Material particle positioning detection method and system based on Fourier dominant frequency phase inversion

Abstract

The invention discloses a material particle positioning detection method and system based on Fourier dominant frequency phase inversion. The method comprises the following steps: S1, collecting a plurality of voltage signals of a plurality of induction coils through an electromagnetic induction device; s2, preprocessing the complex voltage signal of each coil, and extracting the phase of a dominant frequency component through fast Fourier transform; s3, directly extracting an absolute phase from the spectrum by using the global continuity characteristic of the dominant frequency component of the Fourier spectrum; s4, constructing a bidirectional neural network model, training based on the absolute phase data set, and establishing a mapping relation between the phase and the three-dimensional coordinates of the particles; s5, inputting the absolute phase value of each induction coil into the trained reverse neural network model to output the three-dimensional space coordinate position of the particle; according to the method, the problems of insufficient phase information utilization, difficult phase jump processing and high calculation complexity are solved, and high-precision, high-efficiency and high-real-time material internal particle positioning detection is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of material detection and signal processing, and more particularly to a material particle positioning detection method and system based on Fourier principal frequency phase inversion. BACKGROUND

[0002] With the rapid development of advanced manufacturing and material science, the demand for accurate positioning and dynamic monitoring of internal particles in materials is increasingly urgent.

[0003] Traditional material detection technologies mainly include X-ray detection, ultrasonic detection and eddy current detection; the X-ray detection technology has radiation problems, requires protective measures, has high equipment cost, and is difficult to realize continuous real-time monitoring; the ultrasonic detection technology needs to use a coupling agent, has requirements for the surface conditions of the detected material, and the penetration depth is limited by the material properties; the eddy current detection technology mainly detects the surface or near-surface region, and has limited detection capability for deep internal structures.

[0004] As a new detection method, electromagnetic induction detection technology has the advantages of non-contact measurement, good real-time performance, safety and environmental protection; however, the existing electromagnetic induction particle positioning technology mainly faces the following technical challenges in practical application:

[0005] Insufficient use of phase information: traditional electromagnetic induction detection methods mainly focus on the amplitude change of the signal, and the phase data containing more position information is not fully utilized.

[0006] Phase jump processing difficulty: due to the multi-value characteristic of the arctangent function, the phase measurement result is limited to the range of -π to π, and when the true phase value exceeds this range, a sudden jump of 2π will occur, which affects the continuity of the phase data.

[0007] Limitations of existing phase unwrapping algorithms: the main phase unwrapping methods currently used include path integral method, minimum norm method, etc., which are sensitive to noise and have high computational complexity, requiring a large number of path searches and iterative optimization calculations, making it difficult to meet real-time processing requirements.

[0008] Therefore, how to provide a new phase unwrapping method to fully utilize phase information, overcome phase jump and reduce computational complexity, so as to realize high-precision, high-efficiency and strong real-time material internal particle positioning detection is a problem that needs to be solved by those skilled in the art. SUMMARY

[0009] Therefore, the present application provides a material particle positioning detection method and system based on Fourier principal frequency phase inversion to solve some of the technical problems mentioned in the background art.

[0010] In order to achieve the above object, the present application adopts the following technical solutions:

[0011] A material particle positioning detection method based on Fourier main frequency phase inversion, comprising the following steps:

[0012] S1. Collecting complex voltage signals of multiple induction coils through an electromagnetic induction device;

[0013] S2. Preprocessing the complex voltage signals of each coil and extracting the phase of the main frequency component through fast Fourier transform;

[0014] S3. Directly extracting the absolute phase from the frequency spectrum by using the global continuity feature of the main frequency component of the Fourier spectrum;

[0015] S4. Constructing a bidirectional neural network model and training based on the absolute phase data set to establish the mapping relationship between the phase and the three-dimensional coordinates of the particles;

[0016] S5. Inputting the absolute phase values of each induction coil into the trained reverse neural network model to output the three-dimensional spatial coordinate position of the particles.

[0017] Preferably, the electromagnetic induction device includes an excitation coil, an induction coil array, a signal conditioning circuit, and a data acquisition system, wherein the excitation coil generates an alternating magnetic field of a predetermined frequency, the induction coil array includes multiple induction coils and is distributed around the detection area, the signal conditioning circuit preprocesses the induction signal, and the data acquisition system digitizes the signal.

[0018] Preferably, the complex voltage signal collected in step S1 includes a real part signal and an imaginary part signal, wherein the real part signal reflects the in-phase component of the electromagnetic field, and the imaginary part signal reflects the quadrature component of the electromagnetic field.

[0019] The complex voltage signal of each induction coil is represented as:

[0020]

[0021] wherein, is the continuous time domain complex voltage signal of the i-th induction coil, t is the time variable, is the signal amplitude of the i-th coil, is the phase angle, and ω is the angular frequency.

[0022] Preferably, the specific content of step S2 includes:

[0023] S21. Preprocessing the collected complex voltage signal, including removing the direct current component, applying the window function, and anti-aliasing filtering;

[0024] S22. Calculating the frequency spectrum of the preprocessed discrete voltage signal using the fast Fourier transform algorithm.

[0025] S23. Determine the position of the main frequency component through spectrum analysis;

[0026] S24. Extract the phase angle of the main frequency component.

[0027] Preferably, the method for calculating the spectrum in step S22 is:

[0028]

[0029] wherein, is the complex amplitude at index k after discrete Fourier transform, N is the number of FFT points, n is the discrete sampling point number, is the pre-processed discrete voltage signal, k is the spectrum index;

[0030] The phase of the extracted main frequency component in step S24 is:

[0031]

[0032] wherein, φ i is the phase of the main frequency component, is the main frequency component index, which is determined by selecting the item with the maximum amplitude from the spectrum component index.

[0033] Preferably, the method for obtaining the absolute phase in step S3 is:

[0034]

[0035] The unwrap function is naturally realized by the continuity feature of Fourier transform.

[0036] Preferably, the specific content of step S4 for constructing and training the bidirectional neural network model is:

[0037] S41. Training data set construction: take the multi-coil absolute phase obtained in step S3 as input, and take the real three-dimensional coordinates of the particles as output to form a sample pair;

[0038] S42. Forward model training: construct a neural network forward model with particle coordinates as input and phase as output, use mean square error as loss function, and optimize the weight through back propagation algorithm;

[0039] S43. Weight migration: migrate the learned weight in the forward model to the reverse model as parameter initialization;

[0040] S44. Reverse model training: take the multi-coil absolute phase as input and the three-dimensional coordinates of the particles as output, use adaptive optimization algorithm for iterative training to establish the mapping relationship from phase to coordinates;

[0041] S45. Model verification and application: The reverse model is verified by using an independent test set, and a trained reverse neural network model is obtained to realize input of actual collected phase data and output of three-dimensional coordinate positions of particles.

[0042] Preferably, the material particle positioning and detection method based on Fourier main frequency phase inversion further comprises: S6. Independent component analysis method is used to separate independent phase components of different particles, a multi-objective optimization algorithm is used to estimate multiple particle positions at the same time, and spatial filtering technology is used to suppress coupling interference between particles.

[0043] A material particle positioning and detection system based on Fourier main frequency phase inversion is based on the material particle positioning and detection method based on Fourier main frequency phase inversion, and comprises an electromagnetic induction device, a phase extraction module, an absolute phase acquisition module, a model construction and training module, and a particle position inversion module.

[0044] The electromagnetic induction device is used to collect complex voltage signals of multiple induction coils.

[0045] The phase extraction module is used to pre-process the complex voltage signals of each coil, and extract the phase of the main frequency component through fast Fourier transform.

[0046] The absolute phase acquisition module is used to directly extract the absolute phase from the frequency spectrum by using the global continuity feature of the main frequency component of the Fourier spectrum.

[0047] The model construction and training module is used to construct a bidirectional neural network model and train it based on an absolute phase data set, so as to establish a mapping relationship between the phase and the three-dimensional coordinates of the particles.

[0048] The particle position inversion module is used to input the absolute phase values of each induction coil into the trained reverse neural network model to output the three-dimensional spatial coordinate positions of the particles.

[0049] Preferably, the material particle positioning and detection system based on Fourier main frequency phase inversion further comprises a multi-particle detection module, which is used to separate independent phase components of different particles by using independent component analysis method, estimate multiple particle positions at the same time by using a multi-objective optimization algorithm, and suppress coupling interference between particles by using spatial filtering technology.

[0050] Compared with the prior art, the material particle positioning detection method and system based on Fourier main frequency phase inversion provided by the present application introduce fast Fourier transform into the phase unwrapping process, directly extract absolute phase information from the frequency domain, avoid the traditional phase unwrapping process, and realize accurate positioning of the particles in the material by constructing a neural network inversion model. The present application avoids the gradient iteration and cumulative error problems of the traditional phase unwrapping algorithm, significantly improves the calculation efficiency, effectively improves the accuracy of particle positioning by eliminating the phase jump problem, significantly enhances the noise resistance, and is suitable for the detection of different types of particles such as magnetic particles, conductive particles and dielectric particles in metal-based, ceramic-based and polymer-based composite materials, and has broad industrial application prospects. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0052] Figure 1 A material particle positioning detection method based on Fourier main frequency phase inversion provided by the present application is shown in the figure.

[0053] Figure 2 A Fourier transform unwrapping three-dimensional schematic diagram provided by the present application is shown in the figure.

[0054] Figure 3 A frequency domain phase spectrum extraction principle schematic diagram provided by the present application is shown in the figure.

[0055] Figure 4 A frequency domain phase unwrapping processing effect comparison schematic diagram provided by the present application is shown in the figure.

[0056] Figure 5 A bidirectional neural network model schematic diagram provided by the present application is shown in the figure. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0058] The present application discloses a material particle positioning detection method based on Fourier main frequency phase inversion, as shown in Figure 1 , comprising the following steps:

[0059] S1. Collecting complex voltage signals of multiple induction coils by an electromagnetic induction device;

[0060] S2. Preprocessing the complex voltage signals of each coil and extracting the phase of the main frequency component by fast Fourier transform;

[0061] S3. Directly extracting the absolute phase from the frequency spectrum by using the global continuity feature of the main frequency component of the Fourier spectrum;

[0062] S4. Constructing a bidirectional neural network model and training based on the absolute phase dataset to establish the mapping relationship between the phase and the three-dimensional coordinates of the particles;

[0063] S5. Inputting the absolute phase values of each induction coil into the trained reverse neural network model to output the three-dimensional spatial coordinate position of the particles.

[0064] In order to further implement the above technical solutions, the electromagnetic induction device includes an excitation coil, an array of induction coils, a signal conditioning circuit, and a data acquisition system. The excitation coil generates an alternating magnetic field of a predetermined frequency. The array of induction coils includes multiple induction coils and is distributed around the detection area. The signal conditioning circuit preprocesses the induction signal. The data acquisition system digitizes the signal.

[0065] In order to further implement the above technical solutions, the complex voltage signals collected in step S1 include real part signals and imaginary part signals. The real part signals reflect the in-phase component of the electromagnetic field, and the imaginary part signals reflect the quadrature component of the electromagnetic field.

[0066] The complex voltage signal of each induction coil is represented as:

[0067]

[0068] wherein, is the continuous time domain complex voltage signal of the i-th induction coil, t is the time variable, is the signal amplitude of the i-th coil, is the phase angle, and ω is the angular frequency.

[0069] In order to further implement the above technical solutions, the specific content of step S2 includes:

[0070] S21. Preprocessing the collected complex voltage signals, including removing the direct current component, applying the window function, and anti-aliasing filtering;

[0071] S22. Calculating the frequency spectrum of the preprocessed discrete voltage signal using the fast Fourier transform algorithm to improve the calculation efficiency;

[0072] S23. Determine the location of the dominant frequency component through spectrum analysis;

[0073] S24. Extract the phase angle of the main frequency component.

[0074] In this embodiment, the preprocessing of the acquired complex voltage signal includes:

[0075] Remove DC component:

[0076]

[0077] Apply window functions:

[0078]

[0079] Anti-aliasing filtering: Use a suitable low-pass filter to remove high-frequency interference.

[0080] To further implement the above technical solution, step S22, the method for calculating the spectrum using the Fast Fourier Transform algorithm, is as follows:

[0081]

[0082] in, Let N be the complex magnitude at index k after the Discrete Fourier Transform (FFT), where N is the number of FFT points and n is the discrete sampling point number. The signal is the preprocessed discretized voltage signal, and k is the spectral index;

[0083] Step S24, the extracted main frequency component phase is:

[0084]

[0085] Where, φ i The phase of the dominant frequency component, The main frequency component index is determined by selecting the item with the largest amplitude from the spectral component index.

[0086] like Figure 2 The three-dimensional diagram of Fourier transform unwrapping shown illustrates the complex spectral distribution structure of the acquired signal in the frequency domain space, consisting of the real and imaginary parts. This three-dimensional diagram can intuitively reflect the phase continuity of the dominant frequency component and the concentrated spectral energy characteristics.

[0087] like Figure 3 The schematic diagram of frequency domain phase spectrum extraction illustrates the process of determining the dominant frequency component and extracting its phase from the spectrum. The horizontal axis represents frequency, and the vertical axis represents the amplitude and phase change curves. This figure illustrates the key role of Fourier transform in avoiding the traditional phase entanglement problem and verifies that the method of the present invention can directly obtain absolute phase information.

[0088] To further implement the above technical solution, the principle upon which the absolute phase is obtained in step S3 is based:

[0089] The global spectral characteristics of Fourier transform can effectively avoid the phase entanglement problem. The phase of the dominant frequency component can directly reflect the particle position information without complex phase unwrapping processing. The phase continuity is guaranteed by the mathematical properties of Fourier transform, which theoretically eliminates the 2π phase jump problem in traditional methods. The natural unwrapping of the phase is achieved by utilizing the global information in the Fourier frequency domain.

[0090] The method for obtaining the absolute phase is as follows:

[0091]

[0092] The unwrap function is naturally achieved by the continuity characteristic of the Fourier transform.

[0093] In this embodiment, as Figure 4 In (a), the traditional phase unwrapping process typically includes: first, separating the complex voltage signal into real and imaginary parts using an orthogonal reference signal; then calculating the packaged phase, i.e., obtaining the phase value limited to the range [-π, π] using the arctangent function; followed by a complex gradient calculation and iterative unwrapping process to recover the true absolute phase value; such as Figure 4 In (b) of this invention, Fourier transform is used as the basic algorithm for phase unwrapping, which changes the traditional phase processing method and directly performs Fourier transform processing on the acquired complex voltage signal; the phase information of the main frequency component is extracted from the spectrum obtained by the transform; the absolute phase value is directly obtained by utilizing the continuity characteristics of the Fourier frequency domain phase representation, avoiding the traditional phase expansion processing and the 2π jump problem in the traditional method, making the positioning result more accurate and stable; by utilizing the frequency domain filtering characteristics of Fourier transform, noise interference can be effectively suppressed, and frequency domain processing allows selective processing of different frequency components. The phase information of the main frequency component has a better signal-to-noise ratio, thereby improving the stability of the system in noisy environments.

[0094] To further implement the above technical solution, the specific content of step S4, which involves constructing and training the bidirectional neural network model, is as follows:

[0095] S41. Training dataset construction: Using the multi-coil absolute phase obtained in step S3 as input and the true three-dimensional coordinates of the particles as output, sample pairs are formed.

[0096] In this embodiment, a sufficient number of training samples are obtained through finite element simulation and experimental calibration. Each set of samples contains the particle position coordinates and the corresponding coil phase value.

[0097] S42. Forward model training: a neural network forward model with input of particle coordinates and output of phase is constructed, mean square error is used as loss function, and weight is optimized by back propagation algorithm;

[0098] The input and output are defined as:

[0099]

[0100] where X represents the input vector composed of the absolute phases of m inductive coils, φ i represents the absolute phase of the i-th inductive coil, Y represents the real coordinates of the particle;

[0101] The loss function of the forward model is:

[0102]

[0103] where, represents the loss function of the forward model, N represents the total number of samples, represents the phase value predicted by the model, represents the real phase value;

[0104] S43. Weight migration: the learned weights in the forward model are migrated to the backward model as parameter initialization;

[0105] S44. Backward model training: taking multi-coil absolute phase as input and particle three-dimensional coordinates as output, using adaptive optimization algorithm for iterative training, to establish the mapping relationship from phase to coordinates;

[0106] The loss function of the backward model is:

[0107]

[0108] where, represents the loss function of the backward model, N represents the total number of samples, represents the predicted three-dimensional coordinates, represents the real three-dimensional coordinates;

[0109] Adam optimizer is used, learning rate is set to η, and Dropout ratio is p, which is used to suppress overfitting;

[0110] S45. Model verification and application: the independent test set is used to verify the backward model, and the trained backward neural network model is obtained to realize the input of actual collected phase data and output of particle three-dimensional coordinate position.

[0111] In the present embodiment, the present application adopts a bidirectional model collaborative training strategy to optimize the overall performance: first, train the forward model, and after the forward model converges, migrate the weights of the first several feature extraction layers to the backward model as parameter initialization, and randomly initialize the regression head, i.e., the output layer. The forward model is used to learn the mapping relationship between the particle coordinates and the phase distribution, and the backward model realizes the inverse mapping from the phase to the coordinates through transfer learning, as shown in Figure 5 The input layer of the forward model is the three-dimensional coordinate information of the particles, the hidden layer adopts a multi-layer fully connected structure, the number of layers and nodes is determined according to the complexity of the problem, each layer is connected with a batch normalization and an activation function to improve the nonlinear expression ability and convergence speed of the model, and the output layer is the main frequency phase value corresponding to each induction coil. The input of the backward model is the absolute phase value of each induction coil, and the output is the three-dimensional coordinate information of the particles. The backward model is specifically as follows:

[0112] Input layer: data preprocessing is performed, the phase mean and standard deviation calculated for the training set are normalized, and standardization is performed before inputting into the network;

[0113] The hidden layer includes a feature extraction module and a deep nonlinear mapping module. The feature extraction module adopts a multi-layer fully connected structure, is used to map the phase vector to a high-dimensional feature space, and is used to extract the relative coupling information between different coils and the spatial mode of the overall phase field. The deep nonlinear mapping module combines the shallow features and the deep features through a residual connection after the feature extraction is completed, retains the low-order phase coupling information, improves the generalization ability to the particle positions at different depths, and completes the nonlinear mapping from the phase features to the spatial coordinates:

[0114] Output layer: a linear mapping is adopted to directly output the coordinate value.

[0115] In order to further implement the above technical scheme, a material particle positioning and detection method based on Fourier main frequency phase inversion further includes: S6. Independent component analysis method is used to separate the independent phase components of different particles, multi-objective optimization algorithm is used to estimate the positions of multiple particles at the same time, and spatial filtering technology is used to suppress the coupling interference between particles.

[0116] In the present embodiment, step S6 is specifically as follows:

[0117] Independent component analysis: the multi-coil acquisition signal is composed into an observation matrix, and the independent phase components of different particles are separated by using the ICA method;

[0118] Multi-objective optimization: a target function for estimating the positions of multiple particles at the same time is constructed;

[0119]

[0120] Wherein, L represents the total loss function, P represents the number of particles, represents the pth predicted particle position coordinate, represents the pth real particle position coordinate, represents a regularization parameter, R represents an interference term constraint function for reducing mutual interference between particles;

[0121] Spatial filtering: filtering the phase field in the frequency domain or spatial domain, suppressing the coupling interference between adjacent particles, and improving the resolution.

[0122] A material particle positioning detection system based on Fourier main frequency phase inversion, based on a material particle positioning detection method based on Fourier main frequency phase inversion, comprising an electromagnetic induction device, a phase extraction module, an absolute phase acquisition module, a model construction and training module, and a particle position inversion module;

[0123] The electromagnetic induction device is used for collecting complex voltage signals of a plurality of induction coils.

[0124] The phase extraction module is used for pre-processing the complex voltage signal of each coil, and extracting the phase of the main frequency component through fast Fourier transform.

[0125] The absolute phase acquisition module is used for directly extracting the absolute phase from the frequency spectrum by using the global continuity feature of the main frequency component of the Fourier spectrum.

[0126] The model construction and training module is used for constructing a bidirectional neural network model and training based on an absolute phase data set, and establishing a mapping relationship between the phase and the three-dimensional coordinates of the particle.

[0127] The particle position inversion module is used for inputting the absolute phase values of each induction coil into the trained reverse neural network model to output the three-dimensional spatial coordinate position of the particle.

[0128] In order to further implement the above technical solutions, a material particle positioning detection system based on Fourier main frequency phase inversion further comprises a multi-particle detection module, which is used for separating independent phase components of different particles by using independent component analysis method, estimating multiple particle positions simultaneously by using multi-objective optimization algorithm, and suppressing the coupling interference between particles by using spatial filtering technology.

[0129] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same or similar parts of each embodiment can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the related parts can be referred to the method part.

[0130] The foregoing description of the disclosed embodiments enables a person skilled in the art to make or use the application. Modifications of these embodiments will occur to persons of skill in the art, and that the appended claims are intended to cover all such modifications that do not depart from the true spirit and scope of the application. Therefore, the application is not limited to the embodiments shown but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for locating and detecting material particles based on Fourier dominant frequency phase inversion, characterized in that, Includes the following steps: S1. Collect complex voltage signals from multiple induction coils using an electromagnetic induction device; S2. Preprocess the complex voltage signal of each coil and extract the phase of the main frequency component through fast Fourier transform; S3. Utilize the global continuity characteristic of the dominant frequency component of the Fourier spectrum to directly extract the absolute phase from the spectrum; S4. Construct a bidirectional neural network model and train it based on the absolute phase dataset to establish the mapping relationship between phase and particle three-dimensional coordinates; S5. Input the absolute phase values ​​of each induction coil into the trained reverse neural network model to output the three-dimensional spatial coordinates of the particle.

2. The material particle localization and detection method based on Fourier dominant frequency phase inversion according to claim 1, characterized in that, The electromagnetic induction device includes an excitation coil, an induction coil array, a signal conditioning circuit, and a data acquisition system. The excitation coil generates an alternating magnetic field at a preset frequency. The induction coil array contains multiple induction coils distributed around the detection area. The signal conditioning circuit preprocesses the induced signal, and the data acquisition system digitizes the signal.

3. The material particle localization and detection method based on Fourier dominant frequency phase inversion according to claim 1, characterized in that, The complex voltage signal acquired in step S1 includes a real part signal and an imaginary part signal. The real part signal reflects the in-phase component of the electromagnetic field, and the imaginary part signal reflects the quadrature component of the electromagnetic field. The complex voltage signal of each induction coil is represented as: ； in, Let be the continuous time-domain complex voltage signal of the i-th induction coil, where t is the time variable. Let i be the signal amplitude of the i-th coil. ω is the phase angle, and ω is the angular frequency.

4. The material particle localization and detection method based on Fourier dominant frequency phase inversion according to claim 1, characterized in that, The specific content of step S2 includes: S21. Preprocess the acquired complex voltage signal, including removing the DC component, applying a window function, and applying anti-aliasing filtering; S22. The spectrum of the preprocessed discretized voltage signal is calculated using the Fast Fourier Transform algorithm; S23. Determine the location of the dominant frequency component through spectrum analysis; S24. Extract the phase angle of the main frequency component.

5. The material particle localization detection method based on Fourier dominant frequency phase inversion according to claim 4, characterized in that, Step S22, the method for calculating the spectrum using the Fast Fourier Transform algorithm is as follows: ； in, Let N be the complex magnitude at index k after the Discrete Fourier Transform (FFT), where N is the number of FFT points and n is the discrete sampling point number. The signal is the preprocessed discretized voltage signal, and k is the spectral index; Step S24, the extracted main frequency component phase is: ； Where, φ i The phase of the dominant frequency component, The main frequency component index is determined by selecting the item with the largest amplitude from the spectral component index.

6. The material particle localization detection method based on Fourier dominant frequency phase inversion according to claim 1, characterized in that, Step S3, the method for obtaining the absolute phase is as follows: ； The unwrap function is naturally achieved by the continuity characteristic of the Fourier transform.

7. The material particle localization detection method based on Fourier dominant frequency phase inversion according to claim 1, characterized in that, Step S4, which involves constructing and training the bidirectional neural network model, includes the following steps: S41. Training dataset construction: Using the multi-coil absolute phase obtained in step S3 as input and the true three-dimensional coordinates of the particles as output, sample pairs are formed. S42. Forward Model Training: Construct a forward neural network model with particle coordinates as input and phase as output, using mean squared error as the loss function, and optimizing the weights through backpropagation algorithm; S43. Weight Transfer: Transfer the weights learned in the forward model to the backward model and use them as parameter initialization; S44. Reverse Model Training: Using the absolute phase of the multi-coil as input and the three-dimensional coordinates of the particles as output, an adaptive optimization algorithm is used for iterative training to establish a mapping relationship from phase to coordinates; S45. Model Validation and Application: The inverse model is validated using an independent test set. The trained inverse neural network model can output the three-dimensional coordinate position of the particle by inputting the actual phase data.

8. The material particle localization and detection method based on Fourier dominant frequency phase inversion according to claim 1, characterized in that, Also includes: S6. Independent phase components of different particles are separated by independent component analysis, multiple particle positions are estimated simultaneously using a multi-objective optimization algorithm, and spatial filtering is used to suppress coupling interference between particles.

9. A material particle localization and detection system based on Fourier dominant frequency phase inversion, characterized in that, A material particle localization detection method based on Fourier dominant frequency phase inversion according to any one of claims 1-8 includes an electromagnetic induction device, a phase extraction module, an absolute phase acquisition module, a model construction and training module, and a particle position inversion module. An electromagnetic induction device used to collect complex voltage signals from multiple induction coils; The phase extraction module is used to preprocess the complex voltage signal of each coil and extract the phase of the main frequency component through fast Fourier transform. The absolute phase acquisition module is used to extract the absolute phase directly from the spectrum by utilizing the global continuity characteristics of the Fourier spectrum's main frequency component. The model building and training module is used to build a bidirectional neural network model and train it based on the absolute phase dataset, establishing a mapping relationship between phase and particle three-dimensional coordinates; The particle position inversion module is used to input the absolute phase values ​​of each induction coil into the trained inverse neural network model to output the three-dimensional spatial coordinate position of the particle.

10. A material particle localization and detection system based on Fourier dominant frequency phase inversion according to claim 9, characterized in that, It also includes a multi-particle detection module, which uses independent component analysis to separate the independent phase components of different particles, uses a multi-objective optimization algorithm to estimate the positions of multiple particles simultaneously, and uses spatial filtering technology to suppress coupling interference between particles.

Images