An ultrasonic particle size distribution inversion method for suppressing the influence of particle shape

Abstract

This invention relates to the field of particle size measurement technology, and particularly to an ultrasonic particle size distribution inversion method that suppresses the influence of particle shape. The method includes: constructing a standardized attenuation spectrum vector; establishing an ultrasonic frequency domain response matrix for a preset particle geometry, jointly decomposing and extracting common and differential response components, constructing a shape-equivalent forward modeling matrix and a shape difference constraint matrix, and extracting particle morphology feature vectors from the attenuation spectrum vector; constructing a particle size distribution inversion objective function based on the above matrix and feature vectors, including data fitting terms, smoothing constraint terms, and shape robustness constraint terms, adaptively adjusting the frequency channel weights and / or shape constraint penalty intensity using the morphology feature vectors; iteratively solving with non-negative constraints to obtain the shape-equivalent particle size distribution, and outputting characteristic particle size parameters, shape sensitivity indices, and reliability evaluation results. This invention separates particle size and morphology contributions from the mechanistic perspective, adaptively suppresses shape interference, and improves the accuracy and reliability of the inversion.

Description

Technical Field

[0001] This invention relates to the field of particle size measurement technology, and in particular to an ultrasonic particle size distribution inversion method that suppresses the influence of particle shape. Background Technology

[0002] Ultrasonic attenuation spectroscopy detects the frequency-dependent attenuation of ultrasonic waves as they penetrate a particle suspension system. Combined with an appropriate forward acoustic scattering model and mathematical inversion algorithm, it can obtain the particle size distribution and concentration information. This method offers significant advantages such as being non-contact, requiring no dilution, having strong penetration, and enabling real-time online measurement. Therefore, it is widely used in numerous industrial and scientific research fields, including chemical crystallization, pharmaceutical grinding, mineral slurries, food emulsions, and nanomaterials, for online particle size characterization and process quality control.

[0003] However, ultrasonic attenuation signals are extremely sensitive to particle geometry. Currently practical ultrasonic particle size inversion methods are almost all based on the assumption of ideal spherical particles, such as those based on ECAH theory or simplified acoustic attenuation models. When the actual particle shape deviates from spherical, exhibiting needle-like, plate-like, rod-like, polyhedral, or irregular shapes, its acoustic scattering and absorption characteristics differ significantly from those of a sphere of the same volume. In this case, forcibly applying a spherical forward model will lead to severe distortion of the obtained particle size distribution, resulting in false peaks, particle size shifts, or distribution broadening distortions, failing to provide accurate quantitative data for process control and quality evaluation.

[0004] To address the problem of particle shape interference, existing technologies have made some explorations, but the effects are limited: (1) Establishing special acoustic scattering models for specific shapes (such as elongated ellipsoids, oblate ellipsoids, and cylinders), but such models have complex mathematical forms, high computational costs, and require prior knowledge of particle shape type and axis ratio, making them difficult to apply to industrial field systems with variable or unknown morphology. (2) Obtaining morphology parameters using offline or side-by-side equipment such as microscopic imaging, and then correcting the ultrasonic inversion process, not only destroys the core advantage of in-situ online measurement by ultrasonic method, but also the image method has limited sampling volume, making it difficult to reflect the overall morphological statistical characteristics. (3) Introducing empirical shape factors or the concept of equivalent diameter, and adjusting the inversion model by fixing correction coefficients, but this method lacks adaptability. When the particle morphology changes due to changes in raw material batches or crystal morphology, its prediction accuracy drops sharply and its robustness is insufficient. (4) A few studies have attempted to use purely data-driven models (such as deep neural networks) to directly map particle size distribution from decay spectrum and implicitly learn shape influence. However, such methods have poor physical interpretability, extremely weak generalization ability under morphological conditions outside the training data distribution, and the reliability of inversion results cannot be guaranteed. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide an ultrasonic particle size distribution inversion method that suppresses the influence of particle shape, comprising: S1: Obtain the ultrasonic response signal of the particle suspension system under test within a predetermined frequency range, and construct a standardized attenuation spectrum vector based on the ultrasonic response signal; S2: Establish ultrasonic frequency domain response matrices for several preset particle geometries, perform joint decomposition on each ultrasonic frequency domain response matrix, extract common response components that are stable across different particle geometries and differential response components caused by changes in particle geometry, construct a shape equivalent forward modeling matrix based on the common response components, construct a shape difference constraint matrix based on the differential response components, and extract particle morphology feature vectors from the standardized attenuation spectrum vector; S3. Based on the standardized attenuation spectrum vector, the shape equivalent forward modeling matrix, the shape difference constraint matrix, and the particle morphology feature vector, a particle size distribution inversion objective function is constructed. The particle size distribution inversion objective function includes at least a data fitting term, a smoothing constraint term, and a shape robustness constraint term. The particle morphology feature vector is used to adaptively adjust at least one of the frequency channel weights in the data fitting term and the penalty intensity in the shape robustness constraint term. S4. Iteratively solve the objective function of particle size distribution inversion with non-negative constraints to obtain the shape-equivalent particle size distribution of the particle suspension system under test, and output the characteristic particle size parameters, shape sensitivity index and inversion credibility evaluation results based on the shape-equivalent particle size distribution.

[0006] Preferably, step S1 includes: S11: Under the same measurement path and measurement parameters, collect the sample ultrasonic signal of the particle suspension system to be tested and the reference ultrasonic signal of the reference medium, respectively. S12. Perform frequency domain transformation on the ultrasonic signal of the sample and the ultrasonic signal of the reference to obtain the sample amplitude spectrum and the reference amplitude spectrum; S13. Calculate the additional attenuation spectrum caused by particles based on the sample amplitude spectrum and the reference amplitude spectrum; S14. Perform outlier removal, smoothing, noise reduction, and standardization on the additional attenuation spectrum to form the standardized attenuation spectrum vector.

[0007] Preferably, in step S2, establishing the ultrasonic frequency domain response matrix includes: S211: Preset at least three types of particle geometry and determine the range of shape parameter values ​​for each particle geometry; S212: Calculate the theoretical ultrasonic response for each type of particle geometry under preset particle size discrete nodes and predetermined frequency sampling nodes; S213: Arrange the theoretical ultrasonic responses of the same particle geometry at each particle size discrete node and each frequency sampling node according to the frequency dimension and particle size dimension to form the corresponding ultrasonic frequency domain response matrix. S214: Perform dimensional unification and normalization on each ultrasonic frequency domain response matrix to eliminate amplitude scale differences between different particle geometries.

[0008] Preferably, in step S2, the ultrasonic frequency domain response matrices are jointly decomposed and common response components and differential response components are extracted, including: S221: Align the ultrasonic frequency domain response matrices corresponding to the geometry of each particle according to the same frequency dimension and the same particle size dimension, and combine them to form a joint response matrix; S222: Perform subspace decomposition on the joint response matrix to obtain multiple response components sorted by contribution; S223: Calculate the projection consistency index and stability index of each response component in the response matrix corresponding to different particle geometries, and determine the response components whose projection consistency index is higher than the first preset threshold and whose stability index is higher than the second preset threshold as common response components. S224: Identify the remaining response components that were not identified as common response components as differential response components; S225: Construct a common response subspace from the common response components, and construct a differential response subspace from the differential response components.

[0009] Preferably, constructing a shape equivalent forward modeling matrix based on the common response components and constructing a shape difference constraint matrix based on the difference response components includes: S231: Project the basis vectors in the common response subspace back to the original frequency-particle size coordinate system to obtain an equivalent response representation that is stable across different particle geometries; S232: Reorganize the equivalent response representation according to the order of discrete nodes of particle size to form the shape equivalent forward modeling matrix; S233: Project the basis vectors in the differential response subspace back to the original frequency-particle size coordinate system to obtain a sensitive response representation related to changes in particle geometry; S234. Construct a shape difference constraint matrix based on the sensitive response representation, so that the shape difference constraint matrix can be used to characterize the projection amplitude or projection energy of the particle size distribution to be determined in the shape sensitive direction.

[0010] Preferably, in step S2, extracting the particle morphology feature vector from the standardized attenuation spectrum vector includes: S241: Construct a training sample set containing ultrasonic attenuation spectra under different particle morphology categories, particle size distributions, and concentration conditions; S242: Train a feature extraction model using the training sample set, so that the feature extraction model learns a spectral latent representation that is related to particle morphology changes and is at least partially distinguishable from particle size changes; S243: Input the standardized attenuation spectrum vector into the trained feature extraction model to extract intermediate hidden layer features or output layer features; S244: Perform fixed-length mapping on the extracted features to form the particle morphology feature vector.

[0011] Preferably, step S3 includes: S31: Using the standardized attenuation spectrum vector as the observation vector and the shape equivalent orthogonal matrix as the forward mapping matrix, construct the data fitting term; S32: Construct smoothing constraint terms based on the continuous variation of particle size distribution at adjacent particle size nodes; S33: Construct shape robust constraint terms using the shape difference constraint matrix to suppress the response of the particle size distribution to be determined in the shape-sensitive direction; S34: Process the particle morphology feature vector using a mapping function to obtain the channel weight coefficients corresponding to each frequency point and the morphology uncertainty index characterizing the degree of morphology uncertainty; S35: Construct a frequency channel weight matrix based on the channel weight coefficients, and determine the shape robust constraint weight parameters based on the shape uncertainty index; S36: Combine the data fitting term, the smoothing constraint term, and the shape robust constraint term to form the particle size distribution inversion objective function.

[0012] Preferably, the objective function for particle size distribution inversion satisfies the following equation: ,in, To standardize the attenuation spectrum vector, The shape equivalent orthogonal matrix is... Let be the particle size distribution vector to be determined. This is the frequency channel weight matrix constructed based on the particle morphology feature vector z. Here, L represents the smoothing constraint weights, and L is the smoothing constraint operator. The shape robust constraint weights are adaptively determined based on the particle morphology feature vector z. For the shape robust regularization term; Wherein, the shape robust constraint term Specifically Where Adiff is the shape difference constraint matrix. It is a diagonal matrix, and its diagonal elements are negatively correlated with the sensitivity of each frequency point to changes in particle shape. It increases with the increase of the aforementioned morphological uncertainty index.

[0013] Preferably, step S4 includes: S411: Set the initial value, maximum number of iterations, and convergence threshold for the particle size distribution vector to be determined; S412: The particle size distribution inversion objective function is solved using an iterative optimization algorithm to obtain the particle size distribution vector under the current iteration; S413: Apply a non-negativity constraint to the particle size distribution vector in the current iteration, causing components less than zero to be truncated to zero or mapped to non-negativity values; S414: When the difference between the particle size distribution vectors obtained from two adjacent iterations is less than a first preset threshold, or the change in the particle size distribution inversion objective function is less than a second preset threshold, the iteration is terminated and the final particle size distribution vector is output; S415: Calculate the characteristic particle size parameters based on the final particle size distribution vector, and use the shape difference constraint matrix to calculate the projection amplitude or projection energy of the final particle size distribution vector in the shape-sensitive direction as a shape sensitivity index.

[0014] Preferably, the inversion credibility assessment result is generated, including: S421: Calculate the fitting residual index based on the difference between the spectral reconstruction result corresponding to the final particle size distribution vector and the standardized attenuation spectral vector; S422: Apply a preset perturbation to the standardized attenuation spectrum vector and repeatedly perform the inversion solution to obtain several sets of particle size distribution results under perturbation conditions; S423: Calculate the dispersion or consistency index among particle size distribution results under several perturbation conditions; S424: Generate the inversion credibility assessment result based on the fitting residual index, the shape sensitivity index, and the consistency index.

[0015] Compared with the prior art, the beneficial effects of the present invention are: (1) This invention establishes an ultrasonic frequency domain response matrix for various preset particle geometries and performs joint decomposition, extracts common response components and shape difference response components that coexist stably across shapes, constructs a shape equivalent forward modeling matrix based on common components and constructs a shape difference constraint matrix based on difference components, thereby separating particle size contribution and morphology contribution from the ultrasonic response mechanism level. The traditional rigid spherical assumption model is replaced by a forward modeling matrix that is weakly sensitive to changes in particle geometry, thus suppressing particle size inversion deviation introduced by shape interference from the principle level without needing to know the actual shape type and axis ratio parameters of the particles.

[0016] (2) This invention extracts particle morphology feature vectors from the standardized attenuation spectrum vectors and uses these feature vectors to adaptively adjust the frequency channel weights in the data fitting term and / or the penalty intensity in the shape robustness constraint term. This enables automatic weight reduction of frequency ranges in the attenuation spectrum that are severely affected by shape and automatic enhancement of shape constraint penalties when morphology uncertainty increases. This ensures that when the particle morphology of different batches of materials changes, the inversion model can adaptively match the optimal adjustment strategy in real time, avoiding reliance on manual experience to select empirical shape factors. This achieves online automatic adaptation and high robustness of particle size inversion to morphology changes.

[0017] (3) This invention introduces a shape robust constraint term based on the shape difference constraint matrix into the objective function of particle size distribution inversion, and punishes and suppresses the projection component of the particle size distribution to be determined in the shape sensitive response direction. This allows the optimization search process to actively avoid the pseudo solution region caused by the uncertainty of particle morphology. Combined with the shape robust constraint weight determined adaptively based on the particle morphology feature vector, the shape suppression effect is automatically enhanced when the measured spectrum characterizes strong non-spherical features. This ensures that the output equivalent particle size distribution stably approximates the particle volume properties and avoids shape coupling pseudo peaks or distribution distortion.

[0018] (4) This invention generates a shape sensitivity index by calculating the projection energy of the particle size distribution solution in the shape-sensitive direction using the shape difference constraint matrix after the iterative solution is completed. It also outputs the inversion credibility assessment result by combining the fitting residual and the consistency test of the disturbance. This enables the quantification of the shape interference degree of each particle size measurement result and the evaluation of the measurement reliability, thereby ensuring that the measurement result not only gives the particle size value but also includes the quality criterion, providing a traceable measurement credibility basis for industrial online quality control. Attached Figure Description

[0019] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention.

[0020] Figure 1 This is a flowchart of an ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Obviously, the described embodiments are only some, not all, of the embodiments described in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without creative effort are within the scope of protection of this application.

[0022] Those skilled in the art will understand that, unless otherwise stated, the singular forms “a” and “an” used herein, and “the”, may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0023] First Embodiment Please see Figure 1 As shown, this embodiment provides an ultrasonic particle size distribution inversion method to suppress the influence of particle shape, including the following steps: S1: Obtain the ultrasonic response signal of the particle suspension system under test within a predetermined frequency range, and construct a standardized attenuation spectrum vector based on the ultrasonic response signal.

[0024] Preferably, step S1 includes: S11: Under the same measurement path and measurement parameters, the ultrasonic signal of the sample of the particle suspension system to be tested and the reference ultrasonic signal of the reference medium are collected respectively. Specifically, in this embodiment, a broadband ultrasonic signal is emitted to the particle suspension system to be tested using an ultrasonic transmitting transducer, and the transmitted signal is received by an ultrasonic receiving transducer to obtain the sample ultrasonic signal. At the same time, under the same propagation path, excitation conditions and sampling conditions, the reference medium is measured to obtain the reference ultrasonic signal.

[0025] S12. Perform frequency domain transformation on the sample ultrasonic signal and the reference ultrasonic signal to obtain the sample amplitude spectrum and the reference amplitude spectrum. Specifically, in this embodiment, perform fast Fourier transform on the sample ultrasonic signal and the reference ultrasonic signal respectively to obtain the sample amplitude spectrum. and reference amplitude spectrum Additional attenuation spectrum caused by particles It can be represented as: , where L is the length of the ultrasound propagation path.

[0026] In another implementation, decibels can also be used: .

[0027] S13. Calculate the additional attenuation spectrum caused by particles based on the sample amplitude spectrum and the reference amplitude spectrum.

[0028] S14. Perform outlier removal, smoothing, noise reduction, and standardization on the additional attenuation spectrum to form a standardized attenuation spectrum vector.

[0029] For discrete frequency points The i-th element of the normalized attenuation spectrum vector b can be expressed as: ,in, and These represent the mean and standard deviation of the additional attenuation spectrum, respectively.

[0030] S2: Establish ultrasonic frequency domain response matrices for several preset particle geometries, perform joint decomposition on each ultrasonic frequency domain response matrix, extract common response components that coexist stably across different particle geometries and differential response components caused by changes in particle geometry, construct shape equivalent forward modeling matrix based on common response components, construct shape difference constraint matrix based on differential response components, and extract particle morphology feature vectors from standardized attenuation spectrum vectors.

[0031] Preferably, in step S2, establishing the ultrasonic frequency domain response matrix includes: S211: Preset at least three types of particle geometry and determine the range of shape parameter values ​​for each particle geometry. Specifically, in this embodiment, K types of particle geometry are preset.

[0032] S212: Calculate the theoretical ultrasonic response for each type of particle geometry under preset particle size discrete nodes and predetermined frequency sampling nodes.

[0033] S213: Arrange the theoretical ultrasonic responses of the same particle geometry at each particle size discrete node and each frequency sampling node according to the frequency dimension and particle size dimension to form a corresponding ultrasonic frequency domain response matrix. Specifically, in this embodiment, for the k-th type of particle geometry, at the preset frequency sampling node... , , , and particle size discrete nodes , , , Next, the theoretical ultrasonic response is calculated, and the ultrasonic frequency domain response matrix is ​​constructed: ,in, Indicates the geometry of the k-th type of particle at frequency and particle size The theoretical ultrasonic response value under the given conditions.

[0034] S214: Perform dimensional unification and normalization on each ultrasonic frequency domain response matrix to eliminate amplitude scale differences between different particle geometries.

[0035] Preferably, in step S2, the ultrasonic frequency domain response matrices are jointly decomposed and common response components and differential response components are extracted, including: S221: Align the ultrasonic frequency domain response matrices corresponding to the geometry of each particle according to the same frequency dimension and the same particle size dimension, and combine them to form a joint response matrix.

[0036] Combine the response matrices corresponding to the geometry of K types of particles into a joint response matrix: .

[0037] S222: Perform subspace decomposition on the joint response matrix to obtain multiple response components sorted by contribution. Specifically, in this embodiment, singular value decomposition is used as an example: Where U is the left singular vector matrix, Let V be a singular value matrix, and let V be a right singular vector matrix.

[0038] S223: Calculate the projection consistency index and stability index of each response component in the response matrix corresponding to different particle geometries. Response components with projection consistency indices higher than a first preset threshold and stability indices higher than a second preset threshold are identified as common response components. Specifically, in this embodiment, for the r-th response component, calculate its projection consistency index under different particle geometries. In one embodiment, the projection consistency index can be expressed as: ,in, This represents the projection direction of the r-th response component under the geometry of the k-th particle type. Indicates the average projection direction.

[0039] S224: The remaining response components that were not identified as common response components are identified as differential response components. Specifically, in this embodiment, when When the response exceeds a preset threshold, the corresponding response component is identified as a common response component; the remaining response components are identified as differential response components. The common response matrix and differential response matrix are further obtained, denoted as follows: , ,in, For shape equivalent orthogonal matrix, This is the shape difference constraint matrix.

[0040] S225: Construct a common response subspace from common response components, and construct a differential response subspace from differential response components.

[0041] Preferably, constructing a shape equivalent forward modeling matrix based on common response components and constructing a shape difference constraint matrix based on difference response components includes: S231: Projecting the basis vectors in the common response subspace back to the original frequency-size coordinate system yields an equivalent response representation that is stable across different particle geometries; S232: Reorganize the equivalent response representation according to the order of discrete nodes of particle size to form a shape equivalent forward modeling matrix; S233: Projecting the basis vectors in the differential response subspace back to the original frequency-particle size coordinate system yields a sensitive response representation related to changes in particle geometry; S234. Construct a shape difference constraint matrix based on the sensitive response representation, so that the shape difference constraint matrix can be used to characterize the projection amplitude or projection energy of the particle size distribution to be determined in the shape sensitive direction.

[0042] Preferably, in step S2, the particle morphology feature vector is extracted from the standardized attenuation spectrum vector, including: S241: Construct a training sample set containing ultrasonic attenuation spectra under different particle morphology categories, particle size distributions, and concentration conditions. Specifically, in this embodiment, the training sample set includes multiple sets of known particle system samples. Each set of samples includes at least the corresponding ultrasonic attenuation spectrum data, reference particle size distribution data, and particle morphology category labels or morphology parameters. The particle system may include spherical particles, needle-like particles, plate-like particles, rod-like particles, polyhedral particles, and irregular particles, covering different volume fractions, different particle size ranges, and different distribution widths. The training samples may be derived from measured data, acoustic scattering forward modeling simulation data, or a combination of both.

[0043] S242: Train the feature extraction model using the training sample set, so that the feature extraction model... Learn the spectral potential representation that is related to changes in particle morphology and is at least partially distinguishable from changes in particle size.

[0044] The feature extraction model is an improved spectral feature learning model built upon traditional one-dimensional convolutional neural networks and autoencoders. It addresses the problem of the coupling and difficulty in directly separating particle size and morphology information in ultrasonic attenuation spectra. Compared to existing network models that only use single-scale convolutional structures to extract local spectral features, this implementation adds a multi-scale parallel convolution module, a cross-layer residual connection module, and a latent spatial constraint module at the encoding end.

[0045] The multi-scale parallel convolution module is configured with at least two different sizes of one-dimensional convolution kernels to extract narrowband scattering peak features, broadband attenuation trend features, and cross-frequency band variation features, respectively. The cross-layer residual connection module is used to retain shallow spectral details and alleviate gradient decay during deep network training. The latent spatial constraint module is used to reduce the coupling between particle size-related features and morphology-related features, so that the model learns a discriminative latent representation.

[0046] During training, the attenuation spectrum in the training samples undergoes uniform preprocessing, including frequency resampling, outlier removal, smoothing filtering, amplitude normalization, and standardization, forming a fixed-length input vector. This input vector is then fed into the feature extraction model and mapped into a low-dimensional latent feature vector via an encoding network.

[0047] The model training employs a joint loss function for parameter optimization, which includes at least one of the following: spectral reconstruction loss, particle size supervision loss, morphology classification loss, and feature decoupling loss. The network parameters are iteratively updated using the backpropagation algorithm. Once the loss function converges or reaches a preset number of training epochs, the trained feature extraction model is obtained.

[0048] The trained feature extraction model can extract a potential spectral representation from the ultrasonic attenuation spectrum that is sensitive to changes in particle morphology and is at least partially distinguishable from changes in particle size, providing an input basis for subsequent morphology compensation and particle size distribution inversion.

[0049] S243: Input the standardized decay spectrum vector into the trained feature extraction model to extract intermediate hidden layer features or output layer features.

[0050] Specifically, the standardized attenuated spectrum vector corresponding to the suspended particle system is input into the trained feature extraction model, and the spectral feature response is calculated layer by layer according to the network's forward propagation path. The standardized attenuated spectrum vector first passes through a front-end convolutional layer to extract local frequency response features, then passes through a multi-scale feature fusion layer to extract scattering variation features in different frequency bands, and finally forms a high-level semantic feature representation through a deep coding network. According to the requirements of subsequent tasks, intermediate hidden layer features or output layer features are selected from the feature extraction model as target features.

[0051] Specifically, when it is necessary to retain rich local structural information and spectral detail information, intermediate hidden layer features can be selected as particle morphology representation features; when it is necessary to obtain compact and highly discriminative feature representations, output layer features can be selected as input features for subsequent compensation or inversion models. The intermediate hidden layer features or output layer features are preferably fixed-dimensional feature vectors.

[0052] S244: Perform fixed-length mapping on the extracted features to form a particle morphology feature vector. After the feature extraction model is trained, input the standardized attenuation spectrum vector b into the feature extraction model to obtain the particle morphology feature vector z. .

[0053] In one embodiment, the training loss of the feature extraction model can be expressed as: ,in, To reconstruct the loss, Loss due to morphological differentiation This is the balance coefficient.

[0054] S3, Based on standardized attenuation spectrum vector Shape equivalent forward matrix Shape difference constraint matrix and particle morphology feature vector A particle size distribution inversion objective function is constructed, which includes at least a data fitting term, a smoothing constraint term, and a shape robust constraint term. The particle morphology feature vector is used to adaptively adjust at least one of the frequency channel weights in the data fitting term and the penalty intensity in the shape robust constraint term.

[0055] Preferably, step S3 includes: S31: Using the standardized attenuation spectrum vector as the observation vector and the shape equivalent orthogonal matrix as the forward mapping matrix, construct the data fitting term; S32: Construct smoothing constraint terms based on the continuous variation of particle size distribution at adjacent particle size nodes; S33: Construct shape robust constraint terms using the shape difference constraint matrix to suppress the response of the particle size distribution to be determined in the shape-sensitive direction; S34: Use the mapping function to process the particle morphology feature vector to obtain the channel weight coefficients corresponding to each frequency point and the morphology uncertainty index characterizing the degree of morphology uncertainty; S35: Construct a frequency channel weight matrix based on the weight coefficients of each channel, and determine the shape robust constraint weight parameters based on the shape uncertainty index; S36: Combine the data fitting term, smoothing constraint term, and shape robustness constraint term to form the particle size distribution inversion objective function.

[0056] Preferably, the objective function for particle size distribution inversion satisfies the following equation: ,in, To standardize the attenuation spectrum vector, For shape equivalent orthogonal matrix, Let be the particle size distribution vector to be determined. This is the frequency channel weight matrix constructed based on the particle morphology feature vector z. Here, L represents the smoothing constraint weights, and L is the smoothing constraint operator. The shape robust constraint weights are adaptively determined based on the particle morphology feature vector z. For shape-robust regularization terms; Among them, shape robust constraint term Specifically Where Adiff is the shape difference constraint matrix. It is a diagonal matrix, and its diagonal elements are negatively correlated with the sensitivity of each frequency point to changes in particle shape. It increases with the increase of the morphological uncertainty index.

[0057] More preferably, the objective function for particle size distribution inversion can be further expressed as: .

[0058] Frequency channel weight matrix It can be represented as: The weight corresponding to the i-th frequency point can be further defined as: ,in, Let represent the sensitivity of the i-th frequency point to changes in particle shape. This is the adjustment coefficient.

[0059] Shape robust constraint weights It can be represented as: ,in, Based on the basic constraint coefficient, This is the morphology uncertainty index calculated based on the particle morphology feature vector. This is the adjustment coefficient.

[0060] In another embodiment, the actual particle size Shape-equivalent particle size The correction relationship can be expressed as: ,in, It is a mapping function based on shape feature vectors.

[0061] S4. Iteratively solve the objective function of particle size distribution inversion with non-negative constraints to obtain the shape-equivalent particle size distribution of the particle suspension system under test, and output the characteristic particle size parameters, shape sensitivity index and inversion credibility evaluation results based on the shape-equivalent particle size distribution.

[0062] Preferably, step S4 includes: S411: Set the initial value, maximum number of iterations, and convergence threshold of the particle size distribution vector to be determined. Specifically, in this embodiment, the particle size distribution vector to be determined is set... initial value ; S412: An iterative optimization algorithm is used to solve the objective function for particle size distribution inversion, and the particle size distribution vector under the current iteration is obtained; S413: Apply a non-negativity constraint to the particle size distribution vector in the current iteration, causing components less than zero to be truncated to zero or mapped to non-negativity values; S414: When the difference between the particle size distribution vectors obtained from two adjacent iterations is less than a first preset threshold, or the change in the particle size distribution inversion objective function is less than a second preset threshold, the iteration is terminated and the final particle size distribution vector is output. Specifically, in this embodiment, the iteration stops when the following formula is satisfied: ,in, The convergence threshold; S415: Calculate the characteristic particle size parameters based on the final particle size distribution vector, and use the shape difference constraint matrix to calculate the projection amplitude or projection energy of the final particle size distribution vector in the shape-sensitive direction as a shape sensitivity index.

[0063] In the t-th iteration, the particle size distribution vector can be updated as follows: Where F(x) represents the objective function for particle size distribution inversion, Indicates the iteration step size. This represents the non-negative projection operator, used to ensure that each component of the updated particle size distribution vector is non-negative.

[0064] Preferably, the inversion credibility assessment result is generated, including: S421: Based on the difference between the spectral reconstruction result corresponding to the final particle size distribution vector and the standardized attenuation spectral vector, calculate the fitting residual index. Specifically, in this embodiment, after obtaining the final particle size distribution vector... Then, the spectrum reconstruction results are calculated: The fitting residual index can be expressed as: The shape sensitivity index can be expressed as: .

[0065] S422: Apply a preset perturbation to the normalized attenuation spectrum vector b and repeatedly perform the inversion solution to obtain several sets of particle size distribution results under (M) perturbation conditions. .

[0066] S423: Calculate the dispersion or consistency index among the particle size distribution results under several groups of perturbation conditions. Let the particle size distribution results under the perturbation conditions be as follows: Its mean vector is: The consistency index c is calculated using the following formula: ,in, This is the mean vector of the M inversion results.

[0067] S424: Generate the inversion credibility assessment results based on the fitting residual index, shape sensitivity index, and consistency index.

[0068] An inversion confidence score R is generated based on the fitting residual index e, the shape sensitivity index q, and the consistency index c, for example: ,in, , , Let be the weight coefficient, and satisfy... The larger the inversion confidence score R, the better the fit of the current particle size distribution inversion result, the lower the shape sensitivity and the higher the perturbation stability.

[0069] Second Embodiment Based on the same concept, this embodiment also provides a computer device, including a memory and a processor, wherein the memory stores computer-readable instructions, which, when executed by the processor, cause the processor to perform the steps of an ultrasonic particle size distribution inversion method for suppressing the influence of particle shape as described in the embodiment.

[0070] Based on the same concept, the present invention also provides a storage medium storing computer-readable instructions, which, when executed by one or more processors, cause the one or more processors to perform the steps of an ultrasonic particle size distribution inversion method for suppressing the influence of particle shape as described in any one embodiment.

[0071] It is understood that, for the aforementioned ultrasonic particle size distribution inversion method for suppressing the influence of particle shape, if all of them are implemented in the form of software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer server or a network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes: USB flash drive, mobile hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk, and other media capable of storing program code.

[0072] Computer-readable storage media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium may also be any readable medium other than a readable storage medium that can transmit, propagate, or transfer a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0073] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for ultrasonic particle size distribution inversion that suppresses the influence of particle shape, characterized in that, Includes the following steps: S1: Obtain the ultrasonic response signal of the particle suspension system under test within a predetermined frequency range, and construct a standardized attenuation spectrum vector based on the ultrasonic response signal; S2: Establish ultrasonic frequency domain response matrices for several preset particle geometries, perform joint decomposition on each ultrasonic frequency domain response matrix, extract common response components that are stable across different particle geometries and differential response components caused by changes in particle geometry, construct a shape equivalent forward modeling matrix based on the common response components, construct a shape difference constraint matrix based on the differential response components, and extract particle morphology feature vectors from the standardized attenuation spectrum vector; S3. Based on the standardized attenuation spectrum vector, the shape equivalent forward modeling matrix, the shape difference constraint matrix, and the particle morphology feature vector, a particle size distribution inversion objective function is constructed. The particle size distribution inversion objective function includes at least a data fitting term, a smoothing constraint term, and a shape robustness constraint term. The particle morphology feature vector is used to adaptively adjust at least one of the frequency channel weights in the data fitting term and the penalty intensity in the shape robustness constraint term. S4. Iteratively solve the objective function of particle size distribution inversion with non-negative constraints to obtain the shape-equivalent particle size distribution of the particle suspension system under test, and output the characteristic particle size parameters, shape sensitivity index and inversion credibility evaluation results based on the shape-equivalent particle size distribution.

2. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 1, characterized in that, Step S1 includes: S11: Under the same measurement path and measurement parameters, collect the sample ultrasonic signal of the particle suspension system to be tested and the reference ultrasonic signal of the reference medium, respectively. S12. Perform frequency domain transformation on the ultrasonic signal of the sample and the ultrasonic signal of the reference to obtain the sample amplitude spectrum and the reference amplitude spectrum; S13. Calculate the additional attenuation spectrum caused by particles based on the sample amplitude spectrum and the reference amplitude spectrum; S14. Perform outlier removal, smoothing, noise reduction, and standardization on the additional attenuation spectrum to form the standardized attenuation spectrum vector.

3. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 1, characterized in that, In step S2, the ultrasonic frequency domain response matrix is ​​established, including: S211: Preset at least three types of particle geometry and determine the range of shape parameter values ​​for each particle geometry; S212: Calculate the theoretical ultrasonic response for each type of particle geometry under preset particle size discrete nodes and predetermined frequency sampling nodes; S213: Arrange the theoretical ultrasonic responses of the same particle geometry at each particle size discrete node and each frequency sampling node according to the frequency dimension and particle size dimension to form the corresponding ultrasonic frequency domain response matrix. S214: Perform dimensional unification and normalization on each ultrasonic frequency domain response matrix to eliminate amplitude scale differences between different particle geometries.

4. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 3, characterized in that, In step S2, the ultrasonic frequency domain response matrices are jointly decomposed and common and differential response components are extracted, including: S221: Align the ultrasonic frequency domain response matrices corresponding to the geometry of each particle according to the same frequency dimension and the same particle size dimension, and combine them to form a joint response matrix; S222: Perform subspace decomposition on the joint response matrix to obtain multiple response components sorted by contribution; S223: Calculate the projection consistency index and stability index of each response component in the response matrix corresponding to different particle geometries, and determine the response components whose projection consistency index is higher than the first preset threshold and whose stability index is higher than the second preset threshold as common response components. S224: Identify the remaining response components that were not identified as common response components as differential response components; S225: Construct a common response subspace from the common response components, and construct a differential response subspace from the differential response components.

5. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 4, characterized in that, Constructing a shape equivalent forward matrix based on the common response components and constructing a shape difference constraint matrix based on the difference response components, including: S231: Project the basis vectors in the common response subspace back to the original frequency-particle size coordinate system to obtain an equivalent response representation that is stable across different particle geometries; S232: Reorganize the equivalent response representation according to the order of discrete nodes of particle size to form the shape equivalent forward modeling matrix; S233: Project the basis vectors in the differential response subspace back to the original frequency-particle size coordinate system to obtain a sensitive response representation related to changes in particle geometry; S234. Construct a shape difference constraint matrix based on the sensitive response representation, so that the shape difference constraint matrix can be used to characterize the projection amplitude or projection energy of the particle size distribution to be determined in the shape sensitive direction.

6. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 1, characterized in that, In step S2, the particle morphology feature vector is extracted from the normalized attenuation spectrum vector, including: S241: Construct a training sample set containing ultrasonic attenuation spectra under different particle morphology categories, particle size distributions, and concentration conditions; S242: Train a feature extraction model using the training sample set, so that the feature extraction model learns a spectral latent representation that is related to particle morphology changes and is at least partially distinguishable from particle size changes; S243: Input the standardized attenuation spectrum vector into the trained feature extraction model to extract intermediate hidden layer features or output layer features; S244: Perform fixed-length mapping on the extracted features to form the particle morphology feature vector.

7. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 1, characterized in that, Step S3 includes: S31: Using the standardized attenuation spectrum vector as the observation vector and the shape equivalent orthogonal matrix as the forward mapping matrix, construct the data fitting term; S32: Construct smoothing constraint terms based on the continuous variation of particle size distribution at adjacent particle size nodes; S33: Construct shape robust constraint terms using the shape difference constraint matrix to suppress the response of the particle size distribution to be determined in the shape-sensitive direction; S34: Process the particle morphology feature vector using a mapping function to obtain the channel weight coefficients corresponding to each frequency point and the morphology uncertainty index characterizing the degree of morphology uncertainty; S35: Construct a frequency channel weight matrix based on the channel weight coefficients, and determine the shape robust constraint weight parameters based on the shape uncertainty index; S36: Combine the data fitting term, the smoothing constraint term, and the shape robust constraint term to form the particle size distribution inversion objective function.

8. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 7, characterized in that, The objective function for particle size distribution inversion satisfies the following equation: ， in, To standardize the attenuation spectrum vector, The shape equivalent orthogonal matrix is... Let be the particle size distribution vector to be determined. This is the frequency channel weight matrix constructed based on the particle morphology feature vector z. Here, L represents the smoothing constraint weights, and L is the smoothing constraint operator. The shape robust constraint weights are adaptively determined based on the particle morphology feature vector z. For shape-robust regularization terms; Wherein, the shape robust constraint term Specifically Where Adiff is the shape difference constraint matrix. It is a diagonal matrix, and its diagonal elements are negatively correlated with the sensitivity of each frequency point to changes in particle shape. It increases with the increase of the aforementioned morphological uncertainty index.

9. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 1, characterized in that, Step S4 includes: S411: Set the initial value, maximum number of iterations, and convergence threshold for the particle size distribution vector to be determined; S412: The particle size distribution inversion objective function is solved using an iterative optimization algorithm to obtain the particle size distribution vector under the current iteration; S413: Apply a non-negativity constraint to the particle size distribution vector in the current iteration, causing components less than zero to be truncated to zero or mapped to non-negativity values; S414: When the difference between the particle size distribution vectors obtained from two adjacent iterations is less than a first preset threshold, or the change in the particle size distribution inversion objective function is less than a second preset threshold, the iteration is terminated and the final particle size distribution vector is output; S415: Calculate the characteristic particle size parameters based on the final particle size distribution vector, and use the shape difference constraint matrix to calculate the projection amplitude or projection energy of the final particle size distribution vector in the shape-sensitive direction as a shape sensitivity index.

10. The ultrasonic particle size distribution inversion method for suppressing the influence of particle shape according to claim 9, characterized in that, Generate inversion credibility assessment results, including: S421: Calculate the fitting residual index based on the difference between the spectral reconstruction result corresponding to the final particle size distribution vector and the standardized attenuation spectral vector; S422: Apply a preset perturbation to the standardized attenuation spectrum vector and repeatedly perform the inversion solution to obtain several sets of particle size distribution results under perturbation conditions; S423: Calculate the dispersion or consistency index among particle size distribution results under several perturbation conditions; S424: Generate the inversion credibility assessment result based on the fitting residual index, the shape sensitivity index, and the consistency index.

Images