Electrostatic induction electrode array system mimicking shark electroreceptor organs

Abstract

The application discloses an electrostatic induction electrode array system simulating a shark electroreceptor organ, which comprises a charged target, an electrostatic field and a hemispherical electrostatic induction electrode array, wherein a detection electrode of the hemispherical electrostatic induction electrode array comprises a cylinder structure composed of an induction plate, an insulating substrate and a shielding electrode, the inside bottom end of the cylinder structure is the induction plate in the shape of a circular plate, the induction plate is used for sensing the space electrostatic field and is connected to a signal input end of an electrostatic sensor, the insulating substrate is used for electrically separating the induction plate from the shielding electrode, the shielding electrode is connected to a power supply ground of the electrostatic sensor and is used for blocking the influence of the lateral electrostatic field on the induction plate, the detection electrode obtains a current value of the charged target, and the current value is used for representing an electrostatic signal generated when the detection electrode passes through the charged target. The application realizes a high spatial resolution electrostatic field sensor, can improve the sensing area and the spatial resolution of a space electrostatic field of an unmanned platform, and accurately senses the attack direction of a flying charged body.

Description

Technical Field

[0001] This invention relates to the field of electrostatic induction technology, and in particular to an electrostatic induction electrode array system that mimics the electroreceptor organs of sharks. Background Technology

[0002] The ampullae of Lorenzini is an electroreception organ unique to cartilaginous fish such as sharks and rays. In dark or concealed environments, sharks use this sensory organ to perceive the weak electric fields generated by surrounding prey, thus accurately locating their prey. Figure 6 As shown in (A), a dense array of ampullae is distributed around the shark's head and mouth. Each ampulla is connected by a canal containing highly conductive gel, which transmits the spatial electric field from the surface pore to electroreceptor cells at the bottom of the canal. These electroreceptor cells generate nerve impulses in response to changes in the external electric field, which are then transmitted to the central nervous system via nerve fibers. This directional array of ampullae gives the shark a wide-range and high-spatial-resolution ability to perceive its surrounding spatial electric field, providing a significant advantage in hunting and navigation. Unmanned platforms, represented by drones, unmanned vehicles, and unmanned surface vessels (USVs), are characterized by high efficiency, flexibility, and economy. They exhibit a trend towards autonomy, intelligence, and scalability, and have been widely applied and have achieved significant results in daily life and adversarial conflicts. For example, drones are used for logistics delivery, crop protection, and forest fire monitoring; unmanned vehicles are used for battlefield reconnaissance and explosive ordnance disposal; and USVs are used for marine monitoring. In adversarial scenarios, besides electromagnetic interference, unmanned platforms primarily suffer physical attacks from high-speed flying targets such as small arms fire, shrapnel jets, and FPV (Fast Moving Vehicle) collisions. General-purpose sensors on unmanned platforms, such as cameras, radar, and sonar, are unable to detect these high-speed targets. Furthermore, due to limitations in energy, computing power, payload, and cost, unmanned platforms cannot be equipped with complex threat perception systems such as high-speed cameras, early warning radar, or acoustic source localization. Therefore, the lack of perception capabilities for high-speed flying targets in existing unmanned platforms severely restricts their survivability and adaptability in adversarial environments. Researching low-power, low-cost, efficient, agile, and lightweight methods for perceiving high-speed flying targets by incorporating shark electroreceptors has significant scientific and practical value. Summary of the Invention

[0003] To address the above problems, this invention provides an electrostatic induction electrode array system that mimics the electroreceptor organs of sharks.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] An electrostatic sensing electrode array system mimicking the electroreceptor organs of sharks includes: a charged target, an electrostatic field, and a hemispherical electrostatic sensing electrode array. The detection electrode of the hemispherical electrostatic sensing electrode array comprises a cylindrical structure consisting of a sensing plate, an insulating substrate, and a shielding electrode. The inner bottom of the sensing plate is a circular plate-shaped sensing plate used to sense the spatial electrostatic field and connected to the signal input terminal of an electrostatic sensor. The insulating substrate is used to electrically separate the sensing plate from the shielding electrode. The bottom cylindrical shielding electrode is connected to the power ground of the electrostatic sensor to block the influence of the lateral electrostatic field on the sensing plate and improve the spatial directivity of the sensing plate. The detection electrode obtains the current value of the charged target. The current value is amplified and recorded by a subsequent high-impedance electrostatic sensor to characterize the electrostatic signal generated when the charged target passes through the detection electrode.

[0006] Furthermore: the hemispherical electrostatic induction electrode array is distributed on a hemispherical shell-shaped support structure. The central axis of each detection electrode points to the center of the sphere. The detection electrode whose central axis is perpendicular to the bottom surface of the hemisphere is defined as the normal electrode, and its tilt angle is denoted as 0°. The angle between the central axis of the other detection electrodes and the central axis of the normal electrode is defined as its tilt angle. Six detection electrodes are equally spaced on the circumference with tilt angles of 0°, 21°, 42°, and 63°, respectively, and five detection electrodes are equally spaced on the circumference with tilt angles of 36° and 72°.

[0007] Furthermore: the current value of the charged target obtained by the detection electrode includes:

[0008] Establish a Cartesian coordinate system XOY on a horizontal surface, with the unit vectors of the three coordinate axes as follows: and Let the radius of the detection electrode be r, and define the center of its upper surface as the origin O of the spatial coordinate system, with its normal vector... Let α be a vector that passes through the origin O and points perpendicularly to the outside of the circular plate, where α is and The included angle, β is Projection in the XOY plane and The angle between the two sides; the static charge carried by the charged target is Q(t), which changes during flight. The dotted line represents its trajectory, and the velocity vector is... Let x be the tangent vector to the trajectory, and let x be the coordinates of the spatial position. p (t),y p (t),z p (t)), whose unit vector is the position coordinates. and The included angle is δ. and The included angle is The angle between the projection of XOY and the X-axis is γ;

[0009] The electric field components of the target electric field in the direction normal to the probe electrode, calculated using the method of charge images, are as follows:

[0010]

[0011] Where ε₀ is the vacuum permittivity, ε r Let be the dielectric constant of the space medium; from equation (1), it can be concluded that when δ=Nπ, (N=0,1,2...), E n The maximum value is when and When the detector electrodes are located on the same straight line and their normals are perpendicular to the charged target, E n Take the maximum value;

[0012] Let α, β ∈ (0, π / 2) and and If they are located in the same quadrant, then:

[0013]

[0014] Substituting equation (2) into equation (1), we obtain the field strength component in the normal direction of the probe electrode as follows:

[0015]

[0016] set up but

[0017]

[0018] Assuming the charged target is located at position Equation (4) can be simplified to:

[0019]

[0020] When α, β∈(0, π / 2), both are pi / 4, the normal electric field strength is at its maximum. Therefore, according to Gauss's law, the induced charge density σ on the probe electrode surface... s for:

[0021]

[0022] Assuming the charged target carries a constant charge Q0, and the probe electrode is parallel to the horizontal plane (i.e., α = 0), then equation (6) simplifies to:

[0023]

[0024] When x p (t)=0,y p When (t) = 0, σ s Take the maximum value;

[0025] Let d be the distance from the projection of the charged target onto the XOY plane to the origin. p (t), that is

[0026]

[0027] Take d p (t)=0,z p σ when (t) = Δ s The value is a normalized quantity, and Δ is the unit length; when z p When (t)≥6Δ, σ s In 0≤d p The value of (t) ≤ Δ within the circular region is approximately constant; according to Gauss's law, the total charge Q induced on the probe electrode is... s for:

[0028]

[0029] Therefore, when the flight altitude of the charged target is greater than 6 times the radius r of the detection electrode, the charge density induced on the electrode surface can be considered constant; therefore, equation (10) can be simplified to:

[0030]

[0031] According to the law of conservation of charge, the current flowing out of the detector electrode is the change in the amount of charge induced in the detector electrode, that is:

[0032]

[0033] This current value is amplified and recorded by the subsequent high-impedance electrostatic sensor, and is used to characterize the electrostatic signal generated when a charged target passes through the detection electrode.

[0034] Furthermore, the detection electrode obtains the current value of the charged target by acquiring the signal waveform:

[0035] Assuming the probe electrode is parallel to the horizontal plane, the surface charge of the probe electrode can be simplified as follows:

[0036]

[0037] Let the components of the velocity V of the charged target along the coordinate axis be V x V y V z ,So

[0038]

[0039] Assume the charged target has a constant charge of Q0, a constant flight speed of V0, and its velocity direction is parallel to the x-axis along with its flight trajectory. At t=0, it passes through the YOZ plane, i.e., x... p (0) = 0, equation (15) can be simplified to:

[0040]

[0041] The distance between the charged target and the detection electrode is D. p (t), i.e.

[0042]

[0043] but:

[0044]

[0045] Substituting into equation (16), we get

[0046]

[0047] Therefore, when t = 0, equation (19) takes the maximum value, denoted as

[0048]

[0049] Then, equation (19) can be simplified as follows:

[0050]

[0051] From equation (21), we can see that the waveform shape of the induced charge is derived from... Let it be the waveform time scale coefficient τ:

[0052]

[0053] Then equation (21) can be simplified as follows:

[0054]

[0055] Therefore, the waveform of the induced charge on the detection electrode is determined by τ, the flight velocity V(t) of the charged target, and the shortest distance D from the target to the electrode. p (t) have a combined effect, and the effects of the two parameters are inversely proportional. Therefore, substituting equation (23) into the induced current equation (13) yields...

[0056]

[0057] The technological advancements achieved by this invention compared to existing technologies are as follows:

[0058] This invention designs a hemispherical electrostatic induction electrode array, combined with a high-sensitivity electrostatic induction signal amplification circuit, to realize a high spatial resolution electrostatic field sensor. This can improve the sensing area and spatial resolution of the unmanned platform for the spatial electrostatic field, and accurately sense the direction of attack of flying charged objects. Attached Figure Description

[0059] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0060] In the attached diagram:

[0061] Figure 1 This is a schematic diagram of the electrostatic induction electrode array system of the present invention;

[0062] Figure 2 This invention explores the influence of the probe electrode attitude on the normal electric field.

[0063] Figure 3 This is a schematic diagram of the normalized surface charge density of the present invention;

[0064] Figure 4 This is a schematic diagram of the induced charge waveform and its spectrum of the detection electrode of the present invention;

[0065] Figure 5 This is a schematic diagram of the induced current waveform and its spectrum of the detection electrode of the present invention;

[0066] Figure 6 This invention mimics the principle and design of shark electroreceptor organs;

[0067] Figure 7 This is a schematic diagram of the test experiment principle of the present invention;

[0068] Figure 8 This is a design drawing of the two-dimensional attitude control mechanism of the present invention;

[0069] Figure 9 This is a schematic diagram of the original test data of the electrostatic induction signal of the present invention;

[0070] Figure 10 This is a schematic diagram of the normalized time characteristic values ​​of the electrostatic induction signal of the present invention;

[0071] Figure 11 This is a schematic diagram showing the prediction results and errors of Model 1 of the present invention on various datasets;

[0072] Figure 12 This is a schematic diagram showing the prediction results and errors of Model 2 of the present invention on various datasets;

[0073] Figure 13 This is a distribution diagram of the prediction errors for all models in this invention. Detailed Implementation

[0074] The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0075] The electrostatic charging phenomenon of projectiles (i.e., charged flying bodies) has been reported since the 1980s. Due to the electrostatic effects caused by the primer explosion impact, flame and compound powder adhesion, friction between the projectile and the gun barrel, and friction between the projectile and dust and water molecules in the air during flight, high-speed projectiles carry a certain amount of static charge. This charge varies depending on factors such as ammunition type, weapon condition, and environmental conditions, and is distributed within a range of 3-5 orders of magnitude. Small arms projectiles carry static charge in the pC to nC range, while rockets and aircraft carry even greater charges due to their larger surface areas. The static charge on the surface of the projectile generates an electrostatic field in its surrounding space. During flight, this field is disturbed, and can be detected by various electric field sensors. Studies have used cylindrical and window-shaped inductive electrodes combined with charge amplifiers to test the electrostatic induction signal of projectiles. Another study used a cylindrical electrostatic sensor made of steel mesh to test the charge of a 9mm Beretta pistol projectile. Studies have compared the performance of non-contact potential sensors, vector electric field sensors, and charge sensing sensors in detecting projectiles through range experiments. Subsequent work proposed a quasi-electrostatic field sensor array based on varactor diodes, with three sensors placed 3 meters apart. A wired network was used to transmit the test signals to a central data processing unit, and triangulation and wavelet analysis positioning algorithms were used to achieve projectile orientation indication. Other research has utilized a deep learning-assisted self-powered multifunctional electret sensor to identify charged objects in flight. These works have investigated projectile charge measurement, electrostatic signal acquisition, feature analysis, and potential applications, but they are not suitable for unmanned platforms with limited space, payload, and computing power. The main problem is:

[0076] (1) Cylindrical induction electrodes require the flight projectile to penetrate in order to detect the signal. This cannot detect flight projectiles from any direction. Large-size flat electrode or wide-spaced electrode array is not suitable for unmanned platforms with limited space and load, and will affect the stealth and maneuverability of the unmanned platform.

[0077] (2) Electrostatic testing experimental systems generally improve the sensitivity and stability of the experimental system by increasing the induction electrode, shielding interference signals, manually resetting, and controlling the experimental environment. However, the high sensitivity and high stability of the sensor circuit are not taken into account, and the power consumption of the sensor and its adaptability to vibration and shock are not considered.

[0078] (3) Information mining algorithms for electrostatic induction signals all require real-time processing of the entire time series. The algorithms for data acquisition, transmission and processing are highly complex, require high data bandwidth and computing resources, and are not suitable for unmanned platforms with limited edge computing power.

[0079] To address the above problems, this invention, inspired by the electroreceptive organs of organisms such as sharks (the Ampullae of Lorenzini array), proposes an electrostatic induction electrode array with differentiated characteristics in attitude and spatial distribution. This array utilizes the differences in the induction signals to mine target information. First, the influence of electrode parameters on the induction signal is theoretically analyzed. A high-sensitivity, high-precision, and low-noise electrostatic induction signal amplification circuit is designed, capable of flexibly adjusting frequency response characteristics. A prototype system is implemented based on a commercial amplifier. A laboratory simulation system for flying charged objects is built, obtaining an experimental dataset of induction signals from flying charged objects. Symbolic regression machine learning algorithms are used to mine the temporal characteristics of the electrostatic signals, obtaining a mapping function between signal characteristics and the direction of attack of the projectile. This achieves a low-power, low-cost, low-computing-power-requirement, and highly integrated method for sensing the flight trajectory of charged objects, with an omnidirectional prediction error of less than 8 degrees.

[0080] In a non-contact electrostatic testing system consisting of a charged target, an electrostatic field, and a detection electrode, the electrostatic field serves as the medium connecting the target and the electrode. The induced charge on the detection electrode can be calculated using Gauss's law and the law of conservation of charge. To avoid loss of generality, a... Figure 1 The diagram shows an electrostatic detection schematic of a charged target.

[0081] like Figure 1 As shown, the Ground plane is an infinitely large horizontal surface. A Cartesian coordinate system is established on it, with the unit vectors of the three coordinate axes being... and The golden circular plate is a finite-sized, conductive, and grounded detection electrode in space, with radius r. The center of its upper surface is defined as the origin O of the spatial coordinate system, and its normal vector... Let α be a vector pointing perpendicularly outward from the origin O to the outside of the circular plate. The two angles between the normal vector and the spatial coordinate axes determine the spatial attitude of the detection electrode. and The included angle, β is Projection in the XOY plane and The angle between the two spheres is shown. The blue ball is a flying charged target with a static charge of Q(t), which changes during flight. The dotted line represents its trajectory, and its velocity vector is given by... Let x be the tangent vector to the trajectory, and let x be the coordinates of the spatial position. p (t),y p (t),zp (t)), whose unit vector is the position coordinates. and The included angle is δ. and The included angle is The angle between the projection of XOY and the X-axis is γ.

[0082] The electric field components of the target electric field in the direction normal to the probe electrode, calculated using the method of charge images, are as follows:

[0083]

[0084] Where ε₀ is the vacuum permittivity, ε r Let be the dielectric constant of the space medium. From equation (1), it can be seen that when δ = Nπ (N = 0, 1, 2...), E n The maximum value is when and When the detector electrodes are located on the same straight line and their normals are perpendicular to the charged target, E n The value is at its maximum. The spatial orientation of the detection electrode determines the spatial location of the charged target it is most sensitive to, which demonstrates that electrostatic induction has direction selectivity.

[0085] Furthermore, according to Figure 1 Given the geometric relationships and the symmetry of the detection electrodes, we can assume that α, β ∈ (0, π / 2) and and If they are located in the same quadrant, then:

[0086]

[0087] Substituting equation (2) into equation (1), we obtain the field strength component in the normal direction of the probe electrode as follows:

[0088]

[0089] set up but

[0090]

[0091] To visually demonstrate the influence of the probe electrode attitude parameters (α, β) on the induced signal, it is assumed that the charged target is located at position... The above equation can then be simplified to:

[0092]

[0093] When α, β∈(0, π / 2), the variation law of the normalized value of the normal electric field is as follows: Figure 2 As shown, from Figure 2It can be seen that the normal electric field strength is the maximum when both α and β are pi / 4, that is... and When they coincide, the normal field strength is at its maximum, and the maximum value differs from the minimum value by more than double.

[0094] Furthermore, according to Gauss's law, the induced charge density σ on the surface of the probe electrode... s for:

[0095]

[0096] Based on this, the effect of the spatial position of the charged target on the induced charge density σ on the surface of the detection electrode is analyzed. s The influence of the charge on the charged target. To simplify the calculation, it is assumed that the charge Q0 carried by the charged target remains constant and the probe electrode is parallel to the horizontal plane, i.e., α = 0. Then equation (6) simplifies to:

[0097]

[0098] Obviously, when x p (t)=0,y p When (t) = 0, σ s The maximum value is the highest amount of charge induced on the electrode when the charged body reaches directly above it.

[0099] Let d be the distance from the projection of the charged target onto the XOY plane to the origin. p (t), that is

[0100]

[0101] So,

[0102]

[0103] Take d p (t)=0,z p σ when (t) = Δ s The value is a normalized quantity, and Δ is the unit length. Then, the induced charge density σ on the surface of the probe electrode... s The variation law of the relative distance d between the charged body and the detection electrode is as follows: Figure 3 As shown.

[0104] Depend on Figure 3 It can be seen that when z p When (t)≥6Δ, σ s In 0≤d p The values ​​of (t) ≤ Δ within the circular region are approximately constant. According to Gauss's law, the total charge Q induced on the detector electrode... s for:

[0105]

[0106] Therefore, when the flight altitude of the charged target is greater than 6 times the radius r of the detection electrode, the charge density induced on the electrode surface can be considered constant. Thus, equation (10) can be simplified to:

[0107]

[0108] According to the law of conservation of charge, the current flowing out of the detector electrode is the change in the amount of charge induced in the detector electrode, that is:

[0109]

[0110] This current value is amplified and recorded by the subsequent high-impedance electrostatic sensor, and is used to characterize the electrostatic signal generated when a charged target passes through the detection electrode.

[0111] To further visualize the signal waveform without loss of generality, we assume the probe electrode is parallel to the horizontal plane, and the surface charge of the probe electrode is simplified as follows:

[0112]

[0113] Let the components of the velocity V of the charged target along the coordinate axis be V x V y V z ,So

[0114]

[0115] Furthermore, assume the charged target has a constant charge of Q0, a constant flight speed of V0, and its direction of velocity is parallel to the x-axis along with its flight trajectory. At t=0, it passes through the YOZ plane, i.e., x... p (0) = 0, equation (15) can be simplified to:

[0116]

[0117] The distance between the charged target and the detection electrode is D. p (t), i.e.

[0118]

[0119] but:

[0120]

[0121] Substituting into equation (16), we get

[0122]

[0123] Therefore, when t = 0, equation (19) takes the maximum value, denoted as

[0124]

[0125] Then, equation (19) can be simplified as follows:

[0126]

[0127] As can be seen from equation (21), the waveform shape of the induced charge is determined by... Let it be the waveform time scale coefficient τ:

[0128]

[0129] Then equation (21) can be simplified as follows:

[0130]

[0131] Therefore, the waveform of the induced charge on the detection electrode is determined by τ, the flight velocity V(t) of the charged target, and the shortest distance D from the target to the electrode. p (t) have a combined effect, and the effects of the two parameters are inversely proportional. When the waveform coefficients take different values, the charge waveform and its spectrum are as follows: Figure 4 As shown.

[0132] Substituting equation (23) into the induced current equation (13), then

[0133]

[0134] therefore, Figure 4 The current waveforms and their frequency spectra corresponding to each curve are shown in the figure below. Figure 5 As shown, from Figure 4 , 5 As can be seen, the signal energy is mainly concentrated in the low frequency range, requiring the sensor's low-frequency bandwidth to be reduced to around 0.1Hz to effectively amplify the electrostatic induction signal without distortion. When the sensor's low-frequency characteristics are insufficient, the sensor exhibits high-pass filter characteristics, and its distortion response to the induction signal is similar to that of a differentiator.

[0135] Specifically, each electrostatic induction electrode consists of a cylindrical sandwich structure comprising a sensing plate, an insulating substrate, and a shielding electrode, such as... Figure 6As shown in (B), the bottom of the cylinder contains a circular copper induction plate for sensing the spatial electrostatic field and is connected to the signal input terminal of the electrostatic sensor. An insulating substrate made of polyesterimide is used to electrically separate the induction plate from the shielding electrode. The bottomed cylindrical copper shielding electrode is connected to the power ground of the electrostatic sensor to block the influence of lateral electrostatic fields on the induction plate and improve the spatial directivity of the electrostatic induction plate. A higher cylinder height results in better spatial directivity but a weaker sensing signal; a lower cylinder height results in poorer spatial directivity but a stronger sensing signal. In this invention, the induction plate thickness is 1 mm, the diameter is 20 mm, the insulating substrate thickness is 0.5 mm, the shielding electrode radius is 21 mm, and the cylinder height is 20 mm.

[0136] An array of electrostatic induction electrodes is distributed on a hemispherical support structure, with the central axis of each electrode pointing towards the center of the hemisphere. The electrode whose central axis is perpendicular to the bottom surface of the hemisphere is defined as the normal electrode, and its tilt angle is denoted as 0°. The angle between the central axis of the other electrodes and the central axis of the normal electrode is defined as its tilt angle, which is the direction in which the electrode has the highest spatial sensitivity. In this invention, six electrodes are equidistantly arranged on the circumference at tilt angles of 0°, 21°, 42°, and 63°, and five electrodes are equidistantly arranged on the circumference at tilt angles of 36° and 72°.

[0137] The electrostatic induction signal amplification circuit is described in the literature M. Man, M. Wei, Y. Zhang, G. Ma, and Y. Chen, "Biomimetic Measurement Method for Surface Electric Potential Imaging Inspired by Visual Lateral Inhibition," IEEE Transactions on Industrial Electronics, pp. 1-11, 2023, doi:10.1109 / TIE.2023.3314910.

[0138] MHMan and M.Wei, "A Field High Resolution Measurement Method for Irregular Surface Electrostatic Potential," IEEE Transactions on Instrumentation and Measurement, vol.72, pp.1-11, 2023, doi:10.1109 / TIM.2023.3234080.

[0139] The paper, "Remote monitoring method for human body electrostatic potential based on symbolic regression machine learning," by M. Man and M. Wei, in *Measurement Science and Technology*, vol. 34, no. 6, p. 065116, 2023 / 03 / 24, doi:10.1088 / 1361-6501 / acc3b6, details a method with a DC voltage gain of 34dB in the 0.1Hz to 1kHz range, effectively amplifying weak electrostatic induction signals. The flicker noise's 1 / f angular frequency is approximately 30Hz, and the sensor's Gaussian white noise above this frequency is... It's important to note that improving the spatial resolution of electrostatic field testing necessitates reducing the physical size of the sensing electrode, thereby shrinking the sensing area. This introduces a negative consequence: the equivalent coupling capacitance between the charged object and the sensing electrode is drastically reduced, reaching the picofarad or even femtofarad level. This necessitates an amplifier circuit with both extremely small input capacitance and extremely high input resistance to match the equivalent coupling capacitance and improve the voltage division ratio and sensitivity. The use of state-of-the-art positive feedback circuit design techniques (bootstrapping and neutralization) has mitigated this problem to some extent. However, the trade-off between spatial resolution and signal sensitivity in this type of sensor has not yet been completely resolved.

[0140] Each electrode of the electrostatic induction electrode array is connected to an independent amplification circuit to amplify its weak electrostatic induction signal, which is then transmitted to a multi-channel oscilloscope connected to the back end for digital acquisition and recording. This enables multi-channel synchronous recording of the electrostatic field in the surrounding space.

[0141] 3.3 Symbolic Regression Algorithm

[0142] When a projectile passes over an unmanned platform at a distance of ≤10m, the disturbance of the electrostatic field caused by the projectile's static charge is detected and recorded by an electrostatic field sensor, and saved as a set of differentiated time-series signals. Analyzing this data can yield information such as the projectile's velocity, trajectory, and direction. Due to the limited energy, computing power, payload, and cost of the unmanned platform, this invention chooses the symbolic regression algorithm for data mining. This is because symbolic regression uses evolutionary algorithms to search the space of mathematical expressions, aiming to minimize the error between measured and predicted data, and automatically finding the mathematical expressions hidden behind the measured data. The trained symbolic model is easy to deploy without requiring a dedicated hardware or software environment (such as neural networks, vector machines, etc.). This application uses a multi-gene symbolic regression method, combining the population search capability of multi-gene genetic programming (MGGP) and the parameter estimation capability of linear least squares, to find the optimal linear combination of mathematical expressions corresponding to all gene individuals in the population, minimizing the error between the predicted output response and the target output response of the mathematical model. The algorithm principle and implementation details are in the literature M. Man and M. Wei, "Remote monitoring method for human body electrostatic potential based on symbolic regression machine learning," Measurement Science and Technology, vol.34, no.6, p.065116, 2023 / 03 / 24, doi:10.1088 / 1361-6501 / acc3b6.

[0143] The following is a detailed explanation in M. Man, Y. Zhang, G. Ma, Z. Zhang, and M. Wei, "Indoor Localization Method of Personnel Movement Based on Non-Contact Electrostatic Potential Measurements," Sensors, vol. 22, no. 13, p. 4698, 2022.

[0144] The symbolic regression algorithm used in this experiment differs in that it employs a special fitness function. The fitness function is chosen as the circle absolute error between the predicted value (Ye) and the target value (Ya), calculated as follows:

[0145] CAE = min(|Y e -Ya |,360-|Y e -Y a |)

[0146] This is because the direction of the incoming projectile is a point on a circle, and both the predicted and actual incoming directions belong to points on that circle. The values ​​of these points on the circle have a period of 360 degrees. For example, if the actual firing direction is 10°, and the predicted incoming direction is 30°, the prediction error is 20°. When the predicted incoming direction is 350°, the prediction error is also 20°, not 340°, because the interval between 10° and 350° on the circle is 20°. Therefore, CAE is used as the fitness function in this experiment.

[0147] A test scenario for electrostatic induction signals from a flying charged body was constructed in the laboratory, such as... Figure 7 As shown in (a), within a circular laboratory area with a radius of 4m, an electromagnetic catapult module and a two-dimensional attitude control mechanism form a flying charged body launch system, launching a metal cylinder carrying static charge. A mechanical dog equipped with an electrostatic field sensor synchronously collects the spatial electrostatic field disturbance signal caused by the flying charged body.

[0148] 1. Experimental apparatus for charged bodies in flight

[0149] An electromagnetic catapult module and a two-dimensional attitude control mechanism are used to construct a flying charged body launch system. The electromagnetic catapult module consists of a 5-stage copper coil acceleration (0.8mm wire diameter, 195 turns, 20mm outer diameter, 8mm inner diameter, 26mm thickness, 2.4mH inductance). The driving capacitors for each stage of the coil are 2000uF, 1440uF, 1440uF, 1000uF, and 1000uF, respectively. The capacitor charging voltage range is 50V-400V, quantitatively controlled by a contact switch. The guide rail is a PVC round tube (3.2mm radius, 500mm length), and the launching projectile is a stainless steel cylinder (3mm radius, 30mm height). The maximum initial velocity of the projectile is approximately 48m / s. When the capacitor is triggered, the static charge stored in the capacitor flows rapidly through the coil, generating a transient magnetic field that excites the projectile to move within the guide rail. Friction between the projectile and the guide rail generates static charge, resulting in a charged flying body after launch. Repeated experiments have confirmed that this electrification process is relatively stable, and approximately 95% of launch experiments result in the projectile becoming charged.

[0150] The trajectory of a projectile is determined by both the direction of the guide rail and its initial velocity. To accurately and quantitatively control the trajectory of the projectile and improve the repeatability of the experiment, a two-dimensional attitude control mechanism was designed, such as... Figure 8As shown. The control mechanism includes a base, a rotating platform, a rotating drive device, a limit device, and a manual control device. The rotating platform consists of two parts: an azimuth axis and a pitch axis, both supported by two pairs of precision mechanical angular bearings to ensure the axial and radial stiffness and rotational accuracy of the shaft system. The azimuth axis rotation angle range is (-40° to +40°), and the pitch axis rotation angle range is (0° to +15°). Precise control is achieved by sending control signals to the rotating drive device via an electronic handwheel, with an adjustment resolution of 1°.

[0151] 2. Two experimental modes

[0152] Utilizing four sensing electrodes tilted at 42° in a space electrostatic field sensor ( Figure 7 The four colors (red, blue, green, and orange) are labeled as Sensors A, B, C, and D, respectively, to detect the electrostatic field signal of a flying charged object and extract its flight angle information. To verify the effectiveness and versatility of this invention, two types of experiments were designed, named the center-point firing mode experiment and the area sweeping mode experiment, as follows: Figure 7 As shown in (b) and (c). For the center-point firing mode experiment, the electrostatic testing system was located in the center of the experimental field. The projectile launching system aimed at a point 1m above the center of the compound eye electrode and fired, allowing the projectile to pass through the airspace directly above it. The electrostatic testing system recorded four electrostatic induction signals. Then, the position of the launching system was changed at 9-degree intervals, traversing the experimental field once. Experimental results were recorded three times at each position, resulting in a total of 120 sets of data. The difference for the area sweeping mode experiment was that, at each firing position, the system was aimed at the left, center, and right sides respectively, firing three times in each direction, thus recording a total of 360 sets of data.

[0153] 3. Data Processing

[0154] During the experiment, a multi-channel digital oscilloscope (PicoScope 4824) was used to simultaneously record four electrostatic induction signals at a sampling rate of 20kHz. Figure 9 As shown.

[0155] Figure 9 (a) An offset was added to each channel signal in the oscilloscope for easier manual observation. As can be seen from the figure, the four signals exhibit good consistency. The peak values ​​of each signal are amplified and the offset is removed, as shown in the figure. Figure 9 As shown in (b), the signal characteristics conform to Figure 5The electrostatic induction signal of the flying charged body obtained by theoretical analysis shows that the peak value and peak time of the four signals are significantly different, indicating that the system can accurately test the electrostatic induction signal when the flying charged body passes by. Furthermore, the system achieves directional selectivity of electrostatic induction by utilizing the differences in the spatial position and attitude of the sensing electrodes, thus realizing electrostatic testing with spatial filtering characteristics.

[0156] The test results contained DC bias, 50Hz power frequency noise, and high-frequency noise. This was due to the sensor's good low-frequency characteristics, a test bandwidth of up to 100kHz, and the influence of electrostatic discharge during the experiment. Therefore, it was necessary to perform filtering and offset removal data cleaning operations on the collected raw data. The filtering operation used MATLAB's low-pass digital filter function `lowpass()` to reduce noise in the recorded data, with the cutoff frequency parameter set to 10Hz, the steepness parameter set to 0.9999, and the stopband attenuation parameter set to 180dB. The offset removal operation used MATLAB's `detrend()` function, setting the offset removal method to `constant`, i.e., subtracting the DC offset from the raw data. In addition, the signal contained two relatively large noise points. The first noise point, before the electrostatic induction signal, was the electromagnetic radiation signal generated at the moment the projectile separated from the gliding track. The second noise point, after the electrostatic induction signal, was the electrostatic discharge signal generated when a charged flying object collided with protective foam. These two noise components were not the electrostatic field induction signal to be analyzed in this experiment, and therefore were directly eliminated. Finally, using the peak time of the Sensor A signal as the reference point, only the data before and after the reference point for each channel is retained. The data cleaning results are as follows: Figure 9 As shown in (c).

[0157] 4. Feature Extraction

[0158] Due to the differences in the frictional state between the projectile surface and the guide rail surface, the voltage decay of the electromagnetic catapult's energy storage capacitor, and the size of the projectile, the actual charge carried by each launched projectile has a high degree of uncertainty. Therefore, the amplitude of the electrostatic induction signal obtained under the same experimental conditions has a high degree of randomness and cannot be used for information mining. However, the relative time when a charged body passes over different induction electrodes is a fixed value, affected only by the flight speed and the relative position of the electrode array. Therefore, in the experiment, the time difference between the peak times of each signal is used to mine information about the flight trajectory.

[0159] First, by determining the peak values ​​of the four electrostatic induction signals (using the `peak()` function in MATLAB), such as... Figure 10As shown in (a), peaks A, B, C, and D are labeled as PeakA, PeakB, PeakC, and PeakD, respectively. Their horizontal axes represent the peak times, denoted as T1, T2, T3, and T4. Furthermore, the minimum value of the four peak times is set as the start time, and the maximum value as the end time. The interval between the start and end times is defined as the normalized duration of this experiment. Therefore, the time difference between the four peak times and the start time divided by the normalized duration gives their normalized time characteristic values, denoted as the normalized peak times. The calculation method is shown in the equation.

[0160]

[0161] A radar chart of the normalized time characteristic values ​​of four signals obtained from a single experiment, as shown below. Figure 10 As shown in (b). In the first test mode, the normalized time characteristic values ​​of the test data obtained from 40 firing angles, and their radar charts are shown below. Figure 10 As shown in (c, d), it can be seen from the figure that the signal characteristics are significantly correlated with the shooting angle.

[0162] The advantage of this normalization process is that the four time characteristic values ​​are only affected by the firing angle of the projectile, and not by the flight speed and relative distance. The inductive signal waveform corresponds to the dynamic process of the projectile flying over the electrode sensing area. The waveform of the electrostatic induction signal is mainly determined by the time scale coefficient τ, which is the flight speed V(t) and the shortest distance D from the target to the electrode. p (t) The relative distance has a combined effect because, with the electrode structure and attitude fixed, the relative distance determines the sensing area. When the relative distance remains constant but the flight speed changes, the duration and peak times of the four sensing signals also change accordingly. However, the relative intervals of the peak times change in the same proportion, inversely proportional to the flight speed. This proportionality coefficient is precisely reduced when calculating the normalized time characteristic value. Therefore, changes in flight speed do not affect the normalized time characteristic value. Similarly, when the flight speed remains constant but the relative distance changes, the sensing areas of the four electrodes change in the same proportion, and the peak times of the four sensing signals also change in the same proportion, directly proportional to the relative distance. This proportionality coefficient can also be reduced when calculating the normalized time characteristic value. Therefore, changes in relative distance do not affect the normalized time characteristic value.

[0163] 5. Inversion Results

[0164] The symbolic regression algorithm was used to mine the mapping function between the normalized time eigenvalues ​​of the electrostatic induction signal and the firing angle. The firing angle of each experiment was used as the dependent variable of the mapping function, and the normalized time eigenvalues ​​of the four induction signals were used as independent variables. The symbolic regression algorithm was used to optimize this mapping function, with the aim of obtaining a mathematical regression model from the sensor-induced signal to the direction of the incoming charged object.

[0165] This invention conducted three rounds of omnidirectional 360-degree traversal experiments in both center-point firing and area-scanning modes, obtaining six datasets named M1R1 (Mode1Run1), M1R2, M1R3, M2R1, M2R2, and M2R3. Each dataset was then used as training samples for model training, with the remaining data serving as validation samples. A symbolic regression algorithm was run once to obtain an optimal model. Finally, the above process was repeated ten times, with the initial values ​​of the evolution algorithm randomly changed each time while keeping other parameters constant, to obtain the optimal model for each dataset.

[0166] The optimal model trained using the M1R1 dataset is:

[0167] Y e =0.453+0.453T2 cos(T4)-0.211T2+0.506T1 cos(4.07cos(3.07+2.51T2 cos(T2 cos(0.808+2.51T2))))

[0168] Where Ye represents the model estimate of the incoming projectile's direction of attack, and T1-T4 represent the normalized time characteristic values ​​of the four induction signals, respectively. The prediction results of this model on the training dataset M1R1 and the validation datasets M1R2 and M2R1 are as follows: Figure 11 As shown in (a, b, c).

[0169] Figure 11 In (a), the horizontal axis represents the 40 firing angles in the training dataset (traversing one revolution at 9-degree intervals), and the vertical axis represents the angle values ​​(0-360 degrees). The red line represents the target value of the firing angle, the blue line represents the predicted value of the firing angle, and the yellow bars correspond to the prediction error of the firing angle. As shown in the figure, this model has a high prediction accuracy, with a mean absolute error of 3.39 degrees, as indicated by the green line. The model only has larger errors at a few firing angles (such as 45, 54, and 99 degrees), exceeding 10 degrees, which is attributed to the instability caused by electrostatic charging during the experiment. Therefore, the symbolic regression algorithm has sufficiently good modeling and predictive capabilities to meet the requirement of predicting the direction of attack.

[0170] Furthermore, the generalization ability of this model is validated on other datasets. Figure 11(b) shows the prediction results of this model on the validation dataset M1R2. The model's prediction accuracy remains at a high level, with a mean absolute error of 5.55 degrees. Furthermore, the mean absolute error of this model on M1R3 is 4.83 degrees, and the results are similar to this figure, so they will not be repeated. Datasets M1R1, M1R2, and M1R3 all come from the first test mode. Therefore, this model has good generalization ability for the spot-fire test mode, with a prediction absolute error of around 5 degrees.

[0171] Figure 11 (c) shows the model's prediction results on the M2R1 dataset, validating the strafing test pattern. The model's prediction accuracy dropped significantly, with the mean absolute error increasing to 13.01 degrees. In the strafing test pattern, each firing angle was tested three times: left-side firing, center firing, and right-side firing. Therefore, in the strafing pattern, traversing the entire range at 9-degree intervals, 120 sets of data were collected, including 40 sets each for left-side, center, and right-side firing. In the figure, the dark red line represents the model's prediction results for the 40 sets of left-side firing data, the blue line represents the model's prediction results for the center firing data, and the orange line represents the model's prediction results for the right-side firing data. The blue line is closer to the red line than the dark red and orange lines, and the blue error bar is shorter than the dark red and orange lines. This indicates that the model's prediction accuracy for the center firing data is higher, resulting in overfitting, a common phenomenon in machine learning training. This is detrimental to the generalization and application of the model. When the projection of the flight trajectory of the projectile does not pass through the center of the sensor, the model prediction error will increase significantly, greatly reducing the versatility of this method.

[0172] The prediction error of this model on all datasets is as follows: Figure 11 As shown in (d), the model's mean absolute prediction error on the M1R1, M1R2, and M1R3 datasets is around 5 degrees, with few outliers and extreme values ​​not exceeding 40 degrees. On the M2R1, M2R2, and M2R3 datasets, the mean absolute prediction error increases to around 15 degrees, with a significant increase in outliers and a maximum error of 160 degrees. This indicates that the model has good predictive ability for burst fire tests, with an error of approximately 5 degrees. However, its predictive ability for strafing test data is poor, with an error of approximately 15 degrees. The model's generalization ability is weak; fluctuations in the trajectory deviating from the center of the sensor significantly affect prediction accuracy.

[0173] The optimal model trained using the M2R3 dataset is:

[0174] Y e =0.571+T1T2+0.353T1T4+0.0972sin(T2 2)-0.214T4-2.13T1mod(0.571T2-8.03,0.489)

[0175] The prediction results of this model on the training dataset M2R3 and the validation datasets M2R1 and M1R1 are as follows: Figure 12 As shown in (a, b, c).

[0176] Figure 12 In (a) and (b), the mean absolute error of this model on the training dataset M2R3 is 7.22 degrees and the mean absolute error on the validation dataset M2R1 is 7.29 degrees. Figure 12 In (a), when the firing angle is 0, the predicted angle is 357.8 degrees, and when the firing angle is 351 degrees, the predicted angle is 0.02 degrees. Figure 12 In (b), when the firing angle is 9°, the predicted angle is 354.9 degrees. Since the angle values ​​are periodic at 360°, the actual absolute error of the model at these three firing angles is not significant. Therefore, the absolute error distribution of the model is consistent across all data. Furthermore, the mean absolute error of this model on M2R2 is 7.66 degrees, as shown in the results graph. Figure 12 (b) Similarly, this will not be repeated. Therefore, this model has high prediction accuracy for all data in the sweeping pattern, with an absolute error of approximately 7 degrees.

[0177] Figure 12 (c) shows the prediction results of this model on the burst fire pattern dataset M1R1. The model's prediction accuracy did not decrease but rather increased, while the mean absolute error decreased to 5.79 degrees. There are two reasons for this: First, the M1R1 dataset has a smaller volume and stronger regularity, as the trajectory of central firing is relatively easy to control, with the aiming sensor directly above the center. In contrast, the trajectory deviations of left- and right-side firing have higher randomness, requiring manual visual control of aiming offsets, resulting in greater data noise. Second, because the sweep fire pattern data includes burst fire pattern data, Model 2 has learned the patterns inherent in the burst fire pattern data during training. To verify this conclusion, the prediction errors of this model on all datasets are summarized as follows: Figure 12 In (d), the model's mean absolute prediction error on the M1R1, M1R2, and M1R3 datasets is around 6 degrees, with few outliers and extreme values ​​not exceeding 40 degrees. The model's mean absolute prediction error on the M2R1, M2R2, and M2R3 datasets is approximately 7 degrees, with similarly few outliers and extreme values ​​not exceeding 30 degrees. This demonstrates that the model has good predictive ability for both point-fire and scanning model experiments, with a mean error below 8 degrees. Therefore, this model has high prediction accuracy and strong generalization ability; it can accurately predict the angle of attack when a charged flying object passes over the sensor area.

[0178] Furthermore, the optimal models obtained by training on datasets M1R2, M1R3, M2R1, and M2R2 are as follows:

[0179]

[0180] Y e =0.444+0.265T2+1.32T1T2+0.34T1T4-0.627T1-1.49T1mod(T2,0.696)-0.146T2T4cos(T2T3)

[0181] Y e =0.85+0.847T1T2+0.358T1T4-0.182T4-0.311 cos(sin(T2))-2.74T1mod(4.29+0.37T2,0.37)

[0182] Y e =0.556+0.305T1+0.085T2-0.151T4+0.33T1T4+0.122mod(25.2-T2-mod(T1,0.305),-8.23)

[0183] The mean absolute errors of these models on all datasets are as follows: Figure 13 As shown.

[0184] The first three rows show the performance of the optimal models trained on the spot-fire pattern dataset (M1R*) across all datasets. They perform well on the first three columns (M1R* dataset), with an error range of [3, 2, 6, 4], but their performance drops significantly on the last three columns (M2R* dataset), with an error range of [9, 2, 15, 9]. Therefore, the models trained on the spot-fire pattern data exhibit overfitting and poor generalization ability, making them unsuitable for the sweep-fire pattern data. The last three rows show the performance of the optimal models trained on the sweep-fire pattern dataset (M1R*) across all datasets. The error of each model remains around 7 degrees across all datasets, with a fluctuation range of no more than 2 degrees. Therefore, the models trained on the sweep-fire pattern data have strong generalization ability and good versatility, with an omnidirectional prediction error of less than 8 degrees.

[0185] Based on the principle of electrostatic induction, and mimicking the compound eye electrode array, an induction electrode array with attitude and spatial distribution structural characteristics was designed. A high-sensitivity electrostatic induction signal conditioning and amplification circuit was used to achieve long-distance, non-contact measurement of the electrostatic induction signal of a flying charged object. A prototype experimental system was built based on an electromagnetic catapult device to obtain a dataset of electrostatic induction signals from omnidirectionally approaching charged objects. A symbolic regression algorithm was trained to obtain a prediction model of the direction of attack of the charged object. The optimal model's omnidirectional prediction error is less than 8 degrees. This invention is a passive receiving test, without actively emitting any form of energy (e.g., infrared, electromagnetic waves, ultrasound, etc.), thus resulting in very low power consumption. The system is simple, using only 4 electrostatic induction signal amplifiers and a low-cost embedded microcontroller (Raspberry Pi, STM32 series MCU), thus offering low cost, high flexibility, and easy integration. The prediction model is a simple mathematical expression with very low computational complexity, capable of running on any embedded processor, and exhibiting strong model versatility. Therefore, this invention features low power consumption, low cost, low computing power requirements, and high integration, making it highly valuable for application.

[0186] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A system of electrostatic sensing electrode arrays that mimic the electroreceptors of sharks, characterized in that, The application relates to a charged target, an electrostatic field and a hemispherical electrostatic induction electrode array, wherein a detection electrode of the hemispherical electrostatic induction electrode array comprises a cylinder structure composed of an induction plate, an insulating substrate and a shielding electrode, the inside bottom end of the cylinder structure is a circular plate-shaped induction plate used for sensing a space electrostatic field and connected to a signal input end of an electrostatic sensor, the insulating substrate is used for electrically separating the induction plate from the shielding electrode, a bottom-cylindrical shielding electrode connected to a power supply ground of the electrostatic sensor is used for blocking a lateral electrostatic field from affecting the induction plate and improving the spatial directivity of the induction plate, the detection electrode obtains a current value of the charged target, and the current value is a signal amplified and recorded by a high-impedance electrostatic sensor and used for representing an electrostatic signal generated when the charged target passes through the detection electrode. The hemispherical electrostatic induction electrode array is distributed on a hemispherical shell-shaped support structure, the central axis of each detection electrode points to the spherical center, a detection electrode with a central axis perpendicular to the hemispherical bottom surface is defined as a normal electrode, the angle between the central axis of the normal electrode and the central axis of another detection electrode is defined as the inclination angle of the another detection electrode, six detection electrodes are equidistantly arranged on the circumferences with inclination angles of 0, 21, 42 and 63 degrees, and five detection electrodes are equidistantly arranged on the circumferences with inclination angles of 36 and 72 degrees. The detection electrode obtains the current value of the charged target, which comprises the following steps:

2. The electroreception electrode array system that mimics the electroreceptors of a shark of claim 1, wherein, The field intensity component of the target electric field in the normal direction of the detection electrode is calculated by using a mirror charge method, and the formula is as follows: Establish a Cartesian coordinate system XOY on a horizontal surface, with the unit vectors of the three coordinate axes as follows: , and The radius of the gold-plated detection electrode is Define the center of its upper surface circle as the origin of the spatial coordinate system. Its normal vector To pass through the origin A vector pointing perpendicularly outward from the circular plate, where... for and The included angle, for Projection in the XOY plane and The included angle; the amount of static charge carried by the charged target is The trajectory of the line changes during flight; the dotted line represents its motion, and the velocity vector is... Let be the tangent vector of the trajectory, and let be the coordinates of the spatial position. The unit vector of its position coordinates is , and The included angle is , and The included angle is , In the projection of XOY and The included angle of the axis is ; The field intensity component of the detection electrode in the normal direction is obtained by substituting formula (2) into formula (1), and the formula is as follows: （1） wherein is the vacuum permittivity, is the permittivity of the space medium; from equation (1) it can be derived that , is the maximum value, i.e. when and are located on the same straight line, the normal of the detection electrode is perpendicular to the charged target, the value is the maximum; Let and with in the same quadrant, then: （2） Therefore, when the flight height of the charged target is greater than 6 times the radius r of the detection electrode, the charge density on the surface of the electrode can be considered as a constant, therefore, formula (10) can be simplified as formula (11): （3） Let , then （4） Assuming the charged object is located at position then equation (4) can be simplified to: （5） When , the normal electric field strength is maximum, and then, according to Gauss theorem, the surface induced charge density of the detection electrode is: （6） Assume the charged target carries a charge quantity Keeping unchanged, the detection electrode posture is parallel to the horizontal plane, i.e. Then, equation (6) is simplified as: （7） When time, the maximum value; Let the distance from the charged target to the coordinate origin in the XOY plane be i.e. （8） （9） Take the value of the normalized amount, as the unit length; when , , in the circular area of the value is approximately constant; according to Gauss theorem, the total amount of induced charge on the detection electrode is: （10） According to the law of conservation of charge, the current flowing out of the detection electrode is the change amount of the induced charge amount of the detection electrode, that is, formula (12) is obtained. （11） The current value is a signal amplified and recorded by a high-impedance electrostatic sensor and used for representing an electrostatic signal generated when the charged target passes through the detection electrode. （12） （13） The detection electrode obtains the current value of the charged target, which further comprises the following steps of acquiring a signal waveform:

3. The electroreception electrode array system that mimics the electroreceptors of a shark of claim 2, wherein, Supposing that the posture of the detection electrode is parallel to the horizontal plane, the surface charge of the detection electrode is simplified as formula (16). Therefore, t=0, formula (19) takes the maximum value, which is recorded as formula (20). （14） Let the velocity of the charged target be along the coordinate axes respectively , then （15） Let the electric target charge constant be , the flight speed constant , the speed direction and flight trajectory parallel to the x-axis, and the flying plane YOZ at t=0, that is , formula (15) can be simplified as: （16） The distance of the charged target from the detection electrode is , i.e. （17） Therefore, formula (19) is simplified as formula (21). （18） Therefore, formula (21) is simplified as formula (22). （19） ​ （20） ​ （21） From equation (21), the waveform shape of the induced charge is determined by , which is set as the waveform time scale coefficient : （22） ​ （23） Therefore, the waveform of the induced charge by the probe electrode is determined by the flying speed of the charged target and the shortest distance from the target to the electrode together, and the influence of the two parameters is inversely proportional to each other, and then equation (23) is brought into the induced current equation (13), （24）。

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