Non-free field hydrophone low frequency calibration method based on multi-frequency measurement and deep learning

Abstract

The present application belongs to the technical field of low-frequency calibration method of non-free field hydrophone, and particularly relates to a low-frequency calibration method of non-free field hydrophone based on multi-frequency measurement and deep learning, which determines the frequency points for hydrophone calibration, selects a plurality of frequency points in the adjacent frequency band of the frequency points, transmits a sinusoidal pulse signal through a water acoustic emission transducer, receives the sound signal waveform corresponding to each frequency point at the sound pressure measurement point, performs time domain alignment and resampling processing on the received waveform of each frequency point, constructs a two-dimensional waveform graph with time as the horizontal axis and frequency as the vertical axis, the direct sound component in the two-dimensional waveform graph is vertically distributed, and the reflected sound component is distributed at different slopes. A deep learning module based on a U-shaped encoder-decoder network structure is constructed, and the deep learning module is trained and parameter optimized through a two-dimensional waveform data set generated in advance.

Description

Technical Field

[0001] This invention belongs to the technical field of low-frequency calibration methods for non-free-field hydrophones, and particularly relates to a low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning. Background Technology

[0002] As a core component for underwater acoustic signal detection, the accurate calibration of hydrophones' low-frequency / ultra-low-frequency sensitivity is a crucial technical aspect in underwater acoustic engineering, marine exploration, and the development of underwater acoustic equipment. Ideally, hydrophone calibration should be conducted in a free-field environment. However, in practical engineering applications, limitations such as experimental site and tank size make it difficult to achieve a completely free field. In non-free-field environments, multiple sound reflection paths exist, leading to interference from the superposition of direct and reflected sound, and a limited anechoic duration. For low-frequency signals, it is difficult to obtain a sufficient number of steady-state sound cycles, directly affecting the accuracy of direct sound amplitude measurement and thus reducing the precision and reliability of low-frequency calibration. Low-frequency calibration of hydrophones in non-free-field environments has become a core research and application area in the industry. Currently, the CMWA method and time-domain scaled averaging method are the mainstream calibration methods in this field and are widely used in the device calibration of various underwater acoustic subsystems.

[0003] Existing low-frequency calibration methods for non-free-field hydrophones have many technical bottlenecks. These methods generally require high transmit signal bandwidth and are constrained by the Rayleigh limit, which is the reciprocal of the system's echo-free duration. They are prone to significant frequency ambiguity in the low-frequency band, making it difficult to extend the lower limit of the operating frequency.

[0004] To address these issues, the time-domain scaling averaging method attempts to optimize calibration by employing multi-frequency pulse measurement. However, this method only performs direct averaging on the received multi-frequency waveforms, failing to effectively separate direct and reflected sound. Its ability to resolve acoustic signals at extremely low bandwidths is insufficient, failing to overcome the Rayleigh limit. Furthermore, traditional signal processing methods have limited effectiveness in extracting direct sound components in complex, superimposed non-free-field environments, making it difficult to meet the high-precision and wide-application-range requirements of ultra-low frequency calibration for hydrophones. Therefore, developing a new non-free-field hydrophone low-frequency calibration method that overcomes bandwidth limitations and can efficiently identify and separate direct and reflected sound has significant engineering practical implications. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned technical problems by providing a low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning.

[0006] In view of this, the present invention provides a low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning, comprising the following steps: Step 1: Determine the test frequency points for hydrophone calibration, select several frequency points in the adjacent frequency band of the test frequency points, emit sinusoidal pulse signals through the underwater acoustic transducer, and receive the acoustic signal waveforms of the corresponding frequency points at the sound pressure measurement point. Step 2: Perform time-domain alignment and resampling on the received waveforms at each frequency point to construct a two-dimensional waveform diagram with time as the horizontal axis and frequency as the vertical axis. In this two-dimensional waveform diagram, the direct sound component is vertically distributed, and the reflected sound component is slopingly distributed with different slopes. Step 3: Construct a deep learning module based on a U-shaped encoder-decoder network structure, and train and optimize the parameters of the deep learning module using a pre-generated two-dimensional waveform dataset; Step 4: Input the actual two-dimensional waveform obtained in Step 2 into the trained deep learning module, which will then identify and extract the direct sound waveform. Step 5: Measure and calculate the steady-state amplitude of the extracted direct sound waveform, substitute the amplitude calculation result into the hydrophone sensitivity calculation formula, obtain the low-frequency / ultra-low-frequency sensitivity of the hydrophone in a non-free field environment, and complete the low-frequency calibration of the hydrophone.

[0007] Preferably, the specific operation of time-domain alignment of the received waveform in step two includes: accurately determining the arrival time of the direct sound by transmitting a high-frequency sound pulse, taking the arrival time of the direct sound as the zero point of the time axis, and performing time-domain alignment of the direct sound component and the reflected sound component of the received waveform at each frequency point. This time-domain alignment method is applicable to both single-channel reflected sound and multi-channel reflected sound cases.

[0008] Preferably, the specific operation of resampling the received waveform in step two includes: selecting the examination frequency point as the reference frequency, performing time-domain resampling processing on the received waveforms at other frequency points, so that the direct sound components of the received waveforms at different frequency points are aligned and coherent, and the reflected sound components exhibit time-domain misalignment.

[0009] Preferably, the sinusoidal pulse received waveform at each frequency point includes direct sound components and reflected sound components. The envelope of the direct sound is constant except for the transient spikes at the beginning and end of the waveform. The reflected sound has a modulation effect on the waveform envelope. When aligning in the time domain, the time delay difference between the reflected sound and the direct sound and the reverberation time of the pool need to be calibrated.

[0010] Preferably, the training of the deep learning module in step three includes two stages: dataset generation and parameter training. The application of the deep learning module includes a model inference stage, in which the actual two-dimensional waveform is input into the trained model to extract the direct sound waveform.

[0011] Preferably, the specific steps for generating the dataset are as follows: Step 11: Set the frequency point to be calibrated, the number of neighboring sampling frequency points, the number of signal cycles, as well as the transducer resonant frequency and quality factor; Step 12: Simulate and generate the transmission waveform containing the steady-state part and the transducer resonant transient part. Combine different pool sizes and boundary reflection coefficients, and use the impulse response simulation tool to generate a pool impulse response dataset. Step 13: Convolve the transmitted waveform with the water pool impact response and add random noise with different signal-to-noise ratios to construct a received waveform dataset containing reflected sound and noise; only convolve the transmitted waveform with the direct sound part of the water pool impact response without introducing random noise to construct an ideal direct sound waveform dataset. Step 14: Introduce amplitude weighting coefficients to the two types of waveform datasets mentioned above to simulate the frequency non-uniformity of the radiation efficiency of the transmitting transducer; Step 15: Perform time-domain alignment and resampling on the weighted waveform dataset to construct a two-dimensional waveform dataset containing two-dimensional waveforms with interference and two-dimensional waveforms of ideal direct sound.

[0012] Preferably, the specific steps for parameter training are as follows: Step S21: Perform frame segmentation on the two-dimensional waveform to match the number of frequency points and frame length with the input dimension of the neural network, and normalize the data. Step S22: Set the mean squared error function as the loss function, use the Adam optimizer and configure the corresponding learning rate, and set the batch size for model training; Step S23: Input the two-dimensional waveform dataset into the neural network model, use K-fold cross-validation to train the model parameters, and calculate the loss function value after one traversal. Step S24: If the loss function value is lower than the preset threshold, or the difference between the loss function values ​​of two adjacent iterations is lower than the preset threshold, stop model training; otherwise, repeat step S23 to continue training.

[0013] Preferably, in the encoder-decoder structure of the U-shaped network, the left encoder is a downsampling path, and multi-scale feature extraction is achieved through two-dimensional convolution and max pooling; The decoder on the right is an upsampling path, which restores the waveform through transposed convolution and interpolation; skip connections are set between the output of each layer of the encoder and the corresponding layer of the decoder to avoid information loss during the encoding process. The convolution kernel dimension of the two-dimensional convolution operation is 3×3, the convolution stride and padding are both 1, and an activation function layer with the linear rectified function as the activation function is set after each convolution step. The network input is a two-dimensional waveform graph consisting of the number of frequencies multiplied by the number of time-domain sampling points. The network output channel number is 1, which is consistent with the number of input channels.

[0014] Preferably, step five uses a comparison method to calibrate the hydrophone sensitivity, specifically as follows: The standard hydrophone and the hydrophone to be calibrated are placed sequentially at the sound pressure measurement point. The sound pressure value at the measurement point is calculated based on the output voltage amplitude of the standard hydrophone and the known sensitivity level. Then, the output voltage amplitude of the hydrophone to be calibrated is substituted into the comparison method sensitivity calculation formula to obtain the free field sensitivity level of the hydrophone to be calibrated.

[0015] Preferably, step five uses laser interferometry to calibrate the hydrophone sensitivity, specifically as follows: A strip of reflective and sound-transmitting film is placed at the sound pressure measurement point. The vibration velocity of the film is measured using a laser interferometer. The sound pressure value at the measurement point is calculated by combining the density of the water medium, the sound velocity in the water, and the equivalent refractive index of the water medium. After removing the film, the hydrophone to be calibrated is placed at the measurement point. The output voltage amplitude of the hydrophone is measured under the same excitation. The hydrophone's sound pressure sensitivity level is obtained by substituting it into the sensitivity calculation formula of the laser interferometry.

[0016] The beneficial effects of this invention are as follows: This method breaks through the limitation of Rayleigh limit in traditional non-free field hydrophone low-frequency calibration methods. By selecting frequency points in the nearest frequency band to the frequency to be calibrated and carrying out narrowband multi-frequency measurements, and combining time-domain alignment and resampling operations to construct a two-dimensional waveform, the requirements for the bandwidth of the transmitted signal are greatly reduced. This effectively solves the technical problem of significant frequency ambiguity in the low-frequency band, successfully expands the lower limit of the working frequency of hydrophone calibration, realizes ultra-low frequency sensitivity calibration in a non-free field environment, and fills the technical gap of traditional methods in ultra-low frequency calibration.

[0017] This method, relying on a U-shaped network-based encoder-decoder deep learning module, achieves accurate identification and effective separation of direct sound and reflected sound components from various paths in extremely low-bandwidth two-dimensional waveform data. It completely solves the core problem of inaccurate direct sound amplitude measurement caused by superimposed interference from reflected sound in non-free fields. Compared to the time-domain scaling averaging method's direct averaging of multiple waveforms, the deep learning module, trained on a dataset including transducer characteristics, pool parameters, and random noise, can extract direct sound with high accuracy from narrower bandwidth data and is adaptable to different non-free field experimental environments, significantly improving the accuracy and reliability of low-frequency calibration of hydrophones.

[0018] This method boasts excellent engineering compatibility and practicality, directly integrating with existing hydrophone sensitivity calibration principles and devices such as the comparison method, reciprocity method, and laser interferometry, without requiring significant modifications to existing calibration equipment, thus reducing the cost of engineering implementation. Furthermore, its multi-frequency measurement and deep learning-based technical solution offers a clear and highly repeatable operation process, simplifying the signal processing flow for non-free-field low-frequency calibration while ensuring calibration accuracy. This provides a novel technical path for hydrophone calibration in underwater acoustic engineering, marine exploration, and underwater acoustic equipment development, demonstrating broad engineering application and promotional value. Attached Figure Description

[0019] Figure 1 The diagram illustrates the waveform morphology in this invention, where (a) is the waveform transmitted by the transducer and (b) is the waveform received at the sound pressure measurement point. Figure 2 This is a schematic diagram of the frequency selection scheme for multi-frequency measurement in this invention; Figure 3 This is a schematic diagram of the two-dimensional waveform construction process of the present invention, where (a) represents transmitting multi-frequency pulses, (b) represents receiving multi-frequency waveforms, (c) represents time domain alignment (time zero point reset), and (d) represents waveform resampling; Figure 4 This is a diagram of the U-shaped neural network structure designed for this invention; Figure 5 This is a schematic diagram of the implementation process of the present invention, including simulation dataset generation and model training, actual measurement and model inference, etc. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0021] This invention addresses the problems of existing non-free field hydrophone low-frequency calibration methods such as CMWA and time-domain scaled averaging, which have high requirements for transmit signal bandwidth, significant frequency ambiguity, and insufficient extension of the lower limit of operating frequency. It proposes a non-free field hydrophone low-frequency calibration method based on multi-frequency measurement and deep learning.

[0022] Similar to the multi-frequency pulse measurement used in the time-domain scaling average method, this invention also selects frequency points within the frequency band near the frequency to be calibrated to transmit and receive sinusoidal pulse signals. However, this method uses a smaller bandwidth and is not constrained by the Rayleigh limit, which is the reciprocal of the system's anechoic duration. This invention resamples the multi-frequency measurement waveforms to construct a set of resampled two-dimensional waveforms, with the horizontal axis representing time and the vertical axis representing frequency. Unlike the time-domain scaling average method, which directly averages multiple waveforms, the resampling operation in this invention corresponds to the data preprocessing stage, and the resampled two-dimensional waveforms serve as input to the deep learning module. The deep learning module employs a U-shaped network-based encoder-decoder structure. The module is trained and its parameters optimized using a pre-constructed two-dimensional waveform dataset, enabling it to identify and distinguish direct sound and path-reflected sound components from two-dimensional waveform data with extremely low bandwidth (breaking the Rayleigh resolution limit). The amplitude of the direct sound waveform output by the deep learning module is measured and calculated, and then substituted into the hydrophone sensitivity calculation formula of the comparison method, reciprocity method or laser interferometry method to finally achieve low-frequency / ultra-low-frequency sensitivity calibration of hydrophone in non-free field environment.

[0023] The basic principles and methods for hydrophone sensitivity calibration include the comparison method, reciprocity method, and laser interferometry. The specific technology involved in this invention aims to solve the applicability problem of the above-mentioned basic methods and devices under the superposition of low-frequency acoustic reflections in non-free fields, and to expand the lower frequency limit of calibration. Here, the principles and methods of the comparison method and laser interferometry are introduced as examples.

[0024] The working principle of the comparative calibration method is to place the standard hydrophone and the hydrophone being calibrated at the same point in the sound field, with the distance between this measurement point and the transmitting transducer being [missing information]. Under the excitation of a signal source and a power amplifier, the underwater acoustic transducer generates a pulsed sinusoidal sound field with a certain period in the water tank. The output voltage amplitude of a standard hydrophone is [value missing]. The sensitivity level of a standard hydrophone, expressed in decibels, is... This value, after metrological traceability, is a known quantity. Therefore, the sound pressure level at this measurement point can be calculated as follows: (1); in For reference sensitivity, it is usually taken as 1. μPa.

[0025] The amplitude of the output voltage of the hydrophone being calibrated is Based on the above sound pressure values And the output voltage value, the free-field sensitivity level of the hydrophone being calibrated is obtained as follows: (2); The working principle of laser interferometry calibration is to reproduce sound pressure and calibrate hydrophones by measuring the vibration of a thin film in an underwater acoustic field using lasers. A strip-shaped reflective and acoustically transparent film, with a thickness much smaller than the wavelength of the sound wave, is placed in the underwater acoustic field, at a distance from the underwater acoustic transducer that satisfies the far-field condition. The underwater acoustic transducer, excited by a signal source and power amplifier, generates a sinusoidal pulse signal with a certain period in the water tank. Under the influence of the sound field, the film completely follows the movement of the water particles, and the film vibration velocity can be equivalent to the vibration velocity of the sound particles. The film vibration velocity is then measured outside the water tank using a laser interferometer. And measure or calculate the density of the water medium. Speed ​​of sound in water The underwater acoustic pressure at the measurement point is calculated using the following formula: (3); in The equivalent refractive index of the water medium is taken as 1.01.

[0026] After the sound pressure measurement is completed, remove the diaphragm and place the hydrophone to be calibrated in the underwater sound field, ensuring that the sound center of the hydrophone coincides with the sound pressure measurement point. Under the same excitation, the output voltage amplitude of the hydrophone... With sound pressure amplitude The ratio is the hydrophone sensitivity. The hydrophone sensitivity level is obtained by comparing it to the reference sensitivity and taking 20 times the logarithm to base 10, expressed as: (4); The transducer's transmitted waveform and the received waveform at the sound pressure measurement point are as follows: Figure 1 As shown, the transmitted waveform uses a sinusoidal pulse. The transducer's own electroacoustic characteristics cause the start and end segments of the transmitted waveform to exhibit transient features. There are direct sound paths and multiple reflected sound paths between the transmitting transducer and the sound pressure measurement point. The anechoic duration for direct sound amplitude measurement is limited. For low-frequency signals, it is difficult to obtain a sufficient number of steady-state sound cycles, which leads to the low-frequency lower limit problem in hydrophone calibration.

[0027] Multi-frequency measurement and two-dimensional waveform construction; This invention comprises two parts: two-dimensional waveform construction based on multi-frequency measurement and direct sound recovery based on deep learning. The multi-frequency measurement scheme is as follows: Figure 2 As shown.

[0028] The test frequency points for hydrophone calibration, with each test frequency Centered on, in its adjacent frequency band Select K frequency points uniformly It transmits and receives sinusoidal pulses.

[0029] The core of constructing a two-dimensional waveform lies in waveform time-domain alignment and resampling operations. The process and principle of this operation are described below. For a frequency of... The number of cycles is A sinusoidal pulse, after being amplified by a power amplifier, excites the transmitting transducer to generate a sound field. The received waveform at the sound pressure measurement point is represented as follows: (5); Among them, direct sound and reflected sound They are represented as follows: (6); (7); In the formula, Represents frequency carrier signal; The envelope function of the direct sound can be considered a constant, except for the transient spikes at the beginning and end of the waveform. This indicates the modulation of the waveform envelope by the reflected sound; These represent the arrival times of the direct sound and the first reflected sound, respectively. Reverberation time is the time required for the sound pressure level to fully decay after the sound source stops emitting sound.

[0030] The arrival time of direct sound is accurately determined by emitting high-frequency sound pulses. Based on this, the arrival time of the direct sound is taken as the zero point of the time axis, that is, let... The direct sound component and the reflected sound component can be re-expressed as: (8); (9);

[0031] in, This represents the time delay difference between the first reflected sound and the direct sound. This explanation uses a single reflected sound as an example, but the analysis method is still applicable to multiple reflected sound scenarios.

[0032] For acoustic pulses of different frequencies, the coherence of the direct acoustic component of the received waveform is low. Therefore, time-domain resampling is performed to adjust the frequency response. For reference, the frequency is After resampling, the waveforms of the direct sound and the reflected sound can be re-represented as follows: (10) (11); As can be seen, after resampling, the direct sound components of different frequencies are aligned and coherent, while the reflected sound components exhibit temporal misalignment.

[0033] Based on the frequency of observation Nearby narrowband multi-frequency measurement data, after time-domain alignment and waveform resampling, can be used to construct a two-dimensional waveform diagram, such as... Figure 3 As shown. Figure 3 (d) is the final constructed two-dimensional waveform diagram, in which the direct sound component is vertically distributed, while the reflected sound components of each path are slopingly distributed with different slopes. This two-dimensional pattern can be used as the input of the deep learning module.

[0034] Deep Learning-Based 2D Waveform Feature Recognition and Direct Sound Recovery: This invention proposes a deep learning-based method for two-dimensional waveform feature recognition and direct sound recovery. The method consists of two stages: model training and model inference. Model training can be further divided into two steps: dataset generation and parameter training.

[0035] The specific process for generating the dataset is as follows: set the frequency point to be calibrated, the nearest sampling frequency point at the frequency point to be calibrated, and the number of signal cycles; Set the transducer resonant frequency and quality factor (resonance period). The simulation generates the corresponding transmission waveform, which includes the steady-state component and the transient component introduced by transducer resonance; By setting different pool sizes and boundary reflection coefficients, and using an impulse response simulation tool, a pool impulse response dataset is generated. The transmitted waveform is convolved with the water pool impulse response, and random noise with different signal-to-noise ratios is added to construct the received waveform dataset at the sound pressure measurement point. Meanwhile, only the transmitted waveform is convolved with the direct sound component of the water pool impact response, and no random noise is introduced, to construct an ideal direct sound waveform dataset that is noise-free and free from reflected sound interference. Different amplitude weighting coefficients are introduced for different frequency waveforms in the above dataset to simulate the frequency non-uniformity of the radiation efficiency of the transmitting transducer. The waveform dataset above is time-domain aligned and resampled to construct a two-dimensional waveform dataset, which includes two-dimensional waveforms that take into account reflected sound and noise interference. This also includes the ideal direct sound two-dimensional waveform diagram used as a reference. .

[0036] The specific process of parameter training is as follows: The two-dimensional waveform is divided into frames, and the number of frequency points and the frame length should match the input dimension of the neural network. Data normalization; Set the loss function to mean squared error (MSE). The optimizer uses the Adam optimizer, and the learning rate is set. Set the training batch size, which is the number of waveforms contained in each batch; The two-dimensional waveform is used as the input to the neural network model. The model parameters are trained using K-fold cross-validation. The loss function value is calculated after one complete traversal. Training stops when the loss function is lower than a preset threshold or the difference between the loss function values ​​of two adjacent iterations is lower than a preset threshold.

[0037] After the neural network model is trained, it is applied to the processing of actual experimental data. A signal generator produces pulse signals at various frequencies, with parameters consistent with those used in the simulation dataset. These signals are then amplified by a power amplifier and a transmitting transducer to generate a sound field in a water tank. A thin-film / hydrophone receives the waveform at the sound pressure measurement point. The received waveform undergoes time-domain alignment and resampling before being input into the neural network model. The model output is the direct sound waveform. A steady-state segment is selected for amplitude fitting and calculation, and the result is substituted into the sensitivity calculation formula to obtain the hydrophone sensitivity.

[0038] Neural network model structure design: To extract the sound propagation path features and recover the direct sound components contained in a two-dimensional waveform, this invention designs a U-shaped neural network. The input of this network matches the flat matrix dimensionality features presented by the two-dimensional waveform. The U-shaped network is an encoder-decoder structure, as shown below. Figure 4 As shown, the left side is the encoder part corresponding to the downsampling path, used for feature extraction; the right side is the decoder part corresponding to the upsampling path, used for waveform recovery; and the middle is the skip connection.

[0039] The input to the neural network is a two-dimensional waveform, with dimensions of frequency number × time-domain sampling points, which are 11 and 512 respectively. The 6th of the 11 frequency points is the frequency to be calibrated, and the other 10 frequency points are sampling points near the frequency to be calibrated. This input dimension can be adjusted according to actual needs. The blue arrows in the figure represent two-dimensional convolution operations, where the convolution kernel dimension is 3×3, and the convolution stride and padding are both set to 1 to ensure that the height and width of the image do not change. An activation function layer is set after each convolution operation, using a linear rectified function as the activation function. Each convolutional layer has different input and output channels. The first convolutional layer has 1 input channel and 32 output channels, the second convolutional layer has 32 input channels and 32 output channels, and the input and output channel settings of other layers are also marked in the figure. The final output two-dimensional image still maintains 1 channel. The downward green arrow in the encoder section on the left indicates a downsampling operation, which is implemented using max pooling; the upward green arrow in the decoder section on the right indicates an upsampling operation, which is implemented using transposed convolution and interpolation.

[0040] The encoder continuously reduces the width and height of the feature map through convolution and pooling, thereby extracting multi-scale features of the image. The decoder performs image reconstruction based on the image features extracted by the encoder. To avoid information loss during the encoding process, the outputs of each layer of the encoder are directly connected to each layer of the decoder, as shown by the gray arrows in the figure.

[0041] In summary, the specific implementation process of the technical solution of this invention can be given below. Figure 5 .

[0042] The embodiments of this application have been described above with reference to the accompanying drawings. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. This application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning, characterized in that: Includes the following steps: Step 1: Determine the test frequency points for hydrophone calibration, select several frequency points in the adjacent frequency band of the test frequency points, emit sinusoidal pulse signals through the underwater acoustic transducer, and receive the acoustic signal waveforms of the corresponding frequency points at the sound pressure measurement point. Step 2: Perform time-domain alignment and resampling on the received waveforms at each frequency point to construct a two-dimensional waveform diagram with time as the horizontal axis and frequency as the vertical axis. In this two-dimensional waveform diagram, the direct sound component is vertically distributed, and the reflected sound component is slopingly distributed with different slopes. Step 3: Construct a deep learning module based on a U-shaped encoder-decoder network structure, and train and optimize the parameters of the deep learning module using a pre-generated two-dimensional waveform dataset; Step 4: Input the actual two-dimensional waveform obtained in Step 2 into the trained deep learning module, which will then identify and extract the direct sound waveform. Step 5: Measure and calculate the steady-state amplitude of the extracted direct sound waveform, substitute the amplitude calculation result into the hydrophone sensitivity calculation formula, obtain the low-frequency / ultra-low-frequency sensitivity of the hydrophone in a non-free field environment, and complete the low-frequency calibration of the hydrophone. The specific operations for time-domain alignment of the received waveform in step two include: accurately determining the arrival time of the direct sound by transmitting a high-frequency sound pulse, taking the arrival time of the direct sound as the zero point of the time axis, and performing time-domain alignment of the direct sound component and the reflected sound component of the received waveform at each frequency point. This time-domain alignment method is applicable to both single-channel reflected sound and multi-channel reflected sound cases. The specific operations for resampling the received waveform in step two include: selecting the frequency point under consideration as the reference frequency, performing time-domain resampling processing on the received waveforms at other frequency points, so that the direct sound components of the received waveforms at different frequency points are aligned and coherent, and the reflected sound components exhibit time-domain misalignment. The sinusoidal pulse received waveform at each frequency point contains direct sound components and reflected sound components. The envelope of the direct sound is constant except for the transient spikes at the beginning and end of the waveform, while the reflected sound modulates the waveform envelope.

2. The low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning according to claim 1, characterized in that: Step 3, the training of the deep learning module includes two stages: dataset generation and parameter training. The application of the deep learning module includes the model inference stage, which involves inputting the actual two-dimensional waveform into the trained model to extract the direct sound waveform.

3. The low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning according to claim 2, characterized in that: The specific steps for generating the dataset are as follows: Step 11: Set the frequency point to be calibrated, the number of nearest neighbor sampling frequency points, the number of signal cycles, as well as the transducer resonant frequency and quality factor; Step 12: Simulate and generate the transmission waveform containing the steady-state part and the transducer resonant transient part. Combine different pool sizes and boundary reflection coefficients, and use the impulse response simulation tool to generate a pool impulse response dataset. Step 13: Convolve the transmitted waveform with the water pool impact response and add random noise with different signal-to-noise ratios to construct a received waveform dataset containing reflected sound and noise; only convolve the transmitted waveform with the direct sound part of the water pool impact response without introducing random noise to construct an ideal direct sound waveform dataset. Step 14: Introduce amplitude weighting coefficients to the two types of waveform datasets mentioned above to simulate the frequency non-uniformity of the radiation efficiency of the transmitting transducer; Step 15: Perform time-domain alignment and resampling on the weighted waveform dataset to construct a two-dimensional waveform dataset containing two-dimensional waveforms with interference and two-dimensional waveforms of ideal direct sound.

4. The low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning according to claim 3, characterized in that: The specific steps for parameter training are as follows: Step S21: Perform frame segmentation on the two-dimensional waveform to match the number of frequency points and frame length with the input dimension of the neural network, and normalize the data. Step S22: Set the mean squared error function as the loss function, use the Adam optimizer and configure the corresponding learning rate, and set the batch size for model training; Step S23: Input the two-dimensional waveform dataset into the neural network model, use K-fold cross-validation to train the model parameters, and calculate the loss function value after one traversal. Step S24: If the loss function value is lower than the preset threshold, or the difference between the loss function values ​​of two adjacent iterations is lower than the preset threshold, stop model training; otherwise, repeat step S23 to continue training.

5. The low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning according to claim 1, characterized in that: In the encoder-decoder structure of the U-shaped network, the left encoder is a downsampling path, and multi-scale feature extraction is achieved through two-dimensional convolution and max pooling; The decoder on the right is an upsampling path, which restores the waveform through transposed convolution and interpolation; skip connections are set between the output of each layer of the encoder and the corresponding layer of the decoder to avoid information loss during the encoding process. The convolution kernel dimension of the two-dimensional convolution operation is 3×3, the convolution stride and padding are both 1, and an activation function layer with the linear rectified function as the activation function is set after each convolution step. The network input is a two-dimensional waveform graph consisting of the number of frequencies multiplied by the number of time-domain sampling points. The network output channel number is 1, which is consistent with the number of input channels.

6. The low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning according to claim 1, characterized in that: Step five involves using a comparison method to calibrate the hydrophone sensitivity, specifically as follows: The standard hydrophone and the hydrophone to be calibrated are placed sequentially at the sound pressure measurement point. The sound pressure value at the measurement point is calculated based on the output voltage amplitude of the standard hydrophone and the known sensitivity level. Then, the output voltage amplitude of the hydrophone to be calibrated is substituted into the comparison method sensitivity calculation formula to obtain the free field sensitivity level of the hydrophone to be calibrated.

7. The low-frequency calibration method for non-free-field hydrophones based on multi-frequency measurement and deep learning according to claim 1, characterized in that: Step five involves using laser interferometry to calibrate the hydrophone's sensitivity, specifically as follows: A strip of reflective and sound-transmitting film is placed at the sound pressure measurement point. The vibration velocity of the film is measured using a laser interferometer. The sound pressure value at the measurement point is calculated by combining the density of the water medium, the sound velocity in the water, and the equivalent refractive index of the water medium. After removing the film, the hydrophone to be calibrated is placed at the measurement point. The output voltage amplitude of the hydrophone is measured under the same excitation. The hydrophone's sound pressure sensitivity level is obtained by substituting it into the sensitivity calculation formula of the laser interferometry.

Images