Electrified body flight path sensing method based on electrostatic induction principle

Abstract

The invention discloses a charged body flight path sensing method based on an electrostatic induction principle. The charged body flight path sensing method comprises the following steps: capturing an electrostatic field signal generated by a flying charged body through a hemispherical electrostatic induction electrode array; each detection electrode is composed of an induction plate, an insulation substrate and a shielding electrode, the space directivity of the induction plate is effectively improved, and lateral electrostatic field interference is reduced. And an amplification circuit in the rear-stage high-resistance antistatic sensor independently amplifies signals of each detection electrode, and digitally acquires the signals through a multi-channel oscilloscope. A multi-gene symbol regression method is combined with a genetic algorithm and a linear least square method, a mathematical expression is optimized to minimize a prediction and target output error, and a circumference absolute error between a prediction value and a target value is calculated. And finally, filtering and demigration processing are carried out on the collected signals, the time difference of signal peak moments is mined, a time characteristic value data set of the flight path is constructed, and accurate data support is provided for analysis of the flight path of the electrified body.

Description

Technical Field

[0001] The present invention relates to the field of electrostatic induction technology, and in particular to a method for sensing the flight trajectory of a charged body based on the electrostatic induction principle. Background Art

[0002] Unmanned platforms represented by drones, unmanned vehicles, and unmanned boats are efficient, flexible, and economical, showing a trend of autonomy, intelligence, and scalability. They have been widely used in daily life and confrontation and conflict, and have achieved remarkable results. For example, drones are used for logistics distribution, crop protection, and forest fire monitoring, unmanned vehicles are used for battlefield reconnaissance and explosive disposal, and unmanned boats are used for ocean monitoring. In confrontation scenarios, in addition to electromagnetic interference, unmanned platforms are mainly subject to physical attacks from high-speed flying targets such as light weapons shooting, shrapnel jets, and FPV collisions of flying machines. However, general sensors carried by unmanned platforms, such as cameras, radars, and sonars, cannot detect attacks from high-speed flying targets. In addition, due to the limitations of their energy, computing power, payload, and cost, unmanned platforms cannot carry complex threat perception systems such as high-speed cameras, warning radars, or sound source localization. Therefore, existing unmanned platforms lack the ability to perceive high-speed flying targets, which seriously restricts their survivability and adaptability in confrontation environments. It is of great scientific significance and practical value to study the perception method of high-speed flying targets with low power consumption, low cost, high efficiency, agility, small size, and light weight. Summary of the invention

[0003] In order to solve the above problems, the present invention provides a method for sensing the flight trajectory of a charged body based on the principle of electrostatic induction.

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

[0005] A method for sensing the flight trajectory of a charged body based on the principle of electrostatic induction, comprising: a method for sensing the flight trajectory of a charged body based on the principle of electrostatic induction, characterized in that it comprises: a charged target, an electrostatic field and a hemispherical electrostatic induction electrode array, wherein the detection electrode of the hemispherical electrostatic induction electrode array comprises a cylindrical structure composed of an induction plate, an insulating substrate and a shielding electrode, wherein the induction plate at the bottom end thereof is a circular plate-shaped induction plate, which is used to sense the spatial electrostatic field and is connected to the signal input end of the electrostatic sensor, the insulating substrate is used to electrically separate the induction plate from the shielding electrode, the shielding electrode with a bottom cylindrical shape is connected to the power ground of the electrostatic sensor, which is used to block the influence of the lateral electrostatic field on the induction plate and improve the spatial directivity of the induction plate, the detection electrode obtains the current value of the charged target, and the current value is a signal amplified and recorded by a subsequent high-impedance electrostatic sensor, which is used to characterize the electrostatic signal generated when the charged target passes through the detection electrode; the subsequent high-impedance electrostatic sensor comprises an amplification circuit, and each detection electrode of the hemispherical electrostatic induction electrode array is respectively connected to an independent amplification circuit, and is transmitted to a multi-channel oscilloscope connected to the back end for digital acquisition and recording;

[0006] The polygenic symbolic regression method is used, combining the population search capability of the polygenic genetic algorithm and the parameter estimation capability of the linear least squares method, to find the optimal linear combination of the mathematical expressions corresponding to all gene individuals in the population, so that the error between the predicted output response and the target output response is minimized. The fitness function selects the circular absolute error between the predicted value (Ye) and the target value (Ya), and the calculation method is shown in the following formula:

[0007] CAE=min(|Y e -Y a |,360-|Y e -Y a |)

[0008] The hemispherical electrostatic induction electrode array is distributed on a hemispherical shell-shaped support structure, and 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 a normal electrode, and its inclination angle is 0°; the angle between the central axis of other detection electrodes and the central axis of the normal electrode is defined as its inclination angle, and four detection electrodes are equidistantly arranged on the circumference of the inclination angle 42 to detect the electrostatic field signal of the flying charged body, including: a central point shooting mode experiment and a regional scanning mode experiment. For the central point shooting mode experiment, the electrostatic test system is located in the center of the experimental site, and the flying charged body launch system is aimed at the center of the compound eye electrode to launch, so that the flying charged body Pass through the airspace directly above it and record four electrostatic induction signals; then change the position of the launch system at intervals of 9 degrees, traverse the experimental site once, record the experimental results three times at each position, and collect 120 sets of data in total; for the regional sweep mode experiment, when launching at each position, aim at the left, center, and right side of the test system respectively, launch three times in each direction, and record 360 sets of data in total; use a multi-channel digital oscilloscope to synchronously record four electrostatic induction signals, filter and de-bias the collected electrostatic induction signals, and perform data cleaning operations, and use the time difference of the peak moments of each signal to mine the information of the flight trajectory to obtain a time characteristic value data set;

[0009] The hemispherical electrostatic induction electrode array is distributed on a hemispherical shell-shaped support structure, and 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 a normal electrode, and its inclination angle is 0°; the angle between the central axis of other detection electrodes and the central axis of the normal electrode is defined as its inclination angle, and four detection electrodes are equidistantly arranged on the circumference of the inclination angle 42 to detect the electrostatic field signal of the flying charged body, including: a central point shooting mode experiment and a regional scanning mode experiment. For the central point shooting mode experiment, the electrostatic test system is located in the center of the experimental site, and the flying charged body launch system is aimed at the top of the center of the compound eye electrode to launch, so that the flying charged body passes directly above it. The experimental results were recorded three times at each position, and a total of 120 sets of data were collected. For the regional scanning mode experiment, when launching at each position, the left, center, and right sides of the test system were respectively aimed at, and each direction was launched three times, and a total of 360 sets of data were recorded. A multi-channel digital oscilloscope was used to synchronously record the four-way electrostatic induction signals at a sampling rate of 20KHz, and the collected electrostatic induction signals were filtered and de-biased for data cleaning. The time difference of the peak moments of each signal was used to mine the information of the flight trajectory, and a time eigenvalue data set was obtained.

[0010] Further: the data cleaning operation of filtering and de-offsetting the collected electrostatic induction signal includes: the filtering operation uses MATLAB's low-pass digital filter function lowpass() to perform noise reduction on the recorded data, with the cutoff frequency parameter set to 10 Hz, the steepness parameter set to 0.9999, and the stopband attenuation parameter set to 180 dB; the de-offset operation uses MATLAB's detrend() function, setting the offset removal method to constant, that is, the original data minus the DC offset.

[0011] Further: the information mining of the flight trajectory by using the time difference of the peak moments of each signal to obtain the time characteristic value data set includes: determining the peak values ​​of the four electrostatic induction signals, setting the minimum value of the four peak moments as the starting moment, and the maximum value as the ending moment, and the interval from the starting moment to the ending moment is defined as the normalized duration of the test, and the time difference between the four peak moments and the starting moment divided by the normalized duration is the normalized time characteristic value, which is recorded as the normalized peak moment, and the calculation method is shown in the formula;

[0012]

[0013] Further: the detection electrode obtains the current value of the charged target including:

[0014] A Cartesian space coordinate system XOY is established on the horizontal ground, and the unit vectors of the three coordinate axes are and Assume that the radius of the detection electrode is r, and define the center of its upper surface as the origin of the spatial coordinate system O, and its normal vector is the vector passing through the origin O and pointing vertically to the outside of the circular plate, where α is and The angle between The projection on the XOY plane is The amount of static charge carried by the charged target is Q(t), which will change during the flight. The dotted line is its trajectory, and the velocity vector is is the tangent vector of the motion trajectory, and the coordinates of the spatial position are (x p (t),y p (t),z p (t)), the unit vector of its position coordinate is and The angle between them is δ, and The angle is The angle between the projection on XOY and the X-axis is γ;

[0015] The image charge method is used to calculate the field strength component of the target electric field in the normal direction of the detection electrode:

[0016]

[0017] where ε 0 is the vacuum dielectric constant, ε r is the dielectric constant of the space medium; from formula (1), it can be concluded that when δ=Nπ, (N=0,1,2...), E n The maximum value is when and When the detection electrode is located on the same straight line and the normal direction faces the charged target, E n The maximum value;

[0018] Let α, β∈(0,π / 2) and and Located in the same quadrant, then:

[0019]

[0020] Substituting equation (2) into equation (1), we can obtain the field intensity component in the normal direction of the detection electrode:

[0021]

[0022] set up but

[0023]

[0024] Assume that the charged target is located at position Then formula (4) can be simplified as:

[0025]

[0026] When α, β∈(0, π / 2) are both pi / 4, the normal electric field strength is the largest. Then, according to Gauss's theorem, the induced charge density σ on the surface of the detection electrode is s for:

[0027]

[0028] Assume that the charged target carries a charge Q 0 Keeping unchanged, the detection electrode posture is parallel to the horizontal plane, that is, α = 0, then equation (6) is simplified to:

[0029]

[0030] When x p (t)=0,y p When (t) = 0, σ s The maximum value;

[0031] Assume that the distance from the projection of the charged target on the XOY plane to the origin of the coordinate system is d p (t), that is

[0032]

[0033] Take d p (t)=0,z p σ when (t)=Δ s The value is a normalized quantity, Δ is a unit length; when z p When (t)≥6Δ, σ s At 0≤d p The value in the circular region where (t)≤Δ is approximately a constant; according to Gauss's theorem, the total amount of charge induced on the detection electrode Q s for:

[0034]

[0035] Therefore, when the flying height 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 as a constant; therefore, equation (10) can be simplified as:

[0036]

[0037] According to the law of conservation of charge, the current flowing out of the detection electrode is the change in the induced charge of the detection electrode, that is:

[0038]

[0039]

[0040] 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.

[0041] Further: the detection electrode obtains the current value of the charged target and also includes obtaining the signal waveform:

[0042] Assuming that the detection electrode is parallel to the horizontal plane, the surface charge of the detection electrode is simplified to:

[0043]

[0044] Assume that the components of the velocity V of the charged target along the coordinate axis are V x , V y , V z ,So

[0045]

[0046] Assume that the target charge is constant as Q 0, constant flight speed V 0 , the velocity direction and flight trajectory are parallel to the x-axis, and it flies through the YOZ plane at t=0, that is, x p (0) = 0, formula (15) can be simplified to:

[0047]

[0048] The distance between the charged target and the detection electrode is D p (t), that is

[0049]

[0050] but:

[0051]

[0052] Substituting into formula (16), we get

[0053]

[0054] Therefore, when t = 0, the value of formula (19) is the largest, which is expressed as

[0055]

[0056] Then, formula (19) can be abbreviated as:

[0057]

[0058] From equation (21), we can get that the waveform shape of the induced charge is given by Determine, let it be the waveform time scale coefficient τ:

[0059]

[0060] Then formula (21) can be abbreviated as:

[0061]

[0062] Therefore, the waveform of the induced charge of the detection electrode is determined by τ, the flying speed V(t) of the charged target and the shortest distance D from the target to the electrode. p (t) and the influence of the two parameters are inversely proportional. Then, by substituting equation (23) into the induced current equation (13), we get

[0063]

[0064] Compared with the prior art, the present invention has the following technical advances:

[0065] Inspired by the electroreceptive organs (Ampullae of Lorenzini array) of sharks and other creatures, this paper proposes an electrostatic induction electrode array with differentiated characteristics of posture and spatial distribution, and uses the differences in the induction signals of the electrode array 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, which can flexibly adjust the frequency response characteristics, and a prototype system is realized based on a commercial amplifier; a flying charged body laboratory simulation system is built, and an experimental data set of flying charged body induction signals is obtained. The symbolic regression machine learning algorithm is used to mine the time characteristics of the electrostatic signal, and the mapping function between the signal characteristics and the incoming direction of the projectile is obtained, thereby realizing a low-power, low-cost, low-computing-power-demand and highly integrated method for sensing the flight trajectory of charged bodies, with an omnidirectional prediction error of less than 8 degrees. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0067] In the attached picture:

[0068] Figure 1 It is a schematic diagram of the electrostatic induction electrode array system of the present invention;

[0069] Figure 2 The invention detects the influence of the electrode posture on the normal electric field;

[0070] Figure 3 Schematic diagram of normalized surface charge density of the present invention;

[0071] Figure 4 The schematic diagram of the detection electrode induced charge waveform and its spectrum of the present invention;

[0072] Figure 5 The waveform of the induced current of the detection electrode and the schematic diagram of its spectrum of the present invention;

[0073] Figure 6 This is the principle and design diagram of the present invention imitating the shark's electroreceptor organ;

[0074] Figure 7 This is a schematic diagram of the test experiment of the present invention;

[0075] Figure 8 It is the design diagram of the two-dimensional posture control mechanism of the present invention;

[0076] Fig. 9 This is a schematic diagram of the original test data of the electrostatic induction signal of the present invention;

[0077] Fig.10It is a schematic diagram of normalized time characteristic value of electrostatic induction signal of the present invention;

[0078] Fig.11 Schematic diagram of the prediction results and errors of model 1 of the present invention on various data sets;

[0079] Fig.12 Schematic diagram of the prediction results and errors of Model 2 of the present invention on various data sets;

[0080] Fig.13 This is the prediction error distribution diagram of all models of the present invention. DETAILED DESCRIPTION

[0081] The following specific embodiments may be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments. The embodiments of the present invention will be described below in conjunction with the accompanying drawings.

[0082] The phenomenon of electrostatic charging of flying projectiles (i.e., flying charged bodies) has been reported since the 1980s. Due to the charging effects of primer explosion impact, flame and compound powder adhesion, friction between flying projectiles and gun barrels, and friction between flying projectiles and dust and water molecules in the air during flight, high-speed flying projectiles will carry a certain amount of static charge. The amount of charge is related to factors such as ammunition type, weapon status, and environmental conditions. It is distributed in the range of 3-5 orders of magnitude. Light weapons flying projectiles carry static charges in the order of pC to nC. Rockets and aircraft have larger charges due to their large surface areas. The static charge on the surface of a flying projectile will generate an electrostatic field in the space around it. The flight process will disturb the electrostatic field in the space around its trajectory, which can be detected by various electric field sensors. Some studies have used cylindrical and window-shaped sensing electrodes combined with charge amplifiers to test the electrostatic induction signals of flying projectiles. Some studies have used steel mesh to make cylindrical electrostatic sensors and tested the charge of 9mm Beretta pistol flying projectiles. A study compared the flying projectile detection performance of non-contact potentiometric sensors, vector electric field sensors, and charge induction sensors through range experiments, and proposed a quasi-electrostatic field sensor array based on varactor diodes in subsequent work. The three sensors were placed 3 meters apart, and the test signal was transmitted to the central data processing unit using a wired network. The direction of the flying projectile was indicated using positioning algorithms such as triangulation and wavelet analysis. A study used a self-powered multifunctional electret sensor assisted by deep learning to realize the identification of flying charged bodies. The above work has studied the test of the charge quantity of flying projectiles, the acquisition of electrostatic signals of flying projectiles, feature analysis, and potential applications, but it is not suitable for unmanned platforms with limited space, payload, and computing power. The main problems are:

[0083] (1) The cylindrical sensing electrode requires the flying projectile to penetrate in order to detect the signal, which cannot detect flying projectiles from any direction. Large-sized flat electrodes or wide-spaced electrode arrays are not suitable for unmanned platforms with limited space and load, and will affect the concealment and maneuverability of the unmanned platform.

[0084] (2) The electrostatic test experimental system generally improves the sensitivity and stability of the experimental system by increasing the sensing electrode, shielding interference signals, manually resetting, and controlling the experimental environment. The high sensitivity and high stability of the sensor circuit are not taken into account, and the sensor power consumption and adaptability to vibration and shock are not considered.

[0085] (3) The information mining algorithms of electrostatic induction signals require real-time processing of the entire time series. The algorithms for data collection, transmission, and processing are highly complex and require a high amount of data bandwidth and computing resources. They are also not suitable for unmanned platforms with limited edge computing power.

[0086] In view of the above problems, the present invention is inspired by the electroreceptive organs (Ampullae of Lorenzini array) of sharks and other creatures, and proposes an electrostatic induction electrode array with differentiated characteristics of posture and spatial distribution, and uses the differences in the induction signals of the electrode array 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, which can flexibly adjust the frequency response characteristics, and a prototype system is realized based on a commercial amplifier; a flying charged body laboratory simulation system is built, and an experimental data set of flying charged body induction signals is obtained. The symbolic regression machine learning algorithm is used to mine the time characteristics of the electrostatic signal, and the mapping function of the signal characteristics and the incoming direction of the flying projectile is obtained, thereby realizing a low-power, low-cost, low-computing-power-demand and highly integrated method for sensing the flight trajectory of charged bodies, with an omnidirectional prediction error of less than 8 degrees.

[0087] In the non-contact electrostatic test system consisting of a charged target, an electrostatic field, and a detection electrode, the electrostatic field is the medium that connects the target and the electrode. The induced charge of the detection electrode can be calculated using Gauss's theorem and the law of conservation of charge. In order to maintain generality, we establish Figure 1 Schematic diagram of electrostatic detection of charged targets.

[0088] like Figure 1 As shown, the Ground plane is an infinite horizontal ground, on which a Cartesian space coordinate system is established, and the unit vectors of the three coordinate axes are and The golden circular plate is a finite-sized, conductive and grounded detection electrode in space. Its radius is r. The center of its upper surface is defined as the origin O of the spatial coordinate system. Its normal vector is is the vector that passes through the origin O and points vertically to the outside of the circular plate. The two angles between the normal vector and the spatial coordinate axis can determine the spatial posture of the detection electrode. α is and The angle between The projection on the XOY plane is The blue ball is a flying charged target, and the amount of static charge it carries is Q(t), which changes during the flight. The dotted line is its trajectory, and the velocity vector is is the tangent vector of the motion trajectory, and the coordinates of the spatial position are (x p (t),y p (t),z p (t)), the unit vector of its position coordinate is and The angle between them is δ, and The angle is The angle between the projection on XOY and the X-axis is γ.

[0089] The image charge method is used to calculate the field strength component of the target electric field in the normal direction of the detection electrode:

[0090]

[0091] where ε 0 is the vacuum dielectric constant, ε r is the dielectric constant of the space medium. From formula (1), it can be seen that when δ=Nπ, (N=0,1,2...), E n The maximum value is when and When the detection electrode is located on the same straight line and the normal direction faces the charged target, E n The spatial posture of the detection electrode determines the spatial position of the charged target to which it is most sensitive, which shows that electrostatic induction has directional selectivity.

[0092] Furthermore, according to Figure 1 The geometric relationship shown and the symmetry of the detection electrode can be set as α, β∈(0,π / 2) and and Located in the same quadrant, then:

[0093]

[0094] Substituting equation (2) into equation (1), we can obtain the field intensity component in the normal direction of the detection electrode:

[0095]

[0096] set up but

[0097]

[0098] In order to intuitively show the influence of the detection electrode posture parameters (α, β) on the sensing signal, it is assumed that the charged target is located at position The above formula can be simplified to:

[0099]

[0100] When α, β∈(0, π / 2), the change law of the normalized value of the normal electric field is as follows: Figure 2 As shown, from Figure 2 It can be seen that when α and β are both pi / 4, the normal electric field strength is the largest, that is, and When they coincide, the normal field strength is the largest, and the maximum value differs from the minimum value by more than one times.

[0101] Furthermore, according to Gauss's theorem, the induced charge density σ on the surface of the detection electrode is s for:

[0102]

[0103] On this basis, the effect of the charged target spatial position on the induced charge density σ on the detection electrode surface is analyzed. s To simplify the calculation, assume that the charged target carries a charge Q 0 Keeping unchanged, the detection electrode posture is parallel to the horizontal plane, that is, α = 0, then equation (6) is simplified to:

[0104]

[0105] Obviously, when x p (t)=0,y p When (t) = 0, σ s The value is the largest, that is, when the charged body reaches directly above the sensing electrode, the amount of charge induced on the electrode is the highest.

[0106] Assume that the distance from the projection of the charged target on the XOY plane to the origin of the coordinate system is d p (t), that is

[0107]

[0108] So,

[0109]

[0110] Take d p (t)=0,z p σ when (t)=Δ sThe value is a normalized quantity, and Δ is a unit length. Then, the induced charge density σ on the detection electrode surface s , the law of the change of the relative distance d between the charged body and the detection electrode is as follows Figure 3 shown.

[0111] Depend on Figure 3 It can be seen that when z p When (t)≥6Δ, σ s At 0≤d p The value in the circular region where (t)≤Δ is approximately a constant. According to Gauss's theorem, the total amount of charge induced on the detection electrode Q s for:

[0112]

[0113] Therefore, when the flying height 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 as a constant. Therefore, equation (10) can be simplified as:

[0114]

[0115] According to the law of conservation of charge, the current flowing out of the detection electrode is the change in the induced charge of the detection electrode, that is:

[0116]

[0117] 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.

[0118] In order to further analyze the signal waveform intuitively, without loss of generality, it is assumed that the detection electrode posture is parallel to the horizontal plane, and the surface charge of the detection electrode is simplified to:

[0119]

[0120] Assume that the components of the velocity V of the charged target along the coordinate axis are V x , V y , V z ,So

[0121]

[0122] Furthermore, suppose the target charge is constant as Q 0 , constant flight speed V 0 , the velocity direction and flight trajectory are parallel to the x-axis, and it flies through the YOZ plane at t=0, that is, x p (0) = 0, formula (15) can be simplified to:

[0123]

[0124] The distance between the charged target and the detection electrode is D p (t), that is

[0125]

[0126] but:

[0127]

[0128] Substituting into formula (16), we get

[0129]

[0130] Therefore, when t = 0, the value of formula (19) is the largest, which is expressed as

[0131]

[0132] Then, formula (19) can be abbreviated as:

[0133]

[0134] From equation (21), we can see that the waveform of the induced charge is given by Determine, let it be the waveform time scale coefficient τ:

[0135]

[0136] Then formula (21) can be abbreviated as:

[0137]

[0138] Therefore, the waveform of the induced charge of the detection electrode is determined by τ, the flying speed V(t) of the charged target and the shortest distance D from the target to the electrode. p (t) and the influence of the two parameters is inversely proportional. When the waveform coefficient takes different values, the charge waveform and its spectrum are as follows: Figure 4 shown.

[0139] Then, we substitute equation (23) into the induced current equation (13),

[0140]

[0141] therefore, Figure 4 The current waveform and spectrum diagram corresponding to each curve are shown in Figure 5 As shown, from Figure 4 , 5It can be seen that the signal energy is mainly concentrated in the low frequency, requiring the low frequency bandwidth of the sensor to be reduced to about 0.1Hz in order to effectively amplify the electrostatic induction signal without distortion. When the low frequency characteristics of the sensor are insufficient, the sensor has the characteristics of a high-pass filter, and the distortion of the induction signal is the same as the characteristics of a differentiator.

[0142] Specifically, each electrostatic induction electrode is a cylindrical sandwich structure consisting of a sensing plate, an insulating substrate and a shielding electrode, such as Figure 6 (B). The bottom of the cylinder is a copper induction plate in the shape of a circular plate, which is used to sense the spatial electrostatic field and is connected to the signal input end of the electrostatic sensor. The insulating substrate made of polyesterimide is used to electrically separate the induction plate from the shielding electrode. The copper shielding electrode with a bottom cylinder is connected to the power ground of the electrostatic sensor to block the influence of the lateral electrostatic field on the induction plate and improve the spatial directivity of the electrostatic induction plate. The higher the height of the cylinder, the better the spatial directivity, but the weaker the intensity of the induction signal; the lower the height of the cylinder, the worse the spatial directivity, but the stronger the intensity of the induction signal. The present invention sets the induction plate to have a thickness of 1 mm and a diameter of 20 mm, the insulating substrate to have a thickness of 0.5 mm, the shielding electrode radius to 21 mm, and the cylinder to have a height of 20 mm.

[0143] The electrostatic induction electrode array is distributed on a hemispherical shell-shaped support structure, and the central axis of each electrode points to the center of the sphere. The electrode whose central axis is perpendicular to the bottom surface of the hemisphere is defined as the normal electrode, and its inclination angle is 0°. The angle between the central axis of the other electrodes and the central axis of the normal electrode is defined as its inclination angle, that is, the direction in which the spatial sensitivity of this electrode is the highest. The present invention arranges 6 electrodes equidistantly on the circumferences with inclination angles of 0, 21, 42, and 63, and arranges 5 electrodes equidistantly on the circumferences with inclination angles of 36 and 72.

[0144] Electrostatic induction signal amplification circuit, in the literature M.Man, M.Wei, Y.Zhang, G.Ma, and Y.Chen,"Biomimetic Measurement Method for Surface Electric Potential Imaging Inspiredby Visual Lateral Inhibition,"IEEE Transactions on Industrial Electronics, pp.1-11, 2023, doi:10.1109 / TIE.2023.3314910.

[0145] 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.

[0146] 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 2023,doi:10.1088 / 1361-6501 / acc3b6. It is introduced in detail. Its DC voltage gain in the range of 0.1Hz to 1kHz is 34dB, which can effectively amplify weak electrostatic induction signals. The 1 / f corner frequency of flicker noise is about 30Hz, and the sensor Gaussian white noise above this frequency is It should be noted here that in order to improve the spatial resolution of the spatial electrostatic field test, it is necessary to reduce the physical size of the sensing electrode, thereby reducing the sensing area. This also brings a negative impact, that is, the equivalent coupling capacitance between the charged body and the sensing electrode is greatly reduced, reaching the order of picofarads or even femtofarads. This requires the amplifier circuit to have both extremely small input capacitance and extremely high input resistance to match the equivalent coupling capacitance to improve the voltage divider ratio and sensitivity. The use of the most advanced positive feedback circuit design technology (bootstrap, neutralization) has alleviated this problem to a certain extent. However, the mutual constraints between the spatial resolution and signal sensitivity of this type of sensor have not been completely resolved.

[0147] Each electrode of the electrostatic induction electrode array is connected to an independent amplifier circuit to amplify its weak electrostatic induction signal and transmit it to the multi-channel oscilloscope connected at the back end for digital acquisition and recording, thereby realizing multi-channel synchronous recording of the electrostatic field in the surrounding space.

[0148] 3.3 Symbolic Regression Algorithm

[0149] When a flying projectile passes over an unmanned platform at a certain distance (≤10m), the disturbance of the static electric field in space caused by the static charge carried by the flying projectile will be detected and recorded by the electrostatic field sensor and saved as a set of differential time series signals. By analyzing this data, information such as the speed, trajectory, and direction of the flying projectile can be obtained. Since the energy, computing power, load, and cost of the unmanned platform are limited, the present invention selects a symbolic regression algorithm for data mining. This is because symbolic regression uses an evolutionary algorithm to search the mathematical expression space, with the goal of minimizing the error between the measured data and the predicted data, and automatically finds the mathematical expression behind the measured data. The trained symbolic model is easy to deploy without the need for a special hardware and software environment (such as a neural network, vector machine, etc.). This application uses a multi-gene symbolic regression method, combined with the population search capability of the multi-gene genetic algorithm (MGGP) and the parameter estimation capability of the linear least squares method, to find the optimal linear combination of the mathematical expressions corresponding to all gene individuals in the population, so that the error between the predicted output response of the mathematical model and the target output response is minimized. 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 / 242023, doi: 10.1088 / 1361-6501 / acc3b6.

[0150] A detailed explanation is given in M.Man, Y.Zhang, G.Ma, Z.Zhang, and M.Wei,"Indoor Localization Method ofPersonnel Movement Based on Non-Contact Electrostatic PotentialMeasurements,"Sensors,vol.22,no.13,p.4698,2022.

[0151] The difference of the symbolic regression algorithm used in this experiment lies in the special fitness function. The fitness function selects the circle absolute error between the predicted value (Ye) and the target value (Ya), and the calculation method is as follows:

[0152] CAE=min(|Y e -Ya |,360-|Y e -Y a |)

[0153] This is because the direction of the flying projectile is a point on the circumference, and the predicted direction and the actual direction are both points on the circumference, and the values ​​of the points on the circumference are based on a period of 360. For example, if the actual shooting direction is 10°, when the predicted direction is 30°, the prediction error is 20°. When the predicted direction is 350°, the prediction error is also 20° instead of 340°, because the interval between 10° and 350° on the circumference is 20°. Therefore, CAE is used as the fitness function in this experiment.

[0154] A test scenario for the electrostatic induction signal of a flying charged body was built in the laboratory, such as Figure 7 As shown in (a). In a laboratory circular field with a radius of 4m, the electromagnetic catapult module and the two-dimensional attitude control mechanism form a flying charged body launch system to launch a metal cylinder carrying static charge. The robot dog is equipped with an electrostatic field sensor to synchronously collect the spatial electrostatic field disturbance signal caused by the flying charged body.

[0155] 1. Flying charged body experimental device

[0156] The electromagnetic ejection module and the two-dimensional attitude control mechanism form a flying charged body launch system. The electromagnetic ejection module is a 5-level copper coil acceleration (wire diameter 0.8mm, 195 turns, outer diameter 20mm, inner diameter 8mm, thickness 26mm, inductance 2.4mh). The driving capacitors of each level of coil are 2000uF, 1440uF, 1440uF, 1000uF, 1000uF, respectively. The capacitor charging voltage range is (50V-400V), which is quantitatively controlled by the contact switch. The guide rail is a PVC round tube (radius 3.2mm, length 500mm), and the launching flying projectile is a stainless steel metal cylinder (radius 3mm, height 30mm). The maximum initial velocity of the flying projectile is about 48m / s. When the capacitor is triggered, the static charge stored in the capacitor flows quickly through the coil, and the transient magnetic field generated excites the flying projectile to move in the guide rail. The friction between the flying projectile and the guide rail generates static charge, and it becomes a charged flying body after flying out. Repeated experiments have confirmed that this electrification process is relatively stable, and about 95% of launch experiments will cause the flying projectile to be charged.

[0157] The trajectory of the flying projectile is determined by the guide rail pointing and the initial velocity of the flying projectile. In order to accurately and quantitatively control the trajectory of the flying projectile and improve the repeatability of the experiment, a two-dimensional attitude control mechanism is 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 an azimuth axis and a pitch axis, both of which are supported by two pairs of precision mechanical angular bearings to ensure the axial and radial stiffness and rotation accuracy of the axis system. The azimuth axis rotation angle range is (-40° to +40°), and the pitch axis rotation angle range is (0° to +15°). The precise control is achieved by sending a control signal to the rotating drive device through an electronic handwheel, and the adjustment resolution is 1°.

[0158] 2. Two experimental modes

[0159] Using the four sensing electrodes with an inclination angle of 42° in the spatial electrostatic field sensor ( Figure 7 In a, the four colors of red, blue, green and orange are marked, respectively denoted as Sensor A, B, C and D), to detect the electrostatic field signal of the flying charged body and mine its flight angle information. In order to verify the effectiveness and versatility of the present invention, the present invention designs two types of experiments, namely the center point shooting mode experiment and the area scanning mode experiment, such as Figure 7 (b) and (c). For the center point shooting mode experiment, the electrostatic test system is located in the center of the experimental site, and the flying projectile launching system is aimed at 1m above the center of the compound eye electrode to launch, so that the flying projectile passes through the airspace directly above it, and the electrostatic test system records four electrostatic induction signals. Then, the position of the launching system is changed at intervals of 9 degrees, and the experimental site is traversed once. The experimental results are recorded 3 times at each position, and a total of 120 sets of data are collected. The difference for the regional sweeping mode experiment is that when launching at each position, it is aimed at the left, center, and right sides of the test system respectively, and launched 3 times in each direction, so a total of 360 sets of data are recorded.

[0160] 3. Data processing

[0161] During the experiment, a multi-channel digital oscilloscope (PicoScope 4824) was used to synchronously record four-way electrostatic induction signals at a sampling rate of 20KHz. Fig. 9 shown.

[0162] Fig. 9 (a) In order to facilitate manual observation, an offset is added to each channel signal in the oscilloscope. As can be seen from the figure, the four-way signal shows good consistency. The peak part of each signal is amplified and the offset is removed. Fig. 9 As shown in (b), the signal characteristics meet the Figure 5The electrostatic induction signals of the flying charged body were obtained by theoretical analysis, and the peak values ​​and peak moments of the four signals are significantly different, indicating that the system can accurately test the electrostatic induction signals when the flying charged body passes by, and realize the directional selectivity of electrostatic induction by utilizing the differences in the spatial position and posture of the sensing electrodes themselves, thus realizing electrostatic testing with spatial filtering characteristics.

[0163] There are DC bias, 50Hz power frequency noise and high-frequency noise in the test results. This is due to the good low-frequency characteristics of the sensor, the test bandwidth of 100kHz, and the influence of the electrostatic discharge phenomenon in the experiment. Therefore, it is necessary to filter and de-bias the collected raw data. The filtering operation uses MATLAB's low-pass digital filter function lowpass() to reduce the noise of the recorded data. The cutoff frequency parameter is set to 10Hz, the steepness parameter is set to 0.9999, and the stopband attenuation parameter is set to 180dB. The de-biasing operation uses MATLAB's detrend() function to set the de-biasing method to constant, that is, the original data minus the DC offset. In addition, there are two relatively large noise points in the signal. The first noise point is before the electrostatic induction signal. It is an electromagnetic radiation signal generated by the moment when the flying projectile separates from the sliding track. The second noise is after the electrostatic induction signal. It is an electrostatic discharge signal generated by the flying charged body hitting the protective foam. These two parts of noise are not the electrostatic field induction signals to be analyzed in this experiment, so they are directly eliminated. Finally, the peak moment of the SensorA signal is used as the reference point, and only the data of 0.1s before and after the reference point is retained for each channel. The data cleaning results are as follows: Fig. 9 (c) as shown.

[0164] 4. Feature extraction

[0165] Due to the difference in the friction state between the surface of the flying projectile and the surface of the guide rail, the voltage attenuation of the electromagnetic ejection energy storage capacitor, the size of the flying projectile and other factors, the actual amount of charge carried by the flying projectile each time it is launched is highly uncertain. Therefore, the amplitude of the electrostatic induction signal tested under the same test conditions is highly random and cannot be used for information mining. The relative time for the charged body to fly over different sensing electrodes is a fixed value, which is only affected by the flight speed and the relative position of the electrode array. Therefore, in the experiment, the time difference of the peak moments of each signal is used to mine the information of the flight trajectory.

[0166] First, the peak values ​​of the four electrostatic induction signals are determined (using the peak() function of Matlab), as follows: Fig.10As shown in (a), they are marked as PeakA, PeakB, PeakC, and PeakD, and their horizontal axes are the peak moments, recorded as T1, T2, T3, and T4 respectively. Then, the minimum value of the four peak moments is set as the starting time, the maximum value is set as the ending time, and the interval from the starting time to the ending time is defined as the normalized duration of this test. Then, the time difference between the four peak moments and the starting time divided by the normalized duration is their normalized time characteristic value, recorded as the normalized peak moment, and the calculation method is shown in the formula.

[0167]

[0168] The radar chart of the normalized time characteristic values ​​of four signals obtained in one experiment is as follows: Fig.10 (b) In the first test mode, the normalized time characteristic values ​​of the test data obtained at 40 shooting angles and their radar diagrams are shown in Fig.10 As shown in (c, d), it can be seen from the figure that the signal characteristics have an obvious correlation with the shooting angle.

[0169] The advantage of this normalization process is that the four time eigenvalues ​​are only affected by the shooting angle of the flying projectile, but not by the flying speed and relative distance. The induction signal waveform corresponds to the dynamic process of the flying projectile flying over the electrode sensing area. The waveform of the electrostatic induction signal is mainly determined by the time scale coefficient τ, that is, the flying speed V(t) and the shortest distance D from the target to the electrode. p (t) jointly affect, because after the electrode structure and posture are fixed, the relative distance determines the sensing area. When the relative distance remains unchanged and only the flight speed changes, the duration and peak moment of the four-way sensing signal also change accordingly, but the relative interval of the peak moment changes in the same proportion, which is inversely proportional to the flight speed. This proportional coefficient is just reduced when calculating the normalized time eigenvalue. Therefore, the change in flight speed will not affect the normalized time eigenvalue. Similarly, when the flight speed remains unchanged and only the relative distance changes, the sensing areas of the four electrodes change in the same proportion, and the peak moments of the four-way sensing signals also change in the same proportion, which is directly proportional to the relative distance. This proportional coefficient can also be reduced when calculating the normalized time eigenvalue. Therefore, the change in relative distance will not affect the normalized time eigenvalue.

[0170] 5. Inversion results

[0171] The symbolic regression algorithm is used to mine the mapping function between the normalized time eigenvalue of the electrostatic induction signal and the shooting angle. The shooting angle of each experiment is used as the dependent variable of the mapping function, and the normalized time eigenvalue of the four-way induction signal is used as the independent variable. The symbolic regression algorithm is used to optimize this mapping function, hoping to obtain a mathematical regression model from the sensor induction signal to the direction of the charged body.

[0172] The present invention conducted three rounds of omnidirectional 360-degree traversal experiments in two experimental modes, namely, the central point shooting mode and the regional scanning mode, and obtained six data sets, named M1R1 (Mode1Run1), M1R2, M1R3, M2R1, M2R2 and M2R3. Then, each data set was used as a training sample for model training, and the remaining data were used as verification sample sets. The symbolic regression algorithm was run once to obtain a set of optimal models. Finally, the above process was repeated ten times, each time with the initial value of the random evolution algorithm and other parameters unchanged, to obtain the optimal model for each data set.

[0173] The optimal model trained using the M1R1 dataset is:

[0174] Y e =0.453+0.453T 2 cos(T 4 )-0.211T 2 +0.506T 1 cos(4.07cos(3.07+2.51T 2 cos(T 2 cos(0.808+2.51T 2 ))))

[0175] Among them, Ye represents the model estimated value of the incoming direction of the flying projectile, and T1-T4 represent the normalized time characteristic values ​​of the four-way sensing signals. The prediction results of this model on the training dataset M1R1 and the validation datasets M1R2 and M2R1 are shown as follows: Fig.11 As shown in (a, b, c).

[0176] Fig.11 In (a), the horizontal axis is the 40 shooting angles in the training data set (9 degrees intervals for one cycle), the vertical axis is the angle value (0-360 degrees), the red line is the target value of the shooting angle, the blue line is the predicted value of the shooting angle, and the yellow bar corresponds to the prediction error of the shooting angle. As can be seen from the figure, this model has a very high prediction accuracy, with an average absolute error of 3.39 degrees, as shown by the green line. The model only has large errors in individual shooting angles (such as 45, 54 and 99 degrees), reaching more than 10 degrees. It is believed that this is due to the instability of electrostatic charging in the experiment. It can be seen that the symbolic regression algorithm has a good enough modeling and prediction ability to meet the needs of predicting the direction of attack.

[0177] Furthermore, the generalization ability of this model is verified on other datasets. Fig.11(b) is the prediction result of this model on the validation data set M1R2. The prediction accuracy of this model remains at a high level, with an average absolute error of 5.55 degrees. In addition, the average absolute error of this model on M1R3 is 4.83 degrees. The result graph is similar to this graph and will not be repeated here. The data sets M1R1, M1R2, and M1R3 are all from the first test mode. Therefore, this model has a good generalization ability for the burst test mode, and the prediction absolute error is about 5 degrees.

[0178] Fig.11 (c) is the prediction result of this model on the validation strafing test mode data set M2R1. The prediction accuracy of this model has dropped significantly, and the mean absolute error has increased to 13.01 degrees. In the strafing test mode, each shooting angle is shot three times, namely, left-side shooting, center shooting, and right-side shooting. Therefore, in the strafing mode, 120 sets of data will be collected after a 9-degree interval for one week, including 40 sets of data for left-side shooting, center shooting, and right-side shooting. In the figure, the dark red line is the prediction result of the model for 40 sets of left-side shooting data, the blue line is the prediction result of the model for the center shooting data, and the orange line is the prediction result of the model for the right-side shooting data. In the figure, 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 ones. This shows that the prediction accuracy of this model for the center shooting data is higher, resulting in the overfitting phenomenon commonly seen in machine learning training. This is not conducive to the generalization and application of the model. When the projection of the flight trajectory of the flying projectile does not pass through the center of the sensor, the model prediction error will increase significantly, greatly reducing the versatility of this method.

[0179] The prediction error of this model on all datasets is Fig.11 As shown in (d), the average absolute error of the model's prediction on the M1R1, M1R2, and M1R3 datasets is about 5 degrees, and there are few outliers, with the extreme value not exceeding 40 degrees. The average absolute error of the model's prediction on the M2R1, M2R2, and M2R3 datasets increases to about 15 degrees, and the outliers increase significantly, with the maximum error reaching 160 degrees. This shows that this model has good prediction ability for the burst mode test, with an error of about 5 degrees. However, the prediction ability for the sweep mode test data is poor, with an error of about 15 degrees. The generalization ability of this model is weak, and the fluctuation of the trajectory away from the center of the sensor will greatly affect the prediction accuracy.

[0180] The optimal model trained using the M2R3 dataset is:

[0181] Y e =0.571+T 1 T 2 +0.353T 1 T 4+0.0972sin(T 2 2 )-0.214T 4 -2.13T 1 mod(0.571T 2 -8.03,0.489)

[0182] The prediction results of this model on the training data set M2R3 and the validation data sets M2R1 and M1R1 are as follows: Fig.12 As shown in (a, b, c).

[0183] Fig.12 In (a, b), the average absolute error of this model for the training dataset M2R3 is 7.22 degrees, and the average absolute error for the validation dataset M2R1 is 7.29 degrees. Fig.12 In (a), when the shooting angle is 0, the predicted angle is 357.8 degrees, and when the shooting angle is 351 degrees, the predicted angle is 0.02 degrees. Fig.12 In (b), when the shooting angle is 9, the predicted angle is 354.9 degrees. Since the angle value is 360 degrees, the actual absolute error of the model at these three shooting angles is not significant. Therefore, the absolute error distribution of the model on all data is consistent. In addition, the average absolute error of this model on M2R2 is 7.66 degrees, and the result graph is similar to Fig.12 (b) is similar and will not be repeated here. Therefore, this model has a high prediction accuracy for all data in the sweeping mode, with an absolute error of about 7 degrees.

[0184] Fig.12 (c) is the prediction result of this model on the burst mode data set M1R1. The prediction accuracy of this model has not decreased but increased, and the mean absolute error has dropped to 5.79 degrees. There are two reasons for this. First, the amount of data in M1R1 is small and more regular, because the trajectory of central shooting is easier to control, and the shooting is aimed directly above the center of the sensor; while the trajectory deviations of left and right shooting are more random, and the offset of shooting and aiming requires manual intuitive control, resulting in relatively large data noise. Second, because the burst mode data is included in the sweeping mode data, during the training process, Model 2 has learned the rules contained in the burst mode data. To verify this conclusion, the prediction errors of this model on all data sets are summarized as follows. Fig.12In (d), the average absolute error of the prediction of the model on the M1R1, M1R2, and M1R3 datasets is about 6 degrees, and there are few outliers, with the extreme value not exceeding 40 degrees. The average absolute error of the prediction of the model on the M2R1, M2R2, and M2R3 datasets is about 7 degrees, and there are also few outliers, with the extreme value not exceeding 30 degrees. This proves that this model has good prediction ability for both the point-fire mode and the scanning model test, with the average error less than 8 degrees. Therefore, this model has high prediction accuracy and strong generalization ability. When a charged flying object passes over the area above the sensor, the incoming angle can be accurately predicted.

[0185] In addition, the optimal models trained using the datasets M1R2, M1R3, M2R1, and M2R2 are:

[0186]

[0187] Y e =0.444+0.265T 2 +1.32T 1 T 2 +0.34T 1 T 4 -0.627T 1 -1.49T 1 mod(T 2 ,0.696)-0.146T 2 T 4 cos(T 2 T 3 )

[0188] Y e =0.85+0.847T 1 T 2 +0.358T 1 T 4 -0.182T 4 -0.311 cos(sin(T 2 ))-2.74T 1 mod(4.29+0.37T 2 ,0.37)

[0189] Y e =0.556+0.305T 1 +0.085T 2 -0.151T 4 +0.33T 1 T 4 +0.122mod(25.2-T 2 -mod(T 1 ,0.305),-8.23)

[0190] The mean absolute errors of these models on all datasets are as follows: Fig.13 shown.

[0191] The first three rows show the performance of the best models trained using the burst mode dataset (M1R*) on all datasets. They perform well on the first three columns (i.e., the M1R* dataset), with an error range of [3.26.4], while their performance on the last three columns (i.e., the M2R* dataset) drops significantly, with an error range of [9.215.9]. Therefore, the models trained using burst mode data have overfitting and poor generalization ability, and are not suitable for sweep mode data. The last three rows show the performance of the best models trained using the sweep mode dataset (M1R*) on all datasets. The error of each model on all datasets remains at around 7 degrees, with a fluctuation range of no more than 2 degrees. Therefore, the models trained using sweep mode data have strong generalization ability and good versatility, with an omnidirectional prediction error of less than 8 degrees.

[0192] Based on the principle of electrostatic induction, an induction electrode array with posture and spatial distribution structural characteristics is designed by imitating the compound eye electrode array; a high-sensitivity electrostatic induction signal conditioning and amplification circuit is used to realize long-distance, non-contact measurement of the electrostatic induction signal of a flying charged body; a prototype test system is built based on an electromagnetic ejection device to obtain an omnidirectional electrostatic induction signal data set of an incoming charged body, train a symbolic regression algorithm, and obtain a prediction model of the incoming direction of the charged body. The omnidirectional prediction error of the optimal model is less than 8 degrees. The present invention belongs to a passive receiving test and does not actively emit any form of energy (such as infrared, electromagnetic waves, ultrasonic waves, etc.), so the power consumption is very low. The system is simple and only uses a four-way electrostatic induction signal amplifier and a low-cost embedded single-chip microcomputer (Raspberry Pi, STM32 series MCU), so it is low in cost, highly flexible and easy to integrate. The prediction model is a simple mathematical expression with low computational complexity. It can be run by any embedded processor and the model has strong versatility. Therefore, the present invention has the characteristics of low power consumption, low cost, low computing power demand and high integration, and has high application value.

[0193] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of protection of the claims of the present invention.

Claims

1. A method for sensing the flight trajectory of a charged object based on the principle of electrostatic induction, characterized in that: include: A charged target, an electrostatic field and a hemispherical electrostatic induction electrode array, wherein the detection electrode of the hemispherical electrostatic induction electrode array comprises a cylindrical structure composed of an induction plate, an insulating substrate and a shielding electrode, wherein the induction plate at the bottom of the inner portion is in the shape of a circular plate, which is used to sense the spatial electrostatic field and is connected to the signal input end of the electrostatic sensor, the insulating substrate is used to electrically separate the induction plate from the shielding electrode, the shielding electrode with a bottom cylindrical shape is connected to the power ground of the electrostatic sensor, which is used to block the influence of the lateral electrostatic field on the induction plate and improve the spatial directivity of the induction plate, the detection electrode obtains the current value of the charged target, and the current value is amplified and recorded by a subsequent high-impedance electrostatic sensor, which is used to characterize the electrostatic signal generated when the charged target passes through the detection electrode; the subsequent high-impedance electrostatic sensor comprises an amplification circuit, and each detection electrode of the hemispherical electrostatic induction electrode array is respectively connected to an independent amplification circuit, and is transmitted to a multi-channel oscilloscope connected to the back end for digital acquisition and recording; The polygenic symbolic regression method is used, combining the population search capability of the polygenic genetic algorithm and the parameter estimation capability of the linear least squares method, to find the optimal linear combination of the mathematical expressions corresponding to all gene individuals in the population, so that the error between the predicted output response and the target output response is minimized. The fitness function selects the circular absolute error between the predicted value (Ye) and the target value (Ya), and the calculation method is shown in the following formula: CAE=min(|Y e -AND a |,360-|Y e -AND a |) The hemispherical electrostatic induction electrode array is distributed on a hemispherical shell-shaped support structure, and 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 a normal electrode, and its inclination angle is recorded 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 inclination angle, and 4 detection electrodes are equidistantly arranged on the circumference of the inclination angle 42 to detect the electrostatic field signal of the flying charged body, including: a central point shooting mode experiment and a regional scanning mode experiment. For the central point shooting mode experiment, the electrostatic test system is located in the center of the experimental site, and the flying charged body launch system is aimed at the center of the compound eye electrode to launch, so that the flying charged body passes through the airspace directly above it, and records four electrostatic induction signals; then the position of the launch system is changed at intervals of 9 degrees, and the experimental site is traversed once, and the experimental results are recorded 3 times at each position, and a total of 120 sets of data are collected; for the regional scanning mode experiment, when launching at each position, it is aimed at the left, center, and right sides of the test system respectively, and each direction is launched 3 times, and a total of 360 sets of data are recorded; A multi-channel digital oscilloscope is used to synchronously record four electrostatic induction signals. The collected electrostatic induction signals are filtered and de-skewed for data cleaning. The time difference between the peak moments of each signal is used to mine the flight trajectory information and obtain a time eigenvalue data set.

2. The method for sensing the flight trajectory of a charged object based on the electrostatic induction principle according to claim 1 is characterized in that: The data cleaning operation of filtering and de-biasing the collected electrostatic induction signal includes: the filtering operation uses MATLAB's low-pass digital filter function lowpass() to perform noise reduction on the recorded data, with the cutoff frequency parameter set to 10 Hz, the steepness parameter set to 0.9999, and the stopband attenuation parameter set to 180 dB; the de-biasing operation uses MATLAB's detrend() function, setting the de-biasing method to constant, that is, the original data minus the DC offset.

3. The method for sensing the flight trajectory of a charged object based on the electrostatic induction principle according to claim 1 is characterized in that: The method of mining the information of the flight trajectory by using the time difference of the peak moments of each signal to obtain the time characteristic value data set includes: determining the peak values ​​of the four electrostatic induction signals, setting the minimum value of the four peak moments as the starting moment, and the maximum value as the ending moment, and defining the interval from the starting moment to the ending moment as the normalized duration of the test, and dividing the time difference between the four peak moments and the starting moment by the normalized duration to obtain the normalized time characteristic value, which is recorded as the normalized peak moment, and the calculation method is shown in the formula; 4. The method for sensing the flight trajectory of a charged object based on the electrostatic induction principle according to claim 1 is characterized in that: The detection electrode obtains the current value of the charged target including: A Cartesian space coordinate system XOY is established on the horizontal ground, and the unit vectors of the three coordinate axes are and Assume that the radius of the detection electrode is r, and define the center of its upper surface as the origin of the spatial coordinate system O, and its normal vector is the vector passing through the origin O and pointing vertically to the outside of the circular plate, where α is and The angle between The projection on the XOY plane is The amount of static charge carried by the charged target is Q(t), which will change during the flight. The dotted line is its trajectory, and the velocity vector is is the tangent vector of the motion trajectory, and the coordinates of the spatial position are (x p (t),y p (t),z p (t)), the unit vector of its position coordinate is and The angle between them is δ, and The angle is The angle between the projection on XOY and the X-axis is γ; The image charge method is used to calculate the field strength component of the target electric field in the normal direction of the detection electrode: Where ε0 is the dielectric constant of vacuum, ε r is the dielectric constant of the space medium; from formula (1), it can be concluded that when δ=Nπ, (N=0,1,2...), E n The maximum value is when and When the detection electrode is located on the same straight line and the normal direction faces the charged target, E n The maximum value; Let α, β∈(0,π / 2) and and Located in the same quadrant, then: Substituting equation (2) into equation (1), we can obtain the field intensity component in the normal direction of the detection electrode: set up but Assume that the charged target is located at position Then formula (4) can be simplified as: When α, β∈(0, π / 2) are both pi / 4, the normal electric field strength is the largest. Then, according to Gauss's theorem, the induced charge density σ on the surface of the detection electrode is s for: Assuming that the charge Q0 carried by the charged target remains unchanged and the detection electrode posture is parallel to the horizontal plane, that is, α = 0, then equation (6) is simplified to: When x p (t)=0,y p When (t) = 0, σ s The maximum value; Assume that the distance from the projection of the charged target on the XOY plane to the origin of the coordinate system is d p (t), that is Take d p (t)=0,z p σ when (t)=Δ s The value is a normalized quantity, Δ is a unit length; when z p When (t)≥6Δ, σ s At 0≤d p The value in the circular region where (t)≤Δ is approximately a constant; according to Gauss's theorem, the total amount of charge induced on the detection electrode Q s for: Q s =∮ S σ s dS=∫∫ε0ε r E n dxdy (10) Therefore, when the flying height 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 as a constant; therefore, equation (10) can be simplified as: According to the law of conservation of charge, the current flowing out of the detection electrode is the change in the induced charge of the detection electrode, that is: 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.

5. The method for sensing the flight trajectory of a charged object based on the electrostatic induction principle according to claim 4 is characterized in that: The detection electrode obtains the current value of the charged target and also obtains the signal waveform: Assuming that the detection electrode is parallel to the horizontal plane, the surface charge of the detection electrode is simplified to: Assume that the components of the velocity V of the charged target along the coordinate axis are V x , V y , V z ,So Assume that the charge of the charged target is constant at Q0, the flight speed is constant at V0, the speed direction and the flight trajectory are parallel to the x-axis, and it flies through the YOZ plane at t=0, that is, x p (0) = 0, formula (15) can be simplified to: The distance between the charged target and the detection electrode is D p (t), that is but: Substituting into formula (16), we get Therefore, when t = 0, the value of formula (19) is the largest, which is expressed as Then, formula (19) can be abbreviated as: From equation (21), we can get that the waveform shape of the induced charge is given by Determine, let it be the waveform time scale coefficient τ: Then formula (21) can be abbreviated as: Therefore, the waveform of the induced charge of the detection electrode is determined by τ, the flying speed V(t) of the charged target and the shortest distance D from the target to the electrode. p (t) and the influence of the two parameters are inversely proportional. Then, by substituting equation (23) into the induced current equation (13), we get

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