Modeling method of ocean geomagnetic field prediction model

Abstract

The invention discloses a modeling method of an ocean geomagnetic field prediction model, and relates to the technical field of ocean magnetic field prediction. The method comprises the following steps: acquiring ocean ship measurement magnetic field data of a target area, and preprocessing the ocean ship measurement magnetic field data; extracting a magnetic field value according to the preprocessed ocean ship measurement magnetic field data, and constructing a back propagation neural network; and the back-propagation neural network performs ocean ship measurement magnetic field prediction according to the magnetic field value, and optimizes the back-propagation neural network by adopting a genetic optimization algorithm to obtain an ocean geomagnetic field prediction model. Through the method, the nonlinear characteristics of the magnetic field in the marginal area can be accurately represented, hyper-parameters such as network weight, learning rate and hidden layer node number are coded and optimized, the manual parameter adjustment cost is reduced, complex magnetic field distribution is quickly approached, and finally a high-precision ocean geomagnetic field prediction model is constructed.

Description

Technical Field

[0001] The present invention relates to the technical field of ocean magnetic field prediction, and in particular to a modeling method of an ocean geomagnetic field prediction model. Background Art

[0002] As the Earth's inherent fundamental physical field, modeling the geomagnetic field is a core element in safeguarding the marine environment. High-precision ocean magnetic field models not only provide a scientific basis for marine resource exploration, circulation research, and military applications, but also lay an important foundation for sustainable marine development.

[0003] Currently, researchers at home and abroad primarily use two approaches to model ocean magnetic fields: polynomial models and spherical harmonics models. Polynomial models represent geomagnetic elements as polynomial functions of longitude and latitude, using fitting coefficients to characterize regional magnetic field distribution. Spherical harmonics models, based on the principle of magnetic scalar potential expansion, optimize the fitting accuracy of global geomagnetic observation data and increase the model order to resolve the fine structure of the geomagnetic field. Traditional magnetic field modeling methods rely on solving model coefficients to represent the magnetic field conditions in the study area.

[0004] However, although the polynomial model has the advantages of high computational efficiency and ease of real-time processing, its inherent smoothness will suppress high-frequency components of the magnetic field (such as local magnetic anomalies), resulting in reduced spatial resolution. In addition, the model accuracy decreases sharply with increasing distance from the expansion origin, making it difficult to accurately characterize the nonlinear characteristics of the magnetic field in the edge area. The spherical cap harmonic function model may have discontinuities or decreased accuracy at the boundary of the spherical cap region, and there is a boundary effect, which has a limited scope of application. As a linear basis function expansion method, its ability to fit magnetic field mutation signals (such as magnetic anomaly areas) is limited by the linear characteristics of the function basis, and often requires the introduction of high-order terms for compensation, which may cause overfitting problems. Summary of the Invention

[0005] In order to overcome the problems in the existing technology that the ocean magnetic field prediction model is difficult to accurately characterize the nonlinear characteristics of the magnetic field in the edge area and has limited fitting ability in complex magnetic field structures, the purpose of the present invention is to propose a modeling method for the ocean geomagnetic field prediction model, which can accurately characterize the nonlinear characteristics of the magnetic field in the edge area, and at the same time encode and optimize hyperparameters such as network weights, learning rate, and number of hidden layer nodes, reduce the cost of manual parameter adjustment, quickly approximate complex magnetic field distribution, and ultimately construct a high-precision ocean geomagnetic field prediction model.

[0006] To achieve the purpose of the present invention, the present invention adopts the following technical solutions:

[0007] A method for modeling an ocean geomagnetic field prediction model, the method comprising the following steps:

[0008] Acquiring magnetic field data measured by an ocean ship in a target area and preprocessing the magnetic field data measured by the ocean ship;

[0009] Extract magnetic field values ​​based on pre-processed ocean ship magnetic field data and construct a back-propagation neural network;

[0010] The back propagation neural network predicts the ocean ship magnetic field based on the magnetic field value, and the genetic optimization algorithm is used to optimize the back propagation neural network to obtain the ocean geomagnetic field prediction model.

[0011] In the above technical solution, by preprocessing the acquired ocean ship magnetic field data, the practicality and reliability of the ocean ship magnetic field data can be effectively improved, and the difficulty of data processing can be effectively reduced; the constructed back propagation neural network can effectively grasp the changes in the ocean ship magnetic field data, and then predict the ocean ship magnetic field based on the magnetic field value of the ocean ship magnetic field data. During the prediction process, the genetic algorithm used can simultaneously encode and optimize the hyperparameters such as the network weights, learning rate, and number of hidden layer nodes of the back propagation neural network, thereby obtaining an ocean geomagnetic field prediction model. The ocean geomagnetic field prediction model can accurately characterize the nonlinear characteristics of the magnetic field in the marginal area, reduce the cost of manual parameter adjustment, and quickly approximate the complex magnetic field distribution, thereby effectively expanding the scope of application of magnetic field prediction, and thus reducing the labor cost of ocean magnetic field prediction.

[0012] Furthermore, the process of preprocessing the ocean vessel magnetic field data includes:

[0013] The least square method is used to detect trend surface errors and eliminate abnormal data in the magnetic field data measured by ocean vessels.

[0014] Diurnal variation correction is performed on the magnetic field data measured by ocean vessels after gross error detection and abnormal data removal.

[0015] Furthermore, the process of detecting trend surface gross errors of the ocean ship magnetic field data using the least squares method includes:

[0016] Based on the magnetic field data measured by ocean vessels in the target area, a polynomial surface function model is constructed, and the expression is:

[0017]

[0018] The coefficient vector estimation value of the polynomial surface function model is solved by the least squares method The expression is:

[0019]

[0020] Estimates from the coefficient vector Determine the measured value z at the measuring point i Is it abnormal? The expression is:

[0021]

[0022] According to the non-acceptance of the corresponding measurement value z i As the abnormal measurement value z i , and the abnormal measurement value z i The corresponding measurement points are eliminated;

[0023] Where z(x,y) represents the magnetic anomaly value at the measurement point (x,y), a represents the model fitting coefficient to be determined, j represents the order of the model, and σ represents the mean square error.

[0024] Furthermore, the expression for diurnal variation correction of the oceanographic ship magnetic field data after gross error detection and abnormal data removal is:

[0025] ΔT(t)=T(B,L,t)-T0(B,L,t)-T ′ (B,L,t)

[0026] Where (B, L) represents the geographical coordinates of the observation station; T0(B, L, t) represents the normal magnetic field at time t; T(B, L, t) represents the magnetic field intensity value observed by the magnetometer; T ′ (B, L, t) represents the geomagnetic anomaly value; ΔT(t) represents the diurnal change at time t.

[0027] In the above technical solution, the least squares method is used to perform trend surface gross error detection and abnormal data elimination on the ocean ship magnetic field data, which can effectively eliminate the magnetic field outliers in the data, thereby effectively improving the data usability and reducing the calculation requirements for the data; the ocean ship magnetic field data after gross error detection and abnormal data elimination is corrected for daily changes, which can effectively improve the practicality and reliability of the ocean ship magnetic field data.

[0028] Furthermore, the constructed back-propagation neural network includes an input layer, a hidden layer, and an output layer;

[0029] Each layer includes a number of nodes, and the connection status of the nodes between layers is reflected by weights; the hidden layer includes a first hidden layer and a second hidden layer, and the first hidden layer and the second hidden layer both include a number of nodes.

[0030] Furthermore, the process of back propagation neural network predicting the magnetic field measured by ocean ship based on the magnetic field value includes:

[0031] The input layer extracts the corresponding longitude and latitude based on the input magnetic field value, normalizes the longitude and latitude, and transmits them to the hidden layer. The hidden layer makes predictions based on the input longitude and latitude, and transmits the prediction results to the output layer. The output layer denormalizes the prediction results in the form of longitude and latitude, and outputs the magnetic field value of the prediction results. The expression of the whole process is:

[0032]

[0033] Among them, nT(ψ,λ) represents the magnetic field value of the prediction result, (ψ,λ) represents the longitude and latitude of the magnetic field value of the measurement point, represents the weights between hidden layers, represents the bias between hidden layers, represents the weight between the hidden layer and the output layer, b (3) represents the bias between the hidden layer and the output layer, n1 represents the number of nodes in the first hidden layer, n2 represents the number of nodes in the second hidden layer, f represents the tansig activation function of the input layer and the hidden layer, g represents the purelin activation function of the output layer, and h represents the output of the first hidden layer.

[0034] Furthermore, the output h of the first hidden layer is expressed as:

[0035]

[0036] in, Represents the weights and bias from the input layer to the hidden layer, subscript i represents the node index of the first hidden layer, subscript j represents the index of the input layer node, f represents the activation function tansig, lon represents longitude, and lat represents latitude.

[0037] In the above technical solution, considering that the traditional magnetic field prediction model structure is difficult to accurately characterize the nonlinear characteristics of the magnetic field in the edge area during the process of ocean magnetic field prediction, and there may be problems of discontinuity or decreased accuracy, the back propagation neural network is designed to include an input layer, a hidden layer and an output layer; wherein each layer contains a number of nodes, and the connection status of the nodes between layers is reflected by weights; the hidden layer includes a first hidden layer and a second hidden layer, and the first hidden layer and the second hidden layer both include a number of nodes. By designing the tansig activation function in the input layer and the hidden layer, the nonlinear relationship between longitude and latitude and the magnetic field value can be effectively constructed. Designing the purelin activation function in the output layer can effectively improve the flexibility of the output layer, thereby expanding the scope of application of the back propagation neural network and reducing the labor cost of ocean magnetic field prediction.

[0038] Furthermore, the process of optimizing the back propagation neural network using the genetic optimization algorithm includes:

[0039] The weights corresponding to the weights of the back-propagation neural network and the weights corresponding to the weights are encoded as chromosomes, and the expression is:

[0040] Chromosome=[w1,w2,…,w n ,b1,b2,…,bn ]

[0041] Initialize a population consisting of N random individuals, the expression is:

[0042] P0={X1,X2,…,X N}

[0043] Calculating the fitness of each individual in the population, selecting individuals with fitness higher than a preset threshold according to the fitness of each individual in the population for iterative operations of cross-reproduction and mutation, selecting the individual with the highest fitness after the iteration to decode, obtaining the optimal parameters of the back-propagation neural network, and optimizing the parameters of the back-propagation neural network according to the optimal parameters;

[0044] Among them, w i Indicates the weight corresponding to the weight, b i Indicates the weight corresponding to the weight, X N Indicates the Nth chromosome.

[0045] Furthermore, the expression for calculating the fitness of each individual in the population is:

[0046]

[0047] Among them, Fitness represents the designed fitness function, y i represents the true value, represents the predicted value, and MSE represents the mean square error.

[0048] Furthermore, the individual expression for selecting the fitness higher than the preset threshold is:

[0049]

[0050] Among them, P(x i ) represents individuals whose fitness is higher than the preset threshold, f i represents the fitness of the individual, f j Represents the overall fitness of the population.

[0051] In the above technical solution, the genetic algorithm can simultaneously encode and optimize hyperparameters such as the network weights, learning rate, and number of hidden layer nodes of the back-propagation neural network, thereby effectively improving the prediction accuracy of the back-propagation neural network and effectively expanding the scope of application of magnetic field prediction, thereby reducing the labor cost of ocean magnetic field prediction.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention proposes a modeling method for an ocean geomagnetic field prediction model. By preprocessing the acquired ocean ship magnetic field data, the practicability and reliability of the ocean ship magnetic field data can be effectively improved, and the difficulty of data processing can be effectively reduced. The constructed back propagation neural network can effectively grasp the changes in the ocean ship magnetic field data, and then predict the ocean ship magnetic field according to the magnetic field value of the ocean ship magnetic field data. During the prediction process, the adopted genetic algorithm can simultaneously encode and optimize the network weights, learning rate, number of hidden layer nodes and other hyperparameters of the back propagation neural network, thereby obtaining an ocean geomagnetic field prediction model. The ocean geomagnetic field prediction model can accurately characterize the nonlinear characteristics of the magnetic field in the marginal area, reduce the cost of manual parameter adjustment, and quickly approximate complex magnetic field distribution, thereby effectively expanding the scope of application of magnetic field prediction, and thus reducing the labor cost of ocean magnetic field prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A flowchart of the steps of a modeling method for an ocean geomagnetic field prediction model provided in an embodiment of the present application;

[0055] Figure 2 A flowchart of the least squares method and trend surface method for gross error elimination provided in an embodiment of the present application;

[0056] Figure 3 A schematic diagram of the structure of a back propagation neural network provided in an embodiment of the present application;

[0057] Figure 4 Flowchart of the genetic algorithm provided in the embodiment of the present application for parameter optimization of the back propagation neural network;

[0058] Figure 5 Schematic diagram of the magnetic field data measured by an ocean vessel obtained in the experiment provided in the embodiment of the present application;

[0059] Figure 6 This is a graph showing the results of the least squares method and the trend surface method for eliminating gross errors in the experiment provided in the embodiment of the present application;

[0060] Figure 7 A schematic diagram of the prediction results of a traditional magnetic field prediction model in the experiment provided in the embodiments of the present application;

[0061] Figure 8 A schematic diagram of the prediction results of the back propagation neural network before parameter optimization in the experiment provided in the embodiment of the present application;

[0062] Figure 9 This is a schematic diagram of the prediction results of the ocean geomagnetic field prediction model obtained after optimization by a genetic algorithm in the experiment provided in the embodiment of the present application;

[0063] Figure 10A schematic diagram comparing the prediction results of different models in the experiments provided in the embodiments of the present application;

[0064] Figure 11 A schematic diagram of comparative analysis of residuals of a traditional magnetic field prediction model in the experiment provided in the embodiments of the present application;

[0065] Figure 12 Schematic diagram of comparative analysis of residuals of the back propagation neural network before parameter optimization in the experiment provided in the embodiment of the present application;

[0066] Figure 13 Schematic diagram of residual comparison analysis of the ocean geomagnetic field prediction model obtained after genetic algorithm optimization in the experiment provided in the embodiment of the present application. DETAILED DESCRIPTION

[0067] To facilitate understanding of the present invention, the present invention will be described more fully below with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the accompanying drawings. However, the present invention may be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive understanding of the present disclosure.

[0068] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention pertains. The terms used in this specification of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0069] Example 1:

[0070] This embodiment provides a modeling method for an ocean geomagnetic field prediction model. Figure 1 , the method comprises the following steps:

[0071] Step S1: Acquire the magnetic field data measured by the ocean ship in the target area, and pre-process the magnetic field data measured by the ocean ship;

[0072] Step S2: extracting magnetic field values ​​based on the pre-processed ocean ship magnetic field data and constructing a back propagation neural network;

[0073] Step S3: The back propagation neural network predicts the ocean ship magnetic field according to the magnetic field value, and uses a genetic optimization algorithm to optimize the back propagation neural network to obtain an ocean geomagnetic field prediction model.

[0074] In step S1, see Figure 2 The process of preprocessing the ocean ship magnetic field data includes:

[0075] The least square method is used to detect trend surface errors and eliminate abnormal data in the magnetic field data measured by ocean vessels.

[0076] Diurnal variation correction is performed on the magnetic field data measured by ocean vessels after gross error detection and abnormal data removal.

[0077] As a preferred embodiment, the process of detecting trend surface gross errors of ocean vessel magnetic field data using the least squares method includes:

[0078] First, the target area to be detected is selected, and a polynomial surface function model is constructed based on the magnetic field data measured by the ocean ship in the target area. The expression is:

[0079]

[0080] The coefficient vector estimation value of the polynomial surface function model is solved by the least squares method The expression is:

[0081]

[0082] Estimates from the coefficient vector Determine the measured value z at the measuring point i Is it abnormal? Specifically, the trend surface model parameter a of the measurement point is calculated using the least squares method. i A significance test is required to facilitate accurate fitting of magnetic anomalies. i Is it an outlier? After determining the trend surface model parameters by the least squares method, the model is used to calculate the mean square error σ and the estimated value at the measured value, and the estimated value is compared with the original measured value. The expression is:

[0083]

[0084] According to the non-acceptance of the corresponding measurement value z i As the abnormal measurement value z i , and the abnormal measurement value z i The corresponding measurement points are eliminated;

[0085] Where z(x,y) represents the magnetic anomaly value at the measurement point (x,y), a represents the model fitting coefficient to be determined, j represents the order of the model, and σ represents the mean square error.

[0086] As a preferred embodiment, diurnal variation correction is performed on the marine ship magnetic field data after gross error detection and abnormal data removal. Specifically, this embodiment uses the Comprehensive Model Phase (CM series) model to estimate and remove diurnal variation correction. The CM model is used to estimate quiet-day external field signals and remove these signals from the total magnetic field data. The expression is:

[0087] ΔT(t)=T(B,L,t)-T0(B,L,t)-T ′ (B,L,t)

[0088] Where (B, L) represents the geographical coordinates of the observation station; T0(B, L, t) represents the normal magnetic field at time t; T(B, L, t) represents the magnetic field intensity value observed by the magnetometer; T ′ (B, L, t) represents the geomagnetic anomaly value; ΔT(t) represents the diurnal change at time t.

[0089] It can be understood that the use of the least squares method to perform trend surface gross error detection and abnormal data elimination on the ocean ship magnetic field data can effectively eliminate the magnetic field outliers in the data, thereby effectively improving the data usability and reducing the calculation requirements for the data; performing diurnal variation correction on the ocean ship magnetic field data after gross error detection and abnormal data elimination can effectively improve the practicality and reliability of the ocean ship magnetic field data.

[0090] In step S2, a back propagation neural network (BPNN) is constructed, which includes an input layer, a hidden layer, and an output layer;

[0091] Each layer includes a number of nodes, and the connection status of the nodes between layers is reflected by weights; the hidden layer includes a first hidden layer and a second hidden layer, and the first hidden layer and the second hidden layer both include a number of nodes.

[0092] Specifically, see Figure 3 The back propagation neural network is composed of an input layer, a hidden layer (also called an intermediate layer) and an output layer. Each layer can have several nodes, and the connection status of the nodes between layers is reflected by weights. Among them, the input data are longitude (LON) and latitude (LAT), and the input layer is designed to have 2 nodes. The output data is the magnetic field value, and the output layer is designed to have 1 node. The number of nodes in the hidden layer is related to the training accuracy and training cost of the neural network model. Increasing the number of neurons in the hidden layer can improve the accuracy of neural network training, but too many neurons will also affect the complexity of the network, resulting in an increase in training time and the number of weights, affecting the performance of the model. The present invention determines that the number of hidden layers is two, the first layer has 7 nodes, the second layer has 9 nodes, and a total of 16 nodes.

[0093] As a preferred embodiment, the process of predicting the magnetic field measured by an ocean ship according to the magnetic field value by the back propagation neural network includes:

[0094] The input layer extracts the corresponding longitude and latitude based on the input magnetic field value, normalizes the longitude and latitude, and transmits them to the hidden layer. The hidden layer makes predictions based on the input longitude and latitude, and transmits the prediction results to the output layer. The output layer denormalizes the prediction results in the form of longitude and latitude, and outputs the magnetic field value of the prediction results. The expression of the whole process is:

[0095]

[0096] Among them, nT(ψ,λ) represents the magnetic field value of the prediction result, (ψ,λ) represents the longitude and latitude of the magnetic field value of the measurement point, represents the weights between hidden layers, represents the bias between hidden layers, represents the weight between the hidden layer and the output layer, b (3) represents the bias between the hidden layer and the output layer, n1 represents the number of nodes in the first hidden layer, n2 represents the number of nodes in the second hidden layer, f represents the tansig activation function of the input layer and the hidden layer, g represents the purelin activation function of the output layer, and h represents the output of the first hidden layer.

[0097]

[0098] Where, are the weights and biases from the input layer to the hidden layer, where i is the index of the first hidden layer node, j is the index of the input layer node, and f is the activation function "tansig". lon is longitude and lat is latitude.

[0099] It is understandable that, considering that the traditional magnetic field prediction model structure is difficult to accurately characterize the nonlinear characteristics of the magnetic field in the edge area during the ocean magnetic field prediction process, and there may be problems of discontinuity or decreased accuracy, the back propagation neural network is designed to include an input layer, a hidden layer and an output layer; wherein each layer contains a number of nodes, and the connection status of the nodes between layers is reflected by weights; the hidden layer includes a first hidden layer and a second hidden layer, and the first hidden layer and the second hidden layer both include a number of nodes. By designing the tansig activation function in the input layer and the hidden layer, the nonlinear relationship between longitude and latitude and the magnetic field value can be effectively constructed. The purelin activation function is designed in the output layer, which can effectively improve the flexibility of the output layer, thereby expanding the scope of application of the back propagation neural network and reducing the labor cost of ocean magnetic field prediction.

[0100] In this embodiment, by preprocessing the acquired ocean ship magnetic field data, the practicality and reliability of the ocean ship magnetic field data can be effectively improved, and the difficulty of data processing can be effectively reduced; the constructed back propagation neural network can effectively grasp the changes in the ocean ship magnetic field data, and then predict the ocean ship magnetic field based on the magnetic field value of the ocean ship magnetic field data. During the prediction process, the genetic algorithm used can simultaneously encode and optimize the network weights, learning rate, number of hidden layer nodes and other hyperparameters of the back propagation neural network, thereby obtaining an ocean geomagnetic field prediction model. The ocean geomagnetic field prediction model can accurately characterize the nonlinear characteristics of the magnetic field in the marginal area, reduce the cost of manual parameter adjustment, and quickly approximate the complex magnetic field distribution, thereby effectively expanding the scope of application of the magnetic field prediction, and thus reducing the labor cost of the ocean magnetic field prediction.

[0101] Example 2:

[0102] This embodiment further illustrates step S3 in the first embodiment, as follows:

[0103] In step S3, the process of optimizing the back propagation neural network using the genetic optimization algorithm includes:

[0104] The genetic algorithm is based on Darwin's theory of evolution and is an algorithm that simulates the biological evolution process to obtain the optimal solution to a problem. The operations involved mainly include selection, crossover (reproduction), and mutation. The specific steps are as follows:

[0105] A: Chromosome Encoding

[0106] The weights corresponding to the weights of the back-propagation neural network and the weights corresponding to the weights are encoded as chromosomes, and the expression is:

[0107] Chromosome=[w1,w2,…,w n ,b1,b2,…,b n ]

[0108] B: Initial Population

[0109] Initialize a population consisting of N random individuals, the expression is:

[0110] P0={X1,X2,…,X N}

[0111] C: Fitness Function Design

[0112] According to the fitness function designed for each individual, the expression is:

[0113]

[0114] D: Genetic Operators

[0115] Based on the fitness of each individual in the population, individuals with fitness above a preset threshold are selected for iterative crossover and mutation operations. The crossover operation is the primary operation in population reproduction. The idea is to randomly select two individuals from the population and exchange some of their information to generate a new individual. Mutation expands the sample input space. A diverse population is a hallmark of genetic algorithms. It prevents the network from converging to a local optimal solution. Through these operations, the individual with the highest fitness is selected after each iteration.

[0116] After the iteration, the individual with the highest fitness is selected for decoding to obtain the optimal parameters of the back propagation neural network, and the parameters of the back propagation neural network are optimized based on the optimal parameters; the individual with the highest fitness in the final population is selected, and the optimal neural network parameters (weights and thresholds) obtained by decoding are assigned to the BPNN. Subsequently, these derived values ​​are used to train the BPNN. In each training process, the weights and thresholds are adjusted according to the accuracy index to minimize the RMS as much as possible. Once the conditions are met, the algorithm will output the trained back propagation neural network. The specific flow chart is as follows Figure 4 shown.

[0117] Among them, w i Indicates the weight corresponding to the weight, b i Indicates the weight corresponding to the weight, X N represents the Nth chromosome, y i represents the true value, represents the predicted value, and MSE represents the mean square error.

[0118] Specifically, after the fitness of all individuals in the population is calculated, we need to select excellent individuals for subsequent reproduction. The probability of an individual being selected depends on its fitness. The higher the fitness, the greater the probability of being selected. Here, "individual fitness / overall fitness" is used to represent the probability of an individual being selected. The expression for selecting individuals with fitness higher than the preset threshold is:

[0119]

[0120] Among them, P(x i ) represents individuals whose fitness is higher than the preset threshold, f i represents the fitness of the individual, f j Represents the overall fitness of the population.

[0121] In this embodiment, the genetic algorithm can simultaneously encode and optimize hyperparameters such as the network weights, learning rate, and number of hidden layer nodes of the back-propagation neural network, thereby effectively improving the prediction accuracy of the back-propagation neural network and effectively expanding the scope of application of magnetic field prediction, thereby reducing the labor cost of ocean magnetic field prediction.

[0122] Example 3:

[0123] This embodiment provides corresponding experimental data based on the methods described in Example 1 and Example 2, which are as follows:

[0124] Implementing area selection:

[0125] Taking the South China Sea as an example, the longitude and latitude range is (112° to 119° east longitude, 12° to 21° north latitude). This implementation used ship-based magnetic field data.

[0126] Ship-measured magnetic field data extraction:

[0127] There are 130,018 ship-surveyed data points in the study area. By manually filtering out the ship-surveyed data points without magnetic field data and those not at the same sea level, 113,798 data points are retained. The ship-surveyed points on the “SO49” route are retained as check points (see Figure 5 Gray line), and the remaining ship-measured data points are used as training data (see Figure 5 black line).

[0128] Correction of ship-measured magnetic field data:

[0129] Since the ship-based magnetic field data provided by NCEI have a large time span and the observation quality is uneven, there are many gross errors, and most of the data have not been corrected for diurnal variations. After using the CM series model to correct for diurnal variations in the ship-based magnetic field data, the least squares trend surface method was used to remove gross errors. The gross error threshold was set to 2σ, and the number of gross errors removed was 3046 (see Figure 6 Gray gross errors), the number of gross errors accounts for 2.68% of the total number of detections. At the same time, 88,478 ship-measured data points were separated as training data, and 22,274 ship-measured points on the "SO49" route were used as verification points.

[0130] Ocean magnetic field model construction:

[0131] The data obtained after daily variation correction and gross error elimination in the previous step were modeled using traditional methods, BP neural network methods and GA-BP neural network methods, and finally the three methods were analyzed and compared.

[0132] Traditional magnetic field modeling method: The Taylor polynomial model is based on the Taylor series expansion principle. It approximates the spatial variation of the geomagnetic field by performing a Taylor series expansion on the geomagnetic field near a reference point. According to the study area, the coordinate reference point (which can be understood as the center coordinate of the study area) is defined as 115° east longitude and 16° north latitude. The coordinate origin is used to calculate the relative coordinates. Finally, the ocean geomagnetic field model with the smallest RMSE and an order of 15 is obtained as follows Figure 7 shown.

[0133] BP neural network magnetic field modeling method (i.e., back propagation neural network before parameter optimization): Using back propagation neural network for magnetic field modeling, first input the training data, verification data SO49, and prediction data (the prediction resolution of this experiment is designed to be 2 points by 2 points) in sequence. Set the number of input layer nodes, the number of hidden layers and nodes, the number of output layer nodes, the number of training times, the learning rate, and the minimum error of the training target. Finally, after training, the ocean geomagnetic field model with the minimum RMSE is obtained. Figure 8 shown.

[0134] GA-BP neural network magnetic field modeling method (i.e., back propagation neural network after parameter optimization using genetic algorithm): Magnetic field modeling is performed using the back propagation neural network improved by genetic algorithm. Similarly, the training data, verification data SO49 and prediction data are input in sequence (the prediction resolution of this experiment is 2 points by 2 points). The number of input layer nodes, the number of hidden layers and nodes, the number of output layer nodes, the number of training times, the learning rate, the minimum error of the training target, the number of evolutionary iterations, the population size, the crossover probability and the mutation probability, etc. are set. Finally, after training, the ocean geomagnetic field model with the minimum RMSE is obtained, such as Figure 9 shown.

[0135] Comparative analysis of model results:

[0136] The present invention compares and analyzes the ocean magnetic field model constructed by GABP neural network, the interpolation results of original ship measurement data, the model constructed by traditional Taylor method and the model constructed by BP neural network. Figure 10 (b), (c) and (d)) and the original ship-derived geomagnetic field ( Figure 10 (a)) The overall trend is the same, but in the abrupt or abnormal area of ​​the ocean geomagnetic field, the three modeling methods show different fitting effects (see Figure 10 The traditional method has limited fitting ability for complex magnetic field structures (such as high-frequency changes and mutations) and shows the worst fitting effect (see Figure 10(b)), while the neural network method can automatically learn complex magnetic fields, adapt to high-frequency changes and mutation areas, and the constructed ocean geomagnetic field model shows a good fitting effect. In addition, the genetic algorithm is used to optimize the initial weights and thresholds, and then BP is used for local fine-tuning. Combining global exploration and local development, it prevents the BP network from falling into the local optimum near the initial weights, accelerates convergence and reduces the risk of overfitting, improves model accuracy, and the GA-BP neural network fits a more refined effect (see Figure 10 (c) and (d) (lower right grey dashed box).

[0137] Comparative analysis of model residuals:

[0138] To further determine the differences in numerical statistics among the models, the three models were interpolated to the training points for comparison and the fitting ability of the three modeling methods was analyzed. The total number of data was 88,478, and the residual values ​​of the Taylor model prediction values ​​and the training values ​​fell within ±3σ for 86,960 data (accounting for 98.28%) (see Figure 11 Histogram), the residual values ​​of the BPNN model prediction value and the training value fall within ±3σ, with 87611 data (accounting for 99.02%) (see Figure 12 Histogram), the residual values ​​of the GABPNN model prediction value and the training value fall within ±3σ, with 87611 data (accounting for 99.02%) (see Figure 13 Histogram), comparing the three residual histograms, the three magnetic field modeling methods can effectively fit the overall effect of the original data. The neural network contains more residual values ​​within the three-fold error range, indicating that its fitting accuracy for the data is higher. In addition, comparing the residual normal distribution diagrams of the three methods (see Figure 10-13 ), the residual histogram of the neural network model is closer to the normal distribution and the distribution diagram is narrower, which shows that the residuals are mainly concentrated in a smaller range, and the error distribution is more concentrated and uniform, which means that the overall fit of the model to the data is tighter. In addition, the percentage of small residual values ​​in the new method is significantly higher than that of the traditional method, which further shows that the new method has higher accuracy in fitting precision and can more effectively capture the detailed features in the data, especially showing stronger ability in processing local high-frequency signals. Therefore, the back-propagation neural network constructed based on the back-propagation neural network of the present invention can not only better restore local detailed high-frequency signals, but also improve the robustness and reliability of the model.

[0139] Comparative analysis of model accuracy:

[0140] analyze Figure 12 and Figure 13It's difficult to judge the relative merits of the BPNN (back-propagation neural network before parameter optimization) and the GA-BPNN (back-propagation neural network after parameter optimization using a genetic algorithm). To further determine the differences in accuracy between the models, we compared the interpolated training and validation points for each model (see Tables 1 and 2). This comparison revealed that the GA-BPNN had the smallest mean absolute error, root mean square error, and standard deviation, indicating a low overall prediction bias. The errors for most samples were concentrated near zero. The closer the measured values ​​were to the true values, the higher the model's prediction accuracy, and the more concentrated the data, the lower the dispersion. Although the mean absolute error for the validation points varied among the three models, likely due to the limited data at the validation points, the GA-BPNN achieved the lowest overall performance, indicating the best generalization.

[0141] Table 1 Statistical results of the differences between different models and training points

[0142]

[0143] Table 2 Statistical results of the differences between different models and checkpoints

[0144]

[0145] In the present invention, the traditional method relies on high-order terms to fit the nonlinear characteristics and the missing nonlinear information, and is difficult to fit complex magnetic field structures (such as high-frequency mutations, local anomalies). Due to the problem of random initialization of the BP neural network, a BP neural network optimized by genetic algorithm is used here to model the ocean magnetic field, and its feasibility is tested. The present invention uses three methods to model respectively, and compares the result graphs, residual histograms, residual normal distribution graphs and model difference data statistics of the three models. The results obtained by the three modeling methods have a high degree of fit with the results of the original data interpolation on the whole, but the neural network method performs better than the traditional method in the local anomaly area, and is adapted to high-frequency mutations and multi-scale features. The root mean square error accuracy of the GA-BP neural network model is higher than that of the BP neural network model, indicating that the GA-BP neural network significantly improves the efficiency of the network in extracting feature information, and effectively solves the problem of the BP neural network converging to the local optimum due to the randomness of the initial weights.

[0146] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention's description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A modeling method for an ocean geomagnetic field prediction model, characterized in that: The method comprises the following steps: Acquiring magnetic field data measured by an ocean ship in a target area and preprocessing the magnetic field data measured by the ocean ship; Extract magnetic field values ​​based on pre-processed ocean ship magnetic field data and construct a back-propagation neural network; The back propagation neural network predicts the ocean ship magnetic field based on the magnetic field value, and the genetic optimization algorithm is used to optimize the back propagation neural network to obtain the ocean geomagnetic field prediction model.

2. The modeling method of the ocean geomagnetic field prediction model according to claim 1, characterized in that: The process of preprocessing the ocean ship magnetic field data includes: The least square method is used to detect trend surface errors and eliminate abnormal data in the magnetic field data measured by ocean vessels. Diurnal variation correction is performed on the magnetic field data measured by ocean vessels after gross error detection and abnormal data removal.

3. The modeling method of the ocean geomagnetic field prediction model according to claim 2, characterized in that: The process of detecting trend surface gross errors of ocean ship magnetic field data using the least squares method includes: Based on the magnetic field data measured by ocean vessels in the target area, a polynomial surface function model is constructed, and the expression is: The coefficient vector estimation value of the polynomial surface function model is solved by the least squares method The expression is: Estimates from the coefficient vector Determine the measured value z at the measuring point i Is it abnormal? The expression is: According to the corresponding measurement value z i As the abnormal measurement value z i , and the abnormal measurement value z i The corresponding measurement points are eliminated; Where z(x,y) represents the magnetic anomaly value at the measurement point (x,y), a represents the model fitting coefficient to be determined, j represents the order of the model, and σ represents the mean square error.

4. The modeling method of the ocean geomagnetic field prediction model according to claim 2, characterized in that: The expression for diurnal variation correction of the oceanographic ship magnetic field data after gross error detection and abnormal data removal is: ΔT(t)=T(B,L,t)-T0(B,L,t)-T ′ (N,L,t) Where (B, L) represents the geographical coordinates of the observation station; T0(B, L, t) represents the normal magnetic field at time t; T(B, L, t) represents the magnetic field intensity value observed by the magnetometer; T ′ (B, L, t) represents the geomagnetic anomaly value; ΔT(t) represents the diurnal change at time t.

5. The modeling method of the ocean geomagnetic field prediction model according to claim 1, characterized in that: The constructed back propagation neural network includes: input layer, hidden layer and output layer; Each layer includes a number of nodes, and the connection status of the nodes between layers is reflected by weights; the hidden layer includes a first hidden layer and a second hidden layer, and the first hidden layer and the second hidden layer both include a number of nodes.

6. The modeling method of the ocean geomagnetic field prediction model according to claim 5, characterized in that: The process of back propagation neural network to predict the magnetic field of ocean ship measurement based on the magnetic field value includes: The input layer extracts the corresponding longitude and latitude based on the input magnetic field value, normalizes the longitude and latitude, and transmits them to the hidden layer. The hidden layer makes predictions based on the input longitude and latitude, and transmits the prediction results to the output layer. The output layer denormalizes the prediction results in the form of longitude and latitude, and outputs the magnetic field value of the prediction results. The expression of the whole process is: Among them, nT(ψ,λ) represents the magnetic field value of the prediction result, (ψ,λ) represents the longitude and latitude of the magnetic field value of the measurement point, represents the weights between hidden layers, represents the bias between hidden layers, represents the weight between the hidden layer and the output layer, b (3) represents the bias between the hidden layer and the output layer, n1 represents the number of nodes in the first hidden layer, n2 represents the number of nodes in the second hidden layer, f represents the tansig activation function of the input layer and the hidden layer, g represents the purelin activation function of the output layer, and h represents the output of the first hidden layer.

7. The modeling method of the ocean geomagnetic field prediction model according to claim 6, characterized in that: The output h of the first hidden layer is expressed as: in, Represents the weights and bias from the input layer to the hidden layer, subscript i represents the node index of the first hidden layer, subscript j represents the index of the input layer node, f represents the activation function tansig, lon represents longitude, and lat represents latitude.

8. The modeling method of the ocean geomagnetic field prediction model according to claim 6, characterized in that: The process of optimizing the back-propagation neural network using the genetic optimization algorithm includes: The weights corresponding to the weights of the back-propagation neural network and the weights corresponding to the weights are encoded as chromosomes, and the expression is: Chromosome=[w1,w2,…,w n ,b1,b2,…,b n ] Initialize a population consisting of N random individuals, the expression is: P0={X1,X2,…,X N } Calculating the fitness of each individual in the population, selecting individuals with fitness higher than a preset threshold based on the fitness of each individual in the population for iterative genetic operations of cross-reproduction and mutation, selecting the individual with the highest fitness after the iteration to decode, obtaining the optimal parameters of the back-propagation neural network, and optimizing the parameters of the back-propagation neural network based on the optimal parameters; Among them, w i Indicates the weight corresponding to the weight, b i Indicates the weight corresponding to the weight, X N Indicates the Nth chromosome.

9. The modeling method of the ocean geomagnetic field prediction model according to claim 8, characterized in that: The expression for calculating the fitness of each individual in the population is: Among them, Fitness represents the designed fitness function, y i represents the true value, represents the predicted value, and MSE represents the mean square error.

10. The modeling method of the ocean geomagnetic field prediction model according to claim 9, characterized in that: The expression for selecting individuals whose fitness is higher than the preset threshold is: Among them, P(x i ) represents individuals whose fitness is higher than the preset threshold, f i represents the fitness of the individual, f j Represents the overall fitness of the population.

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