AUV movement. The canal structure not only acted as a package to the detector protecting the cilium and crossbeam but also acted as a high-pass filter. Through COMSOL finite element simulation, the correlation between the detector's sensitive microstructure, resonant frequency, and stress on the beam is analyzed, and the dimensions of the diversion cap structure are determined. Additionally, the detector's performance in a wake flow environment is simulated. In the sensitivity calibration experiment, the wake detector exhibits a sensitivity of 147 mV·(m/s) −1 , with a lower detection threshold of 0.3 m/s. The feasibility of the detector to detect a two-dimensional wake flow field is confirmed through vector experiments.