Geomagnetic gradient tensor depth representation learning method and system

Abstract

The application discloses a geomagnetic gradient tensor deep characterization learning method and system, and belongs to the technical field of information processing. The method comprises the following steps: acquiring a geomagnetic three-component data matrix of a magnetic object and establishing an original gradient tensor data set; generating a gradient matrix based on the original gradient tensor data set, orthogonally decomposing the gradient matrix, and obtaining mutually independent rotation invariance features and direction sensitive features; inputting the rotation invariance features and the direction sensitive features into a rotation invariance convolutional neural network for feature extraction; constructing a geometric constraint loss function comprising an angle constraint loss function and a direction constraint loss function, and optimizing a training network; and performing deep characterization on geomagnetic gradient tensor data based on the trained network. The innovative gradient matrix orthogonal decomposition technology solves the problem that rotation invariance and direction sensitivity cannot be considered simultaneously, the feature characterization accuracy is improved by about 30-40%, the processing speed is improved by 2-3 times, and the anti-interference capability is significantly enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of information processing, in particular to a geomagnetic gradient tensor deep representation learning method and system, and more particularly to a method and system for feature extraction and representation of geomagnetic gradient data using deep learning and tensor analysis techniques. BACKGROUND

[0002] Geomagnetic gradient data has wide application value in geological exploration, underwater target detection, intelligent traffic management and other fields. Traditional geomagnetic gradient data processing methods are mainly based on signal processing and statistical analysis, which are difficult to effectively extract deep features in complex geomagnetic fields, and have obvious shortcomings in processing rotation transformation and direction sensitive information.

[0003] With the development of deep learning technology, it is possible to use neural networks to process geomagnetic gradient data. However, existing deep learning methods still have the following problems when processing geomagnetic gradient tensor data: on the one hand, it is difficult to maintain rotation invariance and direction sensitivity at the same time, often resulting in a trade-off situation; on the other hand, the feature representation ability of geomagnetic gradient tensor data is limited, making it difficult to capture complex patterns and internal structures in the data. In addition, existing methods have high computational complexity, limited real-time processing capability, and insufficient stability in high noise environments.

[0004] Therefore, there is an urgent need for a method and system that can effectively process geomagnetic gradient tensor data while maintaining rotation invariance and direction sensitivity, and having efficient feature representation capability. SUMMARY

[0005] The purpose of the present application is to provide a geomagnetic gradient tensor deep representation learning method and system, which aims to solve the problems of existing technology, such as the inability to maintain rotation invariance and direction sensitivity at the same time, limited feature representation capability, low computational efficiency, and insufficient anti-interference capability.

[0006] The present application provides a geomagnetic gradient tensor deep representation learning method, comprising:

[0007] Obtaining a geomagnetic three-component data matrix of a magnetic object, and establishing an original gradient tensor data set based on the geomagnetic three-component data matrix;

[0008] Based on the original gradient tensor data set, a gradient matrix is generated, and the gradient matrix is orthogonally decomposed to obtain rotation invariant features and direction sensitive features, wherein the rotation invariant features and the direction sensitive features are independent of each other;

[0009] The rotation invariant features and the direction sensitive features are input into a rotation invariant convolutional neural network for feature extraction to obtain feature representations;

[0010] construct a geometric constraint loss function comprising an angle constraint loss function and a direction constraint loss function, and train the rotation equivariant convolutional neural network by optimizing the geometric constraint loss function;

[0011] based on the trained rotation equivariant convolutional neural network, the input geomagnetic gradient tensor data is deeply characterized to obtain a target gradient tensor feature.

[0012] As a preferred, the geomagnetic three-component data matrix of the magnetic object is obtained, and the original gradient tensor data set is established according to the geomagnetic three-component data matrix, specifically including:

[0013] The geomagnetic three-component data matrix of a plurality of magnetic objects is obtained and established as a magnetic object geomagnetic three-component data set, the magnetic object geomagnetic three-component data set includes a plurality of elements, and each element contains a geomagnetic three-component data matrix of a magnetic object;

[0014] The first geomagnetic three-component data matrix, the second geomagnetic three-component data matrix and the third geomagnetic three-component data matrix contained in the magnetic object geomagnetic three-component data set are extracted;

[0015] The original spatial three-component data set is established according to the first geomagnetic three-component data matrix, the second geomagnetic three-component data matrix and the third geomagnetic three-component data matrix;

[0016] The original spatial three-component data set is subjected to matrix difference operation to extract the original gradient tensor data set.

[0017] As a preferred, the gradient matrix is generated based on the original gradient tensor data set, and the rotation equivariant feature and the direction sensitive feature are obtained by orthogonal decomposition of the gradient matrix, specifically including:

[0018] The original gradient tensor data set is preprocessed, including zero mean and unit amplitude normalization;

[0019] The original gradient tensor data set after preprocessing is converted into a gradient matrix form;

[0020] An orthogonal decomposition matrix is constructed , wherein R is the orthogonal decomposition matrix, G is the gradient matrix, W is the rotation equivariant feature, is the transpose of the gradient matrix;

[0021] The gradient matrix is decomposed into two-channel information independent of the rotation equivariant feature and the direction sensitive feature by eigenvalue decomposition, wherein the rotation equivariant feature dimension is 4 times the original gradient tensor dimension, and the direction sensitive feature dimension is 2 times the original gradient tensor dimension.

[0022] As preferred, the rotation equivariant convolutional neural network comprises:

[0023] a gradient matrix orthogonal decomposition structure composed of a plurality of convolution modules and a plurality of pooling modules, wherein the convolution module comprises a convolution layer, a ReLU layer, a batch normalization layer and a max pooling layer, and the pooling module is a max pooling layer;

[0024] an orthogonal decomposition module composed of two 3×3 convolution layers and one 1×1 convolution layer, used for decomposing the gradient matrix into double-channel information independent of the rotation equivariant feature and the direction sensitive feature;

[0025] a feature fusion module used for fusing the rotation equivariant feature and the direction sensitive feature to generate a target gradient tensor feature.

[0026] As preferred, the angle constraint loss function is used to constrain the stability of the rotation equivariant feature under rotation transformation, comprising:

[0027] introducing an angle constraint in the feature space to limit the change of the included angle between the feature vectors;

[0028] quantifying the stability of the rotation equivariant feature under rotation transformation;

[0029] ensuring the orthogonality of the feature vectors to avoid information redundancy.

[0030] As preferred, the direction constraint loss function is used to ensure the orthogonality and effectiveness of the direction sensitive feature, comprising:

[0031] constructing a direction constraint loss function to evaluate the quality of the direction sensitive feature;

[0032] introducing a loss metric to quantify the deviation of the direction sensitive feature from the ideal state;

[0033] establishing a feature orthogonality constraint to ensure the capture of complete direction information.

[0034] As preferred, the optimization process of the geometric constraint loss function comprises:

[0035] initializing network parameters to construct an initial feature representation;

[0036] calculating the current feature representation by forward propagation;

[0037] calculating the angle constraint loss function and the direction constraint loss function;

[0038] synthesizing a total loss function for back propagation;

[0039] updating network parameters to optimize feature extraction capability;

[0040] Monitor the loss function trend, and save the optimal network parameters when the convergence condition is reached.

[0041] As preferred, the trained rotation equivariant convolutional neural network is used to deeply characterize the input magnetic gradient tensor data to obtain target gradient tensor features, specifically including:

[0042] The input magnetic gradient tensor data is converted into a 3x3x3 tensor structure;

[0043] The 3x3x3 tensor structure is converted into a 1x27 tensor through a first convolutional layer;

[0044] A first feature tensor of 1x9 is obtained through a first pooling layer;

[0045] Features are extracted through a second convolutional layer to generate a feature matrix;

[0046] The rotation equivariant features and the direction-sensitive features are separated through the orthogonal decomposition module;

[0047] The target gradient tensor feature representation is generated through the feature fusion module.

[0048] As preferred, it also includes:

[0049] The target gradient tensor features are applied to application scenarios such as geological resource exploration, underwater target detection, and intelligent traffic management;

[0050] For geological resource exploration, regional gridding point collection, real-time gradient tensor feature extraction, intelligent identification and labeling of abnormal points, resource distribution three-dimensional modeling and evaluation are performed;

[0051] For underwater target detection, regional scanning collection of magnetic field data, real-time extraction of gradient tensor features, target detection, classification and positioning, trajectory tracking and behavior analysis are performed;

[0052] For intelligent traffic management, multi-point synchronous collection of vehicle magnetic field data, real-time extraction of gradient tensor features, vehicle type identification and flow statistics, traffic state evaluation and early warning release are performed.

[0053] The magnetic gradient tensor deep characterization learning system includes:

[0054] A magnetic gradient data acquisition module is used to obtain a magnetic three-component data matrix of a magnetic object and establish an original gradient tensor data set based on the magnetic three-component data matrix;

[0055] a gradient tensor construction module, configured to generate a gradient matrix based on the original gradient tensor dataset, and perform orthogonal decomposition on the gradient matrix to obtain rotationally invariant features and direction-sensitive features, wherein the rotationally invariant features and the direction-sensitive features are independent of each other;

[0056] a rotationally invariant feature extraction module, configured to input the rotationally invariant features and the direction-sensitive features into a rotationally invariant convolutional neural network to perform feature extraction and obtain feature representations;

[0057] a geometric constraint optimization module, configured to construct a geometric constraint loss function including an angle constraint loss function and a direction constraint loss function, and train the rotationally invariant convolutional neural network by optimizing the geometric constraint loss function;

[0058] a feature application module, configured to perform deep characterization on input magnetic gradient tensor data based on the trained rotationally invariant convolutional neural network, obtain target gradient tensor features, and apply the target gradient tensor features to a related application scenario.

[0059] The beneficial effects of the present application include:

[0060] 1. By means of the innovative gradient matrix orthogonal decomposition technology, the rotationally invariant features and the direction-sensitive features are effectively separated, the problem of difficult to balance the rotation invariance and the direction sensitivity is solved, and the feature characterization accuracy is improved by about 30%-40%.

[0061] 2. A special rotationally invariant convolutional neural network is designed, which significantly improves the feature extraction capability and the processing speed is improved by about 2-3 times compared with the traditional method, and is more suitable for real-time application scenarios.

[0062] 3. The geometric constraint loss function is introduced to ensure the quality and reliability of feature extraction, and the stable feature extraction performance can still be maintained in a high noise environment, and the system signal-to-noise ratio requirement is reduced from ≥15dB of the traditional method to ≥8dB, which is improved by about 7dB.

[0063] 4. The whole process integration from data acquisition to feature application is realized, which has high engineering practicability and scalability, and is suitable for multiple application fields such as geological exploration, underwater target detection and intelligent traffic management. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 The flowchart of the magnetic gradient tensor deep characterization learning method provided by the embodiment of the present application.

[0065] Figure 2 The gradient matrix orthogonal decomposition schematic diagram provided by the embodiment of the present application.

[0066] Figure 3A rotation equivariant convolutional neural network structure schematic diagram provided for an embodiment of the present application.

[0067] Figure 4 A geometric constraint loss function optimization flowchart provided for an embodiment of the present application.

[0068] Figure 5 A geomagnetic gradient tensor deep representation learning system structure schematic diagram provided for an embodiment of the present application. DETAILED DESCRIPTION

[0069] Reference will be made to Figure 1 - Figure 5 The present application will be further described below in conjunction with the drawings and embodiments. It should be understood that the specific embodiments described herein are only for the purpose of illustration and explanation of the present application, and are not intended to limit the present application.

[0070] With reference to Figure 1 The present application provides a geomagnetic gradient tensor deep representation learning method, comprising the following steps:

[0071] S1: Obtain a geomagnetic three-component data matrix of a magnetic object, and establish an original gradient tensor data set according to the geomagnetic three-component data matrix.

[0072] S2: Based on the original gradient tensor data set, generate a gradient matrix, and perform orthogonal decomposition on the gradient matrix to obtain rotation equivariant features and direction sensitive features, wherein the rotation equivariant features and the direction sensitive features are independent of each other.

[0073] S3: Input the rotation equivariant features and the direction sensitive features into a rotation equivariant convolutional neural network for feature extraction to obtain feature representations.

[0074] S4: Construct a geometric constraint loss function comprising an angle constraint loss function and a direction constraint loss function, and train the rotation equivariant convolutional neural network by optimizing the geometric constraint loss function.

[0075] S5: Based on the trained rotation equivariant convolutional neural network, perform deep representation learning on input geomagnetic gradient tensor data to obtain target gradient tensor features.

[0076] The steps are described in detail as follows:

[0077] S1: Obtain a geomagnetic three-component data matrix of a magnetic object and establish an original gradient tensor data set. In an embodiment of the present application, a geomagnetic three-component data matrix of a magnetic object is obtained, and an original gradient tensor data set is established according to the geomagnetic three-component data matrix, specifically comprising:

[0078] First, the geomagnetic three-component data matrices of multiple magnetic objects are acquired and established as a magnetic object geomagnetic three-component dataset. Preferably, data acquisition is performed using a magnetometer acquisition host and a geomagnetic gradient magnetometer, with the sampling frequency set to 100Hz to ensure that the temporal resolution of the data meets the requirements of subsequent processing. The magnetic object geomagnetic three-component dataset includes multiple elements, and each element contains the geomagnetic three-component data matrix of one magnetic object.

[0079] Next, the first, second, and third geomagnetic three-component data matrices are extracted from the geomagnetic three-component dataset of the magnetic object. These three data matrices correspond to the measured values ​​of the magnetic field components in the three orthogonal directions of x, y, and z, respectively.

[0080] Subsequently, an original spatial three-component dataset is constructed based on the first, second, and third geomagnetic three-component data matrices. Here, the elements in the original spatial three-component dataset are geomagnetic spatial three-component data matrices, denoted as... , and , respectively, represent the first, second, and third geomagnetic spatial three-component data matrices.

[0081] Finally, matrix difference operations are performed on the original three-component spatial dataset to extract the original gradient tensor dataset. Matrix difference operations calculate the difference in magnetic fields between adjacent spatial points to obtain spatial gradient information. The original gradient tensor dataset can be represented as:

[0082] ,

[0083] in, The original gradient tensor dataset, For the first Each original gradient tensor data matrix, where n is the number of samples in the dataset. It is The third-order tensor contains the gradient information of the magnetic field components in the x, y, and z directions in three-dimensional space.

[0084] In practice, to improve data quality, the collected data underwent preprocessing, including noise reduction, filtering, and outlier detection. For noise suppression, a bandpass filter was used with cutoff frequencies set at 0.1Hz and 40Hz, effectively filtering out environmental noise and high-frequency interference. For outlier detection, a threshold of mean ± 3 times the standard deviation was set; data points exceeding this range were marked as outliers and interpolated.

[0085] S2: generating a gradient matrix and performing orthogonal decomposition, in an embodiment of the present application, based on the original gradient tensor dataset, a gradient matrix is generated, and the gradient matrix is orthogonally decomposed to obtain rotationally invariant features and direction-sensitive features, specifically including:

[0086] Firstly, the original gradient tensor dataset is preprocessed, including zero-mean and unit amplitude normalization. Zero-mean means that the data is subtracted from the mean, so that the data distribution center is at the origin, which can be expressed as:

[0087] ,

[0088] wherein, is the gradient tensor after zero-mean, and N is the total number of samples in the dataset.

[0089] Unit amplitude normalization means that the data is divided by its module length, so that the data amplitude is uniform, which can be expressed as:

[0090] ,

[0091] wherein, is the normalized gradient tensor, is the module length of , which is calculated as the square root of the sum of squares of each element.

[0092] Next, the preprocessed original gradient tensor dataset is converted into a gradient matrix form. This step is to reconstruct the 3×3×3 third-order tensor into a matrix representation, which is convenient for subsequent processing. The converted gradient matrix is denoted as G, with dimensions wherein m is the sample number, and n is the feature dimension (here, 27, i.e. the dimension after flattening the 3×3×3 tensor).

[0093] Then, an orthogonal decomposition matrix is constructed, wherein R is the orthogonal decomposition matrix, G is the gradient matrix, W is the rotationally invariant feature, is the transpose of the gradient matrix. This form of decomposition has important mathematical significance, which decomposes the gradient matrix into two independent parts of rotationally invariant features and direction-sensitive features.

[0094] Finally, by eigenvalue decomposition, the gradient matrix is decomposed into two-channel information independent of the rotationally invariant features and the direction-sensitive features. Specifically, the matrix G is singular value decomposed (SVD):

[0095] ,

[0096] wherein U and V are orthogonal matrices, is a diagonal matrix containing singular values.

[0097] Based on the SVD decomposition result, the rotation-invariant feature W and the direction-sensitive feature D can be obtained:

[0098]

[0099]

[0100] wherein, and are the singular value diagonal matrices related to the rotation-invariant feature and the direction-sensitive feature extracted from .

[0101] In the present application, the rotation-invariant feature dimension is 4 times the original gradient tensor dimension, and the direction-sensitive feature dimension is 2 times the original gradient tensor dimension. This dimension setting is verified by a large number of experiments, which can maintain the integrity of the information while providing sufficient representation ability.

[0102] The core innovation of this orthogonal decomposition method is that it can separate the information in the gradient tensor into rotation-invariant part and direction-sensitive part, solving the problem that traditional methods are difficult to maintain both characteristics at the same time.

[0103] S3: rotation-invariant convolutional neural network feature extraction, in an embodiment of the present application, the rotation-invariant feature and the direction-sensitive feature are input into a rotation-invariant convolutional neural network for feature extraction to obtain a feature representation. The rotation-invariant convolutional neural network has a special structure design, including:

[0104] a gradient matrix orthogonal decomposition structure composed of multiple convolution modules and multiple pooling modules. The convolution module includes a convolution layer, a ReLU layer, a batch normalization layer and a max pooling layer, and the pooling module is a max pooling layer. Specifically, the convolution layer is responsible for feature extraction, the ReLU layer introduces a nonlinear transformation, the batch normalization layer stabilizes the training process, and the max pooling layer reduces the dimension and extracts significant features.

[0105] an orthogonal decomposition module composed of two 3x3 convolution layers and one 1x1 convolution layer. Two 3x3 convolution layers are used to capture local feature correlation, and one 1x1 convolution layer is used for channel information fusion. The function of this module is to decompose the gradient matrix into two-channel information independent of the rotation-invariant feature and the direction-sensitive feature.

[0106] a feature fusion module for fusing the rotation-invariant feature and the direction-sensitive feature to generate a target gradient tensor feature. This module fuses the two types of features by weighting to form the final feature representation.

[0107] ​​In the network implementation, the first convolutional layer uses 32 3x3 convolutional kernels with a stride of 1 and padding of 1; the second convolutional layer uses 64 3x3 convolutional kernels with a stride of 1 and padding of 1; the two 3x3 convolutional layers in the orthogonal decomposition module each use 128 convolutional kernels, and the 1x1 convolutional layer uses 256 convolutional kernels. These parameter settings are optimized to achieve a good balance between computational efficiency and feature extraction capability.

[0108] The convolution operation can be represented as:

[0109] ,

[0110] wherein, is the input feature map, is the output feature map, W is the convolutional kernel weight, b is the bias term, is the activation function (ReLU), and * represents the convolution operation.

[0111] The ReLU activation function is defined as:

[0112] ,

[0113] The batch normalization operation is defined as:

[0114] ,

[0115] wherein, X is the input, y is the output, is the batch mean, is the batch variance, and are learnable parameters, is a small constant (usually set to ) to prevent division by zero.

[0116] The max pooling operation is defined as:

[0117] ,

[0118] wherein, is the value of position in the input feature map, is the pooling window region centered at , and is the value of position in the output feature map.

[0119] In the specific implementation process, by stacking multiple convolutional modules and pooling modules, a deep network structure is formed, which can extract feature representations from low-level to high-level layer by layer. Preferably, the network depth is set to 5 layers, which is a compromise between model complexity and feature extraction capability.

[0120] S4: Geometric constraint loss function construction and optimization, in an embodiment of the present application, a geometric constraint loss function containing an angle constraint loss function and a direction constraint loss function is constructed, and the rotation equivariant convolutional neural network is trained by optimizing the geometric constraint loss function.

[0121] Firstly, the angle constraint loss function is used to constrain the stability of the rotation equivariant feature under rotation transformation, including: introducing angle constraint in feature space, limiting the change of the included angle between feature vectors; quantifying the stability of the rotation equivariant feature under rotation transformation; ensuring the orthogonality of feature vectors, avoiding information redundancy.

[0122] The angle constraint loss function can be expressed as:

[0123]

[0124] Among them, is the included angle between feature vectors and , calculated as:

[0125]

[0126] N is the number of feature vectors, and are feature vectors in the rotation equivariant feature.

[0127] Then, the direction constraint loss function is used to ensure the orthogonality and effectiveness of the direction sensitive feature, including: constructing a direction constraint loss function to evaluate the quality of the direction sensitive feature; introducing a loss metric to quantify the deviation of the direction sensitive feature from the ideal state; establishing a feature orthogonality constraint to ensure capturing complete directional information.

[0128] The direction constraint loss function can be expressed as:

[0129]

[0130] Among them, is the current direction sensitive feature, is the ideal direction sensitive feature (obtained by prior knowledge or supervision signal), is the Frobenius norm, is the weight coefficient (set to 0.5 in the experiment), M is the dimension of the direction sensitive feature, , represents the inner product of two direction sensitive features.

[0131] Then, the angle constraint loss function and the direction constraint loss function are combined to form the total loss function:

[0132] ​​​ ,

[0133] wherein, is the task-related loss (such as classification loss, regression loss, etc.), 、 and are loss function weight coefficients for balancing the importance of different loss terms. In the experiment, according to the specific application scene, 、 and are respectively 0.3, 0.3 and 0.4, which are the better configuration verified by a large number of experiments.

[0134] Preferably, the optimization process of the geometric constraint loss function comprises:

[0135] 1. Initialize network parameters and construct initial feature representations. Network parameter initialization adopts the He initialization method, which can effectively prevent the problem of gradient disappearance or explosion in deep network.

[0136] 2. Calculate the current feature representation by forward propagation. The input data is processed by each layer of the network to generate the current feature representation.

[0137] 3. Calculate the angle constraint loss function and the direction constraint loss function. According to the current feature representation, the values of the two types of loss functions are calculated.

[0138] 4. Synthesize the total loss function and perform back propagation. The loss terms are combined to form the total loss function, and then the gradient is calculated by the back propagation algorithm.

[0139] 5. Update network parameters and optimize feature extraction capability. The network parameters are updated using the Adam optimizer, the learning rate is initially set to 0.001, and the learning rate decay strategy is adopted, which is decayed to 0.9 times of the original every 10 epochs.

[0140] 6. Monitor the trend of the loss function, and save the optimal network parameters when the convergence condition is reached. The convergence condition is set to be less than 10 -4 for 5 consecutive epochs, or the maximum number of epochs (set to 100) is reached.

[0141] The optimization process adopts a batch processing mode, and the number of samples in each batch is set to 64, which achieves a good balance between calculation efficiency and optimization stability. Early stopping strategy is adopted in the optimization process to avoid overfitting problem.

[0142] S5: Based on the trained network, in an embodiment of the present application, the input geomagnetic gradient tensor data is deeply represented based on the trained rotation equivariant convolutional neural network to obtain the target gradient tensor feature. Specifically, it comprises:

[0143] Firstly, the input geomagnetic gradient tensor data is converted into a 3x3x3 tensor structure. This step is to organize the original geomagnetic data into a standard third-order tensor form, which is convenient for subsequent processing.

[0144] Then, the 3x3x3 tensor structure is converted into a 1x27 tensor through the first convolution layer. The first convolution layer uses 32 3x3 convolution kernels with a step size of 1 and a padding of 1 to convert the input tensor into a feature map, and then the feature map is flattened into a 1x27 vector.

[0145] Then, the first feature tensor of 1x9 is obtained after the first pooling layer. The first pooling layer uses a 3x3 pooling window with a step size of 3 to reduce the dimension of the 1x27 vector to a 1x9 feature tensor.

[0146] Subsequently, the second convolution layer is used to extract features and generate a feature matrix. The second convolution layer uses 64 3x3 convolution kernels with a step size of 1 and a padding of 1 to further extract feature information and form a feature matrix.

[0147] Next, the rotation-invariant features and the direction-sensitive features are separated by the orthogonal decomposition module. The orthogonal decomposition module consists of two 3x3 convolution layers and one 1x1 convolution layer, which decomposes the feature matrix into rotation-invariant features and direction-sensitive features.

[0148] Finally, the target gradient tensor feature representation is generated by the feature fusion module. The feature fusion module combines the rotation-invariant features and the direction-sensitive features into the final target gradient tensor feature through weighted combination.

[0149] The target gradient tensor feature can be represented as:

[0150] ,

[0151] where, is the target gradient tensor feature, is the rotation-invariant feature, is the direction-sensitive feature, and are the feature fusion weighting coefficients, representing the importance of the two types of features. In actual applications, the values of and can be adjusted according to specific task requirements to balance the rotation-invariance and direction-sensitivity.

[0152] Preferably, in the test stage, in order to improve the processing efficiency, model compression techniques including pruning and quantization are adopted. Pruning refers to removing network connections that have less impact on the output, and in the experiment, the pruning threshold is set to the 90th percentile of the absolute value of the weight. Quantization refers to converting 32-bit floating-point parameters to 8-bit integers to reduce computational and storage overhead. After compression, the model size is reduced by about 75%, the inference speed is increased by about 2.5 times, and the accuracy is only decreased by about 1% to 2%, which is an acceptable compromise in practical applications.

[0153] In an embodiment of the present application, the target gradient tensor feature can be applied to geological resource exploration, underwater target detection, or intelligent traffic management, etc.

[0154] For geological resource exploration, the method of the present application performs regional grid point collection, real-time gradient tensor feature extraction, abnormal point intelligent identification and marking, resource distribution three-dimensional modeling and evaluation. Specifically, first, grid points are set in the exploration area, usually with a grid spacing of 5-10 meters to ensure the spatial resolution of the collected data; then real-time magnetic gradient data are collected and features are extracted; then abnormal points are identified by setting a threshold (usually ±3 times the standard deviation of the regional average); finally, a three-dimensional resource model is constructed based on the distribution of abnormal points. Experiments show that the positioning accuracy of the method of the present application in iron ore resource exploration is improved by about 35%, and the exploration efficiency is improved by about 40%.

[0155] For underwater target detection, the method of the present application performs regional scanning of magnetic field data, real-time extraction of gradient tensor features, target detection, classification and positioning, trajectory tracking and behavior analysis. Specifically, first, a underwater magnetic gradient sensor array is used to scan the target area; then the gradient tensor features are extracted in real time; then the target is detected and classified through feature matching, with a classification accuracy of up to 92%; finally, the trajectory is analyzed through continuous tracking. In complex underwater environments, the target detection distance of the method of the present application is improved by about 25% compared to traditional methods, and it can still maintain an identification rate of more than 85% under a signal-to-noise ratio as low as 8dB.

[0156] For intelligent traffic management, the method of the present application performs multi-point synchronous collection of vehicle magnetic field data, real-time extraction of gradient tensor features, vehicle type identification and flow statistics, traffic state evaluation and warning issuance. Specifically, first, a magnetic gradient sensor array is buried at key nodes on the road; then the magnetic field disturbance generated by passing vehicles is collected in real time; then the gradient tensor features are extracted for vehicle identification and statistics; finally, the traffic state is evaluated based on the flow data and a warning is issued. In practical applications, the vehicle identification accuracy is more than 95%, the flow statistics error is controlled within ±3%, and the warning response time is less than 2 seconds, meeting the real-time traffic management requirements.

[0157] Reference Figure 5The application provides a geomagnetic gradient tensor deep characterization learning system, comprising a geomagnetic gradient data acquisition module 1, a gradient tensor construction module 2, a rotationally invariant feature extraction module 3, a geometric constraint optimization module 4 and a feature application module 5.

[0158] The geomagnetic gradient data acquisition module 1 is used for acquiring a geomagnetic three-component data matrix of a magnetic object and establishing an original gradient tensor data set according to the geomagnetic three-component data matrix. The module comprises a magnetometer support, a magnetometer acquisition host and a geomagnetic gradient magnetometer, wherein the geomagnetic gradient magnetometer comprises three triaxial magnetometers which are arranged at equal intervals in space. Preferably, the sensitivity of the triaxial magnetometer is not less than 0.1 nT, and the sampling rate is not less than 100 Hz, so as to meet the high-precision data acquisition requirement.

[0159] The gradient tensor construction module 2 is used for generating a gradient matrix based on the original gradient tensor data set and performing orthogonal decomposition on the gradient matrix to obtain rotationally invariant features and direction-sensitive features, wherein the rotationally invariant features and the direction-sensitive features are independent of each other. The module is responsible for data preprocessing, gradient calculation and orthogonal decomposition, so as to ensure the data quality for subsequent feature extraction.

[0160] The rotationally invariant feature extraction module 3 is used for inputting the rotationally invariant features and the direction-sensitive features into a rotationally invariant convolutional neural network to perform feature extraction and obtain feature representation. The module realizes the forward propagation process of the network, including convolution, activation, normalization and pooling operations and the like, so as to form effective feature representation.

[0161] The geometric constraint optimization module 4 is used for constructing a geometric constraint loss function comprising an angle constraint loss function and a direction constraint loss function and training the rotationally invariant convolutional neural network by optimizing the geometric constraint loss function. The module is responsible for training and optimizing the network, and improves the feature extraction capability by calculating loss, back propagation and parameter updating.

[0162] The feature application module 5 is used for performing deep characterization on input geomagnetic gradient tensor data based on the trained rotationally invariant convolutional neural network, obtaining target gradient tensor features and applying the target gradient tensor features to related application scenarios. The module is the output end of the system and is responsible for applying the extracted features to actual tasks, such as geological exploration, underwater target detection or intelligent traffic management and the like.

[0163] The modules are connected through standardized interfaces to form a complete data processing flow. Preferably, high-speed bus structure is adopted for communication between the modules, and the data transmission rate is not less than 100 MB / s, so as to ensure the real-time performance of the system. The system adopts modular design, so that it is convenient to upgrade and expand, and each module can be individually optimized or replaced according to application requirements.

[0164] In the system implementation, the hardware configuration comprises: a multi-core processor (main frequency >=2.5GHz) is used for a processing platform, memory >=8GB, storage >=256GB SSD; the software architecture comprises an operating system layer, a middleware layer and an application layer, and supports multi-task parallel processing and remote access.

[0165] The system of the application realizes full-process integration from data acquisition to feature application, has high engineering practicability and scalability, can stably operate in various complex environments, and provides a complete solution for geomagnetic gradient data processing.

[0166] The above-described embodiments only express the specific implementation of the application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent of the application. It should be pointed out that for ordinary skilled persons in the art, without departing from the concept of the application, a number of modifications and improvements can be made, which belong to the protection scope of the application.

Claims

1. A geomagnetic gradient tensor depth representation learning method, characterized in that, The method comprises the following steps: obtaining a geomagnetic three-component data matrix of a magnetic object, and establishing an original gradient tensor data set according to the geomagnetic three-component data matrix; based on the original gradient tensor data set, generating a gradient matrix, and performing orthogonal decomposition on the gradient matrix to obtain rotationally invariant features and direction-sensitive features, wherein the rotationally invariant features and the direction-sensitive features are independent of each other; inputting the rotationally invariant features and the direction-sensitive features into a rotationally invariant convolutional neural network for feature extraction to obtain feature representations; constructing a geometric constraint loss function comprising an angle constraint loss function and a direction constraint loss function, and training the rotationally invariant convolutional neural network by optimizing the geometric constraint loss function; based on the trained rotationally invariant convolutional neural network, performing deep characterization on input geomagnetic gradient tensor data to obtain target gradient tensor features; the original gradient tensor data set is preprocessed, including zero mean and unit amplitude normalization; the original gradient tensor data set after preprocessing is converted into a gradient matrix form; by eigenvalue decomposition, the gradient matrix is decomposed into two-channel information independent of each other, wherein the rotationally invariant features have a dimension of 4 times the dimension of the original gradient tensor, and the direction-sensitive features have a dimension of 2 times the dimension of the original gradient tensor. Constructing an orthogonal decomposition matrix where R is an orthogonal decomposition matrix, G is the gradient matrix, W is the rotation eigenvector, is the transpose of the gradient matrix; the method comprises the following steps:

2. The geomagnetic gradient tensor depth representation learning method according to claim 1, characterized in that, obtaining a geomagnetic three-component data matrix of a magnetic object, and establishing an original gradient tensor data set according to the geomagnetic three-component data matrix; extracting a first geomagnetic three-component data matrix, a second geomagnetic three-component data matrix and a third geomagnetic three-component data matrix from the magnetic object geomagnetic three-component data set; establishing an original spatial three-component data set according to the first geomagnetic three-component data matrix, the second geomagnetic three-component data matrix and the third geomagnetic three-component data matrix; performing matrix difference operation on the original spatial three-component data set to extract the original gradient tensor data set. the rotationally invariant convolutional neural network comprises:

3. The geomagnetic gradient tensor depth representation learning method according to claim 1, characterized in that, a gradient matrix orthogonal decomposition structure composed of multiple convolution modules and multiple pooling modules, wherein the convolution module comprises a convolution layer, a ReLU layer, a batch normalization layer and a maximum pooling layer, and the pooling module is a maximum pooling layer; an orthogonal decomposition module composed of two 3x3 convolution layers and one 1x1 convolution layer, used for decomposing the gradient matrix into two-channel information independent of each other; a feature fusion module for fusing the rotationally invariant features and the direction-sensitive features to generate target gradient tensor features. ​ 4. The geomagnetic gradient tensor depth representation learning method according to claim 1, characterized in that, The angle constraint loss function is used to constrain the stability of the rotation equivariant feature under rotation transformation, including: Introducing angle constraints in feature space to limit the change of the included angle between feature vectors; Quantifying the stability of the rotation equivariant feature under rotation transformation; Ensure the orthogonality of the feature vector, avoid information redundancy.

5. The geomagnetic gradient tensor depth representation learning method according to claim 1, characterized in that, The direction constraint loss function is used to ensure the orthogonality and effectiveness of the direction sensitive feature, including: Construct a direction constraint loss function to evaluate the quality of the direction sensitive feature; Introducing loss measurement, quantifying the deviation of the direction sensitive feature from the ideal state; Establish feature orthogonality constraints to ensure complete direction information capture.

6. The geomagnetic gradient tensor depth representation learning method according to claim 1, characterized in that, The optimization process of the geometric constraint loss function includes: Initialize network parameters to build initial feature representation; Through forward propagation, calculate the current feature representation; Calculate the angle constraint loss function and the direction constraint loss function; Synthesize the total loss function and perform back propagation; Update network parameters to optimize feature extraction capability; Monitor the trend of loss function change, save the optimal network parameters when the convergence condition is reached.

7. The geomagnetic gradient tensor depth representation learning method according to claim 3, characterized in that, Based on the trained rotation equivariant convolutional neural network, the input geomagnetic gradient tensor data is deeply characterized to obtain the target gradient tensor feature, specifically including: Convert the input geomagnetic gradient tensor data into a 3×3×3 tensor structure; Convert the 3×3×3 tensor structure to a 1×27 tensor through the first convolutional layer; Get the first feature tensor 1×9 through the first pooling layer; Extract features through the second convolutional layer to generate a feature matrix; Separate the rotation equivariant feature and the direction sensitive feature through the orthogonal decomposition module; Generate the target gradient tensor feature representation through the feature fusion module.

8. The geomagnetic gradient tensor depth representation learning method according to claim 1, characterized in that, Also includes: Apply the target gradient tensor feature to application scenarios such as geological resource exploration, underwater target detection, or intelligent traffic management; For geological resource exploration, perform regional grid point collection, real-time gradient tensor feature extraction, abnormal point intelligent identification and labeling, resource distribution three-dimensional modeling and evaluation; For underwater target detection, perform regional scanning to collect magnetic field data, real-time extraction of gradient tensor features, target detection, classification and positioning, trajectory tracking and behavior analysis; For intelligent traffic management, perform multi-point synchronous collection of vehicle magnetic field data, real-time extraction of gradient tensor features, vehicle type identification and flow statistics, traffic state evaluation and early warning release.

9. A geomagnetic gradient tensor depth characterization learning system, characterized by, It includes: A geomagnetic gradient data acquisition module for obtaining a geomagnetic three-component data matrix of a magnetic object and establishing an original gradient tensor data set based on the geomagnetic three-component data matrix; A gradient tensor construction module for generating a gradient matrix based on the original gradient tensor data set and performing orthogonal decomposition on the gradient matrix to obtain rotation equivariant features and direction sensitive features, wherein the rotation equivariant features and the direction sensitive features are independent of each other; A rotation equivariant feature extraction module for inputting the rotation equivariant features and the direction sensitive features into a rotation equivariant convolutional neural network for feature extraction to obtain feature representation; a geometric constraint optimization module configured to construct a geometric constraint loss function comprising an angle constraint loss function and a direction constraint loss function, and train the rotationally equivariant convolutional neural network by optimizing the geometric constraint loss function; a feature application module configured to perform deep feature representation on input magnetic gradient tensor data based on the trained rotationally equivariant convolutional neural network, to obtain target gradient tensor features, and to apply the target gradient tensor features to a related application scenario; the generating of a gradient matrix based on the original gradient tensor data set, and the orthogonal decomposition of the gradient matrix to obtain rotationally equivariant features and direction-sensitive features, specifically comprising: preprocessing of the original gradient tensor data set, including zero-mean normalization and unit amplitude normalization; conversion of the preprocessed original gradient tensor data set into a gradient matrix form; constructing an orthogonal decomposition matrix where R is an orthogonal decomposition matrix, G is the gradient matrix, W is the rotation eigenvector, is the transpose of the gradient matrix; decomposition of the gradient matrix into two-channel information independent of the rotationally equivariant features and the direction-sensitive features by eigenvalue decomposition, wherein the rotationally equivariant features have a dimension four times that of the original gradient tensor, and the direction-sensitive features have a dimension two times that of the original gradient tensor.

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