A METHOD FOR ENHANCED DETECTION OF AFTERLINE ELECTROMAGNETIC FIELDS BASED ON A CIRCULATING WATER POOL

Abstract

The present invention relates to the field of electromagnetic detection and provides a method for the enhanced detection of wake electromagnetic fields based on a circulating water basin. The present method comprises: the construction of a test setup for wake electromagnetic fields based on a circulating water basin, wherein the model to be tested is fixed in the flow channel of the circulating water basin; the arrangement of Helmholtz coils outside the circulating water basin to generate an enhanced background magnetic field; the periodic variation of the rotational speed of the drive unit and thus the periodic variation of the flow velocity in the circulating water basin; the measurement of the electric field and the magnetic field in the target area; and the processing and analysis of the obtained signals.

Description

23517 Wuhan 2nd Ship Design and Research Institute -1- A Method for Enhanced Detection of Follow-Up Electromagnetic Fields Based on a Circulating Water Basin Technical Field The present invention relates to the field of electromagnetic detection and in particular to a method for enhanced detection of follow-up electromagnetic fields based on a circulating water basin. State of the Art Seawater has high conductivity. When a submarine travels underwater, the conductive seawater is moved in the Earth's magnetic field. This movement intersects the magnetic field lines of the Earth's magnetic field. According to Faraday's law of electromagnetic induction, an electromotive force is induced in the seawater.which generates an electric current. These currents generate an induced electromagnetic field and form the wake electromagnetic field in seawater. This electromagnetic field has a long range and duration. The development of an experimental facility for wake electromagnetic fields and the research of corresponding detection methods are of significant importance and offer potential applications for investigating the mechanisms of wake electromagnetic fields from submarines and developing new detection technologies. Compared to the electromagnetic field of the submarine itself, the wake electromagnetic field generated during operation is relatively weak. Research in this area has only just begun, and there are few published reports on experimental facilities and detection methods. The difficulty in setting up the experimental facility lies in...How to measure the weak wake- 2025 / 5586 BE2025 / 5586 23517 Wuhan 2nd Ship Design and Research Institute -2- Electromagnetic field. Although electromagnetic sensor technology has made great strides, there are still some challenges in applying these advanced sensors directly to wake-measurement electromagnetic field test rigs. There are three main reasons: First, the flow velocity of the surrounding seawater is relatively low when the submarine is submerged, which weakens the wake-measurement electromagnetic field; second, because the Earth's magnetic field is a stationary magnetic field and the flow velocity of the seawater varies slowly, the wake-measurement electromagnetic field is mainly concentrated in the very low frequency range, but electromagnetic sensors have high noise at low frequencies; finally, the Low-frequency ambient noise around the experimental setup can influence the measurement of the trailing electromagnetic field. In the context of the Earth's magnetic field, the trailing electromagnetic field isThe electromagnetic field generated by the submarine while underway is not only extremely weak and has a very low frequency, but is also susceptible to interference from low-frequency electromagnetic noise from the environment. Therefore, there are many challenges in the direct application of advanced electromagnetic sensors to test setups for trailing electromagnetic fields. Description of the Invention: To find an effective method for detecting and testing the trailing electromagnetic field of submarines, the present invention proposes a method for enhanced detection of trailing electromagnetic fields based on a circulating water basin, which improves the testability of the device in the following three areas: First, the main part of the test setup is constructed based on a circulating water basin; the test model is fixed in the basin, and a drive system moves the water in a circulating manner at a fixed speed.so that the trailing electromagnetic field can be monitored in real time and long-term measurements are possible during operation; Secondly, a signal amplification technique was developed for the test setup for measuring the trailing electromagnetic field, which increases the sensitivity of the signal detection and thus improves the reliability of the test results; Thirdly, a signal processing algorithm was developed to extract weak trailing electromagnetic field signals. This algorithm can effectively filter out useful signal features from ambient noise and improve the detection capability of the trailing electromagnetic field signal. In summary,that the presented method for enhanced detection of wake electromagnetic fields based on a circulating water basin significantly improves the detection and testing capabilities of the wake electromagnetic field. It offers new technical means for research into the mechanism of the wake electromagnetic field of submarines and the detection methods and has far-reaching application possibilities in the field of the electromagnetic characteristics of marine targets and their detection. Specifically, the invention offers a method for enhanced detection of wake electromagnetic fields based on a circulating water basin, comprising the following steps: Step (1): Construction of a test setup for wake electromagnetic fields based on a circulating water basin,wherein the test setup comprises at least an annular circulating water basin and a drive device for driving water flow in the basin; Step (2): Place the model to be tested into the circulating water basin and fix the model in the flow channel of the circulating water basin; Step (3): Arrange Helmholtz coils on both sides of the model to be tested outside the circulating water basin, wherein the Helmholtz coils generate an enhanced background magnetic field; 2025 / 5586 BE2025 / 5586 23517 Wuhan 2nd Ship Design and Research Institute -4- Step (4): Periodically change the rotational speed of the drive device and thereby periodically change the flow velocity in the circulating water basin; Step (5): Measure the electric field and the magnetic field in the target area with an electric field sensor and a magnetic field sensor; Step (6): Extraction of relevant characteristic signals from the measurement data using empirical mode decomposition, filtering of the obtained characteristic signals,Performing a fast Fourier transform to convert the signals to a frequency spectrum and extracting the trailing magnetic field and trailing electric field from the time-frequency spectrum, which corresponds to the frequency change of the flow velocity. In a preferred embodiment, the period of change of the rotational speed of the drive unit lies in the range of 0.1 Hz to 2 Hz. In another preferred embodiment, electric field sensors and magnetic field sensors are arranged near the central axis of the Helmholtz coils, so that the measuring ranges of the sensors are covered by a more homogeneous area in which the magnetic field lines run with a homogeneity of more than 95%. In a further preferred embodiment, step (5) includes the use of silver / chloride-silver typical electric field sensors and magnetic fluxgate sensors for measuring the trailing electric field and trailing magnetic field,where the analog signals of the sensors are converted into digital signals by a high-resolution data recorder. In another preferred implementation, in step (1) the empirical mode decomposition is carried out using the following formula: xt = ∑ + 2025 / 5586 BE2025 / 5586 23517 Wuhan2ndShipDesignAndResearchInstitute -5- where the i-teIMFund is denoted as the final remainder term. In a further preferred embodiment, the method also includes: selecting the motor's drive power to ensure that the upper and lower ranges of the flow velocity do not fall below the specified value; using a velocity sensor to measure the flow velocity in the basin; adjusting the motor's drive power; determining the maximum steady-state value of the flow velocity, as well as the maximum drive speed when the flow velocity reaches the steady-state maximum value; removing the velocity sensor; and installing an electric field sensor and a magnetic field sensor.and the periodic adjustment of the drive speed within the range of the maximum speed. In a further preferred embodiment, step (6) comprises the application of empirical mode decomposition to decompose the received electromagnetic signals and retain only the low-frequency signals. In a further preferred embodiment, the method also comprises the use of glass fiber reinforced plastic for the manufacture of the circulating water basin. In another preferred implementation, the filter process comprises: For a discrete time series xL of the electromagnetic field, the window length of the filter is set to n = 2m + 1, where the indices of the electromagnetic data points are selected as (xm, x-m+1, ... x0, x1, ... xm-1, xm), and a -1 degree polynomial is used to fit the electromagnetic data points within the window: Then the electromagnetic data points in the window can form a one-dimensional linear system of equations,21 0121 ...kk yaaxaxax  2025 / 5586 BE2025 / 5586 23517 Wuhan2ndShipDesignAndResearchInstitute -6- where the random error of the matrix fitting is, and is represented as a matrix: n≥k;The parameter matrix A is calculated using the least squares method and then the electromagnetic data points Y are fitted. The value of A is the smallest solution of the parameter matrix A, and the filtered value of Y is: . Explanation of the Principle: The inventors of the present application have discovered two methods for amplifying the wake signal amplitude in the investigation of the wake of submarines: (1) The inventors discovered that the wake electromagnetic field has a low frequency and is therefore susceptible to 1 / f noise from sensors. Therefore, a signal amplification technique was proposed in which the fluid is moved at a fixed cycle speed to achieve a shift in the frequency spectrum of the wake electromagnetic field and to reduce the measurement difficulty by increasing the frequency. (2) The inventors found thatthat the trailing electromagnetic field is not only proportional to the flow velocity of the fluid, but also proportional to the background magnetic field. To reduce the measurement difficulty, 1 0 1 111 1 1 1() 11(1) 1 k mm k mm k mkm yaemm yaemm yaemm            LL MMMMMMM L (21)1(21)1(21)1mmkkmYXAE 1()TTAXXXY& 1()TYXAXXXY& 2025 / 5586 BE2025 / 5586 23517 Wuhan2ndShipDesignAndResearchInstitute -7- another signal amplification technique was introduced, in which a magnetic field generator is used to amplify the background magnetic field in to enhance the lag area. The magnetic field generator consists of a Helmholtz coil pair and a current source. The current source feeds the Helmholtz coils to control the background magnetic field in the lag area and thereby further improve the measurement accuracy. The invention has the following advantages: First: The invention uses a circulating water basin structure,which offers considerable advantages compared to towing tanks. Towing tanks are less advantageous due to the limited lanes and test time, whereas the circulating water tank uses a drive system to circulate the water at a constant speed. This enables long-term simulation of the desired environments without damaging the model through towing, and this simulated environment remains stable. The circulating water tank allows for long-term measurements, which not only facilitates the measurement of the wake electromagnetic field but also enables observations and video recordings through windows of the tank. In addition, the circulating water tank offers advantages such as low investment costs, small footprint, and fast results. Secondly: The invention has developed a signal amplification technique for the experimental setup for measuring the wake electromagnetic field. On the one hand, a frequency shift is achieved by periodically changing the flow velocity,which increases the frequency of the trailing electromagnetic field and reduces the influence of 1 / f noise on the electric and magnetic field sensors. On the other hand, the magnetic field generator is used to amplify the background magnetic field in the trailing region, thereby increasing the signal strength of the trailing electromagnetic field and reducing the measurement difficulty. The invention enables the detection of trailing electric fields with less than 1 μV / and trailing magnetic fields with less than 1 nT, whereas such a weak trailing electromagnetic field would not be detectable at all without the background amplification magnetic field and without periodic flow changes. Thirdly: The invention has developed a data analysis method for extracting weak wake electromagnetic field features. The method combines empirical mode decomposition,The SG filter and the fast Fourier transform. First, the relevant feature signal is extracted from the measurement data using empirical mode decomposition. Then, the SG filter is used to further reduce noise and increase signal purity. Finally, the fast Fourier transform is applied to subject the signal to spectral analysis, thereby thoroughly analyzing and identifying the features of the trailing electromagnetic field. This method improves signal identification and measurement reliability. Description of the drawings: Fig. 1 shows a schematic diagram of the experimental setup for trailing electromagnetic fields used in the embodiment of the present invention. Fig. 2 shows a schematic diagram of the different local structures of the circulating water basin in the embodiment of the present invention, where, from left to right, the water basin structure,The blade, drive shaft, and bearing are shown. Fig. 3 shows a schematic diagram of the overall connection of the circulating water basin in the embodiment of the present invention. Fig. 4 shows a schematic diagram of the water basin impeller in the embodiment of the present invention. 2025 / 5586 BE2025 / 5586 23517 Wuhan 2nd Ship Design and Research Institute -9- Fig. 5 shows the subcritical flow in the channel in the embodiment of the present invention. Fig. 6 shows the user interface for speed control in the embodiment of the present invention. Fig. 7 shows the arrangement of the round Helmholtz coil in the embodiment of the present invention. Fig. 8 shows the spatial magnetic field distribution and the uniform zone division of the Helmholtz coil in the embodiment of the present invention. Fig. 9 shows the frequency spectrum of the wake electric field after data processing during a change in flow velocity with a frequency of 0.2 Hz in the embodiment of the present invention. Fig. 10 shows the frequency spectrum of the wake magnetic field after data processing during a change in flow velocity with a frequency of 0.12 Hz in the embodiment of the present invention. Detailed embodiment The present invention is explained in more detail below with reference to embodiments and the attached drawings, whereby the embodiment of the invention is not limited thereto. The main concept of the inventive method for enhanced detection of wake electromagnetic fields based on a circulating water basin consists of designing a corresponding test system for the wake electromagnetic field generated by a submarine, measuring the wake electromagnetic field, and performing a data analysis.to provide new technical means for the research of wake electromagnetic field mechanisms and remote sensing of submarines. As shown in Fig. 1, the wake electromagnetic field test system in the exemplary embodiment comprises three main parts: the circulating water basin, the magnetic field generator, and the wake electromagnetic field measurement system. All three parts are powered by a single power source. The circulating water basin comprises the main basin, the paddles, the drive shaft, and the motor for the drive shaft. The main basin of the circulating water basin is the central component of the entire device and consists of corrosion-resistant, non-conductive, and non-magnetic material such as fiberglass-reinforced plastic. This material not only resists salt corrosion but also does not interfere with the measurement of the residual electromagnetic field. As shown in Fig. 2, the various parts of the circulating water basin, including the main basin and the paddles,the drive shaft and the bearings. Fig. 3 shows the schematic diagram of the entire connection of the circulating water basin. To ensure a frictionless flow of the fluid, the inside of the basin is designed with a streamlined geometry to reduce fluid resistance and increase flow rate. The test model is fixed in the main body of the circulating basin, and the circulating movement of the fluid generates a wake behind the model, the electromagnetic field of which is measured. The impeller blade is another key element that stimulates the fluid circulation through rotation. Its design must follow the principles of fluid mechanics to maximize efficiency and minimize energy consumption. It is designed in a helical shape. Besides the shape, the material of the blade is also important. It should be made of high-strength and corrosion-resistant material, such as high-quality engineering plastic, 2025 / 5586 BE2025 / 5586 23517 Wuhan 2nd Ship Design and Research Institute -11- to ensure,that it does not deform or corrode during extended periods of operation. The blade is connected to an external drive unit (servo motor) via a drive shaft, with the drive shaft being the central component for power transmission in the system. One end of the drive shaft runs through the outer wall of the circulation basin and is rigidly connected to the blade, while the other end is connected to the output shaft of the servo motor. If a reduction gearbox is used, it is connected to the output shaft of the reduction gearbox. The drive shaft must not only exhibit high strength to meet the demands of high-speed rotation but also offer excellent corrosion resistance. High-quality engineering plastic is selected for the material to ensure sufficient corrosion resistance and mechanical strength. Furthermore, the design of the drive shaft must take into account the dynamic balance of the system.To avoid vibrations and instabilities due to high-speed rotation, the drive shaft is designed to be removable or equipped with quick-connect mechanisms to facilitate installation and maintenance of the equipment, thus improving the system's flexibility. Sealed bearings are mounted on one or both side walls of the circulation basin, with the impeller drive shaft being secured by the sealing bearing on the outer wall. The bearing is the key component connecting the drive shaft to the basin, and its quality directly affects the smooth operation and lifespan of the entire unit. The bearing in the circulation basin is not only responsible for supporting the rotating parts,but must also withstand high loads and be protected against corrosion and damage. Ceramic bearings are selected to adapt to the operating environment. In addition to the above-mentioned components, an automated control system can be used to further improve the overall performance and applicability of the circulation basin. This system precisely controls and adjusts the flow rate of the salt solution via a PLC (Programmable Logic Controller). The operation is as follows: The rotational speed of the rightmost servo motor is entered and converted into the rotational speed of the impeller blade by a 10:1 reduction gear.which generates the flow of water in the circulation basin. The following assumptions are made for calculating the power output, taking into account the input dimensions of the circulation basin: (1) The water flow is one-dimensional and only the steady-state flow velocity is considered; (2) Only one blade interacts with the water flow; (3) The blade is perpendicular to the flow velocity, as shown in Fig. 4. The process of interaction between the water flow and the impeller is shown in Figures 4 and 5. Due to the dynamic exchange between the water flow and the impeller, a difference in water level occurs before and after the impeller. The impeller's power in shallow flow can be estimated as follows: (1) Here, the density of the water, here the density of seawater is = 1.025 × 10⁻⁶ kg / m³, is the width of the impeller, b = 0.14 m, d₂, v₁, v₂ are shown in Figure 5, and d₂ is approximated with 0.2. The motor power is chosen to be 750 W.alsoP=750W.d1 and d2 represent the water level heights at low and high water levels during the blade drive process, v1 and ()2 2212wPbdvvv 2025 / 5586 BE2025 / 5586 23517 Wuhan2ndShipDesignAndResearchInstitute -13- v2 are the flow velocities at low and high water levels (also the flow velocities in front of and behind the impeller). v2 and v1 are in a specific ratio that depends on the shape of the basin. Assuming v2 = C0 • v1, where C0 is the ratio factor of the flow velocity, then the formula can be rewritten as: (2) Here, v1 is the required flow velocity, which can be expressed as follows: (3) The value of v1 is mainly influenced by C0. Experiments have shown that C0 is approximately between 1.5 and 2, so the calculated velocity v1 is between 2.35 m / s and 4.115 m / s. Taking into account the power loss and assuming an effective power of only 400 W, a calculated velocity of 1.91 m / s to 3.337 m / s results. Additionally,Taking into account the kinetic energy loss that occurs when flowing through a basin, multiplied by a factor of 0.8, an upper and lower limit for the flow velocity of approximately 1.528 m / s to 2.669 m / s results, which corresponds to the requirements for a flow velocity of 1.5 m / s. The motor's control system consists of a control circuit, a servo motor, and a drive shaft, with the servo motor being controlled by software control circuit inputs to rotate the blades. The motor has a power output of 750 W, and the speed is regulated via the control circuit. The control interface for the user interface is shown in Fig. 6. The motor can be operated at variable speed (the frequency of the speed change can be adjusted), and this control method allows for changes in the water flow.which provides support for carrying out the test. Preferably, the power of the drive motor is selected before the test to ensure that the upper and lower ranges of the flow velocity do not fall below the specified value. The flow velocity in the basin is measured with a velocity sensor, and the power of the drive motor is adjusted to determine the maximum steady-state value of the flow velocity (the steady-state maximum value refers to the velocity that does not cause any transitional splashing of the water or significant vibrations of the equipment and can reach a certain flow intensity). Once the steady-state maximum velocity is reached,The maximum speed of the drive motor is determined. The speed sensor is removed and replaced by an electric field sensor and a magnetic field sensor. Within the maximum speed range, the speed of the drive motor is periodically adjusted. In this embodiment, the main basin of the circulating water basin is made of glass fiber reinforced plastic, and the blade bearings and blade shields are made of high-quality engineering plastic to ensure that no interference from the electric and magnetic fields is introduced. The drive shaft is fixed to the servo motor via a coupling and connected to the blades via a pin. A splash guard cover can also be attached to the basin, which is secured to the basin by a clip fastener. The bearings on both sides of the blades work together with ceramic bearings and rotate. The bearing unit is attached to the basin through a hole and secured with a retaining ring.to prevent the bearing from falling out. The bottom of the basin is on the same level as the bottom of the engine foundation. The foundation must be fixed against impacts. 2025 / 5586 BE2025 / 5586 23517 Wuhan 2nd Ship Design and Research Institute -15- The effectiveness of this method is demonstrated below through theoretical analysis. The motion of the wake can be described by the equilibrium of mass and momentum, which is represented by the continuity equation and the Navier-Stokes equation, as shown in equation (1): (1) where i is the velocity of the wake motion, p is the pressure of the seawater, ρ is the density of the seawater, and μ is the dynamic viscosity of the seawater. The left-hand side of the Navier-Stokes equation corresponds to the inertial forces, while the right-hand side gives the terms for pressure, viscous forces, and external forces acting on the seawater.represents. Under the influence of the Earth's magnetic field, the wake electric field E and the wake magnetic field B fulfill Maxwell's electromagnetic theory: (2) (3) Here, equations (2) and (3) are the expressions of Maxwell's equations. The conductance density of the induced current in the wake is J = σ(E + v0 × BE), where σ is the electrical conductivity of the seawater, BE is the background magnetic field, and v0 is the speed of the wake motion. It is generally assumed that the conducting current density of the seawater is much greater than the displacement current density, so that the second term on the right-hand side of equation (3) can be neglected. The wake magnetic field can then be represented as follows: (4) 2 0 ()pt  έ     uu uuuF tEB 000tέBJE ()()()()()()()()() 00Ei0E BvBErvrrrrrvBBrr 2025 / 5586 BE2025 / 5586 23517 Wuhan2ndShipDesignAndResearchInstitute -16- (5) From equations(4)and(5) it follows,that the trailing magnetic field is proportional to the flow velocity. By controlling the periodic change in the flow velocity, the measurement frequency of the trailing magnetic field can be increased and the influence of 1 / f noise on the electric and magnetic field sensors reduced. 2. Magnetic Field Generator From equations (4) and (5) it also follows that the trailing magnetic field is proportional to the background magnetic field. The magnetic field generator is used to amplify the background magnetic field in the trailing region, thereby increasing the signal strength of the trailing electromagnetic field and reducing the measurement difficulty. Considering the arrangement of the Helmholtz coils shown in Fig. 7, the two coils have a diameter of 800 mm, a distance of 40 mm, and a current of 2.5 A flows through the coils with a number of turns of 200. Due to the symmetry of the magnetic field distribution of the Helmholtz coils in space, it was sufficient to calculate the magnetic field distribution in the oxy plane.to determine the magnetic field in the entire space. The left image in Fig. 8 shows the magnetic field distribution in the z-direction of the oxy-plane, the right image shows the magnetic field distribution in the By-direction of the oxy-plane, where the magnetic lines divide the uniform areas of 99%, 95%, and 90% in the outside-to-inside direction. For example, the 95% uniform area is overall similar to a spindle shape, with a maximum width of 13 cm. If the maximum length of the 99% uniform area is considered as the limit for the uniform area, the entire area is a rhombus-shaped area with a diagonal length of 13 cm × 25 cm. The area is 0.5 × 13 cm × 25 cm = 33 '' ) 44 ( () VV dvdv μμσ ππ     0E Jr' B ' vBrr r rr'rr 2025 / 5586 BE2025 / 5586 23517 Wuhan 2nd Ship Design and Research Institute -17- 162.5 cm². The sensor size can be determined based on the area of ​​this region, or different Helmholtz coils can be selected according to the sensor size.so that the sensor's measuring range is within a uniform range. 3. Measurement System for the Follow-Up Magnetic Field Silver / silver chloride electric field sensors and fluxgate-type magnetic field sensors are used to measure the follow-up electric field and the follow-up magnetic field. A high-resolution data recorder is used to convert the analog signals from the sensors into digital signals, which facilitates the extraction of the follow-up magnetic field signal by data analysis methods. First, empirical modal analysis (EMD) is used to remove electromagnetic interference in the test process so that the focus is better on the low-frequency range. Then, the SG filter method is applied to process the signals, extract data, and remove outliers. After processing, the optimized data is obtained. Finally, the fast Fourier transform is used,to perform a frequency domain analysis of the data and to calculate the intensity of the wake magnetic field in accordance with the frequencies of the flow velocity changes. This method can provide frequency domain information of the wake magnetic field. (1) Empirical modal analysis (EMD) is an adaptive method for signal decomposition and analysis suitable for nonlinear and non-stationary signals. This method decomposes complex signals into a series of intrinsic modal functions (IMFs), where each IMF represents different frequency and amplitude characteristics of the signal, whose edge frequency changes are relatively stable in a local area. 2025 / 5586 BE2025 / 5586 23517 Wuhan2ndShipDesignAndResearchInstitute -18- The basic idea of ​​EMD is to extract the intrinsic modal functions from the data through iteration, with each iteration generating an IMF. This process continues,until the obtained IMF satisfies the two conditions for the intrinsic modal functions: The number of extrema is equal to or at most 1 greater than the number of zeros in the entire signal range; within each local region, extrema and zeros alternate, and the sum of the absolute differences is minimal. Finally, the original signal can be approximately reconstructed by summing the obtained IMFs. The nuclear form EMD is as follows: For the original magnetic field signal x(t), the EMD decomposition process can be represented as follows: xt = ∑ + (6) where the i-th IMF and the final remainder term are denoted. (2) The SG filter is used for smoothing and noise reduction of data streams and is a time-dependent filtering method based on local polynomial least squares fitting. Its main feature is thatthat the filter maintains the shape and width of the signal when removing noise. As an improvement on the sliding smoothing algorithm, it is mainly used to eliminate interference and has a significant effect on improving the signal-to-noise ratio. The SG filter is an improvement on smoothing filtering. Assuming there is a discrete time series xL of the electromagnetic field, the window length of the filter is set to n = 2m + 1, where the indices of the electromagnetic data points are selected as (xm, x-m+1, ... x0, x1, ... xm-1, xm), and a -1 degree polynomial is used to fit the electromagnetic data points within the window, i.e., these points are magnetic field data points of an sk-1 polynomial model: (7) Then the electromagnetic data points in the window can form a sk-dimensional linear system of equations, (8) where the random error of the matrix fitting isand is represented as a matrix: (9) For the system of equations to have a solution, n ≥ k. The parameter matrix A is calculated using the least squares method, and then the electromagnetic data points Y are fitted. By the least squares method, Aber can be calculated as: (10) is the smallest solution of the parameter matrix A, and the filtered value of Y is: (11) By selecting the appropriate window lengths and the polynomial fit degree k according to the actual application, the smoothing effect of the SG filter can be achieved. (3) By applying the fast Fourier transform, the processed trailing electric field and trailing magnetic field data are converted into 21 0121 ...kk yaaxaxax  1 0 1 111 1 1 1() 11(1) 1 k mm k mm k mkm yaemm yaemm yaemm            LL MMMMMMM L (21)1(21)1(21)1mmkkmYXAE 1()TTAXXXY& 1()TYXAXXXY& 2025 / 5586 BE2025 / 5586 23517 Wuhan2ndShipDesignAndResearchInstitute -20- Spectral diagrams converted,from which the wake magnetic field and wake electric field strengths are extracted in accordance with the frequencies of the flow velocity change in the time domain spectrum. For the time series of the magnetic field TX and the frequency domain sequence FY with a length of m, the calculation formula for the fast Fourier transform is as follows: (12) Where W is my third roots of unit: (13) As shown in Fig. 9 and Fig. 10, the following correspond to the following: the following: at a flow velocity change frequency of 0.2 Hz and the following: the following: magnetic induction strength at a flow velocity change frequency of 0.12 Hz. From the left image in Fig. 9 and the left image in Fig. 10, it can be seen that the weak following electric fields (less than 1 μV / m) and following magnetic fields (less than 1 nT) can be effectively detected by the periodic change of the flow velocity in conjunction with an enhanced background magnetic field. From the right image in Fig. 9 and the right image in Fig. 10 is recognizable,that without the application of signal amplification techniques and data processing, no weak trailing electric fields and trailing magnetic fields can be detected. Although the principles of the present invention have been described in detail with reference to the preferred embodiment, those skilled in the art should understand that the aforementioned embodiments are merely a schematic representation of the implementation of the invention and should not be regarded as limiting the scope of protection of the invention. The details of the embodiments do not constitute a limitation of the scope of protection of the invention. Any obvious changes that may be made to the technical Solutions based on the invention, such as equivalent transformations and simple substitutions, fall within the scope of protection of the invention, provided they do not deviate from the spirit and scope of the invention. 2025 / 5586 BE2025 / 5586