Method for radial cross-section sound pressure correction and prediction of underwater focused ultrasound sound field

Abstract

The application discloses a method for correcting and predicting radial section sound pressure of underwater focused ultrasonic sound field, which comprises the following steps: obtaining an axial scanning signal of the underwater focused ultrasonic sound field and extracting a signal envelope; constructing a proportional correction coefficient based on the ratio of the signal envelope to a theoretical axial sound pressure; modeling the change of the proportional correction coefficient with the axial position by using Gaussian process regression to obtain the corrected axial sound pressure; predicting the radial section beam width of the underwater focused ultrasonic sound field at any axial position; decomposing the existing measured radial section into modes, extracting a spatial mode function and a mode weight coefficient, establishing a prediction model of the change of the mode weight coefficient with the axial position by using Gaussian process regression, reconstructing the preliminary radial section sound pressure distribution at any axial position, and correcting the preliminary radial section by using the corrected axial sound pressure and the predicted beam width. The application can realize the prediction of the radial section sound pressure of the underwater focused ultrasonic sound field at any axial position.

Description

Technical Field

[0001] This invention belongs to the field of underwater ultrasonic testing and sound field measurement technology, specifically relating to a method for correcting and predicting the radial cross-sectional sound pressure of an underwater focused ultrasonic sound field. Background Technology

[0002] Underwater ultrasonic sound field measurement is widely used in underwater acoustic detection, medical ultrasound imaging, non-destructive testing, and industrial measurement. In practical applications, accurate acquisition of the sound field distribution is crucial for system performance evaluation, focusing characteristic analysis, and defect identification. However, in actual measurements, due to the high cost of measurement equipment, the complexity of the scanning process, and the limitations of the measurement environment, it is usually difficult to obtain complete three-dimensional sound field data. Only axial sound field scanning signals and a small amount of radial cross-sectional data at axial positions can be obtained, resulting in a typical sparse distribution of sound field information, which affects the accuracy of sound field prediction and reconstruction.

[0003] Existing sound field prediction methods mainly include interpolation-based prediction methods, numerical simulation-based prediction methods, and data-driven prediction methods. Interpolation-based methods achieve sound field prediction and reconstruction by spatially interpolating existing measurement data. This method is simple to implement but relies on relatively dense measurement data and is prone to large errors under sparse data conditions. Numerical simulation-based methods perform global calculations of the sound field by establishing a sound propagation model. This method can obtain a high-precision sound field distribution, but its high computational complexity and strong dependence on model parameters make it difficult to meet the rapid reconstruction needs of practical engineering. Using machine learning models to fit and predict the sound field based on known training set data improves reconstruction efficiency to some extent, but due to the lack of physical constraints, divergence is prone to occur during extrapolation, leading to unstable prediction results. Furthermore, in actual measurement processes, the axial sound field scanning signal is usually affected by measurement noise and probe position deviation, making it difficult for its amplitude to accurately reflect the true axial sound pressure distribution.

[0004] Therefore, how to achieve unified prediction of the axial and radial sound pressure distributions of the sound field under sparse measurement conditions by using the axial sound field and several sets of radial cross-sectional sound field data at different locations has become a technical problem that needs to be solved. Summary of the Invention

[0005] To address the problems of existing sound field reconstruction methods, such as sparse measurement data and large errors between the maximum sound pressure value at each axial position and the maximum sound pressure value of the corresponding radial section, which makes it difficult to accurately recover the radial section of the sound field, this invention proposes a method for correcting and predicting the radial section sound pressure of an underwater focused ultrasonic sound field. This method performs a Hilbert transform on the signal composed of the maximum sound pressure values ​​at each axial position of the measured axial sound field, and then uses a Gaussian process regression method to construct a function between the measured axial sound pressure and the maximum sound pressure value of the radial section, thus correcting the maximum sound pressure at any axial position; based on the predicted maximum sound pressure at the axial position... A model is established to determine the relationship between beamwidth, acoustic field energy, and maximum axial sound pressure at each axial position, enabling estimation of the beamwidth of the radial cross-section of the underwater focused ultrasonic acoustic field. Singular value decomposition is performed on the measured radial cross-section sound pressure matrix to extract spatial mode functions characterizing the acoustic field distribution. A predictive model is then established using Gaussian process regression to determine the variation of mode weight coefficients with axial position. The preliminary reconstructed cross-section is recovered by superimposing modes at any axial position. Finally, using the predicted beamwidth and maximum axial sound pressure at that position, the preliminary reconstructed cross-section is scaled radially and its maximum sound pressure value is calibrated, thereby achieving continuous correction and prediction of the acoustic field's radial cross-section.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a method for correcting and predicting the radial cross-sectional sound pressure of an underwater focused ultrasonic field, the method comprising: The axial scanning signal of the underwater focused ultrasonic sound field is acquired, and the signal envelope is extracted by Hilbert transform of the axial scanning signal. A proportional correction coefficient is constructed based on the ratio of the signal envelope to the theoretical axial sound pressure. The change of the proportional correction coefficient with the axial position is modeled by Gaussian process regression to predict the proportional correction coefficient at any axial position. The proportional correction coefficient is multiplied by the theoretical axial sound pressure to obtain the corrected axial sound pressure. Predict the radial cross-section beamwidth at any axial position of the underwater focused ultrasonic field; Modal decomposition is performed on the existing measured radial cross section to extract the spatial mode function and mode weight coefficients. A prediction model of the mode weight coefficients changing with axial position is established using Gaussian process regression to predict the mode weight coefficients at any axial position. Based on the predicted mode weight coefficients and the corresponding spatial mode function, the preliminary radial cross section sound pressure distribution at any axial position is reconstructed. The preliminary radial cross section is scaled laterally using the predicted beamwidth, and the amplitude of the scaled cross section is normalized using the corrected axial sound pressure to obtain the final radial cross section sound pressure distribution.

[0007] Furthermore, when modeling the change of the scaling correction coefficient with axial position using Gaussian process regression, for abnormal measurement points, a local neighborhood space set is defined with the axial position of the abnormal measurement point as the center. The axial position coordinates of each normal measurement point in the local neighborhood space set and their corresponding scaling correction coefficients are obtained. The weights of each normal measurement point are determined based on the axial distance between the abnormal measurement point and each normal measurement point and the characteristic scale parameter. The scaling correction coefficients of each normal measurement point are weighted and fused based on the weights to obtain the scaling correction coefficients after correction for the abnormal measurement points.

[0008] Furthermore, predicting the radial cross-section beamwidth at any axial position of the underwater focused ultrasonic sound field includes: The sound field energy parameter is defined as the product of the axial sound pressure and the square of the beamwidth at the corresponding axial position; The beamwidth at the corresponding discrete positions is calculated based on the existing measured radial cross section, and the sound field energy parameters at the corresponding discrete positions are calculated in combination with the corrected axial sound pressure. A linear fit was performed on the variation trend of the sound field energy parameters with axial position to obtain a continuous sound energy distribution function; By using the continuous acoustic energy distribution function and the corrected axial sound pressure, the predicted beamwidth at any axial position is obtained by inverse solution.

[0009] Furthermore, based on existing measured radial cross sections, the beamwidth at corresponding discrete locations is calculated, including: Calculate the peak sound pressure in the existing radial cross section, extract the corresponding isopleth region in the cross section using -3dB of the peak sound pressure as a threshold, and estimate the beamwidth based on the spatial range of the isopleth region.

[0010] Furthermore, modal decomposition is performed on the existing measured radial cross-section, including: The sound pressure data from multiple existing radial cross sections are expanded into vector form and a data matrix is ​​constructed. Singular value decomposition is performed on the data matrix. The column vectors of the left singular matrix are defined as spatial mode functions, and the product of the singular values ​​and the elements of the right singular matrix is ​​defined as the mode weight coefficients at the corresponding axial positions.

[0011] Furthermore, a predictive model for the variation of modal weight coefficients with axial position is established using Gaussian process regression, including: A nonlinear prediction model for the variation of the weight coefficients of each mode with axial position was established using Gaussian process regression. Based on the prediction model, the modal weight coefficients at any axial position are predicted. The predicted modal weight coefficients are then linearly combined and superimposed with the corresponding spatial modal functions to reconstruct the preliminary radial cross-sectional sound pressure distribution at the corresponding axial position.

[0012] Furthermore, the preliminary radial cross-section is laterally scaled using the predicted beamwidth, including: The actual beamwidth of the preliminary radial section is calculated, and the ratio of the predicted beamwidth to the actual beamwidth is defined as the spatial scale scaling factor. The scale transformation of the transverse coordinate system of the preliminary radial section is then performed to achieve the constraint correction of the beamwidth.

[0013] Furthermore, the amplitude of the scaled cross section is normalized using the corrected axial sound pressure, including: The scaled cross section is normalized to make its maximum sound pressure level equal to the corrected axial sound pressure level at the corresponding axial position.

[0014] In a second aspect, the present invention provides a computer device / apparatus / system, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the first aspect.

[0015] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the method described in the first aspect.

[0016] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: This invention extracts the signal envelope using Hilbert transform and constructs proportional correction coefficients using Gaussian process regression, effectively correcting the deviation between axial measured sound pressure and radial cross-sectional peak sound pressure, thus improving the accuracy of axial sound pressure prediction. Based on the physical constraint relationship between acoustic energy parameters and beamwidth, a continuous acoustic energy distribution function is established, enabling reliable estimation of the radial cross-sectional beamwidth at any axial position. By performing modal decomposition on existing radial cross-sections and using Gaussian process regression to establish a prediction model of modal weight coefficients varying with axial position, and combining the predicted beamwidth with corrected axial sound pressure to perform lateral scaling and amplitude normalization on the reconstructed cross-section, this invention achieves high-precision correction and prediction of radial cross-sectional sound pressure distribution at any axial position using only a small amount of existing radial cross-sectional data, effectively overcoming the difficulties of sound field reconstruction under sparse measurement conditions. Attached Figure Description

[0017] Figure 1 This is a flowchart of an underwater focused ultrasonic field radial section sound pressure correction and prediction method according to an embodiment of the present invention; Figures 2A-2E This is a diagram showing measured data of the axial and partial radial sections of the underwater focused ultrasonic sound field according to an embodiment of the present invention; wherein, Figure 2A This is a graph of the axial sound field. Figure 2B This is a radial section sound field distribution diagram at Z=36mm. Figure 2C This is a radial section sound field distribution diagram at Z=40mm. Figure 2D This is a radial section sound field distribution diagram at Z=44mm. Figure 2E The image shows the sound field distribution at the radial section at Z=48mm. Figure 3 This is a diagram showing the original axial sound pressure and the axial sound pressure predicted by Gaussian regression according to an embodiment of the present invention. Figure 4 A diagram showing the beamwidth estimation result obtained after beamwidth constraint modeling according to an embodiment of the present invention; Figure 5 This is a diagram showing the predicted sound pressure distribution of the radial section of the underwater focused ultrasonic field according to an embodiment of the present invention. Detailed Implementation

[0018] 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 and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments provided by this invention without inventive effort are within the scope of protection of this invention.

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

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

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

[0022] This invention addresses the problems in focused ultrasound sound field measurement, such as the limited measurement data and the large error between the maximum sound pressure value at each axial position and the maximum sound pressure value at the corresponding radial section, which makes it difficult to accurately correct and predict the sound pressure of the radial section of the sound field. Combining axial sound pressure prediction, beamwidth constraint modeling and continuous estimation, and radial section reconstruction methods, this invention proposes a method for correcting and predicting the sound pressure of the radial section of the underwater focused ultrasound sound field.

[0023] The underwater focused ultrasonic field radial section sound pressure correction and prediction method of the present invention includes the following steps: (1) Correction of maximum sound pressure in the radial section of the underwater focused ultrasonic field; (2) Estimation of the radial cross-section beamwidth of the underwater focused ultrasonic field; (3) Prediction of the radial section sound pressure of underwater focused ultrasonic field.

[0024] The specific implementation process of the underwater focused ultrasonic field radial section maximum sound pressure correction mentioned in step (1) is as follows: The signal composed of the maximum sound pressure value at each axial position of the measured axial sound field is subjected to Hilbert transform to extract the envelope of the maximum sound pressure signal. Based on the maximum sound pressure value of multiple (at least four) measured radial sections at different axial positions, a function between the axial measured sound pressure and the maximum sound pressure value of the radial section is constructed using the Gaussian process regression method to achieve the correction of the maximum sound pressure at any axial position.

[0025] The underwater focused ultrasonic field radial cross-section beamwidth estimation mentioned in step (2) is specifically implemented as follows: Based on the maximum sound pressure correction value at the axial position obtained in step (1), the beamwidth calculated from multiple measured radial sections at different axial positions is used to establish a model between the beamwidth at each axial position and the sound field energy and the maximum axial sound pressure, thereby realizing the estimation of the radial section beamwidth at any axial position of the underwater focused ultrasonic sound field.

[0026] The underwater focused ultrasonic field radial section sound pressure prediction mentioned in step (3) is specifically implemented as follows: Singular value decomposition was performed on the acoustic pressure matrices of multiple measured radial sections at different axial positions to extract spatial mode functions that characterize the shape, width, and energy distribution of the main lobe of the radial section of the acoustic field. Since the changes in the acoustic field structure at different axial positions are mainly reflected in the changes in the weights of each mode, a nonlinear prediction model in which the weight coefficients of each mode change continuously with the axial position was established using the Gaussian process regression method. The predicted weight coefficients of each mode were combined and superimposed with the corresponding spatial mode functions to reconstruct the preliminary radial section acoustic pressure distribution at the corresponding axial position. Subsequently, the reconstructed section was corrected using the maximum axial acoustic pressure obtained in step (1) and the beamwidth obtained in step (2) to realize the prediction of the radial section acoustic pressure at any axial position of the underwater focused ultrasonic acoustic field.

[0027] Specifically, such as Figure 1 As shown, the underwater focused ultrasonic field radial section sound pressure correction and prediction method of this invention includes the following steps: (1) Correction of maximum sound pressure in the radial section of the underwater focused ultrasonic field; (2) Estimation of the radial cross-section beamwidth of the underwater focused ultrasonic field; (3) Prediction of the radial section sound pressure of underwater focused ultrasonic field.

[0028] The specific implementation process of the underwater focused ultrasonic field radial section maximum sound pressure correction mentioned in step (1) is as follows: First, the axial scan signal... Performing the Hilbert transform involves converting the signal into the maximum sound pressure level at each axial position of the measured axial sound field. Perform a Hilbert transform to construct its analytic signal, and extract its envelope as an approximate representation of the sound pressure amplitude. Its expression is: ; In the formula, The signal envelope is used to represent the sound pressure amplitude. Here, is the axial spatial coordinate, representing the directional dimension of the ultrasonic beam propagation; The variable is the integral variable, representing the displacement in the axial spatial domain; Cauchy principal value, used to process the integral kernel in The strangeness of the place; Pi is a constant. This is the core integral of the Hilbert transform of the original signal.

[0029] Subsequently, the theoretical axial sound pressure calculated based on the measured radial cross section was introduced. And construct the proportional relationship between the actual measurement and the theoretical model, expressed as: ; In the formula, To measure the correction factor for sound pressure relative to theoretical sound pressure; when =1 indicates complete agreement.

[0030] This scaling function reflects the deviation of the actual axial sound pressure in the sound field from the axial sound pressure in the ideal sound field. To improve the numerical stability of the model, a Gaussian process regression method is used to model it, expressed as: ; In the formula, Indicates the test location The mean of the correction coefficients obtained from the prediction; The confidence level of the predicted result; This is the covariance vector between the training samples and the test points. The kernel matrix for the training samples, whose elements are determined by the kernel function. Calculated; To observe the noise variance, it represents the level of random white noise in the measurement system; This is the identity matrix, used for regularization. The target vector is the vector to be observed.

[0031] After training the model, the proportional function at any axial position can be predicted, and the original space can be recovered through exponential transformation to obtain the predicted axial sound pressure, expressed as: ; In the formula, The original axial sound pressure value at any position. This is the estimated value of the proportional function obtained through prediction.

[0032] Furthermore, in actual measurement processes, some measurement points may deviate abnormally due to noise or equipment errors. Directly using these deviations for model training would severely impact prediction stability. Therefore, this invention introduces axial consistency constraints for outlier points, and weights and fuses the neighborhood interpolation results with the ideal axial sound pressure value, expressed as: ; ; In the formula, To detect anomalies The proportional coefficient after weighted fusion correction; For the defined local neighborhood space set; These represent the coordinates of the anomaly location and the coordinates of the reference point within the neighborhood, respectively. For the first The contribution weight of each reference point to the correction of outliers; The characteristic scale parameter is used to control the rate at which the weights decay with distance; through the above processing, stable prediction of axial sound pressure is achieved.

[0033] The underwater focused ultrasonic field radial cross-section beamwidth estimation mentioned in step (2) is specifically implemented as follows: Based on the physical characteristics of sound field propagation, after obtaining the axial sound pressure distribution in step (1), this invention introduces acoustic energy parameters. This is used to characterize the energy distribution characteristics of a sound field during axial propagation. It is defined as the product of the axial sound pressure and the square of the beamwidth, expressed as: ; In the formula, Indicates axial sound pressure. Indicates beamwidth.

[0034] In practice, the sound field distribution is first extracted from the existing measurement cross-sections, and the peak sound pressure level of each cross-section is calculated. Then, using -3dB (i.e. 0.707 times) of the peak sound pressure level as a threshold, the corresponding isopleth region is extracted from the cross-section, and the beamwidth is estimated through the spatial range of this region.

[0035] After obtaining the beamwidth of the existing measurement cross-section, a constraint model based on energy conservation is introduced. By fitting this combined parameter, the transverse energy propagation law of the sound field is modeled. Specifically, acoustic energy parameters are constructed at discrete measurement points. Based on finite measurement cross-section data, acoustic energy parameters are calculated at several discrete locations, and their variation trend with axial position is fitted using a linear model, expressed as: ; In the formula, , The fitting coefficients are denoted as .

[0036] Through this fitting, a continuous acoustic energy distribution function can be obtained. Based on this, combined with the axial sound pressure obtained in step (1) after correction, the beamwidth at each axial position can be obtained by inverse solution, expressed as: ; In the formula, To predict beamwidth; This refers to the axial sound pressure.

[0037] The underwater focused ultrasonic field radial section sound pressure prediction mentioned in step (3) is specifically implemented as follows: After obtaining the maximum axial sound pressure from step (1) and the beamwidth from step (2), it is necessary to reconstruct the actual shape of the sound field during propagation as it changes with the axial position. Singular value decomposition is performed on the sound pressure matrices of the four measured radial sections at different axial positions to extract spatial mode functions that characterize the shape, width, and energy distribution of the main lobe of the radial section of the sound field. Since the changes in the sound field structure at different axial positions are mainly reflected in the changes in the weights of each mode, a nonlinear prediction model is established using the Gaussian process regression method to continuously change the weight coefficients of each mode with the axial position. The predicted weight coefficients of each mode are combined and superimposed with the corresponding spatial mode functions to reconstruct the initial radial section sound pressure distribution at the corresponding axial position. Subsequently, the reconstructed section is corrected using the maximum axial sound pressure from step (1) and the beamwidth from step (2) to achieve prediction of the radial section sound pressure at any axial position of the underwater focused ultrasonic sound field. The specific method is as follows: First, the measured cross-sectional data are expanded into vector form, and a data matrix is ​​constructed. Singular value decomposition is then performed on this matrix, resulting in the following representation: ; In the formula, This is the original data matrix. It is formed by expanding multiple measured sound field cross-sectional data into vectors and then concatenating them. It is a left singular matrix. This is a singular value matrix. The magnitude of each singular value corresponds to the energy or importance of the structure represented by the corresponding singular vector in the data. This is the transpose of the right singular matrix. Expanding the matrix product of equation (10), for the data matrix... any element in (that is, in the first) Axial measurement positions Place, No. The sound pressure value at each horizontal spatial coordinate), and its specific mathematical summation expression is: ; In the formula, Left singular matrix The Line 1 Column elements; This is the k-th diagonal singular value, and its magnitude represents the energy proportion of this mode; represents the corresponding element after the transpose of the right singular matrix; r is the principal mode order after truncation based on energy proportion. To transform the above matrix decomposition result into a sound field spatial mode superposition form with clear physical meaning, this invention uses the spatial mode function... At discrete space points The value at that point is explicitly defined as a left singular matrix. The k-th column vector element: ; At the same time, the known axial position will be measured. Modal weighting coefficients at the location , defined as the product of the singular values ​​and the corresponding elements of the right singular vector: ; Substituting the above two equations, we can realize the continuous modal reconstruction expression of the sound field cross-section at discrete measurement points. Therefore, any cross-section can be represented as a linear combination of several modes, expressed as: ; In the formula, Let the horizontal coordinate at position z on the axis be The sound pressure distribution across the sound field cross section; The selected modal order; The modal weighting coefficient of the k-th mode at the axial position z reflects the degree of contribution of this mode to the sound field; Let be the k-th spatial modal function, which is only related to the cross-sectional spatial structure. Since the changes in the sound field structure at different axial positions are mainly reflected in the changes in the modal weighting coefficients, the variation of the modal weighting coefficients with axial position can be modeled: ; In the formula, For the axial prediction point Modal weighting coefficient estimation at the location; For prediction points The prediction variance of the modal weighting coefficients; For test points The correlation vector between the data and all training sample points; The autocovariance matrix formed by the observed sample points; For the first The equivalent white noise energy of each modal observation data; This is a vector of observed modal weight coefficients extracted from known cross-sectional data; It is an identity matrix.

[0038] After predicting the modal weight coefficients at arbitrary locations, substituting them back into the linear combination formula, and comparing them with the corresponding spatial mode functions... By performing linear superposition, the preliminary reconstructed sound field cross-section at the corresponding location can be calculated. Subsequently, the actual beamwidth of this preliminary reconstructed cross-section is calculated. And introduce the beamwidth predicted in step (2). Define the spatial scale scaling factor A scaling transformation is performed on the transverse coordinate system of the initial reconstructed section to achieve beamwidth constraint correction, expressed as: ; In the formula, This is the cross-sectional sound field distribution after beamwidth scaling correction.

[0039] Finally, to ensure that the reconstruction results are consistent with the axial sound pressure, the cross-section after beamwidth correction is normalized so that its maximum value is equal to the axial sound pressure at the corresponding position, expressed as: ; In the formula, The final reconstructed radial cross-section sound field; This represents the predicted maximum axial sound pressure at this location; Let be the maximum sound pressure level at all (x, y) points on a fixed z-section.

[0040] The above method enables the correction and prediction of the radial cross-sectional sound pressure at any axial position of the underwater focused ultrasonic sound field.

[0041] The following analysis uses underwater acoustic field data measured by an Olympus V314-SU piezoelectric focused ultrasonic transducer in an underwater ultrasonic three-dimensional measurement system with a sampling frequency of 50MHz, a step size of 0.5mm, and a scanning speed of 5-10 measurement points per second. The analysis aims to predict axial sound pressure and beamwidth to reconstruct the ultrasonic acoustic field. 1. Axial acoustic field data and radial acoustic field data at some locations of the underwater focused ultrasonic transducer, see... Figures 2A-2E ;in, Figure 2A This is a graph of the axial sound field. Figure 2B This is a radial section sound field distribution diagram at Z=36mm. Figure 2C This is a radial section sound field distribution diagram at Z=40mm. Figure 2D This is a radial section sound field distribution diagram at Z=44mm. Figure 2E The image shows the sound field distribution at the radial section at Z=48mm.

[0042] 2. Using step (1) to Figures 2A-2E The axial measurement data were processed to obtain the sound pressure correction prediction results, see... Figure 3 .

[0043] 3. Using the corrected axial sound pressure and known cross-sectional measurement data obtained in step (2), the beamwidth at each axial position is obtained, see... Figure 4 .

[0044] 4. Reconstruct the radial section sound field using step (3), see Figure 5 .

[0045] It should be noted that although this embodiment selects four measured radial sections at different axial positions as known data for sound field reconstruction and prediction, this is only the minimum number of measured radial sections required to verify the effectiveness of the method under sparse measurement conditions. In practical applications, the number of measured radial sections can be any number greater than or equal to four; the more measured sections, the higher the accuracy of the prediction model.

[0046] This method can be directly applied to various practical engineering scenarios: In the field of underwater acoustic detection, it can be integrated into a transducer acoustic field calibration system. With only a small amount of axial scanning and a few radial cross-sectional measurements, the radial sound pressure distribution along the entire propagation path can be quickly obtained, enabling transducer directivity calibration and detection performance evaluation, significantly reducing the time and hardware cost of three-dimensional acoustic field scanning. In the field of medical focused ultrasound therapy, it can be embedded in a treatment planning system. Based on limited preoperative acoustic field measurement data, it can accurately predict the radial sound pressure morphology of the focal region at different treatment depths, providing quantitative basis for treatment dose planning and focal region position control, ensuring lesion ablation. This method effectively avoids damage to normal tissues. In the field of industrial non-destructive testing, it can be used for rapid acoustic field calibration of conventional ultrasonic testing probes and phased array ultrasonic probes. For different focal depths formed by phased array electronic focusing, it can quickly predict the radial sound pressure distribution and beamwidth at each focusing depth, complete the probe's lateral resolution calibration, focal domain sound pressure amplitude calibration, and focusing delay parameter verification, optimize the process parameters for quantitative defect detection, and improve the detection rate and dimensional accuracy of minute defects. In addition, this method can also be extended to many other underwater ultrasonic and ultrasonic testing related fields such as ultrasonic imaging performance calibration and acoustic device performance testing.

[0047] In summary, this invention provides a method for correcting and predicting the radial cross-sectional sound pressure of an underwater focused ultrasonic sound field, comprising the following steps: (1) performing Hilbert transform on the signal composed of the maximum sound pressure values ​​at each axial position of the measured axial sound field, extracting the envelope of the maximum sound pressure signal, and constructing a function between the axial measured sound pressure and the maximum sound pressure value of the radial cross-section based on multiple (at least four) measured maximum sound pressure values ​​at different axial positions using the Gaussian process regression method, thereby realizing the correction of the maximum sound pressure at any axial position; (2) based on the predicted maximum sound pressure correction value at the axial position, using multiple (at least four) measured maximum sound pressure values ​​at different axial positions... (3) Based on the axial sound pressure and beamwidth, the measured cross section is decomposed into singular values ​​to extract the spatial mode function. Gaussian process regression is used to establish a prediction model of the mode weight coefficient as the axial position changes. The preliminary reconstructed cross section at any axial position is obtained by mode superposition. Then, the reconstructed cross section is corrected by the beamwidth and the maximum axial sound pressure at the corresponding position, so as to realize the correction and prediction of the sound pressure distribution of the radial cross section of the sound field.

[0048] Furthermore, the present invention also provides a computer device / apparatus / system, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method.

[0049] The present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0050] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more blocks of the flowchart illustrations and / or block diagrams.

[0051] These computer program instructions may also be stored in a computer-readable storage medium capable of directing a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more blocks in a block diagram.

[0052] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable data processing apparatus to produce a computer-implemented process, thereby providing steps for implementing the functions specified in one or more flowcharts and / or one or more blocks in a block diagram.

[0053] It should be noted that, depending on the implementation needs, the various steps / components described in this invention can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0054] Those skilled in the art will readily understand that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for correcting and predicting the radial cross-sectional sound pressure of an underwater focused ultrasonic field, characterized in that, The method includes: The axial scanning signal of the underwater focused ultrasonic sound field is acquired, and the signal envelope is extracted by Hilbert transform of the axial scanning signal. A proportional correction coefficient is constructed based on the ratio of the signal envelope to the theoretical axial sound pressure. The change of the proportional correction coefficient with the axial position is modeled by Gaussian process regression to predict the proportional correction coefficient at any axial position. The proportional correction coefficient is multiplied by the theoretical axial sound pressure to obtain the corrected axial sound pressure. Predict the radial cross-section beamwidth at any axial position of the underwater focused ultrasonic field; Modal decomposition is performed on the existing measured radial cross section to extract the spatial mode function and mode weight coefficients. A prediction model of the mode weight coefficients changing with axial position is established using Gaussian process regression to predict the mode weight coefficients at any axial position. Based on the predicted mode weight coefficients and the corresponding spatial mode function, the preliminary radial cross section sound pressure distribution at any axial position is reconstructed. The preliminary radial cross section is scaled laterally using the predicted beamwidth, and the amplitude of the scaled cross section is normalized using the corrected axial sound pressure to obtain the final radial cross section sound pressure distribution. The prediction of the radial cross-section beamwidth at any axial position of the underwater focused ultrasonic field includes: The sound field energy parameter is defined as the product of the axial sound pressure and the square of the beamwidth at the corresponding axial position; The beamwidth at the corresponding discrete positions is calculated based on the existing measured radial cross section, and the sound field energy parameters at the corresponding discrete positions are calculated in combination with the corrected axial sound pressure. A linear fit was performed on the variation trend of the sound field energy parameters with axial position to obtain a continuous sound energy distribution function; By using the continuous acoustic energy distribution function and the corrected axial sound pressure, the predicted beamwidth at any axial position is obtained by inverse solution.

2. The underwater focused ultrasonic field radial section sound pressure correction and prediction method according to claim 1, characterized in that, When using Gaussian process regression to model the change of the scaling correction coefficient with axial position, for abnormal measurement points, a local neighborhood space set is defined with the axial position of the abnormal measurement point as the center. The axial position coordinates of each normal measurement point in the local neighborhood space set and their corresponding scaling correction coefficients are obtained. The weights of each normal measurement point are determined according to the axial distance between the abnormal measurement point and each normal measurement point and the characteristic scale parameter. Based on the weights, the scaling correction coefficients of each normal measurement point are weighted and fused to obtain the scaling correction coefficients after correction for the abnormal measurement points.

3. The method for correcting and predicting the radial cross-sectional sound pressure of underwater focused ultrasonic sound field according to claim 1, characterized in that, Calculate the beamwidth at the corresponding discrete locations based on the existing measured radial cross section, including: Calculate the peak sound pressure in the existing radial cross section, extract the corresponding isopleth region in the cross section using -3dB of the peak sound pressure as a threshold, and estimate the beamwidth based on the spatial range of the isopleth region.

4. The method for correcting and predicting the radial cross-sectional sound pressure of underwater focused ultrasonic sound field according to claim 1, characterized in that, Modal decomposition of existing measured radial sections, including: The sound pressure data from multiple existing radial cross sections are expanded into vector form and a data matrix is ​​constructed. Singular value decomposition is performed on the data matrix. The column vectors of the left singular matrix are defined as spatial mode functions, and the product of the singular values ​​and the elements of the right singular matrix is ​​defined as the mode weight coefficients at the corresponding axial positions.

5. The method for correcting and predicting the radial cross-sectional sound pressure of underwater focused ultrasonic sound field according to claim 1, characterized in that, A predictive model for the variation of modal weight coefficients with axial position is established using Gaussian process regression, including: A nonlinear prediction model for the variation of the weight coefficients of each mode with axial position was established using Gaussian process regression. Based on the prediction model, the modal weight coefficients at any axial position are predicted. The predicted modal weight coefficients are then linearly combined and superimposed with the corresponding spatial modal functions to reconstruct the preliminary radial cross-sectional sound pressure distribution at the corresponding axial position.

6. The method for correcting and predicting the radial cross-sectional sound pressure of underwater focused ultrasonic sound field according to claim 1, characterized in that, Lateral scaling of the initial radial cross section using the predicted beamwidth includes: The actual beamwidth of the preliminary radial section is calculated, and the ratio of the predicted beamwidth to the actual beamwidth is defined as the spatial scale scaling factor. The scale transformation of the transverse coordinate system of the preliminary radial section is then performed to achieve the constraint correction of the beamwidth.

7. The method for correcting and predicting the radial cross-sectional sound pressure of underwater focused ultrasonic sound field according to claim 1, characterized in that, The amplitude of the scaled cross section is normalized using the corrected axial sound pressure, including: The scaled cross section is normalized to make its maximum sound pressure level equal to the corrected axial sound pressure level at the corresponding axial position.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 7.

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