A vehicle-mounted gravity dynamic error compensation method and device based on intelligent algorithm

Abstract

This application discloses a method and device for on-board dynamic gravity error compensation based on an intelligent algorithm, relating to the field of dynamic gravity measurement technology. The method includes: preliminary screening using the minimum redundancy and maximum correlation criteria and fine selection using a first sparrow search algorithm combined with cross-validation for feature extraction and reconstruction of input data; designing a new loss function using domain knowledge of gravity anomaly measurements as a constraint to construct a PI-LSTM for dynamic error compensation; and finally, optimizing the model hyperparameters of the PI-LSTM using a second sparrow search algorithm. This application uses a swarm intelligence algorithm and PI-LSTM to perform error compensation for on-board dynamic gravity measurement, effectively improving the fitting performance and generalization ability of the error compensation model, thereby improving the accuracy and environmental adaptability of on-board dynamic gravity measurement.

Description

Technical Field

[0001] The present application relates to the field of dynamic gravity measurement technology, and in particular to a vehicle-mounted dynamic gravity error compensation method and device based on an intelligent algorithm. Background Art

[0002] Dynamic gravity measurement, relying on a vehicle, allows for rapid, efficient, and accurate acquisition of regional gravity information, providing insights into underground structures and possessing significant application value in economic development, national defense, basic scientific research, and social development. Vehicle-mounted dynamic gravity measurement, with its advantages of high signal-to-noise ratio, high spatial resolution, flexibility, and ease of establishing baseline information, offers a superior option for the high-precision, efficient, and refined enrichment of Earth's gravity field. However, vehicle-mounted gravity measurement is subject to significant dynamic errors introduced by environmental factors such as road bumps, measurement line conditions, and vehicle maneuvers, posing significant challenges to measurement accuracy. Numerous researchers have made significant efforts to improve the accuracy of dynamic gravity measurement. Li Xiaopeng's team derived a precise compensation model for the tilt error of an inertially stabilized platform, minimizing the impact of short-wave random errors. Addressing the widespread dynamic environmental effects in current operations, Huang Motao proposed a universal model for compensating for residual errors from various dynamic effects, effectively eliminating the impact of highly dynamic measurement environments. Cai Shaokun analyzed the mechanism of strapdown dynamic errors and proposed a universal model to compensate for the dynamic errors of strapdown gravity measurements, effectively suppressing the dynamic errors of gravity measurements. Pan Guowei proposed a method to compensate for the non-modeled errors of strapdown gravity measurements. By estimating the non-modeled errors using real navigation data and trajectory generator data, the internal agreement accuracy was significantly improved.

[0003] Most existing research relies on understanding the principles of dynamic gravity measurement to construct an error compensation model to fit dynamic measurement errors. However, due to incomplete understanding of the error-influencing mechanisms and the complex and changing measurement environment, the accuracy, reliability, and versatility of these models are often difficult to guarantee, making them inapplicable to all measurement processes. In particular, their error suppression effectiveness is severely limited in highly dynamic environments. The Long Short-Term Memory (LSTM) model is a recurrent neural network with a unique structure that offers unique advantages in nonlinear time series prediction. Neural networks that incorporate physical information can leverage the constraints of the physical model to improve the accuracy and generalization of model predictions, combining the advantages of data-driven and physical-mechanism integration. Therefore, for tasks involving both physical laws and time-dependent data, the physical-informed LSTM model is undoubtedly the best solution. It has demonstrated excellent model performance in a variety of application areas, including fault diagnosis, medical image analysis, stock market forecasting, and natural disaster warning. Compensating for dynamic errors in gravity measurements is a regression problem in time series signal processing. Combining LSTM with physical constraints on gravity information can suppress measurement errors introduced by complex dynamic environmental disturbances, for which mathematical models are not yet clear. This plays a crucial role in improving the accuracy and environmental adaptability of vehicle-based dynamic gravity measurements. Therefore, effectively suppressing random, complex, and multi-frequency coupled noise interference during vehicle-based dynamic measurements, constructing a physics-informed long short-term memory (PI-LSTM) model for dynamic error compensation in gravity measurements, and designing hyperparameter optimization strategies for the error compensation model are currently pressing technical challenges in the field of gravity measurement error compensation based on machine learning models. Summary of the Invention

[0004] The purpose of this application is to provide a vehicle-mounted gravity dynamic error compensation method and equipment based on an intelligent algorithm, which can solve the problem that the accuracy, reliability and versatility of the existing error compensation model are difficult to ensure, can effectively suppress the measurement errors introduced by complex dynamic environments, and further improve the vehicle-mounted gravity dynamic measurement accuracy and environmental adaptability.

[0005] To achieve the above objectives, this application provides the following solutions.

[0006] In the first aspect, the present application provides a method for vehicle-mounted gravity dynamic error compensation based on an intelligent algorithm, including: obtaining a dynamic error compensation data set; the dynamic error compensation data set includes a vehicle-mounted state parameter group and a gravity reference value under different operations; using a variational mode decomposition algorithm, the input vector of each dimension in the vehicle-mounted state parameter group is adaptively decomposed into multiple feature vectors to obtain a total feature set; the feature vector is an intrinsic mode function; the set of all input vectors corresponding to the same input vector is a feature in the total feature set; based on the minimum redundancy maximum correlation criterion, the total feature set is preliminarily screened to obtain a preliminary screened feature subset; using the first sparrow search algorithm and the cross-validation algorithm to perform fine feature selection on the preliminary screened feature subset. Screening to obtain the best feature subset; based on the best feature subset, reconstructing data for multiple vehicle state parameter groups in the dynamic error compensation data set to obtain the vehicle state feature vector corresponding to each vehicle state parameter group; constructing a physical information constrained long-short-term memory model; based on the physical laws of gravity information, constructing a total loss function of the physical information constrained long-short-term memory model; using the vehicle state feature vector as input, the gravity reference value as output, and the total loss function as the fitness function value of the second sparrow search algorithm, determining the optimal hyperparameter group of the physical information constrained long-short-term memory model based on the search strategy to obtain a dynamic error compensation model; using the dynamic error compensation model to perform vehicle-mounted gravity dynamic error compensation.

[0007] In a second aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned vehicle-mounted gravity dynamic error compensation method based on an intelligent algorithm.

[0008] According to the specific embodiments provided in this application, this application discloses the following technical effects.

[0009] The present application provides a vehicle-mounted dynamic gravity error compensation method and device based on an intelligent algorithm. The data feature selection scheme based on the minimum redundancy maximum correlation criterion (mRMR) preliminary screening and SSA-CV (sparrow search algorithm-cross validation) fine selection has both computational efficiency and reliability, effectively reducing the interference of non-significantly relevant features on model training, and significantly improving the accuracy of the model; the PI-LSTM formed by embedding the physical constraints of gravity information into the data-driven loss function can greatly reduce the model's requirements for the scale and quality of training data, and significantly improve the accuracy of gravity dynamic measurement error compensation and model generalization ability in high-noise scenarios; the PI-LSTM model hyperparameters are optimized based on the swarm intelligence optimization algorithm, effectively avoiding the model performance degradation problem caused by manual parameter selection, and further improving the model performance; it has certain feasibility, stability and robustness, and is of great value at the theoretical level of machine learning model construction and the engineering level of dynamic gravity measurement, and can be widely used in the measurement and error compensation of marine, underwater and aviation dynamic gravity. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0011] Figure 1 This is a flow chart of a vehicle-mounted gravity dynamic error compensation method based on an intelligent algorithm in one embodiment of the present application.

[0012] Figure 2 This is a schematic diagram of a vehicle-mounted gravity dynamic error compensation method based on an intelligent algorithm in one embodiment of the present application.

[0013] Figure 3 This is a diagram showing the results of an ablation experiment on a test set in one embodiment of the present application.

[0014] Figure 4 This is a result diagram before dynamic error compensation in one embodiment of the present application.

[0015] Figure 5 This is a diagram showing the result after dynamic error compensation in one embodiment of the present application.

[0016] Figure 6 Graphs showing the results before and after dynamic error compensation in one embodiment of the present application. DETAILED DESCRIPTION

[0017] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0018] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0019] In an exemplary embodiment, Figure 1 As shown, a vehicle-mounted gravity dynamic error compensation method based on an intelligent algorithm is provided, including steps 101 to 109.

[0020] Step 101: Obtain a dynamic error compensation dataset. This dataset includes vehicle state parameters and gravity baseline values for different operations. Operations include acceleration and deceleration, start / stop, and turning. The vehicle state parameters include vehicle attitude, velocity, acceleration, position, and measured gravity data. The vehicle state parameters are 13-dimensional input vectors. Vehicle attitude, velocity, acceleration, and position are all 3-dimensional input vectors. The measured gravity data is a 1-dimensional input vector.

[0021] Step 102: Using a variational mode decomposition algorithm, adaptively decompose the input vector for each dimension of the vehicle state parameter set into multiple eigenvectors to obtain a total feature set. The eigenvectors are intrinsic mode functions. The set of all input vectors corresponding to the same input vector is a feature in the total feature set.

[0022] Step 103: Based on the minimum redundancy and maximum relevance criterion, perform preliminary feature screening on the total feature set to obtain a preliminary screened feature subset.

[0023] Step 104: Using the first sparrow search algorithm and the cross-validation algorithm, perform fine feature screening on the initially screened feature subset to obtain the optimal feature subset.

[0024] Step 105: Based on the optimal feature subset, data reconstruction is performed on multiple vehicle state parameter groups in the dynamic error compensation data set to obtain a vehicle state feature vector corresponding to each vehicle state parameter group.

[0025] Step 106: Construct a physical information constrained long short-term memory model. The activation function of the physical information constrained long short-term memory model is the Relu function. The physical information constrained long short-term memory model is trained using the Adam optimizer and passes through a fully connected layer for model output.

[0026] Step 107: Based on the physical laws of gravity information, construct a total loss function of the physical information constrained long short-term memory model.

[0027] Step 108: Using the vehicle state feature vector as input, the gravity reference value as output, and the total loss function as the fitness function value of the second sparrow search algorithm, the optimal hyperparameter group of the physical information constrained long short-term memory model is determined based on the search strategy to obtain a dynamic error compensation model.

[0028] Step 109: Using the dynamic error compensation model, perform vehicle-mounted gravity dynamic error compensation.

[0029] Step 103 specifically includes steps 103 - 1 to 103 - 8 .

[0030] Step 103-1: Calculate the mutual information between each feature and the target variable. The target variable is the gravity reference value. The mutual information is: .

[0031] Where, is the i-th feature With the target variable mutual information. is the feature vector. is the target variable A vector in . is the joint probability distribution. is the eigenvector The marginal distribution of . is a vector The marginal distribution of .

[0032] Step 103-2: Determine the feature corresponding to the maximum mutual information as the initial feature subset.

[0033] Step 103 - 3 : Determine the initial feature subset as the current feature subset.

[0034] Step 103 - 4 : Determine all feature vectors in the total feature set except the current feature subset as candidate features.

[0035] Step 103 - 5 : Based on the minimum redundancy maximum relevance criterion, determine the relevance-redundancy index difference criterion score of each candidate feature and the current feature subset.

[0036] Step 103-6: Add the candidate features corresponding to the maximum relevance-redundancy index difference criterion score to the current feature subset to obtain an updated current feature subset. The maximum relevance-redundancy index difference criterion score is as follows.

[0037] .

[0038] Where, is the jth candidate feature. is the total feature set. is a feature subset. Candidate features With the target variable mutual information. Candidate features With the eigenvector mutual information.

[0039] Step 103-7: Determine the evaluation index of the updated current feature subset. The evaluation index is the difference between relevance and redundancy.

[0040] The formula for correlation is as follows.

[0041] .

[0042] Where, is a feature subset With the target variable correlation. For input data With the target variable mutual information.

[0043] The formula for redundancy is as follows.

[0044] .

[0045] Where, is a feature subset redundancy. is the feature vector pair in the feature subset mutual information.

[0046] Step 103 - 8 : The updated current feature subset is used as the current feature subset, and the process returns to step 103 - 4 until the number of feature vectors in the current feature subset reaches a preset number, and the current feature subset before the update is determined to be the preliminary screening feature subset.

[0047] Step 104 specifically includes steps 104 - 1 to 104 - 5 .

[0048] Step 104-1: Define the individual categories and numbers of the sparrow population. Using the initially selected feature subset as the population dimension, binary encode the first initial population based on the basic principles of the first sparrow search algorithm. Each individual in the first initial population corresponds to a feature subset of the initially selected feature subset.

[0049] Step 104-2: Using multiple feature subsets corresponding to the initial population, perform a 5-fold cross validation on the regression base model to obtain a fitted model. The regression base model is a Gaussian regression model with multiple inputs and a single output.

[0050] Step 104-3: Calculate the root mean square error (RMSE) of the validation set in the fitted model and use the RMSE as the fitness function value for the first sparrow search algorithm. The validation set is a subset of the dynamic error compensation dataset.

[0051] Step 104 - 4 : Iteratively optimize the search strategy based on the first sparrow search algorithm, and gradually find the population individual corresponding to the minimum fitness function value as the first optimal population individual.

[0052] Step 104-5: Determine the feature subset corresponding to the first optimal population individual as the optimal feature subset.

[0053] The formula of the total loss function is as follows.

[0054] .

[0055] in, .

[0056] .

[0057] .

[0058] .

[0059] .

[0060] Where, is the total loss function. is the weight of the physical loss function. is the weight of the monotonicity constraint loss function. is the initial value condition constraining the loss function weight. is the data loss function. is the physical loss function. is the monotonicity constraint loss function. is the initial value condition constraint loss function. is the data loss function value. are the model parameters during training. is the length of the test dataset. Calculates the square root. For the test data set. Input for the model The output value obtained after . For input data. For input data The corresponding model truth value. is the value of the physical loss function. Input for the model The output value obtained after . is the input data at time t. is the intermediate parameter. a 1. a 2 and a 3均 are the coefficients of the Gauss-Markov model. Input for the model The output value obtained after . is the input data at time t-1. Input for the model The output value obtained after . is the input data at time t-2. Input for the model The output value obtained after . is the input data at time t-3. is the monotonicity constraint loss function value. is the monotonicity factor. is a symbolic function. is the height information of the carrier position in the input data. is the initial condition constraint loss function value. Input for the model The output value obtained after . is the input data at the initial moment. is the input data at the initial moment The corresponding model truth value.

[0061] Step 108 specifically includes steps 108-1 to 108-8.

[0062] Step 108 - 1 : Define the population size and the preset number of iterations of the second sparrow search algorithm.

[0063] Step 108-2: Determine a hyperparameter group of the physical information constrained long short-term memory model.

[0064] Step 108-3: Initialize the population based on the parameter boundaries of each variable to be optimized in the hyperparameter group and the population size to obtain a second initial population. One individual in the second initial population corresponds to one hyperparameter group.

[0065] Step 108-4: Substitute each individual in the second initial population into the physical information constrained long short-term memory model, and use the training set to train each physical information constrained long short-term memory model.

[0066] Step 108-5: Use the validation set to determine the total loss of each individual in the second initial population, and use the total loss as the fitness function value of the second sparrow search algorithm.

[0067] Step 108-6: Update the second initial population and return to step 108-4 until the number of iterations reaches the preset number of iterations, and determine the population individual corresponding to the minimum fitness function value as the second optimal population individual.

[0068] Step 108-7: Determine the hyperparameter group corresponding to the second optimal population individual as the optimal hyperparameter group.

[0069] Step 108-8: Substitute the hyperparameter group into the physical information constrained long short-term memory model to obtain a dynamic error compensation model.

[0070] Step 109 specifically includes steps 109-1 to 109-3.

[0071] Step 109-1: Obtain the vehicle status parameter group.

[0072] Step 109 - 2 : Based on the optimal feature subset, reconstruct the vehicle state parameter group to obtain the target vehicle state feature vector.

[0073] Step 109 - 3 : Input the vehicle state feature vector into the dynamic error compensation model to obtain the dynamic error compensation result of the gravity measurement value.

[0074] like Figure 2 In an exemplary embodiment, a vehicle-mounted gravity dynamic error compensation method based on an intelligent algorithm is provided, comprising the following steps.

[0075] Step 1: Determine the model architecture. A machine learning model for dynamic error compensation in gravity anomaly measurements is constructed based on the PI-LSTM. The Relu function is used as the activation function, trained using the Adam optimizer, and a fully connected layer is used for the model output. The model input and output are defined, and the model parameters are initialized, including the number of neurons (Num), the number of training epochs (Epochs), the training batch size (BatchSize), the initial learning rate (LR), the learning rate decay factor (DecayFactor), and the weight coefficients for the physical information constraints. The model input and output must be determined based on the actual needs of dynamic error compensation in gravity measurements, and a training dataset with comprehensive features is constructed. The purpose of this training model is to capture the inherent relationships between the dynamic measurement conditions of the carrier and the gravity anomaly measurement errors. Therefore, the carrier's motion characteristics are used as model inputs, including attitude, velocity, and acceleration in three directions in the Northeastern celestial coordinate system. Because gravity information is closely related to the carrier's position, especially its altitude, the carrier's three-dimensional positioning coordinates are also used as model inputs. Furthermore, gravity anomaly measurements are used as training input data, and the true gravity anomaly values are used as output data for model training. The resulting model output can be used as the measurement result after dynamic error compensation. In summary, the constructed PI-LSTM model has a 13-dimensional input and a 1-dimensional output. Furthermore, the model parameters are initialized based on practical experience in model training.

[0076] Real data collected experimentally is used for model training. This requires measured data for the vehicle's attitude, velocity, acceleration, position, and gravity in three directions in the northeastern sky geographic coordinate system, totaling 13 dimensions of model input. The model output is the gravity baseline value obtained by statically measuring and interpolating along the survey line in advance. The experimental data is divided into training, validation, and test sets in a 4:1:1 ratio. During the training data collection process, the vehicle performs significant acceleration, deceleration, starting, stopping, and turning operations to obtain training data with comprehensive maneuverability characteristics. A machine learning model for dynamic error compensation in gravity anomaly measurements is constructed based on PI-LSTM. The Relu function is used as the activation function, and the Adam optimizer is used for training. A fully connected layer is used for model output. The initialization of the model hyperparameters is manually set based on practical experience, including the number of LSTM neurons, the number of training epochs, the batch size BatchSize, the initial learning rate LR, the learning rate decay factor DecayFactor, and the hyperparameters of physical information constraints. a 1, a 2, a 3. , as well as .

[0077] Step 2: Modal decomposition of input data; Variational mode decomposition (VMD) is used to adaptively decompose the 13-dimensional input data. The input data of each dimension is decomposed into x i ( i ∈[1,13]) intrinsic mode functions (IMFs), so the dimension of the input data will be expanded to sum( x i ).

[0078] Variational modal decomposition is an adaptive, fully non-recursive modal variation and signal processing method. This technology has the advantage of being able to determine the number of modal decompositions. Its adaptability is reflected in determining the number of modal decompositions of a given sequence based on actual conditions. In the subsequent search and solution process, it can adaptively match the optimal center frequency and finite bandwidth of each mode, and can achieve effective separation of inherent modal components and frequency domain division of the signal, thereby decomposing into relatively stable subsequences containing multiple different frequency scales.

[0079] Step 3: Feature selection and data reconstruction: Preliminary screening of feature subsets is performed based on the minimum redundancy maximum relevance (mRMR) criterion, and then fine screening of feature subsets is performed through the first sparrow search algorithm (SSA1) and cross-validation (CV), and the screened data is reconstructed into input data for model training.

[0080] Among them, the preliminary screening of feature subsets based on mRMR includes the following steps.

[0081] Step 3-1: Calculate the mutual information between all features and the target variable. X i and goals C For , the mutual information is calculated as follows.

[0082] .

[0083] Where, x i for X i A feature vector in c is a vector in the target, p ( x i , c ) is the joint probability distribution, p ( x i )and p ( c ) is the marginal distribution.

[0084] Step 3-2: Select the feature with the largest mutual information as the initial feature subsetS 0.

[0085] Step 3-3: Calculate the scores of the candidate feature correlation and redundancy index difference criteria according to the mRMR criterion, which is calculated as follows.

[0086] .

[0087] Step 3-4: Perform incremental feature selection and calculate the feature vector with the highest score x Add to feature subset S middle.

[0088] Step 3-5: Calculate the current correlation D and redundancy R , correlation D is a feature subset S With the goal C The average mutual information, redundancy R is the average mutual information between features within the feature subset S. The calculation formula is as follows.

[0089] .

[0090] .

[0091] Step 3-6: Use the greedy algorithm to gradually add the best individuals in the candidate features to the feature subset so that the evaluation index shown in the following formula reaches the maximum.

[0092] .

[0093] Step 3-7: When the preset number of features is reached or adding features does not significantly improve the model performance, the iteration is terminated. The feature subset at this time S 1 is the input feature data after preliminary screening.

[0094] In addition, the feature subset fine screening based on SSA1 and cross-validation includes the following steps.

[0095] Step 3-8: Define the individual classification and number of sparrow populations. The population dimension is S The dimension of 1 is used, and binary coding is performed based on the basic principle of the sparrow search algorithm to generate the initial population, where 1 or 0 indicates whether the IMF component is selected.

[0096] Step 3-9: Select a subset of undetermined features based on the initial population S A 5-fold cross-validation was then performed, and the regression base model used was a Gaussian regression process with multiple inputs and a single output, which was used to model and fit the unknown functional relationship.

[0097] Step 3-10: Calculate the root mean square error (RMSE) of the model on the validation set and use it as the fitness function value for SSA1 optimization.

[0098] Step 3-11: Perform iterative optimization based on the search strategy of SSA1 and gradually find the population individual with the minimum fitness value.

[0099] Step 3-12: Based on the correspondence between population individuals and feature subset selection, carefully select the globally optimal feature subset.

[0100] Step 3-13: Reconstruct the data based on the optimal feature subset obtained after feature selection to obtain the data set for model training.

[0101] The two-step feature selection strategy combining mRMR and cross-validation takes into account both computational efficiency and model reliability. On the one hand, the feature range is quickly narrowed down through preliminary screening by mRMR, effectively solving the computational efficiency problem. On the other hand, the global optimization and fine selection based on SSA1 and CV improves the reliability of feature selection.

[0102] Step 4: Design the PI-LSTM loss function. Based on the physical laws of gravity information, design the physical constraint loss, monotonicity loss, and initial condition loss and add them to the data-driven loss function. The weighted sum of each loss term is used as the PI-LSTM loss function. Use the training data to train the model under the current parameter conditions and calculate the total loss of the validation set on the resulting model.

[0103] Among them, the design process of the total loss function is as follows.

[0104] Step 4-1: Mean Squared Error as the Data Loss of the Model The formula is as follows.

[0105] .

[0106] Where, are the model parameters during training, S test For the test dataset, N is the length of the test dataset, x For input data, is the model output value, y is the true value of the model.

[0107] Step 4-2: The gravity anomaly satisfies the third-order Gauss-Markov process. The formula for physical information constraints under discrete time conditions is as follows.

[0108] .

[0109] Where,y ( t ) is a time series, a 1. a 2 and a 3 is the coefficient of the Gauss-Markov model, which ranges from [0,1] and satisfies a 1+ a 2+ a 3=1, is Gaussian white noise, based on which the physical loss function of the dynamic error compensation model of gravity anomaly measurement can be designed The formula is as follows.

[0110] .

[0111] Where, x t for t Input data at the moment.

[0112] Step 4-3: The partial derivative of the gravity data with respect to the carrier height satisfies the monotonicity constraint, and a loss function with monotonicity constraint is designed accordingly. The formula is as follows.

[0113] .

[0114] m is the monotonicity factor. If the physical monotonicity is positive, then m =1, otherwise m =-1. h is the height information of the carrier position in the input data, sign is a symbolic function.

[0115] Step 4-4: Dynamic gravity measurement generally starts from the reference point. At this time, the initial gravity value is precisely known. Therefore, the gravity anomaly measurement result also satisfies the following initial value condition constraints:

[0116] .

[0117] Where, x 1 is the input data at the initial moment.

[0118] Step 4-5: The total loss function of PI-LSTM is the weighted sum of data loss and physical constraint loss, as shown in the following formula.

[0119] .

[0120] Where, 、 and are the weights of the corresponding physical constraint losses, ranging from [0,1] and satisfying + + <1.

[0121] Steps 4-6: Use the training data to train the model under the current parameter conditions and calculate the total loss of the validation set on the obtained model.

[0122] Step 5: Iteratively optimize hyperparameters. The calculated total loss is used as the fitness function value of the second sparrow search algorithm (SSA2). Based on the SSA2 search strategy, iterative optimization is performed to find the population individual with the minimum fitness value, which is the current optimal PI-LSTM hyperparameter combination. The model obtained after training is the final dynamic error compensation model.

[0123] The specific process of hyperparameter optimization based on SSA2 includes the following steps.

[0124] Step 5-1: Parameter initialization, define the population size and number of iterations of SSA2.

[0125] Step 5-2: Since the physical constraint weight coefficients satisfy a certain quantitative relationship, select a 1. a 2. 、 and As well as LSTM's Num, Epochs, BatchSize, LR, and DecayFactor, a total of ten variables are used as hyperparameters to be optimized.

[0126] Step 5-3: Based on the practical experience of model training, the parameter boundaries of the variables to be optimized are given, and a feasible solution is randomly generated in the feasible domain to initialize the population.

[0127] Step 5-4: Use the training data to train PI-LSTM under this hyperparameter combination.

[0128] Step 5-5: Calculate the total loss of the validation set on the obtained model and use it as the fitness function value of SSA2.

[0129] Step 5-6: Perform iterative optimization based on the SSA2 search strategy. After each iteration of the population individuals, return to step 5-4 for model training.

[0130] Steps 5-7: Find the population individual with the minimum fitness value and select the optimal PI-LSTM hyperparameter combination based on it.

[0131] Steps 5-8: The model obtained after training is the final gravity measurement dynamic error compensation model.

[0132] The proposed dynamic error compensation method is described in detail through specific embodiments.

[0133] The test vehicle was equipped with a dual-axis laser strapdown inertial navigation system, GNSS equipment, an odometer, and a barometric altimeter. This combined navigation solution provided high-precision navigation data, acquiring the vehicle's attitude, velocity, and position. The vehicle's acceleration was derived by first differencing the calculated velocity. In addition, a platform-mounted gravimeter was used to dynamically measure gravity anomaly data, which together formed a 13-dimensional model input. The experiment was conducted on a closed road. Before dynamic measurement data collection, static measurements were taken every 2 km along the survey line using a CG-5 high-precision relative gravimeter to obtain discrete true gravity anomaly values. These true gravity anomaly values were interpolated and fitted to serve as the model output for the training dataset.

[0134] S1: PI-LSTM uses the Relu function as the activation function and the Adam optimizer for training. A fully connected layer is used for model output. LSTM uses a single-layer 30-neuron structure, 300 training epochs, 32 batches, LR = 0.001 initial learning rate, DecayFactor = 0.2 learning rate reduction factor, and physical information constraint hyperparameters. a 1=0.6, a 2=0.3, a 3=0.1, =0.15, =0.17, =0.18.

[0135] S2: Variational mode decomposition is used to adaptively decompose the input data. The input vector of each dimension is decomposed into several intrinsic mode functions.

[0136] S3: Feature selection and reconstruction of input data. The specific implementation steps are as follows.

[0137] S3-1: Preliminary screening of feature subsets based on the minimum redundancy maximum relevance (mRMR) criterion.

[0138] S3-2: The population dimension of SSA1 is the dimension of the feature subset obtained after the initial screening, and the population is initialized by binary encoding. The population size is set to 20, and the maximum number of iterations is 50.

[0139] S3-3: Fine-tune feature subsets through SSA1 and 5-fold cross-validation.

[0140] S3-4: Reconstruct the filtered data as input data for model training.

[0141] S4: Design the PI-LSTM loss function, embed the physical constraints of gravity information into the data-driven loss function, and then train the model.

[0142] S5: Optimize the hyperparameters of PI-LSTM based on SSA2. The specific implementation steps are as follows.

[0143] S5-1: Determine the hyperparameters to be optimized, including Num, Epochs, BatchSize, LR, DecayFactor, and physical information constraints a 1, a 2, , and There are ten variables in total, so the population dimension is 10.

[0144] S5-2: Define the population size and number of iterations of SSA2. The iterative optimization process includes model training. Due to the limitation of computing resources, the population size and number of iterations should not be too large. Therefore, the population size is set to 10 and the number of iterations is set to 10.

[0145] S5-3: Based on the practical experience of model training, we can set Num∈[5, 100], Epochs∈[50, 500], BatchSize∈[16, 256], LR∈[1e-4, 1e-1], and DecayFactor∈[0.2, 0.5]. The first three variables are integers and therefore need to be integer encoded. The remaining five hyperparameters in the variables to be optimized all have a value range of [0, 1] and satisfy a 1+ a 2<1, + + <1, and randomly generate a feasible solution in the feasible domain to initialize the population.

[0146] S5-4: Use the training data to train PI-LSTM under the current hyperparameter combination, and calculate the total loss of the test set on the resulting model and use it as the fitness function value of SSA2.

[0147] S5-5: Perform iterative optimization until the population individual with the minimum fitness value is found. Based on this, the current optimal PI-LSTM hyperparameter combination is selected. The model obtained after the training is completed is the final gravity measurement dynamic error compensation model.

[0148] Example 1.

[0149] The experimental data is divided into training set, validation set and test set in a ratio of 4:1:1. Based on the dynamic error compensation model obtained after training the training set and validation set, this embodiment uses the test set to test the improvement effect of input data feature screening and reconstruction, physical information constraint embedding loss function and model hyperparameter optimization on LSTM performance, and conducts ablation experiments. The experimental results are shown in Figure 2. Figure 3 The root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) are shown in Table 1, where the abbreviations "FS" and "HO" respectively represent feature screening and hyperparameter optimization, "None" means no processing, and percentage means the percentage of improvement in accuracy of other methods compared to the original data training LSTM (None-LSTM).

[0150] Table 1. Accuracy statistics of LSTM and PI-LSTM test results

[0151]

[0152] Experimental results show that the LSTM model based on feature selection shows significant improvements in error metrics on the test set. Its RMSE, MAE, and MAPE are reduced by 41.1%, 32.8%, and 21.5%, respectively, compared to the model trained with the original feature data. The PI-LSTM model also shows decreases of 29.8%, 31.4%, and 19.5%, respectively, after feature selection. Furthermore, the PI-LSTM demonstrates significant improvements in validation performance on the test set compared to the LSTM model. Before feature selection, the three error metrics were reduced by 21.9%, 12.1%, and 15.4%, respectively, and after feature selection, by 6.98%, 10.3%, and 13.2%, respectively. These results demonstrate that physical information constraints not only enhance model interpretability but also improve fitting accuracy and enhance model generalization. After model hyperparameter selection, the error metrics of the LSTM and PI-LSTM test results can be further reduced, demonstrating that hyperparameter optimization based on SSA2 significantly improves the performance of machine learning models. In summary, the LSTM improved by the three major technical modules of feature screening, integration of physical information and intelligent hyperparameter optimization has the best model performance, with the RMSE, MAE and MAPE achieving the largest improvements of 76.7%, 74.1% and 69.5% respectively, showing significant advantages in time series tasks in complex engineering backgrounds.

[0153] Example 2.

[0154] This example evaluates the effectiveness of on-board dynamic gravity measurement error compensation during stable vehicle operation. After model training, a closed road with good road conditions and no traffic light interference was selected to conduct an on-board dynamic gravity measurement experiment. During the experiment, the vehicle's motion characteristics were kept as stable as possible.

[0155] Experiment 1 involved a one-hour, one-way survey line, maintaining a steady speed of approximately 26 km / h. Four repeated measurements were performed, encompassing two round trips. Static measurements of true gravity anomalies were taken using the CG-5 at intervals of 2 km along the line. These interpolated values served as a baseline for the gravity anomaly along the line, assessing the external accuracy of the dynamic measurement results. The repeated measurements were used to assess the internal accuracy of the results. At the beginning of each repeated measurement, alignment was performed and the navigation solution was restarted to ensure sufficiently accurate integrated navigation results.

[0156] The navigation data and dynamic measurement results of gravity anomalies on each survey line are constructed into a data set according to the model input format, and the input data is feature extracted and reconstructed according to the feature screening method. It is then input into the error compensation model of the trained SSA2 optimized PI-LSTM hyperparameters. The output result is the gravity anomaly measurement result after dynamic error compensation, and the measurement data on each survey line are processed in turn. The results before and after dynamic error compensation of gravity measurement are shown in Figure 2. Figure 4 and Figure 5 The accuracy of the calculated results is shown in Table 2.

[0157] The results show that the overall trend of the measurement results is well consistent with the baseline values, but the impact of unavoidable dynamic interference during the measurement process is also very significant, especially around 18 km of survey line 1 and 5 km of survey line 2. The internal agreement accuracies of survey lines 1-4 were 2.62 mGal, 3.22 mGal, 2.93 mGal, and 1.88 mGal, respectively, and the external agreement accuracies were 3.12 mGal, 4.03 mGal, 3.17 mGal, and 1.88 mGal, respectively. Overall, the internal agreement was 2.71 mGal and the external agreement was 3.14 mGal. This level of accuracy is clearly insufficient for practical engineering applications. After dynamic error compensation, the fluctuation error of gravity anomaly measurement results was effectively suppressed. The internal accuracy of measurement lines 1-4 increased to 0.64mGal, 0.35mGal, 0.42mGal, and 0.31mGal, respectively, and the external accuracy increased to 0.92mGal, 1.03mGal, 1.02mGal, and 0.69mGal, respectively. The overall internal and external accuracy also increased by 83.39% and 70.70%, reaching 0.45mGal and 0.92mGal, respectively. The results show that the accuracy of vehicle-borne gravity anomaly measurements is significantly improved after dynamic error compensation.

[0158] Table 2 Accuracy statistics of measurement results before and after dynamic error compensation in Example 2

[0159]

[0160] Example 3.

[0161] This example examines the effectiveness of the dynamic error compensation model for onboard gravity measurement under highly dynamic vehicle operating conditions. Dynamic gravity measurements were repeated along a different measurement line, with significant acceleration and deceleration during the experiment. Two hours of data were collected under highly dynamic conditions, covering a total distance of approximately 40 km, with two round-trip measurements. The experimental equipment and other conditions were identical to those in Example 2, and the internal and external agreement accuracy was calculated to evaluate model performance. Figure 6 The comparison results before and after dynamic error compensation of gravity anomaly measurement in Example 3 are shown in Table 3, and the accuracy index is calculated.

[0162] Table 3 Accuracy statistics of measurement results before and after dynamic error compensation of Example 3

[0163]

[0164] The results show that before dynamic error compensation, the internal and external agreement accuracies for measurement lines 1 and 2 were 3.36 mGal, 5.11 mGal, and 3.36 mGal and 3.02 mGal, respectively, achieving an overall internal agreement of 3.86 mGal and an external agreement of 4.19 mGal. This indicates that under high-dynamic conditions, measurement results are more significantly affected by dynamic interference, making dynamic error compensation more urgent and practical. After dynamic error compensation, the overall trend of the measurement results on the two repeated measurement lines showed a visible improvement in compliance with the baseline values, with the internal and external agreement accuracies increasing to 0.87 mGal, 1.34 mGal, and 0.87 mGal and 1.31 mGal, respectively. The overall internal and external agreement accuracies also increased by 74.11% and 68.50%, reaching 0.87 mGal and 1.32 mGal, respectively. It can be seen that dynamic error compensation effectively enhances the environmental adaptability of vehicle-mounted gravity measurement, but the measurement results under high dynamic conditions are more strongly disturbed by the movement of the carrier, and the accuracy improvement after dynamic error compensation is not as good as that of Example 2 under stable operating conditions.

[0165] In an exemplary embodiment, a computer device is provided, which may be a server or a terminal. The computer device includes a processor, memory, an input / output (I / O) interface, and a communication interface. The processor, memory, and I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The I / O interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal via a network connection. When executed by the processor, the computer program implements a vehicle-mounted gravity dynamic error compensation method based on an intelligent algorithm.

[0166] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0167] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0168] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0169] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above-mentioned embodiments. In particular, any reference to memory, database, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0170] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0171] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0172] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A vehicle-mounted gravity dynamic error compensation method based on intelligent algorithm, characterized in that: include: Obtaining a dynamic error compensation dataset; The dynamic error compensation data set includes a vehicle state parameter group and a gravity reference value under different operations; Using the variational mode decomposition algorithm, the input vector of each dimension in the vehicle state parameter group is adaptively decomposed into multiple eigenvectors to obtain a total feature set; the eigenvectors are intrinsic mode functions; the set of all input vectors corresponding to the same input vector is a feature in the total feature set; Based on the minimum redundancy and maximum relevance criterion, preliminary feature screening is performed on the total feature set to obtain a preliminary screened feature subset; Using the first sparrow search algorithm and the cross-validation algorithm, the preliminary screened feature subset is subjected to fine feature screening to obtain the best feature subset; Based on the optimal feature subset, reconstructing data of multiple vehicle state parameter groups in the dynamic error compensation data set to obtain a vehicle state feature vector corresponding to each vehicle state parameter group; Construct a physical information constrained long short-term memory model; Based on the physical laws of gravity information, the total loss function of the physical information constrained long short-term memory model is constructed; Using the vehicle state feature vector as input, the gravity reference value as output, and the total loss function as the fitness function value of the second sparrow search algorithm, an optimal hyperparameter set of the physical information constrained long short-term memory model is determined based on a search strategy to obtain a dynamic error compensation model; Using the dynamic error compensation model, performing vehicle-borne gravity dynamic error compensation; The total loss function is: ； in, ; ； ； ； ； Where, is the total loss function; is the weight of the physical loss function; is the weight of the monotonicity constraint loss function; is the initial value condition constraint loss function weight; is the data loss function; is the physical loss function; is the monotonicity constraint loss function; is the initial value condition constraint loss function; is the data loss function value; are the model parameters during training; is the length of the test dataset; Calculates square roots; is the test dataset; Input for the model The output value obtained after For input data; For input data The corresponding model truth value; is the value of the physical loss function; Input for the model The output value obtained after is the input data at time t; is the intermediate parameter; a 1. a 2 and a 3均 are the coefficients of the Gauss-Markov model; Input for the model The output value obtained after is the input data at time t-1; Input for the model The output value obtained after is the input data at time t-2; Input for the model The output value obtained after is the input data at time t-3; is the monotonicity constraint loss function value; is the monotonicity factor; is a symbolic function; is the height information of the carrier position in the input data; is the initial condition constraint loss function value; Input for the model The output value obtained after is the input data at the initial moment; is the input data at the initial moment The corresponding model truth value.

2. The vehicle-mounted gravity dynamic error compensation method based on intelligent algorithm according to claim 1 is characterized in that: The operations include: acceleration and deceleration operations, start and stop operations, and turning operations; The vehicle-mounted state parameter group includes: carrier posture, carrier speed, carrier acceleration, carrier position and gravity measurement data; The vehicle state parameter group is a 13-dimensional input vector; The carrier posture, the carrier velocity, the carrier acceleration and the carrier position are all 3D input vectors; The measured gravity data is a 1-dimensional input vector.

3. The vehicle-mounted gravity dynamic error compensation method based on intelligent algorithm according to claim 1 is characterized in that: Based on the minimum redundancy and maximum relevance criterion, the total feature set is preliminarily screened to obtain a preliminarily screened feature subset, specifically including: Calculate the mutual information between each feature and the target variable respectively; the target variable is the gravity reference value; Determine the features corresponding to the maximum mutual information as the initial feature subset; Determine the initial feature subset as the current feature subset; Determine all feature vectors in the total feature set except the current feature subset as candidate features; Based on the minimum redundancy and maximum correlation criterion, the correlation-redundancy index difference criterion score of each candidate feature and the current feature subset is determined respectively; The candidate features corresponding to the maximum relevance-redundancy index difference criterion score are added to the current feature subset to obtain an updated current feature subset; Determine the evaluation index of the updated current feature subset; The updated current feature subset is used as the current feature subset, and the process returns to step "determining all feature vectors in the total feature set except the current feature subset as candidate features" until the number of feature vectors in the current feature subset reaches a preset number, and the current feature subset before the update is determined to be the preliminary screening feature subset.

4. The vehicle-mounted gravity dynamic error compensation method based on intelligent algorithm according to claim 3 is characterized in that: The mutual information is: ; Where, is the i-th feature With the target variable Mutual information of is the eigenvector; is the target variable A vector in ; is the joint probability distribution; is the eigenvector The marginal distribution of is a vector The marginal distribution of The maximum relevance-redundancy index difference criterion score is: ； Where, is the jth candidate feature; is the total feature set; is a feature subset; Candidate features With the target variable Mutual information of Candidate features With the eigenvector Mutual information of The evaluation index is the difference between relevance and redundancy; The correlation is: ； Where, is a feature subset With the target variable relevance; For input data With the target variable Mutual information of The redundancy is: ； Where, is a feature subset Redundancy; is the feature vector pair in the feature subset mutual information.

5. The vehicle-mounted gravity dynamic error compensation method based on intelligent algorithm according to claim 1 is characterized in that: Using the first sparrow search algorithm and the cross-validation algorithm, the preliminary screened feature subset is subjected to fine feature screening to obtain the best feature subset, specifically including: Define the individual classification and number of the sparrow population, use the preliminary screened feature subset as the population dimension, and generate a first initial population by binary encoding based on the first sparrow search algorithm; one individual in the first initial population corresponds to a feature subset of the preliminary screened feature subset; Using multiple feature subsets corresponding to the initial population, a 5-fold cross-validation is performed on the regression base model to obtain a fitting model; the regression base model is a Gaussian regression model with multiple inputs and a single output; Calculating the root mean square error of the validation set in the fitted model, and using the root mean square error as the fitness function value for the first sparrow search algorithm to perform optimization; the validation set is a subset of the dynamic error compensation dataset; Based on the search strategy of the first sparrow search algorithm, iterative optimization is performed to gradually find the population individual corresponding to the minimum fitness function value as the first optimal population individual; Determine the feature subset corresponding to the first optimal population individual as the optimal feature subset.

6. The vehicle-mounted gravity dynamic error compensation method based on intelligent algorithm according to claim 1 is characterized in that: The activation function of the physical information constrained long short-term memory model is a ReLU function; The physical information constrained long short-term memory model is trained using the Adam optimizer and is used for model output through a fully connected layer.

7. The vehicle-mounted gravity dynamic error compensation method based on intelligent algorithm according to claim 1 is characterized in that: The vehicle state feature vector is used as input, the gravity reference value is used as output, and the total loss function is used as the fitness function value of the second sparrow search algorithm. Based on the search strategy, the optimal hyperparameter set of the physical information constrained long short-term memory model is determined to obtain a dynamic error compensation model, which specifically includes: Define the population size and preset number of iterations of the second sparrow search algorithm; Determine the set of hyperparameters for the physical information constrained long short-term memory model; Initialize the population based on the parameter boundary and population size of each variable to be optimized in the hyperparameter group to obtain a second initial population; one individual in the second initial population corresponds to one hyperparameter group; Substituting each individual in the second initial population into the physical information constrained long short-term memory model, and using the training set to train each physical information constrained long short-term memory model; The total loss of each individual in the second initial population is determined using the validation set, and the total loss is used as the fitness function value of the second sparrow search algorithm; Update the second initial population and return to step "substituting each individual in the second initial population into the physical information constrained long short-term memory model, and training each physical information constrained long short-term memory model using the training set" until the number of iterations reaches the preset number of iterations, and determine the population individual corresponding to the minimum fitness function value as the second optimal population individual; Determine the hyperparameter group corresponding to the second optimal population individual as the optimal hyperparameter group; Substituting the hyperparameter group into the physical information constrained long short-term memory model, a dynamic error compensation model is obtained.

8. The vehicle-mounted gravity dynamic error compensation method based on intelligent algorithm according to claim 1 is characterized in that: Using the dynamic error compensation model, vehicle-mounted gravity dynamic error compensation is performed, specifically including: Get the vehicle status parameter group; Based on the optimal feature subset, reconstructing the vehicle state parameter group to obtain a target vehicle state feature vector; The vehicle-mounted state feature vector is input into the dynamic error compensation model to obtain an error compensation result of the gravity measurement value.

9. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the vehicle-mounted gravity dynamic error compensation method based on an intelligent algorithm as described in any one of claims 1 to 8.

Images