A novel biomimetic sensor system for vibration source perception of autonomous underwater vehicles based on artificial lateral lines

The perception of vibration sources can be used to detect, classify, locate, and track autonomous underwater vehicles (AUVs), which is of great importance for ocean scientific research and naval applications. The artificial lateral lines system (ALLS) is a promising technique to sense underwater vibration sources. However, most current ALLS research focuses on perception mechanism and biomimetic sensor design. The design of a systematic ALLS that is ready for practical applications is still an unsolved problem. To this end, a novel biomimetic sensor system is proposed in this work for the purpose of developing a practical ALLS for AUVs. In order to determine the distribution of the developed biomimetic sensors in the AUVs, hydromechanics modelling and simulation of the artificial lateral lines were implemented to investigate the pressure response mechanisms of the AUVs in terms of the position, frequency and amplitude of the vibration source(s). Subsequently, an experimental AUV was equipped with biomimetic sensors to evaluate the performance of the vibration source perception. Experimental tests were conducted to analyze the relationship between the measured AUV pressure and the distance, frequency and amplitude of the vibration source. Analysis results demonstrate that the experimental measurements were consistent with simulation results. Based on the relationship between the sensor measurements and the vibration source, a neural network model was used to identify the coordinates, frequency and amplitude of the vibration source, producing an identification accuracy of 93%. Hence, the proposed ALLS is effective for vibration source perception of AUVs.


Introduction
The perception of vibration sources can be used to detect, classify, locate, and track underwater targets and it is of great strategic importance for underwater communication and navigation, ship safeguarding, position monitoring of submarines, underwater weapons and anti-submarine helicopters. Currently, ultrasonic waves, visual images and electro magnetic devices are often used to perceive vibration sources of autonomous underwater vehicles (AUVs) [1]. As a most popular device, sonar can perceive the position of AUV vibration sources and attitudes/positions via radio waves [2]. However, due to the shielding effect of water, radio signals cannot travel far. In complex underwater environments, the performance of sonar with respect to vibration source detection may be decreased. Optics sensors can perceive AUV vibration sources but light phenomena such as refraction and darkness strongly interfere with their applications in motion control, positioning and environ mental perception of underwater vehicles. Furthermore, electromagnetic waves are severely attenuated in water [3,4]. Consequently, current methods using ultrasonic waves, visual images and electro magnetic devices may suffer from low detection accuracy for AUV vibration sources.
Sensing the surrounding vibration sources accurately in complex underwater environments is a challenging task. Inspired by fish laterals, which enable fishes to effectively perform prey tracking, obstacle avoiding, group travel, information exchange, and long-range migration [5][6][7], a new sensing and navigation positioning technology is proposed, namely, the artificial lateral lines system (ALLS) [8]. ALLS is a promising technique in compensating existing technologies to improve the identification accuracy of underwater vibration sources. However, most current ALLS research focuses on the perception mechanism and biomimetic sensor design [9]. The design of a systematic ALLS that is ready for practical applications is still an unsolved problem.
In order to address the aforementioned issue in ALLS, this paper aims to develop a practicable and applicable ALLS for AUVs. The contributions of this paper are described as follows.
(1) A novel ALLS is developed using high-precision pressure sensors with optimal design of sensor distribution. (2) A practical AUV experimental device equipped with the proposed ALLS is developed to perform vibration source perception/positioning. This paper is organized as follows. Section 2 reviews the related work in vibration source perception/positioning of AUVs. In section 3, according to the basic theory of fluid mechanics, a mathematical model is established to locate the AUV vibration sources. The mathematical relationship between the vibration source coordinates and the surface pressure of the lateral line carrier is described. Numerical simulation is carried out in section 4 to investigate the optimal distribution of pressure sensors in the ALLS. The experimental AUV device is introduced in section 5. The characteristics of the ALLS surface pressure caused by vibration sources with different coordinates, frequency and amplitude are analyzed. Section 6 draws the main conclusions.

Related work
The lateral lines of fish have been studied in various fields such as biology, neurology and engineering. Fish predation and obstacle avoidance actions are the result of an interaction of multiple sensory organs, such as chemical perception, acoustic perception, and mechanical sideline perception. Fish can also evade danger through taste buds and the olfactory system. It has been discovered that most fish mainly rely on the lateral line system to achieve omni-directional vibration perception, obstacle avoidance, communication, group travel, and target positioning [10][11][12][13]. The lateral line system is a sensory system that fish can use to sense water flow and pressure gradients. It consists of thousands of arrays of surface neurons [14]. Each neuron contains several cilia bundles, sealed in a gelatinous shell. Fluids may trigger the neurons to enable fish to identify near-field objects and water currents [15,16]. Coombs and Conley [17][18][19] found that the mottled sculpin can always locate vibrating objects. If the surface neurons are removed from one side of the sculpin, the initial positioning angle error may increase from 20° to 60°. As a result, it can be deduced that fish rely mainly on the lateral line system to achieve accurate positioning of vibrating objects. Janssen and Corcoran [20] found that as long as the lateral line system of the mottled sculpin is intact, it can not only determine the direction of the source, but also the distance to the source and the change in vibration intensity. However, the estimated position is limited to short distance (approximately the length of a fish body). Enger et al [21] discovered that Lepomis macrochirus only reacts strongly to balls with vibration frequency below 10 Hz in a dark environment. Furthermore, Yang et al [22] used surface micromachining to manufacture a set of miniaturized hot wire speed sensors (HWAs) to perform dipole source positioning and hydrodynamic wake monitoring. Chen et al [23] developed an ALLS for hydrodynamic object tracking whereas the developed system is yet to be used in practice. Yang et al [24] designed a carrier with a sensor array using a 3-degree-of-freedom mechanical arm and carried out experiments on tracking and positioning of vibration sources. They also built a corresponding ALLS tester [25]. A PVC pipe (89 mm in diameter) was used to imitate the fish body to study the 3D positioning ability of the ALLS. Good results were obtained in their experiments. McConney et al [26] designed a biomimetic hydrogel-covered cilia sensor system through precision casting. The performance of object detection is enhanced by two orders of magnitude [26]. When detecting a 50 Hz dipole source with 15 mm in distance, a speed sensitivity of 2.5 µm s −1 was achieved. Mohsen et al [27] developed a sensitive artificial ciliary flow sensor, which can be mounted on a miniature membrane with a floating electrode. Simulations were conducted using the developed sensor to detect a 35 Hz dipole source. The position and distance of the underwater dipole source were identified accurately.
Most of the existing research on ALLS mainly focuses on theoretical analysis and experimental testing in sensor design, flow velocity perception, vibration source perception and positioning, and obstacle shape recognition. Practical ALLS devices that are suitable for AUVs have not been found yet. This paper will address this concern by developing a novel practical ALLS for AUVs.

Hydromechanics of the proposed ALLS
The hydromechanics model of the proposed ALLS assumes that the fluid is incompressible, satisfying the continuity equation, Euler equation, and Navier-Stokes equation. The fluid is also non-viscous and non-rotating, consistent with the potential flow theory.

Euler equations
When the source vibrates, a force is generated on the surrounding water flow that gives rise to changes in the flow environ ment [28][29][30]. Applying Newton's second law to a small volume element in the fluid (see figure 1) we get where, in a small volume δA, δ F is the micro force, δm is the volume mass and a is the volume acceleration. δ F can be decomposed into orthogonal force components δF n . (n =1, 2, …, 6). The vertical force components are δF 1 and δF 2 . Normal stress and shear stress are expressed as follows: Combined with the Taylor series expansion, the force comp onents on the hexahedron can be expressed as follows: where δ x , δ y and δ z are the normal stress in the x, y and z directions, σ xx is the component of ∂x in the x direction, τ z is the shear stress in the z direction, and τ zx is the component of τ z in the x direction. The balanced expressions of forces in the x-axis, y-axis, and z-axis are The resultant forces of the hexahedron may be expressed as follows: where ρ is the volume density, î , ĵ and k are unit vectors in the x, y and z directions, respectively, V is the speed vector, ∂ V ∂t is the time-varying acceleration, and V · ∇ V denotes the convection acceleration. Supposing that the gravity has a component g x in the x direction, we derive where u, v, and w are the three directions of the fluid. In nonviscous fluid, there is no shear stress, only normal stress. The vector expression is as follows: where Δp denotes the pressure gradient, represents the acceleration and µ∇ 2 V represents the viscous force. Equation (14) is the Euler equation in the ideal fluid while for practical problems the viscous fluids are often used. Equation (14) can be rewritten for viscous fluids by adding a viscous force term according to the Navier-Stokes equations (3): where µ∇ 2 V is the viscous force term.

Plane potential flow theory
An incompressible, non-rotating ideal flow is called a potential flow. Its potential function satisfies the Laplace equation in equation (16): where ϕ is the potential function. There is no shear stress in the ideal fluid. The fluid microcell can only slide along but cannot pass through the surface of the object. Therefore, the impenetrable condition is satisfied.
where υ denotes the fluid velocity, v b denotes the speed of the object, and n denotes a normal vector.
According to the boundary conditions of the object, the potential function can be obtained in a complex water area. Let us assume the source coordinates of the vibration dipole (x 0 , y 0 ), point coordinates (x 0 + δ x0 , y 0 ). The dipole potential function can be expressed as When (δ x0 → 0), the potential function can be simplified to Figure 2 shows the working flow diagram of vibration source location. First, the potential function and velocity potential are obtained according to the Laplace equation and potential flow theory. Then the relationship between speed and pressure is obtained by the Euler equation. Lastly, the coordinates of the vibration source can be calculated by solving the Laplace equation. Figure 3 depicts the mathematical model of vibration source positioning. When a ball vibrates in an ideal fluid, the vibration of the object will continuously influence the surrounding fluid that, causing the flow of the fluid. However, the energy is limited. The fluid movement is mainly concentrated in the water area near the vibrating object [28,29].  The instantaneous displacement of the ball vibration can be expressed as [30,31]

Mathematical model of the positioning
The instantaneous speed of the ball is The Laplace equation has a solution 1/r, where r is the distance to the origin. When the ALLS is away from the vibration source, the general form of the solution to the Laplace equation may be expressed as where a is a constant (because the flow of incompressible fluid through any closed surface should be zero, a = 0) and Q = uR 3 /2, where u and R denote the speed and radius of the vibration source, respectively. Therefore, the potential function can be expressed in equation (24): where n denotes the normal vector of the direction of motion of the vibration source, which can be approximated by cosθ, and u = A · ω · sin(ωt). Hence, the potential function can be further expressed as In an arbitrary vector field with zero rotation, the velocity caused by the potential flow can be described by a scalar gradient. Substituting v = Δϕ into the Euler equation yields Equation (28) can be rewritten as where f(t) is an arbitrary function of time. Since velocity is equal to the derivative of the potential function with respect to the coordinates, ϕ may vary with time. If f(t) = 0, then the distribution of pressure in the flow field becomes where p 0 is the pressure at infinity point in the flow field. If the flow is a potential flow and the fluid is incompressible, the velocity of the water flow caused by the vibration is very small (i.e. ∂ϕ ∂t v 2 ). Thus, the squared term ρv 2 2 in equation (30) can be ignored. The formula for the pressure and velocity of the sensor at a distance r is then expressed as where (x 1 , y 1 ) is the sensor coordinate.

The establishment of the simulation model
The FLUENT software is used to implement the simulation. Figure 4 shows the simulation model. The simulation area is set to 2000 × 1200 mm as illustrated in figure 4(a). The simulation model is 550 mm in length and 160 mm in diameter. The mesh types are triangular meshes and the solver type is based on pressure. The operating pressure is 10 325 Pa, the gravity acceleration is 9.8 N kg −1 , the velocity-inlet size is set to zero, and the pressure-outlet is set to zero. As illustrated in figure 4(b), the omni-directional perception of the lateral carriers is enabled by setting the vibration source to four different positions in the simulation. These four positions are located directly in front of the lateral line carriers at different angles from the lateral line carriers, perpendicular to the lateral line carriers or parallel to the lateral line carriers.    Figure 5 illustrates the simulation results of the dynamics and the static pressures that are perceived by a lateral line carrier at a certain frequency and varying distances. The x-axis denotes the time, the y-axis denotes the grid sequence, and the z-axis denotes the pressure variations.
The pressure variations at different positions, 50, 100, 200 and 300 mm in front of the carrier were analyzed. Figure 6 shows the analysis results. As can be seen in figure 6(a), the pressure variations on the left and right sides exhibit a certain symmetry, and the distance is inversely proportional to the pressure. In figure 6(b), the pressure is proportional to the vibration frequency.   According to the simulation results, the dynamic pressure is almost zero, and hence it can be ignored here. The static pressure can approximate the total pressure. The total pressure data is the actual pressure measured by the sensor during the experiment. Therefore, only the total pressure is analyzed below. Figures 7  and 8 show the analysis results of the surface pressure variations from different angles to the ALLS carriers. When the vibration source is located at 45° with the center of the ball head, the extreme point of the pressure appears at the 58th grid sequence in figure 7. The computed angle is θ = 48.44°, which is 3.44° greater than the true value of 45°. Similarly, as depicted in figure 8, when the vibration source is at 56.31°, the computed angle is 59.61°. These results demonstrate that when the vibration source is at a certain angle with the lateral line carrier, the general orientation of the stimulation signal can be determined by the distribution point of the maximum pressure of the ball head. Figure 9 shows the analysis results of the pressure distribution when the vibration sources are parallel to the ALLS carriers. In figure 9(a), at the distance of 100 mm ahead of the ALLS carriers the extreme pressure point corresponds to the 383th grid node while for a 150 mm distance it corresponds to the 330th grid node in figure 9(b). When the distance is 200 mm, the extreme pressure point corresponds to the 280th grid node in figure 9(c). The extreme pressure point in figure 9(e) corresponds to the 180th grid node. As a result, when the vibration source moves parallel along the carrier, the grid node corresponding to the extreme pressure point will decrease with increasing distance. Figure 10 illustrates the analysis results of the pressure distribution when the vibration sources are perpendicular to ALLS carriers. In the simulation, the distance is varied with constant frequency. As can be seen in figure 10, the pressure perceived by the lateral line carrier is inversely proportional to the distance.

Perpendicular to ALLS carriers.
In summary, the surface pressure distribution characteristics of the ALLS carriers can be obtained through simulation analysis. The distance between the vibration source and the carrier is inversely proportional to the perceived pressure, and the vibration frequency is proportional to pressure. These results demonstrate that the carriers are able to sense the pressure signals and the intensity changes in specific directions.

Experimental setup
The ALLS carrier, as illustrated in figure 11, was designed and manufactured to implement the experimental tests in this study. Twenty-five high-precision pressure sensors (MS5803-07BA) were selected and installed in the carrier. These pressure sensors were sealed to the housing, and a battery and a microcontroller were imbedded inside the carrier.
The inside devices were connected to the outside through a watertight connector. The whole system was sealed with O-rings. Figure 12 describes the carrier in detail. The entire system was driven by a 12 V lithium battery. The supply voltage to each sensor was 3.3 V. The microcontroller transmitted the data to the signal processing system through the TTL-232 cable. The signal processing system was programmed using C# language to receive and store pressure data in real time. The acquisition frequency was 12 Hz. The experimental platform is illustrated in figure 13. The size of the pool was 2000 × 1500 × 1200 mm. The water-depth was 1000 mm, the water temperature was 13 °C, and the atmospheric pressure was 1.01 × 10 5 Pa. Table 1 lists the experimental parameter settings.

The experimental results
The pressure measured by the sensor was affected by many uncontrollable factors that included, but were not limited to, the variations in the weather, altitude, temperature, water depth, and also sensor hardware [32][33][34]. The true pressure change was depicted through the discrepancy between the sensor measured pressure and the hydrostatic pressure. The measurements of the 25 pressure sensors in the water are illustrated in figure 14.
Since the measurements of the sensors presented slight fluctuations, a filtering processing was applied to the sensory signals. Figure 15(a) shows the pressure waveform of sensor No. 25 at the front end of the carrier. Figure 15(b) shows the frequency spectrum of the pressure using fast Fourier transform. It can be observed that the frequency spectrum of the pressure is corrupted by noise and there are few significant amplitude characteristics. Figure 15(c) shows the filtered signal, where the noise has been effectively depressed. Figure 16 illustrates the pressure distribution of the 25 sensors. The extreme pressure point appeared at 13 s on sensor No. 25, which was installed in front of the carrier. The maximum pressure was ±80 Pa. The pressure fluctuations of the other 24 sensors were within the range of ±30 Pa.
A comparison analysis between the simulation and experimental data is depicted in figure 17 when the vibration source frequency is 3 Hz. Certain similarities can be observed between the simulation and experimental results. The maximum, minimum, mean and kurtosis of the experimental result are respectively 18 Pa, 81 Pa, 53.7 Pa and 2.7 while for the simulation result they are 3.5 Pa, 81.1 Pa, 52.3 Pa and 2.1. Hence, the statistics of the experimental data are close to those calculated from the simulation data. However, due to sensor and background noise the degree of variation of the experimental curve is more severe than that of the simulation curve.

Relationship between pressure and frequency.
When the vibration source was located at 50 mm in front of the carrier, the amplitude was 10 mm and the frequencies were 1, 3 and 5 Hz, respectively. The data fitting was applied to the measurement of sensor No. 25. Figure 18 compares the data fitting results of the experimental and the simulation results. The obtained data fitting functions are  (33) where p e indicates the pressure of the experimental data, p s indicates the pressure of the simulation data, and ω indicates the vibration frequency.
As can be seen in figure 18, the simulated pressure is larger than the experimental one. The pressure on the surface of the carrier increases with frequency. Because the experiment test was conducted with low vibration frequencies, the sensor measurement may be subject to sensor and background noise.
After noise filtering, the sensor measured value can be smaller than the simulated value.
Nevertheless, the pressure is directly proportional to the frequency of the vibration source. Thanks to the data fitting, the mathematical relationship between the pressure and the frequency at a certain distance is obtained. The maximum pressure can then be used to estimate the source vibration frequency.

Relationship between pressure and distance.
The pressure change on the carrier surface was analyzed when the vibration source (10 mm and 3 Hz) was in the vertical  direction of the carrier. Figure 19 shows the relationships between pressure and distance. The data fitting functions of the exper imental and the simulation results are P e = −0.000205d 3 + 0.0389d 2 − 2.68d + 86. 19 (34) P s = −0.000126d 3 + 0.0247d 2 − 2.15d + 98.67. (35) The pressures in the experiment and the simulation decrease with increasing distance in figure 19. It is evident that the effective range for identifying the vibration source by an underwater vehicle equipped with an ALLS is limited. The experimental carrier may only sense the range within 0-2 BL (the length of the lateral line carrier) for very low frequency of the vibration sources. However, the sensing range may increase for large vibration frequency because the pressure is proportional to the frequency of the vibration sources.   ) while the y-axis error is huge. The reason for this large error in the y direction is probably that the theoretical formula is derived from the ideal fluid, which is incompressible and conforms to the non-rotational flow of the potential flow theory, while in a real experimental environment the fluid will not be ideal. The theoretical formula can only determine the approximate orientation (1D coordinates) and intensity of the vibration source, such as sensing the stimulus signal and the approximate distance and intensity at a certain part of the carrier body (head, torso, tail, etc). At this point, the lateral line carrier already has the ability to sense the orientation and intensity of the stimulus signal.

Vibration source identification
In order to achieve accurate positioning and localization, neural network learning is employed. Since the concept of  an artificial neural network (ANN) has been proposed, it has been rapidly developed and widely used in many applications [35]. In this paper, the ANN learning method is used to realize accurate perception of the coordinates, frequency and amplitude of the vibration source [36]. The ANN model is implemented by simulating the human brain, such as the nonlinear network structure of the simulated nervous system, as shown in figure 20. The artificial neuron is the basic unit of an ANN model, and its function is to realize multiple input values corresponding to a single output value. In figure 20, p = [p 1 , p 2 , . . . , p R ] T is the output vector of the neuron, w = [w 1 , w 2 , . . . , w R ] is the weight vector, and θ is the     threshold of the neuron. If the weighted sum of the neuron input vector is greater than θ, then the neuron is activated. In this research, ANN was used to identify the coordinates of the vibration source, the amplitude, and the vibration frequency. The mean square error performance analysis was conducted using the network topology (see figure 21), where w indicates the weight, b indicates the offset, and ~ indicates the activation function.
Experimental data were used for the training, verification and testing of the ANN model. The training, verification and test of the experimental data have all reached a level of 0.97, as depicted in figure 22. The identification accuracy of the vibration frequency was 98.93%, as shown in figure 23(a).
The accuracy of the amplitude recognition reached 98.33%, as shown in figure 23(b). The accuracy of the recognition of the coordinates reached 98.93%, as shown in figure 23(c). In this paper, three different coordinates of the vibration source were trained. The best positioning accuracy of the vibration source was obtained when the vibration source was perpend icular to the carrier. The results indicate that the lateral line of the linear array sensor is most sensitive to vibration sources.
When the characteristic parameters (frequency, position and amplitude) of the vibration sources change, the pressure of the lateral line surface carrier changes accordingly. Through the training and computational intelligence of the  ANN algorithm, it becomes possible to achieve accurate recognition of vibration sources.

Conclusion and future work
In this research work, a prototypical topology of an ALLS is developed for underwater vehicles. The ALLS was designed and fabricated to successfully identify the coordinates, amplitudes, and frequencies of underwater vibration sources. The relevant mathematical model was established based on the principles of fluid mechanics, and the subsequent mathematical model was established as a relationship between the pressure and the characteristic parameters of the vibration sources.
The technology of fluid simulation enabled the analysis of the pressure changes caused by the position of the vibration source, the frequency, and also the amplitude. There follows a summary of the variation rules pertaining to the ALLS carrier's surface pressure. When the vibration frequency and amplitude are constant, the distance from the vibration source to the carrier is inversely proportional to the pressure perceived by the carrier. The position of the grid node that corresponds to the maximum pressure on the surface of the carrier is consistent with the horizontal coordinates of the vibration source. An azimuth of the vibration source may be determined by the location of the pressure maximum point. Moreover, it is shown that the lateral line carrier may detect changes in the vibration source position.
The mathematical relationship between pressure and the distance to the vibration source, the pressure and vibration frequency may be summed up through the application of the neural network learning algorithm. The algorithm also identifies the characteristic parameters of the vibration source: (1) Frequency identification: the maximum recognition accuracy was reached at 96.34%. source was perpendicular to the direction of the artificial lines.
The analysis results of this research also suggest that it may be helpful in improving the identification accuracy using vibration source sensing and flow field sensing in the underwater vehicles. The developed ALLS may have practical applications in underwater vehicles as well as deep-sea applications.
Future research will include (1) position tracking of the moving vibration sources; (2) new vibration source identification algorithms such as beamforming algorithms, genetic algorithms and least squares; and (3) perception of middle and long distances. Furthermore, although the MS5803-07BA sensor has excellent long-term stability, it is limited by accuracy, acquisition frequency and measurement range. We will consider sensors with higher precision and acquisition frequency in future.