A multi-frequency electromagnetic feature fusion abrasive grain identification method
By using multi-frequency series sensors and the Levenberg-Marquardt optimization algorithm, the problems of hardware parasitic parameters and nonlinear models in online oil monitoring of large mechanical equipment were solved, achieving high accuracy and real-time performance in abrasive particle identification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN ENG UNIV
- Filing Date
- 2026-06-08
- Publication Date
- 2026-07-31
AI Technical Summary
Existing technologies for online monitoring of oil in large mechanical equipment suffer from problems such as measurement distortion caused by deep coupling between hardware parasitic parameters and physical response, intermodulation interference during multi-frequency detection, difficulty in analytically solving nonlinear models, and poor convergence of conventional optimization algorithms, which affect the accuracy and real-time performance of abrasive particle identification.
A multi-frequency complex observation matrix is acquired using a multi-frequency series sensor. Parasitic parameter interference is removed by complex domain calibration of the hardware system. A multi-dimensional joint inversion objective function of the time harmonic field is constructed. The Levenberg-Marquardt optimization algorithm is used for iterative optimization to extract the equivalent diameter, conductivity and relative permeability of the abrasive particles.
It achieves a robust environment against hardware influences, high-precision decoupling of multiple physical properties of abrasive particles, and global convergence and extreme speed of the solution process, thereby improving the accuracy and real-time performance of abrasive particle identification.
Smart Images
Figure CN122330253B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of signal processing, sensor information fusion, and intelligent monitoring of mechanical conditions, and in particular to a method for identifying abrasive particles by fusing multi-frequency electromagnetic features. Background Technology
[0002] In online oil monitoring of large mechanical equipment, electromagnetic induction sensors are widely used to capture metal particles in lubricating oil. However, existing signal processing and parameter identification methods suffer from the following serious theoretical and technical shortcomings: 1. The deep coupling between hardware parasitic parameters and physical response leads to absolute measurement distortion. In practical detection systems, the weak induced electromotive force output by the sensor coil must be conditioned by complex front-end analog circuitry (including preamplifiers, bandpass filters, etc.). These hardware circuits inevitably introduce uncertain gain amplification factors. A and the system's inherent phase shift i Meanwhile, geometric manufacturing errors in the coil itself can also cause the shape factor to deviate from the theoretical value. Most existing technologies directly utilize the amplitude or phase of the measured voltage for threshold determination or artificial neural network training, failing to completely separate the "hardware modulation term" from the "abrasive intrinsic response term" at the physical mechanism level. This method, lacking absolute physical quantity calibration, makes the recognition algorithm extremely fragile; once the circuit experiences temperature drift or the sensor probe is replaced, the original recognition model becomes invalid. Secondly, existing technologies often face the challenge of intermodulation interference at the hardware level when attempting to introduce multi-frequency detection. If a multi-frequency mixed current is directly applied to the same set of excitation coils, electromagnetic fields of different frequencies will nonlinearly superimpose in the same physical space. Due to the complexity of the magnetic field distribution in the detection area and the nonlinear characteristics that ferromagnetic materials may exhibit, severe interference noise will be generated between the frequency components. This not only exponentially increases the complexity of the back-end signal processing circuit but also significantly reduces the signal-to-noise ratio for extracting signals from tiny abrasive particles. Furthermore, to improve detection sensitivity, existing sensors often increase the sensitivity field strength by reducing the inner diameter of the coil or increasing the number of turns. However, this approach significantly increases the signal pulse width when particles pass through, leading to severe signal overlap problems at high abrasive particle concentrations, which in turn affects the accuracy of particle counting. Due to the lack of an architecture that can effectively distribute frequency characteristics in physical space, existing technologies struggle to acquire the complete electromagnetic polarization trajectory of abrasive particles as a function of frequency at a single monitoring node, limiting the in-depth identification of the properties of heterogeneous abrasive particles under complex wear conditions.
[0003] 2. The high nonlinearity of the forward analytical model hinders direct analytical solutions. According to the time-harmonic electromagnetic field polarization theory, the complex magnetic susceptibility χ of metal particles under an alternating magnetic field a It contains complex wavenumbers kAnd the extremely complex nonlinear mathematical expression of the spherical Bessel function. In this expression, the particle diameter... d Electrical conductivity s and relative permeability m r These elements are intertwined within trigonometric functions and complex algebraic expressions. This deep nonlinear coupling means that, given the observed complex voltage values, it is impossible to directly derive the analytical inverse solution of the parameters through algebraic transformations. Traditional linearization approximation methods (such as Taylor first-order expansions) produce significant truncation errors when dealing with nonferromagnetic particles dominated by the high-frequency skin effect, leading to material identification results that deviate severely from the true values.
[0004] 3. The curse of convergence in conventional optimization algorithms for solving complex problems with multiple parameters. To address the problem of inverting nonlinear equations, some studies have attempted to introduce conventional optimization algorithms (such as the steepest descent method or the Newton-Raphson method). However, due to the complex non-convex characteristics of the objective function in the abrasive particle inversion problem (multiple minima coexisting with "canyons" and "plains"), the steepest descent method is prone to "sawtooth" oscillations near the optimal solution, resulting in extremely slow convergence or even stagnation. While the Newton method exhibits second-order convergence near the minima, it requires the initial guess to be extremely close to the true solution and necessitates the calculation of the complex Hessian matrix. Once the Hessian matrix is non-positive definite, the Newton method will diverge directly. Lacking an iterative inversion framework that can balance global search robustness with local convergence speed, existing optimization methods often get trapped in local optima, leading to catastrophic misjudgments of the output abrasive particle diameter and material parameters. Summary of the Invention
[0005] This invention proposes a multi-frequency electromagnetic feature fusion abrasive particle identification method. It acquires a multi-frequency complex observation matrix using a multi-frequency series sensor, removes parasitic parameter interference through hardware system complex domain calibration, constructs a time-harmonic field multi-dimensional joint inversion objective function, and uses the Levenberg-Marquardt optimization algorithm to iteratively optimize and invert the extraction of the abrasive particle's equivalent diameter, conductivity, and relative permeability. This addresses the problems in existing abrasive particle identification methods, such as measurement distortion caused by hardware parasitic parameter coupling, the inability to directly solve the highly nonlinear time-harmonic field model analytically, and the poor convergence of conventional optimization algorithms leading to misjudgment of abrasive particle parameters.
[0006] A multi-frequency electromagnetic feature fusion abrasive particle identification method includes the following steps: S1. Obtain the multi-frequency complex observation matrix of unknown abrasive particles through a multi-frequency series sensor; S2. Perform hardware system complex domain absolute calibration on the multi-frequency complex observation matrix, remove hardware parasitic parameter interference, and obtain the target observation matrix of the intrinsic electromagnetic polarization characteristics of abrasive particles. S3. Construct a multidimensional joint inversion objective function based on time-harmonic electromagnetic field theory; S4. The Levenberg-Marquardt optimization algorithm is used to iteratively optimize the multidimensional joint inversion objective function and extract the physical parameters of unknown abrasive particles. S5, the equivalent diameter, intrinsic conductivity, and relative permeability of the output abrasive grains.
[0007] Furthermore, in S1, the multi-frequency complex observation matrix is the measured complex voltage observation matrix. M x Its expression is:
[0008] M x Through multi-frequency series sensors N Each detection unit applies an excitation frequency. f 1, f 2, ..., f N Extract the extreme values of the in-phase components of transient pulses at each frequency. X n and orthogonal component extrema Y n The following is constructed: n This is the serial number of the detection unit. N This represents the total number of detection units.
[0009] Furthermore, S2 includes the following steps: S21. Select a reference sample with known material and size, and obtain its reference complex electromagnetic signal and theoretical reference response characteristics at each excitation frequency; S22. Based on the measured reference complex electromagnetic signal and the theoretical reference response characteristics, construct the system comprehensive compensation coefficient; S23. The measured complex voltage observation matrix is adjusted using the system's comprehensive compensation coefficient. M x Data cancellation and feature reconstruction are performed to obtain the target observation matrix.
[0010] Furthermore, S3 includes the following steps: S31. Based on the time-harmonic electromagnetic field theory, define the forward mapping operator. F (P, oh n Given abrasive particle parameter vector P, its frequency oh n Predicted physical response D prd,n for:
[0011] in, D prd,n middle prd It is an abbreviation of predicted, meaning D prd,n It is composed of the forward mapping operator F (P, oh n The theoretical prediction value obtained from the calculation, n It is a subscript index, corresponding to the first... n One excitation frequency, complex wave number , Angular frequency, equivalent radius a = d / 2, d The equivalent diameter of the abrasive grains. s For electrical conductivity, m r The relative permeability, m 0 is the permeability of free space. k n For the first n The complex wave number corresponding to each excitation frequency; S32, will N The complex residual is decomposed into 2 N The real residual vector e(P) of dimension:
[0012] Where Re(·) is the complex real part extraction operator, and Im(·) is the complex imaginary part extraction operator. D prd,N (P) is the first N A predicted complex response, D obs,N (P) is the first N The measured complex response, where obs is an abbreviation for observed, indicates... D obs,N (P) is a complex signal obtained through actual measurement by a sensor. N It is a subscript, corresponding to the first... N Given several excitation frequencies, a global nonlinear objective function is constructed based on the least squares criterion to quantify model errors. E (P):
[0013] Where, e(P) T For the transpose of e(P), i For the summation index, for the summation index, for the summation index of 2 N Sum of the residual elements e i (P) 2 The residual vector is the firsti The core of the inversion is to solve P. * =arg min P E (P), P * arg min is the optimal parameter vector obtained from the inversion solution. P For mathematical operators, it means to make the objective function E (P) The independent variable P that reaches its minimum value.
[0014] Furthermore, in S4, the Levenberg-Marquardt optimization algorithm employs a high-precision central difference method for numerical approximation:
[0015] Among them, J i,j The Jacobian matrix is the first... i row and number j Column elements, The residual vector is the first i Each component e i For the parameter vector of the first j Each component First-order partial derivative, P k For the first k The parameter vector for the next iteration is a vector containing all the parameters to be optimized, u j For the first j A unit vector in each parameter direction, Δ P j For adaptive difference step size, k For the number of iterations, When the parameter vector is at the th j When the first parameter is positively disturbed in one direction, the second parameter is... i The calculated value of each error term, When the parameter vector is at the th j When the first parameter is negatively disturbed in one direction, the second parameter is... i The calculated value of each error term.
[0016] Furthermore, in S4, the Levenberg-Marquardt optimization algorithm controls the iteration through a non-negative damping factor λ, with the parameter update amount ΔP... k Obtained through the regularized normal equation:
[0017] Among them, J k For the first k Jacobian matrix of the next iteration For J k transpose, for A diagonal matrix consisting of the diagonal elements of P, e(P) k ) is the first k In each iteration, the residual vector is formed by the difference between the predicted response and the observed target response. If the objective function error decreases after iteration, the damping factor λ is decreased; if the error increases, the damping factor λ is increased.
[0018] Furthermore, in S4, the iterative loop continues until any of the following strict stopping criteria are met: Gradient norm of the objective function ; relative rate of change of parameters ; Reaching the maximum allowed number of iterations K max , in, J in the gradient vector T The maximum absolute value of each component in e This is the gradient convergence threshold. This is the ratio of the norm of the parameter update in this iteration to the norm of the current parameter vector. The convergence threshold for parameter variation. K max This represents the maximum allowed number of iterations.
[0019] Furthermore, in S5, after convergence and shutdown, the final optimal parameter vector P is output. * The equivalent diameter of the output abrasive grains d Intrinsic conductivity s and relative permeability m r .
[0020] A storage medium storing a computer program, which, when executed by a processor, implements the above-described multi-frequency electromagnetic feature fusion abrasive particle identification method.
[0021] A terminal includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described multi-frequency electromagnetic feature fusion abrasive particle identification method.
[0022] Compared with the prior art, the present invention achieves significant beneficial effects through the above technical solution: 1. Completely broke through hardware bottlenecks, achieving a leap in environmental robustness. By introducing a system error compensation mechanism based on the reference response, this method successfully cancels out the phase shift, gain, and geometric deviations introduced by the sensor hardware during computation. The input data processed by the inversion algorithm is the intrinsic physical response, reducing the impact of temperature drift, component aging, and probe replacement on the material identification results.
[0023] 2. High-precision joint decoupling of multiple physical properties of abrasive particles was achieved. To address the parameter interleaving phenomenon in abrasive signals, this method does not rely on any empirical formulas or scalar thresholds, but instead directly establishes a rigorous 2D model within the complex plane. N A real residual matrix. Utilizing the evolution of the real and imaginary parts of complex impedance across different frequency bands as constraints, the algorithm can simultaneously output the diameter, conductivity, and permeability of abrasive particles, truly achieving precise quantitative separation of the properties of non-ferromagnetic particles (such as distinguishing between copper and brass) and ferromagnetic particles. This is achieved by unifying and simplifying the morphology to an equivalent diameter. d The algorithm avoids the computational cost trap of attitude evolution, ensuring high efficiency in recognition.
[0024] 3. It endows the solution process with excellent global convergence and extreme speed. To address the extremely non-convex objective function terrain caused by the complex Bessel model of time-harmonic electromagnetic fields, the Levenberg-Marquardt (LM) core algorithm introduced in this invention exhibits unparalleled mathematical superiority. Its adaptively controlled damping factor λ allows the algorithm to robustly approach the valley (avoiding divergence) like gradient descent when the initial guess deviates significantly from the true solution; and when approaching the global optimum, it smoothly transitions to the Gauss-Newton method, achieving extremely rapid quadratic convergence dominated by the Hessian matrix. This algorithm design fundamentally solves the problem of traditional optimization methods easily getting trapped in local minima or oscillatory stagnation in the complex domain. The inversion time of a single particle attribute is compressed to the millisecond level, fully meeting the extremely high real-time requirements of online monitoring of industrial oil. Attached Figure Description
[0025] Figure 1 The diagram shows the multi-frequency cascade structure and the spatial frequency domain mapping mechanism, where, Figure 1 (a) is a diagram of the overall architecture of a multi-frequency sensor with N detection units connected in series. Figure 1 (b) is a schematic diagram of the spatiotemporal feature mapping principle; Figure 1 (c) is a diagram of the construction process of the multidimensional complex observation matrix; Figure 2 This is a flowchart of a multi-frequency electromagnetic feature fusion abrasive particle identification method according to the present invention. Detailed Implementation
[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0027] The algorithm framework of this invention first briefly relies on a multi-frequency series hardware structure to acquire basic data. This structure includes a non-magnetic insulated flow tube serving as a sensor channel and multiple detection units arranged equidistantly in series along the axial direction of the non-magnetic insulated flow tube. Each detection unit is a three-coil structure wound around the non-magnetic insulated flow tube, consisting of excitation coils on both sides and an induction coil in the middle. The multiple detection units are physically independent, and each unit is subjected to a different excitation frequency. The excitation coil is energized with an anti-phase harmonic current to excite an alternating main magnetic field. The induction coil is used to collect the secondary scattered field signal generated when abrasive particles pass through the detection area and outputs a complex induced voltage signal. Subsequently, the focus is fully expanded to the calibration and stripping of the characteristic complex plane, the mathematical reconstruction of the forward observation model, and the nonlinear iterative optimization mechanism in high-dimensional space. The specific invention content and technical solution are as follows: 1. Acquisition of basic data (importing multi-frequency complex observation matrix) The input source for this method is a multidimensional complex observation matrix. It utilizes a pre-deployed multi-frequency cascaded sensor (containing...) N Each detection unit is subjected to an excitation frequency. f 1, f 2, ..., f N When unknown abrasive particles pass through the hardware channel, the system extracts the in-phase component extrema of transient pulses at each frequency through quadrature phase-sensitive demodulation. X n and orthogonal component extrema Y n Therefore, the basic input data for the algorithm is constructed—the measured complex voltage observation matrix. M x :
[0028] The matrix contains the holographic physical fingerprints of particles under different time harmonic energy fields, but the data is still deeply contaminated by the parasitic parameters of the front-end hardware.
[0029] 2. Hardware system complex domain absolute calibration and interference removal mechanism To address the interference from parasitic parameters introduced by the sensor coil and front-end analog circuit, this method introduces a system error compensation mechanism before feature extraction to eliminate the modulation of the real physical signal by hardware gain and inherent phase shift.
[0030] Step 2.1: Obtaining the reference electromagnetic response A reference sample with known material and dimensional characteristics is selected, and its reference complex electromagnetic signals at various excitation frequencies are acquired using a pre-set multi-frequency series sensor. Based on the electromagnetic theory of alternating magnetic fields, the theoretical reference response characteristics of the reference sample under ideal conditions are determined.
[0031] Step 2.2: Construction of system compensation coefficients and signal restoration Based on the measured reference complex electromagnetic signal and the theoretical reference response characteristics, a system comprehensive compensation coefficient including the hardware link transfer function and spatial shape deviation is constructed.
[0032] Step 2.3: Target signal restoration and feature reconstruction For the measured complex voltage observation matrix of any unknown abrasive grain, the algorithm performs data cancellation and feature reconstruction by calling the aforementioned system comprehensive compensation coefficients. This step directly eliminates the influence of parasitic parameters of the hardware system, outputting a target observation matrix that eliminates measurement distortion. This matrix only represents the intrinsic electromagnetic polarization characteristics of the unknown abrasive grain governed by physical laws, serving as a pure input source for subsequent multi-dimensional iterative identification.
[0033] 3. Construction of the multidimensional joint inversion objective function After obtaining clean observation data D obs Subsequently, the core task of this invention is to find a set of optimal abrasive intrinsic parameter vectors P = [ d , s , m r ] T This allows the response value predicted based on the theoretical model to approximate the observed value.
[0034] Step 3.1: Encapsulation of the forward prediction model Based on time-harmonic electromagnetic field theory, the forward mapping operator is defined. F (P, oh n For a given parameter vector P, its frequency... oh n Predicted physical response D prd,n for:
[0035] In the formula, the complex wave number equivalent radius a = d / 2.
[0036] Step 3.2: Realize the residual vector and the objective function Since traditional nonlinear optimization algorithms have the most mature theoretical guarantees in the real number domain, this method will... N The complex residual is decomposed into 2 N The real residual vector e(P) of dimension:
[0037] Based on the least squares criterion, a global nonlinear objective function is constructed to quantify model error. E (P):
[0038] The core of inversion is solving P. * = arg min P E (P).
[0039] 4. Core Iterative Decoupling Mechanism Based on Levenberg-Marquardt (LM) Algorithm Given the objective function E (P) Due to its highly nonlinear nature and the presence of extreme "canyon" terrain, this invention innovatively employs the Levenberg-Marquardt (LM) algorithm as the core solver. The LM algorithm cleverly combines the global robustness of gradient descent with the local rapid convergence of the Gauss-Newton method.
[0040] Step 4.1: Dynamic solution of the Jacobian matrix In the k In this iteration, the algorithm needs to calculate the residual vector with respect to the parameter vector P. k The first-order partial derivative matrix, i.e., the Jacobian matrix. .
[0041] Because the formula for complex magnetic susceptibility is applicable d , s , m r The analytical derivative is extremely complex and easily affected by truncation errors. This method uses a high-precision central difference method for numerical approximation.
[0042] Where u j For the first j A unit vector in each parameter direction, Δ P j For adaptive differential step size.
[0043] Step 4.2: Adaptive update of damping factor (Marquardt strategy) The core of the LM algorithm lies in the introduction of a non-negative damping factor λ. The iterative update amount of the parameters ΔP... k The following regularized normal equation is obtained by solving:
[0044] The trust region modulation strategy of this invention is as follows: Calculate the updated trial solution and the change in the objective function .
[0045] (1) If (Error decrease): This indicates that the current iteration step was successful, and the local linearization assumption holds. The algorithm accepts the update. and reduce the damping factor (e.g., make This makes the algorithm more inclined to use the Gauss-Newton method, which has a second-order convergence speed, in the next step, thus accelerating the approach to the bottom.
[0046] (2) If (Increased error): This indicates excessive nonlinearity, and the trial solution has escaped the trust region. The algorithm refuses to update (hold). ), and significantly increase the damping factor (e.g., make At this point, the diagonal elements of the matrix are absolutely dominant, and the update equation degenerates into... This means performing a conservative search with small steps along the steepest descent direction, ensuring the absolute convergence of the algorithm in harsh terrain.
[0047] Step 4.3: Convergence Determination and Physical Parameter Reconstruction Output The iterative loop continues until any of the following strict halting criteria are met: (1) Gradient norm of the objective function (Default 10) -8 ).
[0048] (2) Relative rate of change of parameters (Default 10) -8 ).
[0049] (3) Reach the maximum allowed number of iterations (Default 500 times).
[0050] After the algorithm converges and stops, it outputs the final optimal parameter vector P. * The system software interface will synchronously display the equivalent diameter of the decoupled abrasive particles. d (Accurate to the micrometer level), intrinsic conductivity s (Used to determine the specific metal alloy grade) and relative permeability m r (Used to determine ferromagnetic / nonferromagnetic properties).
[0051] This embodiment takes a ship's main engine oil online monitoring system with a set of three-frequency series sensors (the frequencies are set to 50kHz, 100kHz, and 150kHz respectively) as an example to explain in detail how to use the software algorithm system of the present invention to decouple and inversely deduce the absolute properties of an unknown abrasive grain in real time.
[0052] Step 1: System preheating and baseline calibration (obtaining...) C n ) In the initial system startup with clean oil, a standard reference sample of known material and size is introduced. The system's host computer software calls the forward analytical model to calculate the theoretical physical response of the sample at three frequency points. Simultaneously, the underlying hardware captures the three complex voltage peak matrices output when the sample passes through the sensor. Based on the measured reference matrix and the theoretical physical response, the algorithm control module constructs the system's comprehensive compensation coefficients and permanently caches them in the software configuration library, thus completing the recording and isolation of hardware phase delay and gain disturbances.
[0053] Step 2: Online capture and stripping of unknown abrasive grain signals When the main unit is powered off and a piece of abrasive material of unknown origin passes through the pipe, the hardware system outputs a measured voltage matrix. The algorithm immediately retrieves the cached system comprehensive compensation coefficients and performs decoupling and cancellation operations on the measured matrix to obtain the absolute intrinsic observation matrix of the unknown abrasive particle, providing clean feature input for subsequent identification.
[0054] Step 3: Initialization and High-Speed Optimization Iteration of the LM Algorithm The algorithm sets a general-purpose initial guess vector in the parameter space. and initialize the LM damping factor. .
[0055] Entering the core iteration loop (the first iteration) k Second-rate): First, based on the current situation The predicted response of the three frequency bands was calculated using the time-harmonic field complex magnetic susceptibility formula. .
[0056] Subsequently, the predicted values and absolute observed values were calculated. The 6-dimensional real residual vector between (These correspond to the real and imaginary differences of the three frequency bands, respectively).
[0057] Calculate using the central difference method Jacobian partial derivative matrix .
[0058] Construct and solve the incremental equations with Marquardt damping terms: .
[0059] Calculate the error after the trial step. If the error decreases, accept the step size. and will The step size is reduced to one-tenth of its original value (to accelerate convergence); if the error increases, the step size is rejected, and the error is... Magnify tenfold (to enhance optimization stability).
[0060] Step 4: Converge Output After approximately 12 millisecond-level rapid iterations, the gradient norm of the objective function plummeted to... The following conditions have triggered a shutdown.
[0061] The algorithm finally outputs a converged solution P. * Equivalent diameter electrical conductivity relative permeability .
[0062] Based on the inversion data, the host computer expert system accurately determined that the abrasive particles were "148-micron 304 stainless steel debris", thereby guiding maintenance personnel to conduct targeted inspections of the wear condition of the hydraulic pump plunger.
[0063] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.
Claims
1. A multi-frequency electromagnetic feature fusion abrasive particle identification method, characterized in that, Includes the following steps: S1. Obtain the multi-frequency complex observation matrix of unknown abrasive particles through a multi-frequency series sensor; S2. Perform hardware system complex domain absolute calibration on the multi-frequency complex observation matrix, remove hardware parasitic parameter interference, and obtain the target observation matrix of the intrinsic electromagnetic polarization characteristics of abrasive particles. S3. Construct a multidimensional joint inversion objective function based on time-harmonic electromagnetic field theory, including the following steps: S31. Based on the time-harmonic electromagnetic field theory, define the forward mapping operator. F (P, ω n Given abrasive particle parameter vector P, its frequency ω n Predicted physical response D prd,n for: in, D prd,n middle prd It is an abbreviation of predicted, meaning D prd,n It is composed of the forward mapping operator F (P, ω n The theoretical prediction value obtained from the calculation, n It is a subscript index, corresponding to the first... n One excitation frequency, complex wave number , Angular frequency, equivalent radius a = d / 2, d The equivalent diameter of the abrasive grains. σ For electrical conductivity, μ r The relative permeability, μ 0 is the permeability of free space. k n For the first n The complex wave number corresponding to each excitation frequency; S32, will N The complex residual is decomposed into 2 N The real residual vector e(P) of dimension: Where Re(·) is the complex real part extraction operator, and Im(·) is the complex imaginary part extraction operator. D prd,N (P) is the first N A predicted complex response, D obs,N (P) is the first N The measured complex response, where obs is an abbreviation for observed, indicates... D obs,N (P) is a complex signal obtained through actual measurement by a sensor. N It is a subscript, corresponding to the first... N Given several excitation frequencies, a global nonlinear objective function is constructed based on the least squares criterion to quantify model errors. E (P): Where, e(P) T For the transpose of e(P), i For the summation index, for the summation index, for the summation index of 2 N Sum of the residual elements e i (P) 2 The residual vector is the first i The core of the inversion is to solve P. * =arg min P E (P), P * argmin is the optimal parameter vector obtained by inversion solution. P For mathematical operators, it means to make the objective function E (P) The independent variable P that reaches its minimum value; S4. The Levenberg-Marquardt optimization algorithm is used to iteratively optimize the multidimensional joint inversion objective function and extract the physical parameters of unknown abrasive particles. S5, the equivalent diameter, intrinsic conductivity, and relative permeability of the output abrasive grains.
2. The multi-frequency electromagnetic feature fusion abrasive particle identification method according to claim 1, characterized in that, In S1, the multi-frequency complex observation matrix is a real measured complex voltage observation matrix M x The expression is: M x Through multi-frequency series sensors N Each detection unit applies an excitation frequency. f 1, f 2, ..., f N Extract the extreme values of the in-phase components of transient pulses at each frequency. X n and orthogonal component extrema Y n The following is constructed: n This is the serial number of the detection unit. N This represents the total number of detection units.
3. The multi-frequency electromagnetic signature fusion abrasive particle identification method of claim 2, wherein, S2 includes the following steps: S21. Select a reference sample with known material and size, and obtain its reference complex electromagnetic signal and theoretical reference response characteristics at each excitation frequency; S22. Based on the measured reference complex electromagnetic signal and the theoretical reference response characteristics, construct the system comprehensive compensation coefficient; S23, the system is integrated compensation coefficient to the measured complex voltage observation matrix M x Data cancellation and feature reconstruction are performed to obtain a target observation matrix.
4. The multi-frequency electromagnetic signature fusion abrasive particle identification method of claim 1, wherein, In S4, the Levenberg-Marquardt optimization algorithm uses a high-precision central difference method for numerical approximation: Among them, J i,j The first Jacobian matrix i row and number j Column elements, The residual vector is the first i Each component e i For the parameter vector of the first j Each component First-order partial derivative, P k For the first k The parameter vector for the next iteration is a vector containing all the parameters to be optimized, u j For the first j A unit vector in each parameter direction, Δ P j For adaptive difference step size, k For the number of iterations, When the parameter vector is at the th j When the first parameter is positively disturbed in one direction, the second parameter is... i The calculated value of each error term, When the parameter vector is at the th j When the first parameter is negatively disturbed in one direction, the second parameter is... i The calculated value of each error term.
5. The multi-frequency electromagnetic signature fusion abrasive particle identification method of claim 4, wherein, In S4, the Levenberg-Marquardt optimization algorithm controls the iteration through a non-negative damping factor λ, and the iterative update of the parameters ΔP k The normal equation is obtained by regularization: Among them, J k For the first k Jacobian matrix of the next iteration For J k transpose, for A diagonal matrix consisting of the diagonal elements of P, e(P) k ) is the first k In each iteration, the residual vector is formed by the difference between the predicted response and the observed target response. If the objective function error decreases after iteration, the damping factor λ is decreased; if the error increases, the damping factor λ is increased.
6. The multi-frequency electromagnetic signature fusion abrasive particle identification method of claim 5, wherein, In S4, the iterative loop continues until any of the following strict stopping criteria are met: Gradient norm of objective function ; Parameter relative change rate ; reaching the maximum allowed number of iterations K max , in, J in the gradient vector T The maximum absolute value of each component in e This is the gradient convergence threshold. This is the ratio of the norm of the parameter update in this iteration to the norm of the current parameter vector. The convergence threshold for parameter variation. K max This represents the maximum allowed number of iterations.
7. The multi-frequency electromagnetic signature fusion abrasive particle identification method of claim 6, wherein, In S5, after convergence and shutdown, the final optimal parameter vector P is output. * The equivalent diameter of the output abrasive grains d Intrinsic conductivity σ and relative permeability μ r .
8. A storage medium having stored thereon a computer program, characterized in that When the computer program is executed by the processor, it implements the multi-frequency electromagnetic feature fusion abrasive particle identification method according to any one of claims 1-7.
9. A terminal, characterized by comprising: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the multi-frequency electromagnetic feature fusion abrasive particle identification method according to any one of claims 1-7.