An underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement method, system, device and medium

Abstract

This invention relates to the field of underwater welding technology and discloses a method and system for modeling and coherently enhancing the error propagation of underwater phased array nonlinear ultrasonic echoes. The method includes: establishing a unified error propagation model encompassing array element amplitude deviation, additional phase error, array element position deviation, and sound velocity disturbance; constructing a channel frequency domain transfer function based on a standard scatterer with known scattering characteristics and compensating for the measured echo; introducing a minimum variance distortionless response beamforming method based on amplitude and phase correction; optimizing the array output power distribution; and achieving real-time updating and stable output of the array channel response based on laboratory calibration and on-site dynamic correction phase calibration mechanisms, and by introducing an environmental correction factor. This invention enables quantitative analysis of the coherent superposition efficiency of nonlinear harmonics and accurate recovery of the amplitude and phase consistency of array channels under complex environments; it can improve the distinguishability of nonlinear harmonic signals and the stability and reliability of detection results in complex underwater environments.

Description

Technical Field

[0001] This invention relates to the field of underwater phased array technology, and in particular to a method, system, device and medium for modeling and coherent enhancement of nonlinear ultrasonic echo error propagation in underwater phased arrays. Background Technology

[0002] To ensure the long-term safe service of marine engineering structures and achieve highly sensitive detection of early micro-damage in underwater welds, the application of phased array technology in array ultrasonic testing and imaging has significantly improved the detection capability of internal defects in complex structures. For example, the full-matrix acquisition-based full-focusing imaging method, by delaying and coherently combining signals from each transmitting and receiving channel of the array, can achieve high-resolution imaging and has become an important technical means for the fine inspection of complex components. With the improvement of hardware system performance, multi-element phased array systems can flexibly adjust the element delay, effective aperture, and excitation mode through program control, thereby forming a controllable sound field distribution in the target area and improving the adaptability and spatial resolution of the detection. Building on this, existing technologies have attempted to introduce nonlinear ultrasonic testing methods into phased array systems, extracting local nonlinear response features under array excitation conditions to balance spatial resolution with high sensitivity to micro-damage. By optimizing the frequency response of the receiving system to match the harmonic frequency band, the detectability of weak nonlinear echo signals can be enhanced to a certain extent.

[0003] However, under multi-element excitation and multi-path propagation conditions, the formation and superposition process of the nonlinear sound field becomes more complex, and phase distortion and uneven energy distribution easily occur between different channels, affecting the stability and consistency of the imaging results. Meanwhile, as the array data scale increases, the defect localization and imaging process becomes highly dependent on post-processing algorithms, resulting in high computational complexity and difficulty in meeting real-time detection requirements. Therefore, existing technologies still lack systematic theoretical models to support the formation mechanism and stable characterization of nonlinear scattering signals under underwater array focusing conditions, particularly regarding error propagation and coherent enhancement. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method and system for modeling and coherent enhancement of nonlinear ultrasonic echo error propagation in underwater phased arrays to solve the problems of current underwater phased array models not comprehensively considering multi-source errors, difficulty in evaluating the coherent superposition effect of nonlinear harmonics, poor applicability of traditional array calibration methods in underwater near-field multipath environments, and difficulty in effectively separating weak nonlinear harmonic signals, resulting in decreased calibration accuracy.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] In a first aspect, the present invention provides a method for modeling and coherent enhancement of underwater phased array nonlinear ultrasonic echo error propagation, comprising:

[0008] For the nonlinear harmonic echo signals received by each channel in the array, a receiving model including the ideal scattering response and the actual disturbance is established, and the phase residual parameter used to measure the degree of coherence loss of each channel is extracted to quantitatively describe the influence of multi-source error on the nonlinear harmonic coherent superposition efficiency.

[0009] Based on a standard scatterer, the frequency domain transfer function of each channel of the array is calibrated to obtain the comprehensive transfer characteristics of each channel. An amplitude and phase compensation operator is constructed, and the compensation operator is used to perform consistency compensation correction on the echo signal of the target under test.

[0010] After consistency compensation and correction, each channel signal is constructed into a multi-channel array signal vector. The covariance matrix of the signal vector is calculated. A steering vector is established according to the target direction. Adaptive weights are calculated through minimum variance distortionless response beamforming. The compensated signal is coherently fused to enhance nonlinear harmonic components and suppress interference.

[0011] A joint calibration mechanism combining laboratory benchmark calibration and on-site dynamic correction is constructed. The initial transfer function of each channel of the array is obtained in advance as a benchmark. The channel response offset caused by environmental changes is measured in real time using a reference scatterer. An environmental correction factor is extracted, and the compensation parameters are corrected online based on the environmental correction factor to achieve dynamic compensation.

[0012] As a preferred embodiment of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method described in this invention, the method includes: for the nonlinear harmonic echo signals received by each channel in the array, establishing a receiving model that includes ideal scattering response and actual disturbance, and extracting phase residual parameters to measure the degree of coherence loss of each channel, so as to quantitatively describe the influence of multi-source errors on the nonlinear harmonic coherent superposition efficiency, including:

[0013] Set array number Each array element receives an ideal nonlinear harmonic signal;

[0014] Based on the ideal nonlinear harmonic signal, the receiver model is constructed by introducing array element amplitude response deviation, channel additional phase error, array element position and path error and environmental noise.

[0015] Based on the aforementioned receiving model, with ideal weights as superposition coefficients, coherent superposition is used to fuse multi-channel signals to obtain the array output amplitude under error conditions.

[0016] Based on the array output amplitude expression, the array element position and path error components and the channel additional phase error components are combined and defined as the phase residual parameter;

[0017] Based on the assumption that the phase residual follows a zero-mean small perturbation distribution, an approximate quantitative relationship between the array output power gain and the variance of the phase residual is established, and it is determined that the coherent superposition efficiency loss depends on the dispersion of the phase residual.

[0018] As a preferred embodiment of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement method described in this invention, wherein: in the receiving model, the array element amplitude response deviation is quantified by the harmonic output power degradation factor to the expected value of the coherent superposition gain.

[0019] The sound velocity disturbance in environmental noise is transformed into an additional phase error component through the product of wavenumber change and propagation distance, and the corresponding component is proportional to the propagation distance.

[0020] As a preferred embodiment of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method described in this invention, the method includes: calibrating the frequency domain transfer function of each channel of the array based on a standard scatterer to obtain the comprehensive transfer characteristics of each channel; constructing amplitude and phase compensation operators; and using these compensation operators to perform consistency compensation correction on the echo signal of the target under test, including:

[0021] A standard scatterer with stable scattering characteristics is deployed at a known location, and the calibration signal received by each channel is obtained;

[0022] After averaging the noise suppression through multiple measurements, the frequency domain integrated transfer function of each channel is calculated. The frequency domain integrated transfer function includes the combined effects of array element amplitude response deviation, channel additional phase error, array element position and path error, and sound speed disturbance.

[0023] Based on the comprehensive transfer function, a compensation operator is constructed to perform frequency domain inversion compensation on the echo signal of the target under test, so that the response of each channel is normalized to the ideal reference level, thereby realizing frequency domain amplitude and phase consistency control.

[0024] As a preferred embodiment of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method described in this invention, the comprehensive transfer function error of each channel after compensation includes: amplitude response deviation term and phase residual term; after compensation, the phase residual between each channel is controlled within a range that matches the requirements of array coherence processing.

[0025] As a preferred embodiment of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement method described in this invention, the method includes: constructing a multi-channel array signal vector from the consistent compensation-corrected signals of each channel; calculating the covariance matrix of the signal vectors; establishing a steering vector based on the target direction; calculating adaptive weights through minimum variance distortionless response beamforming; and coherently fusing the compensated signals to enhance nonlinear harmonic components and suppress interference, including:

[0026] The compensated multi-channel signals are used to form an array signal vector, and the covariance matrix of the signal vector at the harmonic frequency is calculated.

[0027] Based on the target detection direction and array geometric parameters, a guiding vector reflecting the spatial phase delay of each array element relative to the reference point is constructed;

[0028] Using the guide vector as a linear constraint, solve for the weight vector that minimizes the total output power of the array while ensuring distortion-free output of the target direction signal;

[0029] The weight vector is used to calculate the multi-channel compensated signal to obtain the coherently enhanced array output signal.

[0030] As a preferred embodiment of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method described in this invention, the method includes: constructing a joint calibration mechanism combining laboratory benchmark calibration and on-site dynamic correction; pre-obtaining the initial transfer function of each channel of the array as a benchmark; using a reference scatterer to measure the channel response offset caused by environmental changes in real time; and extracting environmental correction factors, including:

[0031] In a controlled laboratory environment, the array is calibrated across the entire frequency band using a standard scatterer, and the initial transfer function of each channel is obtained as the intrinsic response benchmark.

[0032] A reference scatterer at a known location is deployed at the actual testing site to measure the received signal of each channel under the current environmental conditions;

[0033] By calculating the ratio of the field-received signal to the theoretically received signal based on the laboratory intrinsic response, correction factors reflecting the impact of environmental changes on the response of each channel are extracted.

[0034] The correction factor is multiplied by the initial transfer function to obtain the updated transfer function suitable for the current detection environment, which is used for online dynamic compensation of the signal under test.

[0035] Secondly, the present invention provides an underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement system, comprising:

[0036] The error model construction module is used to establish a receiving model that includes the ideal scattering response and the actual disturbance for the nonlinear harmonic echo signals received by each channel in the array, and to extract the phase residual parameter used to measure the degree of coherence loss of each channel, so as to quantitatively describe the influence of multi-source error on the nonlinear harmonic coherent superposition efficiency.

[0037] The channel calibration and compensation module is used to calibrate the frequency domain transfer function of each channel of the array based on a standard scatterer, obtain the comprehensive transfer characteristics of each channel, and construct amplitude and phase compensation operators. The compensation operators are then used to perform consistency compensation and correction on the echo signal of the target under test.

[0038] The multi-channel coherent enhancement module is used to construct a multi-channel array signal vector from the signals of each channel after consistency compensation and correction, calculate the covariance matrix of the signal vector, establish a steering vector according to the target direction, calculate adaptive weights through minimum variance distortionless response beamforming, and coherently fuse the compensated signal to enhance nonlinear harmonic components and suppress interference.

[0039] The joint calibration and dynamic correction module is used to construct a joint calibration mechanism that combines laboratory benchmark calibration with on-site dynamic correction. The initial transfer function of each channel of the array is obtained in advance as a benchmark. The channel response offset caused by environmental changes is measured in real time using a reference scatterer. An environmental correction factor is extracted, and the compensation parameters are corrected online based on the environmental correction factor to achieve dynamic compensation.

[0040] Thirdly, the present invention provides a computer device, comprising:

[0041] Memory and processor;

[0042] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of an underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement method.

[0043] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method.

[0044] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention establishes a unified error propagation model that includes array element amplitude deviation, additional phase error, array element position deviation, and sound velocity disturbance, clarifying the influence relationship of various errors on harmonic output and achieving quantitative analysis of nonlinear harmonic coherent superposition efficiency; it constructs a channel frequency domain transfer function based on a standard scatterer with known scattering characteristics and compensates for the measured echo, achieving accurate recovery of array channel amplitude and phase consistency under complex environments; and, based on amplitude and phase correction, it introduces a minimum variance distortionless response beamforming method to improve the distinguishability of nonlinear harmonic signals by optimizing the array output power distribution; furthermore, it combines a calibration mechanism that integrates laboratory calibration with on-site dynamic correction, and by introducing an environmental correction factor, achieves real-time updating and stable output of the array channel response. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a schematic diagram of the overall process of an underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method according to an embodiment of the present invention.

[0047] Figure 2 This is a schematic diagram illustrating the specific process of an underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method according to an embodiment of the present invention.

[0048] Figure 3 This is a schematic diagram of the simulation results of eight-channel phase residuals in an underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method according to an embodiment of the present invention.

[0049] Figure 4 This is a schematic diagram of the statistical distribution of harmonic signal-to-noise ratio under multiple random experiments in an underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method according to an embodiment of the present invention. Detailed Implementation

[0050] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0051] Example 1, referring to Figure 1 As an embodiment of the present invention, a method for modeling and coherent enhancement of underwater phased array nonlinear ultrasonic echo error propagation is provided, comprising:

[0052] S100: For the nonlinear harmonic echo signals received by each channel in the array, a receiving model including the ideal scattering response and the actual disturbance is established, and the phase residual parameter used to measure the degree of coherence loss of each channel is extracted to quantitatively describe the influence of multi-source error on the nonlinear harmonic coherent superposition efficiency.

[0053] Based on the above, S100 introduces phase residual as a key characterization parameter by uniformly modeling the error, which is used to characterize the degree of coherence loss during multi-channel superposition and analyze its influence on the output signal strength and stability.

[0054] S200: Based on a standard scatterer, the frequency domain transfer function of each channel of the array is calibrated to obtain the comprehensive transfer characteristics of each channel, and amplitude and phase compensation operators are constructed. The compensation operators are used to perform consistency compensation correction on the echo signal of the target under test.

[0055] Based on the above, in order to eliminate the differences in response of each channel in S200, a standard scatterer with stable scattering characteristics and known geometric dimensions is selected as a reference source to calibrate the array system. The specific process includes: (1) deploying the standard scatterer at a known location to obtain the actual received signal of each channel; (2) suppressing the influence of random noise through multiple measurements and averaging; (3) estimating the comprehensive transmission characteristics of each channel; and (4) constructing a unified compensation operator to normalize the amplitude and phase of the subsequent signal to be measured. After compensation, the signals of each channel achieve consistency in the frequency domain, which can significantly reduce the influence of system errors on nonlinear harmonic signals, thereby improving the detectability of weak signals.

[0056] S300: Constructs the signals of each channel after consistency compensation and correction into a multi-channel array signal vector, calculates the covariance matrix of the signal vector, establishes a steering vector according to the target direction, calculates adaptive weights through minimum variance distortionless response beamforming, and performs coherent fusion on the compensated signal to enhance nonlinear harmonic components and suppress interference.

[0057] Based on the above, after completing the channel consistency compensation, S300 constructs the multi-channel signals into an array vector form and performs collaborative processing. Specifically, it includes: (1) constructing a statistical characteristic description of the multi-channel signals; (2) establishing array guidance information according to the direction of the target; designing adaptive weights to keep the target direction signal output without distortion while minimizing the overall output energy; and (4) achieving effective suppression of interference, reverberation and noise in non-target directions.

[0058] This process can further enhance nonlinear harmonic components, thereby improving the signal-to-noise ratio and spatial resolution of the signal.

[0059] S400: Construct a joint calibration mechanism that combines laboratory benchmark calibration with on-site dynamic correction. The initial transfer function of each channel of the array is obtained in advance as a benchmark. The channel response offset caused by environmental changes is measured in real time using a reference scatterer. An environmental correction factor is extracted, and the compensation parameters are corrected online based on the environmental correction factor to achieve dynamic compensation.

[0060] Based on the above, in order to improve the stability of the system in real complex environments, S400 constructs a joint calibration strategy of laboratory calibration and field correction. Specifically, it includes: (1) performing full-band, multi-directional scanning calibration of the array in a controllable environment and establishing a channel response database; (2) deploying reference scatterers in the actual detection environment and acquiring the channel response under the current environment in real time; (3) extracting the response offset caused by environmental changes by comparing the laboratory calibration results with the field measurement results; and (4) correcting the original calibration parameters online to achieve dynamic compensation.

[0061] It should be noted that existing underwater phased array detection methods are typically based on linear echo models, failing to adequately consider the multi-source error coupling effects on nonlinear harmonic signals during propagation. In particular, they lack unified modeling of factors such as channel amplitude and phase errors, element position deviations, and sound velocity disturbances, leading to a significant decrease in coherent superposition efficiency in complex environments. Furthermore, existing methods often employ simple amplitude normalization or fixed phase correction strategies, making it difficult to accurately compensate for dynamic errors in different channels. This can easily result in the accumulation of residual phase deviations, making it difficult to separate weak nonlinear signals from noise. Therefore, by establishing a multi-channel nonlinear echo error propagation model through steps S100-S400, introducing a standard scatterer for channel consistency calibration compensation, and combining this with frequency-domain adaptive coherent enhancement processing, the coherent superposition efficiency and signal-to-noise ratio of nonlinear harmonic echoes can be improved, thereby enhancing the stability and reliability of detection results in complex underwater environments.

[0062] Example 2, refer to Figures 1-2 As an embodiment of the present invention, based on the above embodiment, a method for modeling and coherent enhancement of underwater phased array nonlinear ultrasonic echo error propagation is provided. The method includes:

[0063] S100: For the nonlinear harmonic echo signals received by each channel in the array, a receiving model including the ideal scattering response and the actual disturbance is established, and the phase residual parameter used to measure the degree of coherence loss of each channel is extracted to quantitatively describe the influence of multi-source error on the nonlinear harmonic coherent superposition efficiency.

[0064] In the embodiments of this application, reference is made to Figure 2Step one includes the following steps A1-A5:

[0065] A1: Set the array number Each array element receives an ideal nonlinear harmonic signal;

[0066] Specifically, let the array's first... The second harmonic frequency received by each array element Ideal scattered signal at for:

[0067] (1)

[0068] in, This represents the amplitude of the second harmonic. represents an imaginary number; Indicates the first The position of each array element; Angular frequency; For time; For wave number.

[0069] A2: Based on the ideal nonlinear harmonic signal, the receiver model is constructed by introducing array element amplitude response deviation, channel additional phase error, array element position and path error, and environmental noise.

[0070] Specifically, in actual underwater environments, due to factors such as differences in array element channel response, array element installation position errors, and random disturbances in sound velocity, the received signal will deviate from the ideal form. Taking all the above factors into consideration, the first... The actual received signal of each array element can be modeled as:

[0071] (2)

[0072] in, For the first Channel amplitude response deviation; Add phase error to the channel; For the position and path error of array elements; This is environmental noise.

[0073] A3: Based on the aforementioned receiving model, using ideal weights as superposition coefficients, coherent superposition is employed to fuse multi-channel signals, thereby obtaining the array output amplitude under error conditions;

[0074] Specifically, in A3, to improve the harmonic signal-to-noise ratio, coherent superposition is used to fuse multi-channel signals; the array output can be defined as:

[0075] (3)

[0076] in, Representing the ideal weights, by substituting the actual signal and ignoring the noise term, we can obtain the expected output amplitude:

[0077] (4)

[0078] in, express One channel.

[0079] A4: Based on the array output amplitude expression, the array element position and path error components and the channel additional phase error components are combined and defined as the phase residual parameter;

[0080] Specifically, in A4, to characterize the comprehensive impact of phase error, the first... The phase residual of the channel is:

[0081] (5)

[0082] It should be noted that, The residual, which combines position error and channel phase error, is a key parameter that determines the stacking efficiency.

[0083] A5: Based on the assumption that the phase residual follows a zero-mean small perturbation distribution, an approximate quantitative relationship between the array output power gain and the variance of the phase residual is established, and it is determined that the coherent superposition efficiency loss depends on the dispersion of the phase residual.

[0084] Specifically, based on A4 ,when It follows a zero-mean, small-perturbation distribution and can be expanded using a second-order Taylor expansion of the exponential function. Ignoring terms of order three and above, we get:

[0085] (6)

[0086] in, This represents the sample variance of the phase residual.

[0087] Furthermore, it is necessary to decompose the various error sources constituting the phase residual and analyze the influence mechanisms of amplitude deviation, position error, and sound velocity disturbance one by one. In the embodiment of this application, in the receiving model described in S100:

[0088] The first type of error is the amplitude response deviation of the array elements; its impact on the expected value of the coherent superposition gain is quantified by the harmonic output power degradation factor.

[0089] Specifically, the amplitude inconsistency coefficient is defined as follows: ,in For gain deviation. Define the harmonic output power degradation factor. :

[0090] (7)

[0091] It should be noted that its physical meaning is the power gain loss relative to an ideal uniform response when only amplitude error exists.

[0092] like With zero mean and zero variance For independent and identically distributed random variables, then The expectation is:

[0093] (8)

[0094] when When the amplitude dispersion is large, it has a small impact on the average gain, but its random fluctuations will still introduce volatility and affect stability.

[0095] The second type of error is: the position and path error of the array elements;

[0096] Specifically, let the deviation vector between the actual position and the nominal position of the array element be... Then the propagation distance error is ,in Let be the unit vector in the target direction. The resulting phase error is:

[0097] (9)

[0098] Comparing formula (24), formula (9) directly relates the array element position installation accuracy to the system phase residual.

[0099] The third type of error is the sound velocity disturbance and path error in environmental noise; it is converted into an additional phase error component through the product of wavenumber change and propagation distance, and the corresponding component is proportional to the propagation distance.

[0100] Specifically, the speed of sound in water is affected by factors such as temperature, salinity, and depth, and can be expressed as follows: ,in The nominal speed of sound, This is a random perturbation. The corresponding change in wavenumber is:

[0101] (10)

[0102] For a transmission distance of For the channel, the additional phase error caused by sound speed disturbance is:

[0103] (11)

[0104] Equation (11) shows that long-distance channels are more sensitive to sound speed disturbances, which is a key factor to consider for shallow sea long baseline arrays or large aperture phased array systems.

[0105] Overall, Equation (6) provides a quantitative relationship between the multi-channel coherent superposition efficiency and the phase error variance from a statistical perspective; while the array element position deviation (Equation 9), sound velocity disturbance (Equation 11), and channel phase inconsistency together constitute the main sources of phase error, and their variances are superimposed to form This, in turn, determines the coherent gain attenuation of the harmonic signal; simultaneously, the amplitude inconsistency error is mitigated by a factor. This further affects the output power, thus forming a unified characterization model of the multi-source error on the nonlinear echo fusion performance.

[0106] S200: Based on a standard scatterer, the frequency domain transfer function of each channel of the array is calibrated to obtain the comprehensive transfer characteristics of each channel, and amplitude and phase compensation operators are constructed. The compensation operators are used to perform consistency compensation correction on the echo signal of the target under test.

[0107] In the embodiments of this application, reference is made to Figure 2 Step two includes the following steps B1-B3:

[0108] B1: Deploy a standard scatterer with stable scattering characteristics at a known location and obtain the calibration signal received by each channel;

[0109] For example, in B1, a standard body with known geometric dimensions and stable scattering characteristics, such as a metal sphere or a plate, can be selected as the reference source.

[0110] Specifically, assuming the standard scatterer is located at a certain orientation of the array, its theoretical scattering response can be modeled as follows:

[0111] (12)

[0112] in, The complex scattering amplitude of the standard body; Wave number; For standard body to the first The distance between each array element.

[0113] In actual measurement, the first The calibration signal received by the channel is:

[0114] (13)

[0115] in, For the first The channel's integrated transfer function.

[0116] B2: After averaging the noise through multiple measurements, calculate the frequency domain integrated transfer function of each channel. The frequency domain integrated transfer function includes the combined effects of array element amplitude response deviation, channel additional phase error, array element position and path error, and sound speed disturbance.

[0117] Specifically, based on B1 Its error can be expressed as:

[0118] ;

[0119] Here The amplitude error is caused by the harmonic output power degradation factor. express; For channel phase; This refers to the positional error; For sound speed perturbation; This is additive noise. By averaging multiple measurements, the noise can be effectively suppressed, thus the frequency domain synthesis transfer function can be estimated as follows:

[0120] (14)

[0121] B3: Based on the comprehensive transfer function, a compensation operator is constructed to perform frequency domain inversion compensation on the echo signal of the target under test, so that the response of each channel is normalized to the ideal reference level, thereby realizing frequency domain amplitude and phase consistency control.

[0122] Specifically, for any target echo... The compensated signal is:

[0123] (15)

[0124] So, the overall transfer function error after second harmonic calibration compensation It can be represented as:

[0125] (16)

[0126] In this embodiment of the application, in S200, the comprehensive transfer function error of each channel after compensation includes: amplitude response deviation term and phase residual term; after compensation, the phase residual between each channel is controlled within a range that matches the requirements of array coherent processing.

[0127] Specifically, the range that matches the requirements of array coherent processing is not a fixed value, but is determined by the quantitative relationship in formula (6).

[0128] It should be noted that this compensation operator normalizes the response of each channel to an ideal reference level, achieving frequency domain amplitude-phase consistency control. After compensation, the signal of each channel can be regarded as an ideal observation containing only the physical scattering characteristics and propagation effects of the target.

[0129] Overall, S100 is derived based on the time domain, while S200 is derived based on the frequency domain. S200, based on formula (16), requires a Fourier transform to inversely deduce S100. The error factors of S100, including the element amplitude and phase errors, position deviations, and sound velocity disturbances established by S100, can be uniformly and equivalently represented as the channel complex transfer function. The S200 achieves this through a standard scatterer. Experimental estimations are used to construct a strict correspondence between the error model and calibration compensation, thereby achieving consistent correction of multi-channel nonlinear echoes.

[0130] S300: Constructs the signals of each channel after consistency compensation and correction into a multi-channel array signal vector, calculates the covariance matrix of the signal vector, establishes a steering vector according to the target direction, calculates adaptive weights through minimum variance distortionless response beamforming, and performs coherent fusion on the compensated signal to enhance nonlinear harmonic components and suppress interference.

[0131] In the embodiments of this application, reference is made to Figure 2 Step three includes the following steps C1-C4:

[0132] C1: Construct an array signal vector from the compensated multi-channel signals and calculate the covariance matrix of the signal vector at the harmonic frequency.

[0133] Specifically, to quantify the enhancement effect of compensation on nonlinear harmonic components, the harmonic signal-to-noise ratio (HSNR) is defined as follows:

[0134] (17)

[0135] in, The signal power at the second harmonic frequency. This represents the total power of noise and reverberation within the same frequency band; this indicator directly reflects the identifiability of weak nonlinear signals.

[0136] After single-channel compensation, the multi-channel signal needs to be filtered to further suppress interference and enhance harmonic components. Let the compensated multi-channel signal vector be... Its frequency domain form is Define the array covariance matrix:

[0137] (18)

[0138] in, This represents the conjugate transpose. The steering vector corresponding to the desired harmonic direction is... , its first Each component is .

[0139] C2: Based on the target detection direction and array geometric parameters, construct a steering vector that reflects the spatial phase delay of each array element relative to the reference point;

[0140] C3: Using the aforementioned guiding vector as a linear constraint, solve for the weight vector that minimizes the total output power of the array while ensuring distortion-free output of the target direction signal;

[0141] Specifically, in C2-C3, after amplitude and phase compensation is completed, minimum variance distortionless response (MVDR) weights are introduced. The weighting minimizes the total output power while ensuring distortion-free output in the harmonic direction, thus effectively suppressing interference and reverberation in undesirable directions. Therefore, the beamformer solves the following optimization problem:

[0142] (19)

[0143] The solution is:

[0144] (20)

[0145] C4: Calculate the multi-channel compensated signal using the weight vector to obtain the coherently enhanced array output signal.

[0146] Specifically, based on the above calculations, the output signal of the multi-channel coherent fusion array can be obtained as follows:

[0147] (twenty one)

[0148] Overall, S200 has eliminated the amplitude-phase inconsistency between channels, enabling phase alignment of multi-channel signals in the target direction. S300 can directly utilize the aligned array data, where the nonlinear harmonic components in the target direction have good coherence between channels, while interference and reverberation from non-target directions remain incoherent or non-directional. The minimum variance distortionless response beamformer used in this step can allow signals (including nonlinear harmonics) from the target direction to pass without attenuation, and suppress the power of background noise from other directions to a minimum, achieving stable extraction of weak nonlinear harmonics from complex underwater backgrounds.

[0149] S400: Construct a joint calibration mechanism that combines laboratory benchmark calibration with on-site dynamic correction. The initial transfer function of each channel of the array is obtained in advance as a benchmark. The channel response offset caused by environmental changes is measured in real time using a reference scatterer. An environmental correction factor is extracted, and the compensation parameters are corrected online based on the environmental correction factor to achieve dynamic compensation.

[0150] In the embodiments of this application, reference is made to Figure 2 Step four includes steps D1-D4:

[0151] D1: In a controlled laboratory environment, the array is calibrated across the entire frequency band using a standard scatterer, and the initial transfer function of each channel is obtained as the intrinsic response benchmark.

[0152] Specifically, to improve calibration robustness and overcome the sensitivity of a single calibration method to environmental changes, a standard scatterer is used to perform a full-band, all-around scan of the array in an anechoic pool or a controlled environment to obtain the initial transfer function of each channel.

[0153] (twenty two)

[0154] D2: Deploy reference scatterers at known locations at the actual testing site and measure the received signals of each channel under the current environmental conditions;

[0155] Specifically, in actual testing environments, factors such as sound velocity fluctuations and platform attitude changes can introduce additional errors. Therefore, a reference scatterer at a known location is deployed at the testing site, and its echo is measured.

[0156] (twenty three)

[0157] in, This is the integrated transfer function under the field environment.

[0158] D3: By calculating the ratio of the field-received signal to the theoretically received signal based on the laboratory intrinsic response, a correction factor reflecting the impact of environmental changes on the response of each channel is extracted.

[0159] Specifically, based on the integrated transfer function in the field environment of D2, a correction factor is defined:

[0160] (twenty four)

[0161] in, The ratio reflects the relative change in channel response caused by environmental changes.

[0162] D4: Multiply the correction factor by the initial transfer function to obtain the updated transfer function suitable for the current detection environment, which is used for online dynamic compensation of the signal under test.

[0163] Specifically, the channel transfer function ultimately used for actual detection is:

[0164] (25)

[0165] This enables online compensation for environmental changes.

[0166] Therefore, the output signal of the jointly calibrated multi-channel coherent fusion array is:

[0167] (26)

[0168] It should be noted that Equation (26) is the mechanism for the combined effect of harmonic signals to complete error propagation, calibration compensation, array fusion coherence enhancement.

[0169] Overall, step S400 is mainly used for dynamic joint calibration, updating formula (21) in step S300. By updating the channel transfer function in real time, it ensures that the amplitude and phase consistency achieved in S200 and the accuracy of the steering vector on which S300 depends can be maintained in changing environments, guaranteeing the robustness and long-term reliability of the entire process. Without dynamic updates, the calibration accuracy may gradually decrease with environmental changes, and the error model in S100 may deviate from reality, while the beamforming performance in S300 may degrade.

[0170] Example 3, referring to Figures 3-4 Based on the above embodiments, this embodiment provides an application simulation experiment of underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method to verify the feasibility and advantages of the present invention.

[0171] Figure 3 The diagram shows a simulation of the phase residuals of eight channels, where (a) represents the phase residuals of each channel before compensation, and (b) represents the phase residuals of each channel after compensation. It illustrates that without compensation, the echo signals of each channel exhibit significant phase deviations. Simulation results show that the phase residuals of the multiple channels fluctuate within a large range, with some channels having deviations close to or exceeding ±10°, far exceeding the phase consistency requirements for coherent array superposition. This results in difficulties in effectively superimposing the multi-channel signals and dispersing harmonic energy. To address these issues, this embodiment first uses a standard scatterer to uniformly calibrate the array. Specifically, a reference target with stable scattering characteristics is deployed at a known spatial location, and calibration echo data for each channel is obtained. Noise effects are suppressed through multiple measurements, and the comprehensive transmission characteristics of each channel are estimated. Corresponding amplitude and phase compensation operators are then constructed. After using these compensation operators to perform consistency correction on the echoes of the target under test, the signals of each channel are unified in the frequency domain.

[0172] Simulation results show that the phase residuals of each channel are significantly reduced after compensation, with most channels controlled within ±3° (i.e., a range matching the requirements of array coherent processing), thus meeting the phase consistency requirements of array coherent processing. Based on the channel consistency compensation, coherent superposition processing is performed on the multi-channel signals. By uniformly weighting and synthesizing the compensated channel signals, the nonlinear harmonic components in the target direction are enhanced, while random noise and uncorrelated interference are effectively suppressed during the superposition process.

[0173] Figure 4 This diagram illustrates the statistical distribution of harmonic signal-to-noise ratio (SNR) under multiple randomized experiments, demonstrating the use of the Monte Carlo method in this embodiment for multiple randomized simulations. In each simulation, channel errors and noise are regenerated, and the calibration and compensation process is repeated to obtain the statistical distribution of the harmonic SNR. It can be seen that compared to the uncompensated case, the overall SNR of the compensated harmonic signal is significantly improved, with the distribution clearly concentrated in the high SNR region and the fluctuation range reduced. The average improvement reaches and exceeds 20%, indicating that this method can stably improve the detectability of nonlinear echoes under random error conditions.

[0174] Therefore, the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method proposed in this invention can quantitatively predict the attenuation of harmonic superposition efficiency due to phase residuals, achieve high-precision amplitude and phase compensation using standard scatterers, and dynamically adapt to changes in the underwater environment through a two-stage joint strategy. The phase residual between channels can be controlled within 3°, and the harmonic signal-to-noise ratio is improved by no less than 20%, significantly improving the reliability and imaging quality of underwater weld damage detection.

[0175] Example 4 illustrates a schematic scheme for underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement method. It should be noted that the technical solution of this underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement system belongs to the same concept as the above-described underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement method. Details not described in detail in this example of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement system can be found in the description of the above-described underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement method.

[0176] This embodiment provides an underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement system, including:

[0177] The error model construction module is used to establish a receiving model that includes the ideal scattering response and the actual disturbance for the nonlinear harmonic echo signals received by each channel in the array, and to extract the phase residual parameter used to measure the degree of coherence loss of each channel, so as to quantitatively describe the influence of multi-source error on the nonlinear harmonic coherent superposition efficiency.

[0178] The channel calibration and compensation module is used to calibrate the frequency domain transfer function of each channel of the array based on a standard scatterer, obtain the comprehensive transfer characteristics of each channel, and construct amplitude and phase compensation operators. The compensation operators are then used to perform consistency compensation and correction on the echo signal of the target under test.

[0179] The multi-channel coherent enhancement module is used to construct a multi-channel array signal vector from the signals of each channel after consistency compensation and correction, calculate the covariance matrix of the signal vector, establish a steering vector according to the target direction, calculate adaptive weights through minimum variance distortionless response beamforming, and coherently fuse the compensated signal to enhance nonlinear harmonic components and suppress interference.

[0180] The joint calibration and dynamic correction module is used to construct a joint calibration mechanism that combines laboratory benchmark calibration with on-site dynamic correction. The initial transfer function of each channel of the array is obtained in advance as a benchmark. The channel response offset caused by environmental changes is measured in real time using a reference scatterer. An environmental correction factor is extracted, and the compensation parameters are corrected online based on the environmental correction factor to achieve dynamic compensation.

[0181] This embodiment also provides a computer device applicable to underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method proposed in the above embodiment.

[0182] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements a method for modeling and coherently enhancing the error propagation of underwater phased array nonlinear ultrasonic echoes as proposed in the above embodiments.

[0183] The storage medium proposed in this embodiment and the method for modeling and coherent enhancement of underwater phased array nonlinear ultrasonic echo error propagation proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0184] From the above description of the implementation methods, those skilled in the art will clearly understand that the present invention can be implemented using software and necessary general-purpose hardware. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0185] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for modeling and coherent enhancement of underwater phased array nonlinear ultrasonic echo error propagation, characterized in that, include: For the nonlinear harmonic echo signals received by each channel in the array, a receiving model including the ideal scattering response and the actual disturbance is established, and the phase residual parameter used to measure the degree of coherence loss of each channel is extracted to quantitatively describe the influence of multi-source error on the nonlinear harmonic coherent superposition efficiency. Based on a standard scatterer, the frequency domain transfer function of each channel of the array is calibrated to obtain the comprehensive transfer characteristics of each channel. An amplitude and phase compensation operator is constructed, and the compensation operator is used to perform consistency compensation correction on the echo signal of the target under test. After consistency compensation and correction, each channel signal is constructed into a multi-channel array signal vector. The covariance matrix of the signal vector is calculated. A steering vector is established according to the target direction. Adaptive weights are calculated through minimum variance distortionless response beamforming. The compensated signal is coherently fused to enhance nonlinear harmonic components and suppress interference. A joint calibration mechanism combining laboratory benchmark calibration and on-site dynamic correction is constructed. The initial transfer function of each channel of the array is obtained in advance as a benchmark. The channel response offset caused by environmental changes is measured in real time using a reference scatterer. An environmental correction factor is extracted, and the compensation parameters are corrected online based on the environmental correction factor to achieve dynamic compensation.

2. The underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method as described in claim 1, characterized in that, For the nonlinear harmonic echo signals received by each channel in the array, a receiving model incorporating both ideal scattering response and actual disturbance is established. Phase residual parameters, used to measure the coherence loss of each channel, are extracted to quantitatively describe the impact of multi-source errors on the coherent superposition efficiency of nonlinear harmonics, including: Set array number Each array element receives an ideal nonlinear harmonic signal; Based on the ideal nonlinear harmonic signal, the receiver model is constructed by introducing array element amplitude response deviation, channel additional phase error, array element position and path error and environmental noise. Based on the aforementioned receiving model, with ideal weights as superposition coefficients, coherent superposition is used to fuse multi-channel signals to obtain the array output amplitude under error conditions. Based on the array output amplitude expression, the array element position and path error components and the channel additional phase error components are combined and defined as the phase residual parameter; Based on the assumption that the phase residual follows a zero-mean small perturbation distribution, an approximate quantitative relationship between the array output power gain and the variance of the phase residual is established, and it is determined that the coherent superposition efficiency loss depends on the dispersion of the phase residual.

3. The underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method as described in claim 2, characterized in that, In the receiving model, the amplitude response deviation of the array element is quantified by the harmonic output power degradation factor to determine its impact on the expected value of the coherent superposition gain. The sound velocity disturbance in environmental noise is transformed into an additional phase error component through the product of wavenumber change and propagation distance, and the corresponding component is proportional to the propagation distance.

4. The underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method as described in claim 3, characterized in that, Based on a standard scatterer, the frequency domain transfer function of each channel of the array is calibrated to obtain the comprehensive transfer characteristics of each channel. Amplitude and phase compensation operators are then constructed, and these compensation operators are used to perform consistency compensation correction on the echo signal of the target under test, including: A standard scatterer with stable scattering characteristics is deployed at a known location, and the calibration signal received by each channel is obtained; After averaging the noise suppression through multiple measurements, the frequency domain integrated transfer function of each channel is calculated. The frequency domain integrated transfer function includes the combined effects of array element amplitude response deviation, channel additional phase error, array element position and path error, and sound speed disturbance. Based on the comprehensive transfer function, a compensation operator is constructed to perform frequency domain inversion compensation on the echo signal of the target under test, so that the response of each channel is normalized to the ideal reference level, thereby realizing frequency domain amplitude and phase consistency control.

5. The underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method as described in claim 4, characterized in that, The compensated integrated transfer function error of each channel includes: amplitude response deviation term and phase residual term; after compensation, the phase residual between each channel is controlled within a range that matches the requirements of array coherent processing.

6. The underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method as described in claim 5, characterized in that, The signals from each channel after consistency compensation correction are constructed into a multi-channel array signal vector. The covariance matrix of the signal vector is calculated, a steering vector is established according to the target direction, and adaptive weights are calculated through minimum variance distortionless response beamforming. The compensated signals are then coherently fused to enhance nonlinear harmonic components and suppress interference, including: The compensated multi-channel signals are used to form an array signal vector, and the covariance matrix of the signal vector at the harmonic frequency is calculated. Based on the target detection direction and array geometric parameters, a guiding vector reflecting the spatial phase delay of each array element relative to the reference point is constructed; Using the guide vector as a linear constraint, solve for the weight vector that minimizes the total output power of the array while ensuring distortion-free output of the target direction signal; The weight vector is used to calculate the multi-channel compensated signal to obtain the coherently enhanced array output signal.

7. The underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method as described in claim 6, characterized in that, A joint calibration mechanism combining laboratory benchmark calibration and on-site dynamic correction is constructed. The initial transfer function of each channel of the array is pre-obtained as a benchmark. The channel response shift caused by environmental changes is measured in real time using a reference scatterer, and environmental correction factors are extracted, including: In a controlled laboratory environment, the array is calibrated across the entire frequency band using a standard scatterer, and the initial transfer function of each channel is obtained as the intrinsic response benchmark. A reference scatterer at a known location is deployed at the actual testing site to measure the received signal of each channel under the current environmental conditions; By calculating the ratio of the field-received signal to the theoretically received signal based on the laboratory intrinsic response, correction factors reflecting the impact of environmental changes on the response of each channel are extracted. The correction factor is multiplied by the initial transfer function to obtain the updated transfer function suitable for the current detection environment, which is used for online dynamic compensation of the signal under test.

8. An underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement system, using the method described in any one of claims 1-7, characterized in that, include: The error model construction module is used to establish a receiving model that includes the ideal scattering response and the actual disturbance for the nonlinear harmonic echo signals received by each channel in the array, and to extract the phase residual parameter used to measure the degree of coherence loss of each channel, so as to quantitatively describe the influence of multi-source error on the nonlinear harmonic coherent superposition efficiency. The channel calibration and compensation module is used to calibrate the frequency domain transfer function of each channel of the array based on a standard scatterer, obtain the comprehensive transfer characteristics of each channel, and construct amplitude and phase compensation operators. The compensation operators are then used to perform consistency compensation and correction on the echo signal of the target under test. The multi-channel coherent enhancement module is used to construct a multi-channel array signal vector from the signals of each channel after consistency compensation and correction, calculate the covariance matrix of the signal vector, establish a steering vector according to the target direction, calculate adaptive weights through minimum variance distortionless response beamforming, and coherently fuse the compensated signal to enhance nonlinear harmonic components and suppress interference. The joint calibration and dynamic correction module is used to construct a joint calibration mechanism that combines laboratory benchmark calibration with on-site dynamic correction. The initial transfer function of each channel of the array is obtained in advance as a benchmark. The channel response offset caused by environmental changes is measured in real time using a reference scatterer. An environmental correction factor is extracted, and the compensation parameters are corrected online based on the environmental correction factor to achieve dynamic compensation.

9. A computer device, characterized in that, include: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherent enhancement method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores computer-executable instructions, which, when executed by a processor, implement the steps of the underwater phased array nonlinear ultrasonic echo error propagation modeling and coherence enhancement method according to any one of claims 1 to 7.

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