Airborne laser bathymetry echo signal inversion method based on physical information neural network

Abstract

This invention belongs to the field of airborne laser bathymetry echo signal processing technology, and specifically relates to an airborne laser bathymetry echo signal inversion method based on a physical information neural network. First, grid points aligned with the preprocessed input data space are generated in the physical domain. These grid points are then used as input to the physical equations to obtain the theoretical waveform. A neural network architecture module is established, and the original measurement data is loaded into a convolutional neural network for training. After training, the data loss is calculated, and the physical loss is calculated by comparing the theoretical waveform with the training results of the convolutional neural network. In the loss function fusion module, the physical loss and data loss are combined through a weighted summation. Then, the Adam optimizer is used to update the network parameters, and training is repeated until the output model is obtained. This invention, based on a physical information neural network data processing method, utilizes a deep learning neural network to quickly invert depth and ocean information, thus broadening its application range.

Description

Technical Field

[0001] This invention belongs to the field of airborne laser depth sounding echo signal processing technology, specifically relating to an airborne laser depth sounding echo signal inversion method based on a physical information neural network. Background Technology

[0002] Seabed topographic data is an indispensable data foundation for marine economic development, marine scientific research, and marine military applications. Airborne lidar systems can quickly and efficiently acquire height information of ground and sea surface targets and depth information of seabed targets. They feature high accuracy, wide coverage, high measurement point density, short measurement cycle, low power consumption, ease of management, and high mobility, making them particularly suitable for shallow waters, rocky reefs, minefields, and other sea areas that affect ship navigation. This enables seamless mapping of coastlines and facilitates exploration and development in a wider range of areas. Data processing of echo signals is a core step in lidar depth sounding technology. Due to the complexity of the environment, the characteristics of the depth sounding waveform vary greatly, and the signal-to-noise ratio is relatively low, making data processing very difficult and prone to problems such as inaccurate inversion models, difficulties in data fusion, and low computational efficiency. Summary of the Invention

[0003] In response to the shortcomings of existing technologies, the inventors have developed a method for inverting airborne laser bathymetry echo signals based on physical information neural networks through long-term practical research. Based on the physical information neural network data processing method, a deep neural network is designed by establishing a model, which can quickly invert depth and ocean information.

[0004] The airborne laser bathymetry echo signal inversion method based on physical information neural network of the present invention is as follows:

[0005] Step 1: Data Acquisition and Preprocessing: Raw laser depth sounding data is acquired through airborne radar; then the acquired raw data is classified, transformed, and filtered to obtain input data that can be recognized by the convolutional neural network.

[0006] Step 2: Establish a physical equation constraint module to embed the physical laws of laser depth sounding into a neural network; generate grid points in the physical domain that are spatially aligned with the preprocessed input data, and use these grid points as input to the physical equations to obtain the theoretical waveform.

[0007] The physical equation is:

[0008] ;

[0009] Where C is the calibration coefficient, D is the distance between the detector and the water surface, H is the water depth, n is the refractive index of water, and R0 is the water surface reflectivity. R is the laser pulse width. b For underwater reflectivity, The absorption coefficient of water body, t air t represents the round-trip time in the air. total This represents the total propagation time.

[0010] Step 3: Establish the neural network architecture module: used to build a convolutional neural network; load the original measurement data and enter the convolutional neural network for training.

[0011] Step 4: After training, the mean squared error loss is output as the data loss.

[0012] Step 5: Compare the theoretical waveform with the training results of the convolutional neural network.

[0013] Step 6: Establish a loss function fusion module to balance the optimization objectives of data-driven and physical constraints.

[0014] Step 7: Establish a training optimization module for updating the parameters of the neural network.

[0015] Step 8: Repeat steps 4 to 7 until the required number of training iterations is reached, and output the model data; the model data includes neural network weight parameters, optimized physical model parameters, and structured data of predicted water depth and confidence level.

[0016] Furthermore, in step two, grid points aligned with the preprocessed input data space are generated within the physical domain. Specifically, data-physical field alignment is achieved by performing radial basis function interpolation at the grid nodes. The interpolation expression is:

[0017] ;

[0018] Where x is the spatial location of the point to be interpolated, x j Let j be the spatial location of the j-th raw laser depth sounding data point. Here, N is the radial basis function, and N is the number of original data points used for interpolation. j It is data point x j The weighting coefficients are p, which is the option for compensating for system errors.

[0019] Furthermore, in the physical equations:

[0020] The round-trip time in the air ;

[0021] Round trip time in water ;

[0022] The total propagation time ;

[0023] in It is the speed of light in the air. It is the speed at which light travels through water;

[0024] because, Laser pulse time domain The expression;

[0025] Therefore, the water surface echo signal is:

[0026] ;

[0027] Among them, water surface reflectivity These are constants measured based on actual experimental scenarios;

[0028] According to Beer-Lambert's law, the water decay coefficient is... ;

[0029] The underwater echo signal is:

[0030] ;

[0031] Among them, underwater reflectivity These are constants measured based on actual experimental scenarios;

[0032] The total echo signal received by the detector is:

[0033] P(t) = ;

[0034] Among them, geometric attenuation factor C is the calibration coefficient;

[0035] The physical equations can be obtained by rearranging the above equations:

[0036] .

[0037] Furthermore, the physical equation constraint module calculates the equation residuals using automatic differentiation technology and incorporates the residuals as soft constraints into the loss function.

[0038] Furthermore, the neural network architecture module includes:

[0039] Input layer: Receives raw laser depth measurement data;

[0040] Convolutional layer: It consists of multiple convolutional kernels. The size of the convolutional kernel is determined by the length of a single acquired signal, and the number is dynamically adjusted according to the depth measurement data. Each layer is followed by a pooling layer.

[0041] Linear layer: Composed of fully connected layers, outputting water depth prediction results.

[0042] Furthermore, in step three, the original measurement data is loaded and trained into the convolutional neural network. Specifically, depending on the amount of data, the convolutional neural network structure can be divided into multiple convolutional layers and pooling layers stacked together.

[0043] The output features of the convolutional layer can be represented as:

[0044] ;

[0045] Where x[t] is the laser echo signal, t is the sampling time interval, w[k] is the convolution kernel, and n is the convolution kernel length. This represents the convolution operation.

[0046] The pooling layer compresses the output features of the convolutional layer to achieve dimensionality reduction while retaining feature information. The model employs max pooling, taking the maximum value within a window size of m. Its expression is:

[0047] y[t]=max(x[t], x[t+1], ..., x[t+m-1]).

[0048] Furthermore, in step five, the theoretical waveform is compared with the training results of the convolutional neural network. Specifically, the difference between the theoretical physical model and the predictions of the convolutional neural network is quantified using mean square error, constraining the network output to conform to physical laws. The calculation formula is as follows:

[0049] ;

[0050] Among them, y theory The theoretical waveform generated based on the physical model of laser depth sounding, y pred The waveform is the predicted output of the convolutional neural network, where N is the number of predicted waveform points and L is the mean square error loss. phy This is a physical loss.

[0051] Furthermore, the loss function of the loss function fusion module is a weighted summation form, which combines physical loss and data loss through weighted summation, and its form is:

[0052] L= ;

[0053] in, The physical loss weights are decreased as the number of training rounds increases to ensure that the results are closer to reality. Weight the data loss; For physical loss, This results in data loss.

[0054] Furthermore, the training optimization module employs the Adam optimizer, utilizes gradient descent to update network parameters, and dynamically adjusts the physical loss weights. The learning rate.

[0055] The beneficial effects of this invention are:

[0056] By combining physical equations with neural networks, and using a physical information neural network data processing method, a deep neural network is designed to process airborne laser depth sounding echo signals through model building. Compared with traditional methods, this method is faster in computation, more interpretable, requires less data, is less sensitive to noise, has a faster fitting speed, lower requirements on equipment, and has a wide range of practical applications. Attached Figure Description

[0057] Figure 1 This is a flowchart of the inversion method of the present invention.

[0058] Figure 2 This is a structural diagram of the convolutional neural network of this invention.

[0059] Figure 3 This is a comparison chart of the results from convolutional neural networks and physical information neural networks. Detailed Implementation

[0060] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. These embodiments are described in sufficient detail to enable those skilled in the art to understand and practice the invention. Logical, implementation, and other changes may be made to the embodiments without departing from the spirit and scope of the invention. Therefore, the following detailed description should not be construed as limiting, and the scope of the invention is defined solely by the claims.

[0061] See Figure 1 and Figure 2 This invention proposes a method for inverting airborne laser bathymetry echo signals based on a physical information neural network. The specific steps are as follows:

[0062] Step 1: Data Acquisition and Preprocessing; Raw laser depth sounding data is acquired through airborne radar; The acquired raw data is then classified, transformed, and filtered to obtain input data that can be recognized by a convolutional neural network.

[0063] Step 2: Establish a physical equation constraint module to embed the physical laws of laser depth sounding into the neural network. Within the physical domain, generate grid points spatially aligned with the preprocessed input data. Specifically, data-physical field alignment is achieved by performing radial basis function interpolation at the grid nodes. The interpolation expression is:

[0064] ;

[0065] Where x is the spatial location of the point to be interpolated, x j Let j be the spatial location of the j-th raw laser depth sounding data point. Here, N is the radial basis function, and N is the number of original data points used for interpolation. j It is data point x j The weighting coefficients are p, which is the option for compensating for system errors.

[0066] Finally, the discretized control equations are embedded into the neural network loss function in the form of residuals, forming a deep learning framework with physical consistency.

[0067] The grid points are used as input to the physical equations, and the theoretical waveforms are obtained by substituting them into the physical equations.

[0068] The physical equation is:

[0069] ;

[0070] Where D is the distance between the detector and the water surface, H is the water depth, n is the refractive index of water, and R0 is the water surface reflectivity. R is the laser pulse width parameter. b For underwater reflectivity, The absorption coefficient of water body, t air t represents the round-trip time in the air. total This represents the total propagation time.

[0071] Among them, the round-trip time in the air ;

[0072] Round trip time in water ;

[0073] Total transmission time ;

[0074] It is the speed of light in the air. It is the speed at which light travels through water.

[0075] because, Laser pulse time domain The expression;

[0076] The water surface echo signal is:

[0077] ;

[0078] Among them, water surface reflectivity These are constants measured based on actual experimental scenarios.

[0079] According to Beer-Lambert's law, the water decay coefficient is... ;

[0080] The underwater echo signal is:

[0081] ;

[0082] Among them, underwater reflectivity These are constants measured based on actual experimental scenarios;

[0083] For clear water bodies, water echo signals can be ignored. Depth inversion is mainly related to surface echo signals and bottom echo signals. P(t) represents the evolution of the relative intensity of the total echo signal received by the detector over time, which includes the surface reflected echo signal. and underwater reflected echo signal The total echo signal received by the detector is:

[0084] P(t) = ;

[0085] in, Given the geometric attenuation factor, for diffuse underwater surfaces, normalized detector area and reflection characteristics, the geometric attenuation factor is... It can be approximated as C is the calibration coefficient, from which we can obtain

[0086] ;

[0087] The physical equations can be obtained by rearranging the above equations:

[0088] .

[0089] The physical equation constraint module calculates the equation residuals using automatic differentiation technology and incorporates the residuals as soft constraints into the loss function.

[0090] Step 3: Establish the neural network architecture module: used to build the convolutional neural network. Load the original measurement data and train the convolutional neural network. The training method is as follows: Figure 2 As shown, depending on the amount of data, the structure of a convolutional neural network can be divided into multiple convolutional layers and pooling layers stacked together. 。

[0091] The output features of a convolutional layer can be represented as:

[0092] ;

[0093] Where x[t] is the laser echo signal, t is the sampling time interval, w[k] is the convolution kernel, and n is the convolution kernel length. This represents the convolution operation.

[0094] A convolution kernel acts like a "detector," scanning the echo signal through convolution operations to extract local features, thereby reducing the number of parameters and lowering computational costs.

[0095] Pooling layers compress the output features of convolutional layers to achieve dimensionality reduction while preserving feature information. This prevents overfitting and further reduces the computational cost of subsequent layers. The model employs max pooling, taking the maximum value within a window of size m. Its expression is:

[0096] y[t]=max(x[t], x[t+1], ..., x[t+m-1] );

[0097] The neural network architecture module mainly includes:

[0098] Input layer: Receives raw laser depth measurement data;

[0099] Convolutional layer: It consists of multiple convolutional kernels. The size of the convolutional kernel is determined by the length of a single acquired signal, and the number is dynamically adjusted according to the depth measurement data. Each layer is followed by a pooling layer.

[0100] Linear layer: Composed of fully connected layers, outputting water depth prediction results.

[0101] Step 4: After training, the mean squared error loss is output as the data loss. Figure 1 Step 4 of the process.

[0102] Step 5: Compare the theoretical waveform with the training results of the convolutional neural network. Quantify the difference between the theoretical physical model and the predictions of the convolutional neural network using the mean square error (MSE). Constrain the network output to conform to physical laws. The calculation formula is as follows:

[0103] ;

[0104] Where y theory The theoretical waveform generated based on the physical model of laser depth sounding, y pred Let N be the predicted waveform output by the convolutional neural network, and N be the number of predicted waveform points. The mean squared error loss L... phy For physical loss ( Figure 1 (Steps 5 and 6 of the process). This ensures that the network strictly adheres to the physical laws of laser energy attenuation while fitting the data. Physical parameters in the model, such as the attenuation coefficient, can be automatically optimized through gradient descent to adapt to the optical characteristics of different water bodies.

[0105] Step Six: Establish a loss function fusion module to balance the optimization objectives of data-driven and physical constraints. The loss function of the loss function fusion module is a weighted summation form, combining physical loss and data loss through weighted summation, with the following form:

[0106] L= ;

[0107] in: The physical loss weights are decreased as the number of training rounds increases to ensure that the results are closer to reality. Weight the data loss; For physical loss, This results in data loss.

[0108] Step 7: Establish a training optimization module for updating the neural network parameters. This module uses the Adam optimizer, employs gradient descent to update network parameters, and dynamically adjusts the physical loss weights. The learning rate.

[0109] Step 8: Repeat steps 4 through 7 until the required number of training iterations is reached, then output the model. The model data mainly includes neural network weight parameters, optimized physical model parameters, and structured data for predicted water depth and confidence levels. This output data retains the nonlinear fitting capability of the deep learning model while ensuring that the prediction results conform to the attenuation law of laser light in water through embedded physical parameters. It can be directly deployed to an airborne laser depth sounding radar system to achieve real-time, physically reliable depth measurement analysis.

[0110] Based on the depth sounding device built in the laboratory, convolutional neural networks and physical information neural networks were used to model and predictively analyze a small number of collected experimental data samples. Figure 3 As can be seen, the physical information neural network exhibits significant advantages when the amount of data is limited, and its measurement error is significantly lower than that of the traditional convolutional neural network method.

[0111] This difference stems primarily from the inherent characteristics of the two models: Convolutional Neural Networks, as a purely data-driven deep learning method, rely heavily on large-scale, high-quality training data for performance, and are prone to overfitting or insufficient generalization under small sample conditions; while Physical Information Neural Networks, by embedding physical laws into the neural network architecture, significantly reduce the dependence on the amount of data, enabling the model to maintain strict adherence to physical laws even when training samples are insufficient. Therefore, its prediction results not only have higher accuracy but also exhibit better physical rationality.

[0112] Therefore, in application scenarios where experimental costs are high or data acquisition is difficult, the physical information neural network method can overcome the limitations of traditional data-driven models and provide a new technical path for achieving high-precision and high-robustness measurements.

[0113] It is impossible to describe all possible combinations of components or methods in order to describe the above embodiments; however, those skilled in the art will recognize that further combinations and arrangements of the various embodiments are possible. Therefore, the embodiments described herein are intended to cover all such changes, modifications, and variations that fall within the scope of the appended claims. Furthermore, the term "comprising" as used in the specification or claims is interpreted in a manner similar to the term "including," as interpreted when used as a conjunction in the claims. Additionally, the use of any term "or" in the specification of the claims is intended to mean "non-exclusive or."

Claims

1. An airborne laser depth sounding echo signal inversion method based on a physical information neural network, characterized in that, The specific method is as follows: Step one, data acquisition and pretreatment: obtain the raw data of laser sounding through the airborne radar, classify, convert and filter the obtained raw data, and obtain the input data that can be recognized by the convolutional neural network; Step two, establish a physical equation constraint module for embedding the physical law of laser sounding into the neural network; generate grid points in the physical domain that are aligned with the preprocessed input data space, and use the grid points as the input of the physical equation to obtain the theoretical waveform; The physical equation is: ； where C is a calibration factor, D is the detector distance from the water surface, H is the water depth, n is the water refractive index, R0 is the water surface reflectivity, is the laser pulse width parameter, R b is the water bottom reflectivity, is the water absorption coefficient, i.e. the attenuation coefficient, t air is the air round-trip time, t total is the total propagation time; Step three, establish a neural network architecture module: load the original measurement data into the convolutional neural network for training; Step four, after training, the mean square error loss is obtained as the data loss output; Step five, compare the theoretical waveform with the convolutional neural network training result; Step six, establish a loss function fusion module for balancing the optimization objectives of data-driven and physical constraints; Step seven, establish a training optimization module for parameter updating of the neural network; Step eight, repeat steps four to seven until the training times requirement is met, and output the model data; the model data includes neural network weight parameters, optimized physical model parameters, predicted water depth and confidence structured data.

2. The method of claim 1, wherein, In step two, the grid points in the physical domain that are aligned with the preprocessed input data space are generated, specifically, the data-physical field alignment is realized by radial basis function interpolation at the grid nodes, and the interpolation expression is: ； where x is the spatial position of the point to be interpolated, x j is the spatial position of the jth laser depth measurement raw data point, is the radial basis function, N is the number of raw data points used for interpolation, j is the weight coefficient of the data point x j , and p is the option for compensating system error.

3. The method of claim 1, wherein, In the physical equation: the air round trip time ; Water round trip time ; the total propagation time ; wherein is the speed of propagation of light in air, is the speed of propagation of light in water; Due to, Expression of the time domain of the laser pulse of the laser pulse; Therefore, the water surface echo signal is: ； wherein the water surface reflectivity is a constant measured according to the actual experimental scenario; According to the Beer-Lambert law, the water attenuation coefficient is ; The water bottom echo signal is: ； wherein the water reflectance is a constant measured from an actual experimental scenario; The total echo signal received by the detector is: P(t) = P0+ P1t ; wherein the geometric attenuation factor C is a calibration coefficient; The physical equation is obtained by arranging the above equation: 。 4. The method of claim 3, wherein, The physical equation constraint module calculates the equation residual through automatic differentiation technology and integrates the residual as a soft constraint into the loss function.

5. The method of claim 1, wherein, The neural network architecture module includes: Input layer: accepts laser sounding raw data; Convolution layer: composed of multiple convolution kernels, the size of the convolution kernel is determined by the length of a single collected signal, and the number is dynamically adjusted according to the depth data, and each layer is connected to a pooling layer; Linear layer: composed of fully connected layers, outputting water depth prediction results.

6. The method of claim 5, wherein, In step three, the original measurement data is loaded into the convolutional neural network for training, specifically, according to the data size, the convolutional neural network structure can be divided into multiple convolution layers and pooling layers stacked; The output feature of the convolution layer is represented as: ； where x[t] is the laser return signal, t is the sampling time interval, w[k] is the convolution kernel, and n is the length of the convolution kernel, denotes a convolution operation; The pooling layer compresses and reduces the dimension of the output feature of the convolution layer while retaining the feature information, and the maximum pooling operation is used in the model, which takes the maximum value within a window size of m, and its expression is: y[t]=max(x[t], x[t+1],..., x[t+m-1] )).

7. The method of claim 1, wherein, In step five, the theoretical waveform is compared with the convolutional neural network training result, specifically, the difference between the theoretical physical model and the convolutional neural network prediction is quantified by the mean square error, and the network output is constrained to comply with the physical law, and the calculation formula is: ； wherein y theory is a theoretical waveform generated based on a laser depth measurement physical model, y pred is a predicted waveform output by the convolutional neural network, N is the number of waveform prediction points, and the mean square error loss L phy is a physical loss.

8. The method of claim 1, wherein, The loss function of the loss function fusion module is in the form of weighted summation, and the physical loss and data loss are combined by weighted summation, and the form is: L= ； wherein, is a physical loss weight, which decreases with the increase of training rounds, to ensure that the result is closer to reality; is a data loss weight; is a physical loss, is a data loss.

9. The method of claim 8, wherein, The training optimization module adopts an Adam optimizer, uses a gradient descent method to update network parameters, and dynamically adjusts a learning rate of a physical loss weight. ​

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