Method for cancelling vibration noise of a magnetoelectric sensing element

Abstract

This application relates to the field of magnetoelectric sensing technology, specifically a method for canceling vibration noise in a magnetoelectric sensing element. The method comprises: acquiring a magnetoelectric sensing element signal and a single-electrode reference signal, and performing a Fast Fourier Transform to obtain a frequency domain signal of the magnetoelectric sensing element and a frequency domain signal of the single-electrode reference; determining a coherence function based on a pre-set coherence threshold; constructing a vibration transfer function based on the coherence function, the frequency domain signal of the magnetoelectric sensing element, and the frequency domain signal of the single-electrode reference; constructing a vibration component in the magnetoelectric sensing element signal based on the vibration transfer function and the frequency domain signal of the single-electrode reference; and subtracting the frequency domain signal of the magnetoelectric sensing element from the vibration component to obtain the frequency domain signal after vibration noise cancellation. This application solves the problem of phase and amplitude mismatch and signal residuals caused by the inability to dynamically adjust compensation parameters due to a fixed physical structure by flexibly adjusting the coherence threshold.

Description

Technical Field

[0001] This application relates to the field of magnetoelectric sensing technology, and in particular to a method for canceling vibration noise of a magnetoelectric sensing element. Background Technology

[0002] Magnetoelectric sensing elements are widely used in various magnetic field measurement and control systems, but their piezoelectric relative is extremely sensitive to vibration, and even weak vibration can generate strong noise, which seriously limits their engineering applications.

[0003] To suppress noise, existing technologies employ symmetrical hardware design, mechanical differential compensation, or polarization offsetting to physically cancel out vibration interference. However, these suppression methods are all based on filtering with fixed physical characteristics and cannot cope with non-stationary, time-varying vibration excitations in complex environments. When faced with non-stationary, time-varying vibration excitations, the fixed physical structure cannot dynamically adjust compensation parameters, resulting in phase and amplitude mismatch and signal residuals. Summary of the Invention

[0004] This application provides a method for canceling vibration noise of a magnetoelectric sensing element, which at least solves the problem in related technologies where the fixed physical structure cannot dynamically adjust the compensation parameters, resulting in phase and amplitude mismatch and signal residual.

[0005] In a first aspect, embodiments of this application provide a method for canceling vibration noise of a magnetoelectric sensing element, including: The magnetoelectric sensing element signal and the single-electrode reference signal are acquired and subjected to fast Fourier transform to obtain the frequency domain signal of the magnetoelectric sensing element and the frequency domain signal of the single-electrode reference. The coherence function is determined based on a pre-set coherence threshold; Based on the coherence function, the frequency domain signal of the magnetoelectric sensing element, and the single-electrode reference frequency domain signal, a vibration transfer function is constructed. Based on the vibration transfer function and the single-electrode reference frequency domain signal, the vibration component in the magnetoelectric sensing element signal is constructed. The difference between the frequency domain signal of the magnetoelectric sensing element and the vibration component is calculated to obtain the frequency domain signal after vibration noise cancellation.

[0006] In some embodiments, determining the coherence function based on a pre-set coherence threshold includes: In the full frequency domain, the coherence function at each frequency is compared with the coherence threshold; If the coherence function is greater than the coherence threshold, then the value of the coherence function is retained; If the coherence function is less than the coherence threshold, then the coherence function is assigned a value of zero.

[0007] In some embodiments, determining the coherence function based on a pre-set coherence threshold includes: Set multiple sets of undetermined coherence thresholds, and determine the coherence function corresponding to each set of undetermined coherence thresholds according to each set of undetermined coherence thresholds; According to the coherence function corresponding to any set of undetermined coherence thresholds, the frequency domain signal after vibration noise cancellation corresponding to that set of undetermined coherence thresholds is calculated; Based on the frequency domain signal after vibration noise cancellation corresponding to any set of undetermined coherence thresholds, calculate the residual power and frame rate leakage power; Based on the residual power and the frame rate leakage power, the evaluation index corresponding to any set of undetermined coherence thresholds is calculated. Select the evaluation index with the smallest value from the evaluation indices corresponding to the undetermined coherence thresholds in each group, and use the evaluation index with the smallest value corresponding to the undetermined coherence threshold as the coherence threshold.

[0008] In some embodiments, calculating the residual power includes: The residual power is calculated according to the formula for calculating residual power. The formula for calculating the residual power is set as follows: ; in, The residual power, The total number of sampling points. For any sampling point, The residual time-domain signal is obtained by performing an inverse fast Fourier transform on the frequency-domain signal after the vibration noise has been canceled.

[0009] In some embodiments, calculating the frame rate leakage power includes: The frame rate leakage power is calculated according to the formula for calculating frame rate leakage power. The formula for calculating the frame rate leakage power is set as follows: ; in, The frame rate leakage power, This represents the total number of positive frequency spectral lines. For any positive frequency spectral line, Let be the power spectral density at any frequency point, which is obtained by calculating the square of the amplitude of the frequency domain signal after vibration noise cancellation.

[0010] In some embodiments, calculating the frequency domain signal after vibration noise cancellation corresponding to any set of undetermined coherence thresholds according to the coherence function corresponding to any set of undetermined coherence thresholds includes: Acquire the time-domain signal output from the magnetoelectric sensing element and the time-domain signal output from a single electrode; Divide the time window into multiple time windows in chronological order; Calculate the variance of the time-domain signal amplitude output by the magnetoelectric sensing element in each time window; The time-domain signal output by the magnetoelectric sensing element within the time window with the smallest variance is selected as the magnetoelectric sensing element signal corresponding to the undetermined coherence threshold, and the time-domain signal output by the single electrode within the time window is selected as the single electrode reference signal corresponding to the undetermined coherence threshold. Based on the magnetoelectric sensing element signal and the single-electrode reference signal corresponding to each group of undetermined coherence thresholds, the frequency domain signal after vibration noise cancellation corresponding to each group of undetermined coherence thresholds is obtained.

[0011] In some embodiments, constructing the vibration transfer function based on the coherence function, the frequency domain signal of the magnetoelectric sensing element, and the single-electrode reference frequency domain signal includes: The vibration transfer function is set as follows: ; in, Let be the vibration transfer function. The transfer function is... The coherence function is obtained based on the frequency domain signal of the magnetoelectric sensing element and the single-electrode reference frequency domain signal.

[0012] In some embodiments, the transfer function includes: ; in, The power spectrum of the single-electrode reference signal is obtained from the single-electrode reference frequency domain signal. The cross-power spectrum is obtained from the frequency domain signal of the magnetoelectric sensing element.

[0013] In some embodiments, after obtaining the frequency domain signal after vibration noise cancellation, the method further includes: By using inverse fast Fourier transform, the frequency domain signal after vibration noise cancellation is transformed into a time domain signal, and then weighted and superimposed in time order to form a time-continuous vibration noise cancellation time domain signal.

[0014] In some embodiments, the weighted superposition according to time order includes: Weighted superposition is performed according to the superposition calculation formula; The superposition calculation formula is set as follows: ; in, The time-domain signal is the result of canceling out the vibration noise, which is continuous in time. The m-th frame is the residual time-domain signal. For Hanning Window.

[0015] Compared to related technologies, the vibration noise cancellation method of the magnetoelectric sensing element provided in this application embodiment, by flexibly adjusting the coherence threshold to adapt to the full-frequency vibration noise cancellation calculation, solves the problem of phase and amplitude mismatch and signal residual caused by the inability to dynamically adjust compensation parameters due to the fixed physical structure. It realizes accurate signal reconstruction, improves the adaptive suppression capability under complex non-stationary vibration environment, and enhances the robustness and stability in complex environment.

[0016] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a method for canceling vibration noise of a magnetoelectric sensing element according to an embodiment of this application; Figure 2 This is a structural diagram of a magnetoelectric sensing element package adapted to a method for canceling vibration noise of a magnetoelectric sensing element according to an embodiment of this application. Figure 3 This is a structural diagram of a magnetoelectric sensing element adapted to a method for canceling vibration noise of a magnetoelectric sensing element according to an embodiment of this application. Figure 4 This is a structural diagram of a single electrode adapted to a method for canceling vibration noise of a magnetoelectric sensing element according to an embodiment of this application. Figure 5 This is another flowchart of a method for canceling vibration noise of a magnetoelectric sensing element according to an embodiment of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the application is described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments provided in this application without inventive effort are within the scope of protection of this application.

[0019] Obviously, the accompanying drawings described below are merely some examples or embodiments of this application. Those skilled in the art can apply this application to other similar scenarios based on these drawings without any creative effort. Furthermore, it is understood that although the efforts made in this development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this application, any changes to design, manufacturing, or production based on the technical content disclosed in this application are merely conventional technical means and should not be construed as insufficient disclosure of this application.

[0020] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment that is mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application may be combined with other embodiments without conflict.

[0021] Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms “a,” “an,” “an,” “the,” and similar words used in this application do not indicate quantity limitation and may indicate singular or plural. The terms “comprising,” “including,” “having,” and any variations thereof used in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or modules (units) is not limited to the listed steps or units, but may also include steps or units not listed, or may include other steps or units inherent to these processes, methods, products, or devices. The terms “connected,” “linked,” “coupled,” and similar words used in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. “Multiple” used in this application refers to two or more. “And / or” describes the relationship between related objects, indicating that three relationships may exist; for example, “A and / or B” can represent: A alone, A and B simultaneously, and B alone. The character " / " generally indicates that the preceding and following objects are in an "or" relationship. The terms "first," "second," and "third" used in this application are merely to distinguish similar objects and do not represent a specific ordering of the objects.

[0022] Magnetoelectric sensing elements can convert magnetic field signals into electrical signals, and have broad application prospects in magnetic field measurement and control systems. However, because the piezoelectric phases in magnetoelectric composite materials are extremely sensitive to vibration, even weak vibration interference can generate strong noise in the sensing element, severely reducing the signal-to-noise ratio of magnetic anomaly signals. This has become a core bottleneck restricting the engineering application of high-sensitivity magnetoelectric weak magnetic sensors.

[0023] To suppress vibration noise, existing technologies mainly employ symmetrical hardware structure design or mechanical differential compensation schemes. The core idea is to cancel out vibration interference at the physical level through symmetrical arrangement of physical structures or offsetting of piezoelectric layer polarization directions.

[0024] However, existing structural compensation designs are essentially based on filtering with fixed physical characteristics, which cannot cope with non-stationary and time-varying vibration excitation in complex environments. When the vibration frequency fluctuates, the fixed physical structure cannot dynamically adjust the compensation parameters, which can easily lead to phase and amplitude mismatch, resulting in severe signal residuals, weakening the signal-to-noise ratio of magnetic anomaly signals, and causing poor robustness and real-time performance of signal suppression.

[0025] Meanwhile, the high-precision differential structure has extremely stringent requirements for assembly consistency. Even a small process deviation can lead to a significant drop in the common mode rejection ratio, and the actual noise reduction effect is far lower than the theoretical value. In addition, the complex mechanical structure increases the system size, manufacturing cost and the difficulty of operation and maintenance throughout the entire life cycle.

[0026] To address the aforementioned issues, this application provides a method for canceling vibration noise in magnetoelectric sensing elements. This method does not rely on complex hardware structures and can adaptively track vibration changes while accurately protecting the target magnetic signal.

[0027] like Figure 1 As shown in the embodiment of this application, a method for canceling vibration noise of a magnetoelectric sensing element is provided, including: S101: Acquire the magnetoelectric sensing element signal and the single-electrode reference signal, and perform a fast Fourier transform to obtain the magnetoelectric sensing element frequency domain signal and the single-electrode reference frequency domain signal.

[0028] A method for canceling vibration noise of a magnetoelectric sensing element, adapted to this application, is proposed, along with a compensation structure for the magnetoelectric sensing element package, such as... Figure 2 As shown, the compensated magnetoelectric sensing element package includes a multi-layer structure: the upper layer is the magnetoelectric sensing element, the middle layer is a rigid plate, and the lower layer is a single electrode. The magnetoelectric sensing element and the single electrode are fixed to the upper and lower sides of the rigid plate, and after fixing, they are encapsulated in a rigid encapsulation box. The compensated magnetoelectric sensing element package achieves the in-phase response of the sensor to vibration noise from the hardware source, synchronously acquiring vibration signals and avoiding time delay.

[0029] like Figure 3As shown, the magnetoelectric sensing element has a sandwich structure, consisting of two layers of magnetostrictive material on the top and bottom, and a layer of piezoelectric material in the middle. The magnetostrictive layer deforms under the action of an external magnetic field, and this deformation is transmitted to the middle piezoelectric layer. The piezoelectric layer converts the mechanical strain into an electrical signal output through the piezoelectric effect, thereby realizing the conversion of magnetic field signal into electrical signal.

[0030] like Figure 4 As shown, the single electrode is a single crystal wafer with the middle piezoelectric layer remaining after removing the upper and lower magnetostrictive materials from the magnetoelectric sensing element. It only responds to the stress generated by vibration and does not respond to magnetic field signals.

[0031] This application adds a single electrode with the magnetostrictive layer removed as a reference channel. Combined with vibration noise cancellation methods, it dynamically estimates the vibration transfer function using the frequency domain coherence characteristics between the reference channel and the magnetoelectric sensing element channel, and reconstructs the vibration component in the magnetoelectric sensing element signal in real time. Finally, this component is stripped from the mixed magnetoelectric sensing element signal to recover the target magnetic anomaly signal. This application eliminates the need for complex mechanically symmetrical structures, high-precision matching processes, or additional vibration sensors for compensation, avoiding the problem of reduced common-mode rejection capability caused by structural asymmetry, processing errors, etc., thereby reducing system size, manufacturing difficulty, and overall cost.

[0032] Furthermore, this application uses a rigid encapsulation box to fix the magnetoelectric sensing element and single electrode to the upper and lower sides of a rigid plate, achieving in-phase vibration noise at the hardware source. Simultaneously, it works with the acquisition circuit to complete high-quality signal acquisition, and then achieves precise noise stripping by combining frequency domain coherence analysis, vibration transfer function estimation, and vibration noise cancellation methods. The hardware structure and software algorithm work together to form a complete vibration noise suppression closed loop, resulting in superior overall suppression performance compared to existing solutions that solely rely on hardware compensation.

[0033] Meanwhile, the rigid encapsulation structure ensures that the two sensors can synchronously sense vibration excitation without time delay. The acquisition circuit can perform high-fidelity acquisition of extremely weak signals of about 1 pC. Together, they ensure the high consistency and reliability of the single-electrode reference signal and the magnetoelectric sensing element signal, providing a high-quality input foundation for subsequent algorithms and fundamentally improving the accuracy of vibration noise suppression.

[0034] Specifically, the signal output by the magnetoelectric sensing element and the signal output by the single electrode are acquired by the acquisition circuit. The magnetoelectric sensing element output includes the target magnetic anomaly signal and vibration noise, while the single electrode output is a single electrode reference signal related to the vibration noise. Therefore, the single electrode reference signal can be used as a reference template for vibration noise.

[0035] Subsequently, the signals output by the magnetoelectric sensing element and the signals output by the single electrode are preprocessed. The preprocessing includes, but is not limited to, removing the DC component, bandpass filtering, and normalization. Preprocessing eliminates baseline drift and out-of-band noise interference, thereby improving the stability of subsequent frequency domain analysis.

[0036] S102, determine the coherence function based on the pre-set coherence threshold.

[0037] The coherence function can quantify the degree of linear correlation between two channels at various frequencies. High coherence means that the frequency component mainly comes from the vibration excitation that is felt together, while low coherence indicates that the frequency is mainly the target magnetic signal or unrelated noise. Therefore, the coherence function can be used as a reliable criterion to distinguish between vibration noise and magnetic anomaly signals.

[0038] S103, based on the coherence function and the frequency domain signal of the magnetoelectric sensing element and the single-electrode reference frequency domain signal, constructs the vibration transfer function.

[0039] This transfer function can characterize the amplitude scaling and phase delay relationship of vibration noise from the reference channel to the magnetoelectric sensing element channel. Due to the introduction of the coherence function, the transfer function retains an effective value only at high coherence frequencies and is compressed to near zero at low coherence frequencies, thus realizing frequency-selective extraction of vibration transmission characteristics.

[0040] S104. Based on the vibration transfer function and the single-electrode reference frequency domain signal, the vibration component in the magnetoelectric sensing element signal is constructed. The frequency domain signal of the magnetoelectric sensing element is subtracted from the vibration component to obtain the frequency domain signal after vibration noise cancellation.

[0041] Since the vibration components are reconstructed and canceled only at high coherence frequencies, while the cancellation terms are zero and the spectrum remains unchanged at low coherence frequencies, this method can accurately suppress vibration noise while completely preserving the target magnetic anomaly signal.

[0042] In this application, the collected signal data can be processed by a host computer.

[0043] In this embodiment, the coherence function is used as the vibration criterion, and precise cancellation is performed only in the frequency band where the vibration interference has strong coherence. This effectively avoids the false elimination of the target magnetic anomaly signal caused by blind fitting in the traditional adaptive filtering algorithm, improves the reconstruction accuracy of weak magnetic anomaly signals, and achieves adaptive suppression of vibration noise without relying on complex hardware symmetrical structures.

[0044] In some embodiments, determining the coherence function based on a pre-set coherence threshold includes: In the full frequency domain, the coherence function at each frequency is compared with the coherence threshold.

[0045] If the coherence function is greater than the coherence threshold, the value of the coherence function is retained, and vibration noise cancellation is performed at the frequency corresponding to the coherence function.

[0046] If the coherence function is less than the coherence threshold, the coherence function is assigned a value of zero, and vibration noise cancellation is not performed at the frequency corresponding to the coherence function.

[0047] In this embodiment, the magnitude of the coherence function reflects the linear correlation strength between the two channels at a given frequency, while the coherence threshold serves as a quantization threshold for determining whether the frequency belongs to the dominant vibration frequency. If the coherence function at a certain frequency is greater than the coherence threshold, the frequency is determined to be the dominant vibration frequency, the value of the coherence function is retained, and vibration noise cancellation is performed at that frequency. High coherence means that the frequency component has consistent propagation characteristics in both channels, conforming to the physical propagation laws of vibration noise; therefore, performing cancellation at this frequency is a reasonable and safe operation. If the coherence function is less than the coherence threshold, the frequency is determined to be mainly a magnetic anomaly signal or non-common-source noise, the coherence function is assigned a value of zero, and vibration noise cancellation is not performed at this frequency. Low coherence means that the frequency component does not have a linear correlation in the two channels; forced cancellation would destroy the spectral structure of the target magnetic signal. A dynamic confidence mask was constructed by using a coherence threshold to achieve frequency-selective vibration noise cancellation. This ensures that vibration noise is effectively suppressed while preventing the target magnetic anomaly signal from being mistakenly eliminated, thus achieving synergistic optimization between efficient vibration noise suppression and complete protection of the target magnetic signal.

[0048] Existing adaptive filtering methods typically process the entire frequency band uniformly, which can easily attenuate the target magnetic anomaly signal while suppressing vibration noise. This application calculates the coherence function between the single-electrode reference signal and the magnetoelectric sensor signal, constructing the vibration transfer function only at high coherence frequencies and implementing frequency-selective cancellation, while keeping the original signal unchanged at low coherence frequencies. This achieves effective separation of vibration noise from the target magnetic signal. This method can accurately track the frequency changes of vibration noise, significantly reduce the distortion of the target magnetic signal, and improve the reconstruction accuracy of weak magnetic anomaly signals.

[0049] Meanwhile, traditional adaptive filtering algorithms continuously update filter weights at non-vibration frequencies, which can easily lead to false cancellation of target magnetic anomaly signals. This application utilizes frequency domain coherence as the vibration criterion, performing noise cancellation only on frequency components that are highly correlated between the single-electrode reference signal and the magnetoelectric sensor signal, while completely preserving the target magnetic signal corresponding to low coherence frequencies. This achieves synergistic optimization between efficient vibration noise suppression and complete protection of the target magnetic signal, effectively improving the system's detection sensitivity and signal-to-noise ratio.

[0050] In some embodiments, determining the coherence function based on a pre-set coherence threshold includes: Set multiple sets of undetermined coherence thresholds, and determine the coherence function corresponding to each set of undetermined coherence thresholds.

[0051] Based on the coherence function corresponding to any set of undetermined coherence thresholds, the frequency domain signal after vibration noise cancellation corresponding to that set of undetermined coherence thresholds is calculated.

[0052] Based on the frequency domain signal after vibration noise cancellation corresponding to any set of undetermined coherence thresholds, calculate the residual power and frame rate leakage power.

[0053] Based on residual power and frame rate leakage power, the evaluation index corresponding to any set of undetermined coherence thresholds is calculated.

[0054] Select the evaluation index with the smallest value from the evaluation indices corresponding to each group of undetermined coherence thresholds. The evaluation index with the smallest value corresponds to the undetermined coherence threshold as the coherence threshold.

[0055] Specifically, the optimal frequency domain processing block length is determined simultaneously during the process of determining the optimal coherence threshold.

[0056] Multiple sets of candidate parameters are set, each including an undetermined coherence threshold and an undetermined frequency domain processing block length. The undetermined coherence threshold and the undetermined frequency domain processing block length differ between different sets of candidate parameters. The coherence threshold determines which frequency components participate in vibration noise cancellation, and the frequency domain processing block length determines the frequency resolution and coherence estimation accuracy of the Fast Fourier Transform analysis. Therefore, different parameter combinations will produce different frequency domain signals after vibration noise cancellation. For each set of candidate parameters, a complete vibration noise cancellation process is performed once to obtain the corresponding frequency domain signal after vibration noise cancellation.

[0057] The calculation formula for the evaluation indicators is constructed and set as follows: .

[0058] in, For residual power, For frame rate leakage power, This is the proportionality coefficient. .

[0059] The residual power and frame rate leakage power are both calculated based on the frequency domain signal after vibration noise cancellation.

[0060] By iterating through all candidate parameters and calculating the evaluation index for each group of candidate parameters according to the evaluation index calculation formula, the group of candidate parameters with the smallest evaluation index is selected as the optimal parameters. The undetermined coherence threshold is taken as the optimal coherence threshold, and the undetermined frequency domain processing block length is taken as the optimal frequency domain processing block length. Vibration noise is canceled according to the optimal coherence threshold and the optimal frequency domain processing block length, which ensures that the residual noise is minimized and avoids large frame rate leakage caused by frame truncation.

[0061] Furthermore, the frequency domain processing block length is used to calculate the frequency resolution, and the formula for calculating the frequency resolution is: .

[0062] in, For frequency resolution, The sampling frequency, which can be manually set according to actual needs, represents the number of times the signal of the magnetoelectric sensing element is sampled per unit time, and determines the time resolution of the discrete signal. The frequency domain processing block length is determined by calculating the frequency resolution to establish the spacing between adjacent frequency points in the Fast Fourier Transform spectrum. Frequency resolution directly affects the accuracy of frequency identification, cross-power spectrum calculation, and coherence function calculation during vibration noise cancellation. Higher frequency resolution improves the ability to distinguish between similar frequency components, helping to avoid misjudging effective magnetic signals and vibration noise, but it increases data processing latency. Therefore, this application rationally selects the frequency domain processing block length based on the sampling frequency, target signal bandwidth, and the real-time requirements of the algorithm.

[0063] In this embodiment, the method for setting the coherence threshold is further defined. Since the coherence distribution characteristics differ under different vibration environments, a fixed threshold value cannot adapt to all operating conditions. Therefore, it is necessary to find the optimal threshold value among multiple sets of data. Each threshold value will generate a different coherence function, thus affecting which frequencies are marked as vibration and which frequencies are retained, ultimately leading to different cancellation results. By calculating the residual power, the vibration noise energy remaining in the signal after cancellation is quantified, reflecting the noise reduction depth. By calculating the frame rate leakage power, the degree of spectral diffusion caused by frame processing is quantified, reflecting the spectral fidelity. Both evaluate the quality of the cancellation result from different dimensions. By weighted summing of the residual power and frame rate leakage power, an evaluation index is obtained, achieving a unified quantification of noise reduction depth and spectral fidelity. The minimum evaluation index means that the set of parameters has achieved the best balance between clean noise reduction and spectral fidelity, thus adapting to changes in noise characteristics under different vibration conditions. The optimal noise reduction parameters can be obtained without manual parameter tuning, significantly improving the robustness and stability of the system in complex environments compared to traditional fixed-parameter methods.

[0064] This application proposes a method for setting the coherence threshold and frequency domain processing block length. By searching for the optimal coherence threshold and frequency domain processing block length among multiple sets of undetermined data, the algorithm parameters are adaptively adjusted, enabling the application to adapt to changes in noise characteristics under different vibration conditions. Compared with traditional fixed-parameter filtering methods, this application can effectively suppress single-frequency vibration, multi-frequency vibration, and random non-stationary vibration noise, avoiding the degradation of suppression performance due to parameter mismatch, thereby improving the robustness and stability of the system in complex environments.

[0065] In some embodiments, calculating the residual power includes: The residual power is calculated using the formula for residual power.

[0066] The formula for calculating residual power is set as follows: .

[0067] in, For residual power, This represents the total number of sampling points. For any sampling point, The residual time-domain signal is obtained by performing an inverse fast Fourier transform on the frequency-domain signal after the vibration noise has been canceled.

[0068] In this embodiment, averaging the squared amplitudes of the residual time-domain signal at each sampling point essentially calculates the average power of the residual signal. Since the residual time-domain signal is the signal remaining after frequency domain cancellation, its energy primarily comes from residual vibration noise that was not completely canceled. The magnitude of the residual power directly reflects the remaining energy level after the vibration noise is suppressed; the smaller the residual power, the more thoroughly the vibration noise is canceled and the better the noise reduction effect. By calculating the residual power, this application provides an objective and quantifiable evaluation index for the noise reduction effect under different parameter combinations, making the automatic parameter search process data-driven and ensuring that the finally selected parameters achieve the optimal vibration noise suppression effect.

[0069] In some embodiments, calculating frame rate leakage power includes: The frame rate leakage power is calculated using the formula for calculating frame rate leakage power.

[0070] The formula for calculating frame rate leakage power is set as follows: .

[0071] in, For frame rate leakage power, This represents the total number of positive frequency spectral lines. For any positive frequency spectral line, Let be the power spectral density at any frequency point. The power spectral density is obtained by calculating the square of the amplitude of the frequency domain signal after vibration noise cancellation.

[0072] In this embodiment, the power spectral density of the residual frequency domain signal is summed across all frequency points in the full frequency band. Since framing processing causes signal energy to diffuse from its originally concentrated frequency points to neighboring frequency points, this spectral leakage results in additional energy distribution across the entire frequency band for the residual frequency domain signal. The magnitude of the frame rate leakage power directly reflects the level of leakage energy diffused across the entire frequency band due to framing truncation. A higher leakage power indicates more severe damage to the signal's spectral structure caused by framing processing, potentially leaking vibrational energy into the magnetic signal band and causing interference. Therefore, this application quantifies the degree of damage to the spectral structure caused by framing processing by calculating the frame rate leakage power. It considers not only the noise reduction depth but also spectral fidelity, avoiding the use of excessively small block lengths for noise reduction, which could lead to severe spectral leakage and contamination of the magnetic signal band.

[0073] In some embodiments, the frequency domain signal after vibration noise cancellation corresponding to any set of undetermined coherence thresholds is calculated according to the coherence function corresponding to that set of undetermined coherence thresholds, including: The time-domain signal output from the magnetoelectric sensing element and the time-domain signal output from the single electrode are acquired.

[0074] The two signals are acquired synchronously through the acquisition circuit, ensuring that the main channel and the reference channel signals are strictly aligned on the time axis. Since the time delay is eliminated at the hardware source, the phase relationship in the subsequent frequency domain analysis has high reliability.

[0075] Multiple time windows are divided according to chronological order.

[0076] Calculate the variance of the time-domain signal amplitude output by the magnetoelectric sensing element in each time window.

[0077] Specifically, the time-domain signal output by the preprocessed magnetoelectric sensing element and the time-domain signal output by the single electrode are divided into multiple time windows. The variance of the amplitude of the time-domain signal output by the magnetoelectric sensing element in each time window is calculated, and the time window with the smallest variance is selected as the vibration estimation segment to reduce the influence of the target magnetic anomaly signal on the vibration feature extraction.

[0078] The formula for calculating the variance of the time-domain signal output by the magnetoelectric sensing element is set as follows: .

[0079] in, Let be the time-domain signal sample value output by the magnetoelectric sensing element within the i-th time window. Let be the mean of the signal within the i-th window. The total number of samples, For any sampling point, denoted as the variance of the time-domain signal amplitude output by the magnetoelectric sensing element.

[0080] The variance of signal amplitude quantitatively reflects the severity of signal fluctuations. When a magnetic anomaly signal appears, the signal fluctuation increases significantly, leading to an increase in variance. Conversely, when there is only vibration noise, the signal fluctuation is small, leading to a decrease in variance. Therefore, the magnitude of variance can be used as an effective indicator to determine whether a magnetic anomaly signal exists within a window.

[0081] The time-domain signal output by the magnetoelectric sensing element within the time window with the smallest variance is selected as the magnetoelectric sensing element signal corresponding to the undetermined coherence threshold, and the time-domain signal output by the single electrode within this time window is used as the single electrode reference signal corresponding to the undetermined coherence threshold.

[0082] Since the time window with the smallest variance is selected, the probability and energy of magnetic anomaly signals appearing within this time window are the lowest. Therefore, the signals within this time window are almost pure vibration noise components and can be used as pure samples for vibration feature extraction.

[0083] Based on the magnetoelectric sensing element signals and single-electrode reference signals corresponding to each set of undetermined coherence thresholds, the frequency domain signals after vibration noise cancellation corresponding to each set of undetermined coherence thresholds are obtained.

[0084] In this embodiment, by calculating the variance and screening the usable magnetoelectric sensing element signals and single-electrode reference signals, since the signal fluctuation increases significantly when the magnetic anomaly signal appears, while the fluctuation is small when there is only vibration noise, the time window with the smallest variance is selected as the vibration estimation segment, and the magnetoelectric sensing element signals and single-electrode reference signals in it are used to calculate the frequency domain signal after vibration noise cancellation, thereby obtaining a more satisfactory coherence threshold, so as to minimize the impact of the magnetic anomaly signal on subsequent vibration modeling.

[0085] In some embodiments, a vibration transfer function is constructed based on the coherence function, the frequency domain signal of the magnetoelectric sensing element, and the single-electrode reference frequency domain signal, including: The vibration transfer function is set as follows: .

[0086] in, Let be the vibration transfer function. For transfer functions, The coherence function is obtained from the frequency domain signal of the magnetoelectric sensing element and the single-electrode reference frequency domain signal.

[0087] In this embodiment, the original vibration transfer function is directly multiplied by the coherence function, and the original transfer function is frequency-dependently weighted using the coherence function. At frequencies with high coherence, the coherence function approaches 1, and the vibration transfer function is almost equal to the complete transfer function. Therefore, the complete vibration transfer characteristics are preserved at these frequencies, enabling accurate reconstruction of vibration components and cancellation. At frequencies with low coherence, the coherence function approaches 0, and the vibration transfer function is compressed to near zero. Therefore, the cancellation term at these frequencies is almost zero, and the spectrum remains unchanged. This application, through coherence weighting, ensures that the cancellation action is strictly limited to high coherence frequencies and automatically disables cancellation at low coherence frequencies to protect the magnetic signal. This achieves precise frequency-selective suppression of vibration noise, fundamentally avoiding the problem of false cancellation of target magnetic anomaly signals caused by the uniform processing across the entire frequency band in traditional adaptive filtering algorithms.

[0088] In some embodiments, the coherence function is calculated using the following formula: .

[0089] in, The self-power spectrum of the single-electrode reference signal. For cross power spectrum, This is the power spectrum of the signal from the magnetoelectric sensing element.

[0090] Specifically, the formula for calculating the power spectrum of the signal from a magnetoelectric sensing element is as follows: .

[0091] In some embodiments, the formula for calculating the transfer function includes: .

[0092] in, This is the self-power spectrum of the single-electrode reference signal, which is obtained from the single-electrode reference frequency domain signal. The cross-power spectrum is obtained from the frequency domain signal of the magnetoelectric sensing element.

[0093] Specifically, the formula for calculating the self-power spectrum of the single-electrode reference signal is as follows: .

[0094] Specifically, the formula for calculating the cross power spectrum is: .

[0095] in, Total number of frames For any frame, For the first Frame, frequency The spectral value of the single-electrode reference signal at that location is obtained by performing a fast Fourier transform on the single-electrode reference signal. For the first Frame, frequency The signal spectrum value of the magnetoelectric sensing element at the location is obtained by performing a fast Fourier transform on the magnetoelectric sensing element signal.

[0096] In this embodiment, the self-power spectrum of the single-electrode reference signal describes the energy distribution of the single-electrode reference signal at each frequency, and the cross-power spectrum describes the degree of coordinated change of the two channel signals at each frequency. The transfer function obtained by the ratio of the two represents the amplitude scaling ratio and phase delay from the reference channel to the magnetoelectric sensing element channel at each frequency. Since both the self-power spectrum and the cross-power spectrum of the single-electrode reference signal are calculated based on the statistical averaging of multiple frames of data, they can effectively suppress the interference of random noise and instantaneous disturbances on the transfer function estimation, making the estimation results statistically stable and reliable. This application provides an accurate amplitude and phase model basis for the subsequent accurate reconstruction of vibration components through the transfer function, ensuring the accuracy of vibration component reconstruction, enabling the frequency domain cancellation algorithm to perform subtraction operations based on an accurate physical model, and improving the accuracy and stability of vibration noise cancellation.

[0097] In some embodiments, a vibration component in the magnetoelectric sensing element signal is constructed based on the vibration transfer function and a single-electrode reference frequency domain signal. The difference between the frequency domain signal of the magnetoelectric sensing element and the vibration component is calculated to obtain the frequency domain signal after vibration noise cancellation, including: The magnetoelectric sensing element signal and the single-electrode reference signal are processed in a frame-by-frame frequency domain. The full-band spectrum of the magnetoelectric sensing element signal and the full-band spectrum of the single-electrode reference signal in each frame are obtained by fast Fourier transform.

[0098] The vibration component in the magnetoelectric sensing element signal is obtained by multiplying the vibration transfer function and the full-band spectrum of the single-electrode reference signal. The vibration component reconstructs the amplitude and phase of the magnetoelectric sensing element signal component caused by vibration in any frame.

[0099] Vibration noise is canceled point by point across the entire frequency band. The difference between the full-band spectrum of the magnetoelectric sensing element signal and the vibration component in the magnetoelectric sensing element signal is calculated to obtain the frequency domain signal after vibration noise cancellation.

[0100] Specifically, the calculation formula for vibration noise cancellation is as follows: .

[0101] in, The vibration component in the signal of the magnetoelectric sensing element. Let be the vibration transfer function. This represents the full-band spectrum of the signal from the magnetoelectric sensing element. This represents the full-band spectrum of the single-electrode reference signal.

[0102] because The term is 0 in the low coherence frequency band, and the cancellation term is 0 in the low coherence frequency band, so the spectrum remains unchanged. At the high coherence frequency, effective difference calculation is performed.

[0103] In this application, vibration noise cancellation is performed on the full-band signal, but the cancellation action is only effective at high coherence frequencies.

[0104] In some embodiments, after obtaining the frequency domain signal after vibration noise cancellation, the method further includes: By using inverse fast Fourier transform, the frequency domain signal after vibration noise cancellation is transformed into a time domain signal, and then weighted and superimposed in time order to form a time-continuous vibration noise cancellation time domain signal.

[0105] In this embodiment, the frequency domain signal is represented by a spectrum with frequency as the independent variable. However, in practical applications, a time domain waveform needs to be output for subsequent analysis, display, or storage. Therefore, an inverse transformation must be used to restore the processing result to a time domain waveform. Since a framing strategy is used in the signal processing, each frame's time domain signal corresponds to only a short time window. Therefore, the time domain signals of each frame need to be weighted and superimposed in chronological order to form a time-continuous vibration noise-cancelled time domain signal. Framing processing divides a long sequence signal into short frames for independent processing. The boundaries between frames need to be smoothly spliced ​​to restore the continuous signal. Direct splicing leads to discontinuities and abrupt boundary changes between frames; therefore, weighted superposition is necessary to achieve a smooth transition between frames. This application, through inverse transformation and reconstruction, completely restores the denoised time domain waveform. The overlapping and adding splicing method effectively eliminates the discontinuities and boundary effects that may be introduced by framing processing, ensuring the integrity and continuity of the output signal. This allows the denoised magnetic anomaly signal to be directly applied to practical engineering systems.

[0106] In some embodiments, the weighted summation is performed in chronological order, including: Weighted superposition is performed according to the superposition calculation formula.

[0107] The superposition calculation formula is set as follows: .

[0108] in, The time-domain signal is the result of canceling out the vibration noise, which is continuous in time. The residual time-domain signal of the m-th frame is obtained by performing an inverse fast Fourier transform on the frequency-domain signal after vibration noise cancellation. For Hanning Window.

[0109] In this embodiment, the specific method of weighted superposition is further defined. Hanning windows are applied to the time-domain signals after inverse transformation of each frame for amplitude modulation. Then, the corresponding positions of each frame on the time axis are accumulated, and finally, the sum of the squares of the window weights is used for normalization. The Hanning windows approach zero at both ends, effectively suppressing spectral leakage at frame boundaries. The accumulation and normalization operations ensure the correct recovery of signal amplitude in the overlapping areas of each frame. Since adjacent frames overlap, multiple frames may simultaneously cover the same point in time. The numerator is the sum of the weighted contributions of multiple frames at that moment, and the denominator is the sum of the squares of all covered window weights at that moment. The ratio of these two values ​​precisely achieves a normalized weighted average of the contributions of each frame. The weighted superposition method of this application ensures a smooth transition between frames in the overlapping area, effectively suppresses reconstruction distortion caused by boundary effects, and restores the original amplitude of the signal. Ultimately, it achieves high-fidelity continuous time-domain magnetic anomaly signal output, providing a reliable data foundation for subsequent magnetic anomaly signal identification and interpretation.

[0110] In some embodiments, it also includes: By using mirror filling, signal data symmetrical to the data at each end of the time-domain signal after the cancellation of time-continuous vibration noise is added.

[0111] Specifically, during the weighted superposition process, the overlap rate is pre-set to 75% to ensure good continuity between adjacent data frames, reduce distortion caused by inter-frame splicing, and improve the smoothness of the time-domain signal after weighted superposition.

[0112] The overlap rate can be modified according to actual needs. After modification, the signal is reconstructed by weighted superposition according to the corresponding positions of each frame.

[0113] After the overlap rate is modified, the movement step size between two adjacent frames changes. For example, when the overlap rate is 50%, the movement step size is 50% of the frequency domain processing block length. When the overlap rate is 75%, the movement step size is 25% of the frequency domain processing block length.

[0114] Therefore, different overlap rates only affect the size of the overlapping area and the movement step between frames, and do not change the calculation principle of overlapping addition.

[0115] For each frame, the time-domain signal obtained by inverse fast Fourier transform is first multiplied by a Hanning window to obtain the windowed frame signal.

[0116] Based on a pre-set overlap rate, adjacent frames have overlapping regions. At each moment on the output time axis, the windowed frame signals of multiple different frames are simultaneously covered. For each moment on the output time axis, the contributions of all frames covering that moment are weighted and accumulated according to the superposition calculation formula, and then normalized to restore the original amplitude, thus reconstructing a continuous and complete denoised time-domain signal.

[0117] At both ends of the signal, the number of covered frames is relatively small, which can easily lead to amplitude instability. To address this, this application employs a mirror padding strategy, supplementing each end of the denoised time-domain signal with a data segment symmetrical to the boundary. This ensures that the first and last frames also receive the same number of frames as other frames, thereby eliminating reconstruction distortion caused by boundary effects.

[0118] For example, the original sequence is a, b, c, d, which becomes d, c, b, a, a, b, c, d, d, c, b, a after mirroring.

[0119] Furthermore, this application also provides an evaluation algorithm that calculates the vibration noise suppression amount by measuring the change in signal power before and after denoising, so as to quantitatively evaluate the algorithm's effect on vibration noise suppression under single-frequency vibration, multi-frequency vibration, and non-stationary vibration environments.

[0120] Specifically, the residual power ratio is first calculated, which is used to evaluate the cancellation effect.

[0121] The residual power ratio can be expressed as: .

[0122] in, To process the total energy of the signal before processing, This represents the total energy of the processed signal.

[0123] The formula for calculating the total energy of the signal before processing is as follows: .

[0124] The formula for calculating the total energy of the processed signal is: .

[0125] in, To complete the signal obtained after vibration noise cancellation, The signal from the magnetoelectric sensing element is obtained in S101.

[0126] Secondly, the vibration and noise suppression amount is calculated according to the formula for calculating the vibration and noise suppression amount. The formula for calculating the vibration and noise suppression amount is as follows: The unit is dB. The larger the value of the vibration noise suppression, the better the vibration noise cancellation effect.

[0127] like Figure 5 As shown, in practical applications, the process of this application includes, in sequence: data preprocessing, parameter adaptive search, frequency domain modeling and coherence weighting, frame-by-frame frequency domain cancellation and denoising signal reconstruction.

[0128] Specifically, in data preprocessing, the magnetoelectric sensing element signal and the single-electrode reference signal are acquired through the acquisition circuit. The magnetoelectric sensing element signal includes vibration noise and target magnetic anomaly signal, while the single-electrode reference signal serves as a reference for the vibration noise signal. After acquisition, both the magnetoelectric sensing element signal and the single-electrode reference signal undergo DC component removal, bandpass filtering, and standardization.

[0129] Specifically, in the parameter adaptive search, multiple time windows are first divided, and the variance of the time-domain signal amplitude output by the magnetoelectric sensing element is compared to determine the time window with the smallest variance. This determines the corresponding time period, during which the magnetoelectric sensing element signal and the single-electrode reference signal are used for subsequent calculations. Next, a parameter search is performed, using residual power and frame rate leakage power as references to select the optimal parameters from multiple sets of undetermined coherence thresholds and undetermined frequency domain processing block lengths.

[0130] Specifically, in frequency domain modeling and coherence weighting, the coherence function is first calculated, and then revalued across the entire frequency domain based on the coherence threshold. Next, based on the coherence function and the transfer function, a vibration transfer function is constructed, quantifying the vibration components in the magnetoelectric sensing element signal for easier subsequent elimination.

[0131] Specifically, in the frame-by-frame frequency domain cancellation and denoised signal reconstruction, the frame-by-frame frequency domain cancellation is first completed according to the calculation formula of vibration noise cancellation. Then, the frequency domain signal after vibration noise cancellation is transformed into a time domain signal through inverse fast Fourier transform. Subsequently, weighted superposition is performed to reconstruct the denoised time domain signal.

[0132] Finally, the suppression effect can be evaluated by calculating the amount of vibration and noise suppression.

[0133] This application has wide applications in fields such as magnetic anomaly detection, industrial non-destructive testing, biomagnetic measurement, geophysical exploration, and intelligent sensing system integration. Firstly, systems for submarine magnetic anomaly detection, geomagnetic navigation, and unexploded ordnance detection often operate on platforms subject to strong vibrations. This application can effectively suppress vibration noise and improve target recognition capabilities in complex environments, which is of great significance for enhancing the practicality and reliability of high-sensitivity weak magnetic detection systems. Secondly, vibration interference is also a common problem in fields such as industrial non-destructive testing, structural health monitoring, and wearable medical devices. This application can achieve high-precision suppression of vibration noise without increasing system size and complexity, thus having broad application prospects in these fields. Finally, with the development of the Internet of Things, edge computing, and intelligent sensing technologies, the demand for low-power, miniaturized, and high-real-time vibration noise suppression solutions is becoming increasingly urgent.

[0134] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0135] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for canceling vibration noise of a magnetoelectric sensing element, characterized in that, include: The magnetoelectric sensing element signal and the single-electrode reference signal are acquired and subjected to fast Fourier transform to obtain the frequency domain signal of the magnetoelectric sensing element and the frequency domain signal of the single-electrode reference. The coherence function is determined based on a pre-set coherence threshold; Based on the coherence function, the frequency domain signal of the magnetoelectric sensing element, and the single-electrode reference frequency domain signal, a vibration transfer function is constructed. Based on the vibration transfer function and the single-electrode reference frequency domain signal, the vibration component in the magnetoelectric sensing element signal is constructed. The difference between the frequency domain signal of the magnetoelectric sensing element and the vibration component is calculated to obtain the frequency domain signal after vibration noise cancellation.

2. The method for canceling vibration noise of a magnetoelectric sensing element according to claim 1, characterized in that, The coherence function is determined based on a pre-set coherence threshold, including: In the full frequency domain, the coherence function at each frequency is compared with the coherence threshold; If the coherence function is greater than the coherence threshold, then the value of the coherence function is retained; If the coherence function is less than the coherence threshold, then the coherence function is assigned a value of zero.

3. The method for canceling vibration noise of a magnetoelectric sensing element according to claim 1, characterized in that, The coherence function is determined based on a pre-set coherence threshold, including: Set multiple sets of undetermined coherence thresholds, and determine the coherence function corresponding to each set of undetermined coherence thresholds according to each set of undetermined coherence thresholds; According to the coherence function corresponding to any set of undetermined coherence thresholds, the frequency domain signal after vibration noise cancellation corresponding to that set of undetermined coherence thresholds is calculated; Based on the frequency domain signal after vibration noise cancellation corresponding to any set of undetermined coherence thresholds, calculate the residual power and frame rate leakage power; Based on the residual power and the frame rate leakage power, the evaluation index corresponding to any set of the undetermined coherence thresholds is calculated. Select the evaluation index with the smallest value from the evaluation indices corresponding to the undetermined coherence thresholds in each group, and use the evaluation index with the smallest value corresponding to the undetermined coherence threshold as the coherence threshold.

4. The method for canceling vibration noise of a magnetoelectric sensing element according to claim 3, characterized in that, The calculation of residual power includes: The residual power is calculated according to the formula for calculating residual power. The formula for calculating the residual power is set as follows: ; in, The residual power, The total number of sampling points. For any sampling point, The residual time-domain signal is obtained by performing an inverse fast Fourier transform on the frequency-domain signal after the vibration noise has been canceled.

5. The method for canceling vibration noise of a magnetoelectric sensing element according to claim 3, characterized in that, The calculation of frame rate leakage power includes: The frame rate leakage power is calculated according to the formula for calculating frame rate leakage power. The formula for calculating the frame rate leakage power is set as follows: ; in, The frame rate leakage power, This represents the total number of positive frequency spectral lines. For any positive frequency spectral line, Let be the power spectral density at any frequency point, which is obtained by calculating the square of the amplitude of the frequency domain signal after vibration noise cancellation.

6. A method for canceling vibration noise of a magnetoelectric sensing element according to any one of claims 3-5, characterized in that, The step of calculating the frequency domain signal after vibration noise cancellation corresponding to any set of undetermined coherence thresholds according to the coherence function of that set of undetermined coherence thresholds includes: Acquire the time-domain signal output from the magnetoelectric sensing element and the time-domain signal output from a single electrode; Divide the time window into multiple time windows in chronological order; Calculate the variance of the time-domain signal amplitude output by the magnetoelectric sensing element in each time window; The time-domain signal output by the magnetoelectric sensing element within the time window with the smallest variance is selected as the magnetoelectric sensing element signal corresponding to the undetermined coherence threshold, and the time-domain signal output by the single electrode within the time window is selected as the single electrode reference signal corresponding to the undetermined coherence threshold. Based on the magnetoelectric sensing element signal and the single-electrode reference signal corresponding to each group of undetermined coherence thresholds, the frequency domain signal after vibration noise cancellation corresponding to each group of undetermined coherence thresholds is obtained.

7. The method for canceling vibration noise of a magnetoelectric sensing element according to claim 1, characterized in that, The construction of the vibration transfer function based on the coherence function, the frequency domain signal of the magnetoelectric sensing element, and the single-electrode reference frequency domain signal includes: The vibration transfer function is set as follows: ; in, Let be the vibration transfer function. The transfer function is... The coherence function is obtained based on the frequency domain signal of the magnetoelectric sensing element and the single-electrode reference frequency domain signal.

8. The method for canceling vibration noise of a magnetoelectric sensing element according to claim 7, characterized in that, The transfer function includes: ； in, The power spectrum of the single-electrode reference signal is obtained from the single-electrode reference frequency domain signal. The cross-power spectrum is obtained from the frequency domain signal of the magnetoelectric sensing element.

9. A method for canceling vibration noise of a magnetoelectric sensing element according to claim 1, characterized in that, After obtaining the frequency domain signal after vibration noise cancellation, it also includes: By using inverse fast Fourier transform, the frequency domain signal after vibration noise cancellation is transformed into a time domain signal, and then weighted and superimposed in time order to form a time-continuous vibration noise cancellation time domain signal.

10. A method for canceling vibration noise of a magnetoelectric sensing element according to claim 9, characterized in that, The weighted summation according to time order includes: Weighted superposition is performed according to the superposition calculation formula; The superposition calculation formula is set as follows: ; in, The time-domain signal is the result of canceling out the time-continuous vibration noise. The m-th frame is the residual time-domain signal. For Hanning Window.

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