Real-time fitting method for ground subsidence measurement data based on evolutionary algorithm

Abstract

The application discloses a kind of surface subsidence measurement data real-time fitting method based on evolutionary algorithm, S1.Acquire surface subsidence measurement data set;S2.The surface subsidence measurement data set is preprocessed;S3.Surface subsidence measurement data feature matrix is generated;S4.Radial basis function neural network model for surface subsidence measurement data fitting is constructed;S5.The parameters of initial surface subsidence measurement data fitting function are optimized using alpha evolutionary algorithm;S6.The input surface subsidence measurement data is predicted using the optimized surface subsidence measurement data fitting function.The application effectively improves the calculation efficiency, nonlinear expression capacity and global optimization capacity of surface subsidence measurement data fitting, and can be widely applied to surface subsidence monitoring, infrastructure safety assessment and mine subsidence prediction multiple scenes.

Description

Technical Field

[0001] This invention relates to the field of land subsidence measurement technology, and in particular to a real-time fitting method for land subsidence measurement data based on an evolutionary algorithm. Background Technology

[0002] With the development of surface monitoring technology, surface subsidence measurement has become an important research topic in many fields, including infrastructure safety assessment, mine subsidence prediction, groundwater resource management, and geological disaster early warning. Currently, surface subsidence measurement usually relies on various monitoring methods such as global navigation satellite systems, synthetic aperture radar, and lidar to obtain surface subsidence data. However, surface subsidence data is often affected by environmental factors, measurement errors, and multi-source data fusion bias, resulting in large data noise, obvious nonlinear characteristics, and a large time scale, making it a challenge to accurately fit the surface subsidence trend.

[0003] Currently, the fitting methods for surface subsidence measurement data mainly include traditional statistical regression methods, machine learning methods, and physical modeling methods. Among them, traditional statistical regression methods rely on fixed mathematical models, which are difficult to adapt to the dynamic changes of complex nonlinear subsidence processes. When the subsidence rate changes significantly over time, the fitting accuracy is low. Machine learning methods can capture the nonlinear characteristics of surface subsidence data to a certain extent, but they usually rely on large-scale labeled data for training and have high computational costs. They are also prone to computational delays in high-frequency data stream processing. In addition, although physical modeling methods can deduce subsidence trends based on geomechanical principles, they are highly dependent on input parameters and are difficult to adapt to the subsidence characteristics of different regions and environments in practical engineering applications.

[0004] Therefore, existing technologies for real-time fitting of surface subsidence measurement data suffer from problems such as low computational efficiency, fitting accuracy affected by dynamic changes, easy getting trapped in local optima during the optimization process, lack of adaptability, and insufficient ability to identify abnormal data. There is an urgent need for a method that can improve computational efficiency, enhance model adaptability, and optimize fitting accuracy to meet the real-time monitoring needs of surface subsidence measurement. Summary of the Invention

[0005] One objective of this invention is to propose a real-time fitting method for surface subsidence measurement data based on an evolutionary algorithm. This invention effectively improves the computational efficiency, nonlinear expression ability, and global optimization ability of surface subsidence measurement data fitting, and can be widely applied to multiple scenarios such as surface subsidence monitoring, infrastructure safety assessment, and mining area collapse prediction.

[0006] A real-time fitting method for surface subsidence measurement data based on an evolutionary algorithm according to an embodiment of the present invention includes the following steps: S1. Obtaining a surface subsidence measurement dataset;

[0007] S2. Preprocess the surface subsidence measurement dataset to obtain a standardized surface subsidence measurement dataset;

[0008] S3. Perform time-series analysis on standardized surface subsidence measurement data to generate a surface subsidence measurement data feature matrix;

[0009] S4. Construct a radial basis function neural network model for fitting surface subsidence measurement data, and initialize the parameters of the radial basis function neural network model to obtain the initial surface subsidence measurement data fitting function;

[0010] S5. The parameters of the fitting function for the initial surface subsidence measurement data are optimized using the Alpha Evolutionary Algorithm to obtain the optimized fitting function for the surface subsidence measurement data.

[0011] S6. The optimized surface subsidence measurement data fitting function is used to predict the input surface subsidence measurement data, output the surface subsidence trend fitting curve, and calculate the fitting error, trend change rate, and prediction confidence interval index.

[0012] Optionally, S1 includes the following steps:

[0013] S11. Obtain the surface subsidence measurement dataset, which includes global navigation satellite system measurement data, synthetic aperture radar measurement data, and lidar point cloud measurement data:

[0014] D GNSS ={(x i ,y i ,t i ,h i | i = 1, 2, ..., N GNSS};

[0015] D InSAR ={(x j ,y j ,t j ,h j |j=1,2,...,N InSAR};

[0016] D LiDAR ={(x k ,y k ,t k ,h k |k=1,2,...,N LiDAR};

[0017] Where x, y represent geographic coordinates, t represents a timestamp, h represents the ground elevation, and N GNSS N InSAR N LiDARThese represent the number of sampling points for Global Navigation Satellite System measurement data, Synthetic Aperture Radar measurement data, and LiDAR point cloud measurement data, respectively.

[0018] S12. Perform spatial reference coordinate system transformation on the surface subsidence measurement dataset to unify the coordinate datum of the surface subsidence measurement dataset, resulting in a surface subsidence measurement dataset under a unified spatial reference coordinate system:

[0019] "′

[0020] D aligned =D GNSS ∪D InSAR ∪D LiDAR ;

[0021] "′

[0022] Among them, D GNSS D InSAR and D LiDAR These represent global navigation satellite system measurement data, synthetic aperture radar measurement data, and lidar point cloud measurement data, respectively, in a unified spatial reference coordinate system.

[0023] Optionally, S2 includes the following steps:

[0024] S21. Using wavelet transform to process the surface subsidence measurement dataset D in a unified spatial reference coordinate system. aligned Denoising is performed to remove random noise from the surface subsidence measurement data, resulting in a denoised surface subsidence measurement dataset.

[0025] S22. The Mahalanobis distance analysis method is used to detect outliers in the denoised surface subsidence measurement dataset, and the outlier degree of each data point is calculated:

[0026]

[0027] Among them, M i The Mahalanobis distance between the surface settlement measurement data points is μ. h Let Σ be the mean vector of the height of the surface subsidence measurement data. h This is the covariance matrix of the elevation of the surface subsidence measurement data;

[0028] Set threshold M th When M i >M th When this happens, data points are identified as anomalous data points, and a set of anomalous data points is marked.

[0029] S23. Perform interpolation correction on the set of abnormal data points. Use spline interpolation to calculate the correction value of the abnormal data points. Replace the original data points with the corrected abnormal data points to obtain the corrected surface settlement measurement dataset.

[0030] S24. The corrected surface subsidence measurement dataset was standardized using the mean-standard deviation normalization method, resulting in the standardized surface subsidence measurement dataset D. standardized .

[0031] Optionally, S3 includes the following steps:

[0032] S31. Based on the changing trends of time series data, the time difference method is used to calculate the surface subsidence rate characteristics of each measurement point, which is used to reflect the degree of change in surface subsidence within different time intervals:

[0033]

[0034] Among them, v i Let represent the surface subsidence rate at time i. Let t be the standardized ground elevation value of the i-th measurement point. i -t i-1 The time interval between two consecutive observations is used to calculate the instantaneous rate of surface subsidence.

[0035] S32. By calculating the rate of change of subsidence rate, the characteristics of surface subsidence acceleration are captured, which can be used to reflect the intensification or deceleration of surface subsidence trends:

[0036]

[0037] Among them, a i This represents the surface subsidence acceleration at the i-th measurement point, reflecting the acceleration at that point at time t. i The trend of settlement rate change at time, v i Let be the surface subsidence rate at the i-th measurement point, and represent the intensity of subsidence change at the current moment, t. i -t i-1 For time intervals;

[0038] S33. A polynomial fitting method is used to model the trend of surface subsidence data, depicting the global trend of nonlinear changes in surface subsidence:

[0039]

[0040] in, Let c0, c1, ..., c be the fitted settlement trend value for the i-th measurement point. n t represents the fitting coefficient. i For timestamps;

[0041] S34. The settlement data is converted to the frequency domain using the Fast Fourier Transform method to identify potential periodic characteristics of surface settlement:

[0042]

[0043] Where H(f) represents the spectral amplitude of the surface subsidence data at the f-th frequency, reflecting the dominant frequency of periodic subsidence, and j is the imaginary unit, selecting the dominant frequency f with the largest amplitude in the spectrum. max As a major periodic feature of surface subsidence:

[0044] f max =argmaxH(f);

[0045] Among them, f max It represents the main periodic information of settlement data, used to analyze periodic settlement phenomena caused by geological structure, climate change or underground engineering construction factors;

[0046] S35. Based on the comprehensive calculations of surface subsidence rate characteristics, surface subsidence acceleration characteristics, nonlinear trend characteristics of surface subsidence, and periodic characteristics of surface subsidence, a feature matrix of surface subsidence measurement data is constructed:

[0047]

[0048] Optionally, S4 includes the following steps:

[0049] S41. Construct a radial basis function neural network model for fitting surface settlement measurement data. Define the input layer of the radial basis function neural network model, which receives the feature matrix F of the surface settlement measurement data. subsidence As input, let the number of neurons in the input layer be d, then the input layer neurons are represented as follows:

[0050] X = [x1, x2, ..., x d ];

[0051] Where X is the input neuron vector, x i The characteristic variables representing surface subsidence measurement data, where d=4 corresponds to the dimensions of velocity characteristics, acceleration characteristics, nonlinear trend characteristics, and periodic characteristics;

[0052] S42. Define the hidden layers of the radial basis function neural network model, using Gaussian radial basis functions as activation functions:

[0053]

[0054] Among them, H j Let X be the output of the j-th hidden layer neuron, and C be the input neuron vector. j Let σ be the j-th center vector. j Let be the scaling parameter of the j-th radial basis function, controlling the response range of the neuron, ∥XC j∥ represents the Euclidean distance between the input neuron and the center vector. Let m be the total number of neurons in the hidden layer. The output vector of the hidden layer is represented as:

[0055] H = [H1,H2,...,H] j ];

[0056] S44. Define the output layer of the radial basis function neural network model. The output layer is used to calculate the fitting result of the surface subsidence measurement data and obtain the initial surface subsidence measurement data fitting function:

[0057]

[0058] Where y is the fitted output of the surface subsidence measurement data, W is the weight matrix from the hidden layer to the output layer, and b is the bias term of the output layer. This represents the fitted surface settlement height value at the i-th measurement point.

[0059] Optionally, S5 includes the following steps:

[0060] S51. Generate initial solutions for multiple fitting parameters to form an optimization population. Set the population size to P and initialize the population individuals Θ. 0 :

[0061]

[0062] in, Let be the parameter vector of the p-th individual, containing the weight matrix W, bias term b, and hidden layer center vector C of the radial basis function neural network, i.e.:

[0063]

[0064] S52. Combining surface subsidence measurement data feature matrix F subsidence The sample size for fitness evaluation is calculated using the sample dimension N.

[0065] P = αN;

[0066] Where α is the population size coefficient;

[0067] S53. Using mean squared error and model complexity penalty terms as optimization objectives, calculate the fitness of individuals in the population, and define the fitness function f(θ). p )Measure the fitting error of an individual:

[0068]

[0069] in, This represents the actual surface settlement height. To use the p-th individual parameter θ p The calculated fitted height value, λ∥θp ∥ 2 is the regularization term;

[0070] S54. Optimize using the alpha evolutionary algorithm and adaptively adjust the evolutionary operator according to the evolutionary stage:

[0071] In the global exploration stage (G < G1), use the alpha hybrid strategy to combine genetic algorithm and differential evolution for wide-area search:

[0072]

[0073] where, θ r g , θ s g , θ t g are randomly selected different individuals, and F is the scaling factor;

[0074] Adopt the elite retention mechanism to retain the current optimal individual:

[0075]

[0076] In the local development stage (G1 ≤ G < G2), use the alpha adaptive mutation strategy to select the optimal individual for local fine-tuning:

[0077]

[0078] where, p best,p is the individual optimal solution, g best is the global optimal solution of the population, c1 and c2 are adaptive weight coefficients, and r1 and r2 are random numbers;

[0079] Combine gradient descent optimization to adjust the parameters of the optimal individual:

[0080]

[0081] where, η is the learning rate, is the gradient of the fitness function;

[0082] S55. Optimize the computational complexity using the dynamic weight adjustment strategy, and set the weight adjustment factor λ g :

[0083]

[0084] where, λ min and λ max are the lower and upper limits of the weight adjustment factor respectively;

[0085] S56. Determine whether the optimization has reached the convergence condition. If the convergence condition is met, output the optimal fitting parameters; otherwise, return to S53 to continue iterative optimization and finally obtain the optimized surface subsidence measurement data fitting function.

[0086] Optionally, S56 includes the following steps:

[0087] S561. Based on the optimization objective of the fitting function of the surface subsidence measurement data, calculate the mean fitness of the optimized population in the current generation g:

[0088]

[0089] in, This represents the average fitness value of the current population, where P is the number of individuals in the optimal population. Let be the fitness function value of the p-th individual in the g-th generation. The fitness function measures the degree of error in the fitting function of the surface subsidence measurement data.

[0090] S562. Calculate the fitness variance based on the current population fitness distribution. To measure the convergence of the population:

[0091]

[0092] in, The standard deviation of the fitness of the optimized population is represented by the standard deviation of ... fitness of the optimized population. The gradual convergence to the preset value indicates that the fitness of individuals in the population tends to be consistent;

[0093] S563. Determine if the convergence condition is met. Set a convergence threshold. If the following conditions are met, the optimization process is considered to have converged:

[0094] and

[0095] Wherein, ∈1 is the fitness convergence threshold, and ∈2 is the fitness variance threshold;

[0096] S564. Determine the optimal fitting parameters. When the convergence condition is met, select the best individual from the current generation as the optimal parameters for the final surface subsidence measurement data fitting function:

[0097]

[0098] Where, θ best The fitting parameters for the optimized surface subsidence measurement data include the weight matrix, bias term, and hidden layer center vector of the radial basis function neural network model, namely:

[0099] θ best ={W best ,bbest C best};

[0100] S565. If the convergence condition is not met, continue the optimization iteration, return to S53 to recalculate the fitness of individual populations, and perform the next generation of iterative optimization based on the alpha evolution algorithm until the convergence condition is met.

[0101] S566. Obtain the optimized fitting function for the surface subsidence measurement data:

[0102]

[0103] in, W represents the fitted surface settlement height value for the i-th measurement point. best H is the optimal hidden-to-output layer weight matrix after optimization of the Alpha Evolutionary Algorithm. i Let b be the output vector of the hidden layer of the radial basis function neural network. best This is the optimal bias term after optimization by the Alpha Evolutionary Algorithm.

[0104] The beneficial effects of this invention are:

[0105] (1) This invention proposes an adaptive hybrid optimization strategy. During the evolution process, the algorithm can adjust the optimization operator according to the dynamic changes of the surface subsidence data. In the global search stage, it combines genetic algorithm and differential evolution to conduct wide-area exploration. In the local optimization stage, it adopts particle swarm optimization combined with gradient descent for fine-tuning and adopts an elite retention mechanism to ensure that the best individual is retained. The alpha evolution algorithm can adaptively adjust the strategy according to the search stage, reduce unnecessary calculations, improve the convergence speed, and enable the fitting process to be optimized in a short time, thereby improving real-time computing capabilities.

[0106] (2) This invention uses a radial basis function neural network as the fitting model for land subsidence measurement data, and optimizes the parameters of the neural network through the alpha evolution algorithm. By utilizing the local response characteristics of the Gaussian radial basis function, the model can more accurately capture the nonlinear characteristics of land subsidence and perform accurate fitting at different time scales. In addition, the adaptive weight adjustment mechanism is combined to ensure that the optimal balance is found between computational complexity and fitting accuracy.

[0107] (3) This invention proposes an adaptive convergence determination mechanism based on fitness mean and variance. That is, in each generation of evolution, the fitness mean and fitness variance of the current optimization population are calculated to ensure that the optimization process is searched in the global range. When the fitness mean of the population reaches a preset threshold and the fitness variance converges, the algorithm automatically terminates the optimization to ensure the acquisition of the global optimal solution. The convergence strategy can reduce the computational overhead and avoid getting trapped in local optima while ensuring global optima. Attached Figure Description

[0108] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0109] Figure 1 This is a flowchart of a real-time fitting method for surface subsidence measurement data based on an evolutionary algorithm, as proposed in this invention. Detailed Implementation

[0110] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0111] refer to Figure 1 A real-time fitting method for surface subsidence measurement data based on evolutionary algorithm, comprising the following steps: S1. Obtaining surface subsidence measurement dataset;

[0112] S2. Preprocess the surface subsidence measurement dataset to obtain a standardized surface subsidence measurement dataset;

[0113] S3. Perform time-series analysis on standardized surface subsidence measurement data to generate a surface subsidence measurement data feature matrix;

[0114] S4. Construct a radial basis function neural network model for fitting surface subsidence measurement data, and initialize the parameters of the radial basis function neural network model to obtain the initial surface subsidence measurement data fitting function;

[0115] S5. The parameters of the fitting function for the initial surface subsidence measurement data are optimized using the Alpha Evolutionary Algorithm to obtain the optimized fitting function for the surface subsidence measurement data.

[0116] S6. The optimized surface subsidence measurement data fitting function is used to predict the input surface subsidence measurement data, output the surface subsidence trend fitting curve, and calculate the fitting error, trend change rate, and prediction confidence interval index.

[0117] In this embodiment, S1 includes the following steps:

[0118] S11. Obtain the surface subsidence measurement dataset, which includes global navigation satellite system measurement data, synthetic aperture radar measurement data, and lidar point cloud measurement data:

[0119] D GNSS ={(x i ,y i ,t i ,h i| i = 1, 2, ..., N GNSS};

[0120] D InSAR ={(x j ,y j ,t j ,h j |j=1,2,...,N InSAR};

[0121] D LiDAR ={(x k ,y k ,t k ,h k |k=1,2,...,N LiDAR};

[0122] Where x, y represent geographic coordinates, t represents a timestamp, h represents the ground elevation, and N GNSS N InSAR N LiDAR These represent the number of sampling points for Global Navigation Satellite System measurement data, Synthetic Aperture Radar measurement data, and LiDAR point cloud measurement data, respectively.

[0123] S12. Perform spatial reference coordinate system transformation on the surface subsidence measurement dataset to unify the coordinate datum of the surface subsidence measurement dataset, resulting in a surface subsidence measurement dataset under a unified spatial reference coordinate system:

[0124] "′

[0125] D aligned =D GNSS ∪D InSAR ∪D LiDAR ;

[0126] "′

[0127] Among them, D GNSS D InSAR and D LiDAR These represent global navigation satellite system measurement data, synthetic aperture radar measurement data, and lidar point cloud measurement data, respectively, in a unified spatial reference coordinate system.

[0128] In this embodiment, S2 includes the following steps:

[0129] S21. Using wavelet transform to process the surface subsidence measurement dataset D in a unified spatial reference coordinate system. aligned Denoising is performed to remove random noise from the surface subsidence measurement data, resulting in a denoised surface subsidence measurement dataset.

[0130] S22. The Mahalanobis distance analysis method is used to detect outliers in the denoised surface subsidence measurement dataset, and the outlier degree of each data point is calculated:

[0131] M i =(h i ″ -μ h ) T Σ h -1 (h i ″ -μ h );

[0132] Among them, M i The Mahalanobis distance between the surface settlement measurement data points is μ. h Let Σ be the mean vector of the height of the surface subsidence measurement data. h This is the covariance matrix of the elevation of the surface subsidence measurement data;

[0133] Set threshold M th When M i >M th When this happens, data points are identified as anomalous data points, and a set of anomalous data points is marked.

[0134] S23. Perform interpolation correction on the set of abnormal data points. Use spline interpolation to calculate the correction value of the abnormal data points. Replace the original data points with the corrected abnormal data points to obtain the corrected surface settlement measurement dataset.

[0135] S24. The corrected surface subsidence measurement dataset was standardized using the mean-standard deviation normalization method, resulting in the standardized surface subsidence measurement dataset D. standardized .

[0136] In this embodiment, S3 includes the following steps:

[0137] S31. Based on the changing trends of time series data, the time difference method is used to calculate the surface subsidence rate characteristics of each measurement point, which is used to reflect the degree of change in surface subsidence within different time intervals:

[0138]

[0139] Among them, v i Let represent the surface subsidence rate at time i. Let t be the standardized ground elevation value of the i-th measurement point. i -t i-1 The time interval between two consecutive observations is used to calculate the instantaneous rate of surface subsidence.

[0140] S32. By calculating the rate of change of subsidence rate, the characteristics of surface subsidence acceleration are captured, which can be used to reflect the intensification or deceleration of surface subsidence trends:

[0141]

[0142] Among them, a i This represents the surface subsidence acceleration at the i-th measurement point, reflecting the acceleration at that point at time t. i The trend of settlement rate change at time, v i Let be the surface subsidence rate at the i-th measurement point, and represent the intensity of subsidence change at the current moment, t. i -t i-1 For time intervals;

[0143] S33. A polynomial fitting method is used to model the trend of surface subsidence data, depicting the global trend of nonlinear changes in surface subsidence:

[0144]

[0145] in, Let c0, c1, ..., c be the fitted settlement trend value for the i-th measurement point. n t represents the fitting coefficient. i For timestamps;

[0146] S34. The settlement data is converted to the frequency domain using the Fast Fourier Transform method to identify potential periodic characteristics of surface settlement:

[0147]

[0148] Where H(f) represents the spectral amplitude of the surface subsidence data at the f-th frequency, reflecting the dominant frequency of periodic subsidence, and j is the imaginary unit, selecting the dominant frequency f with the largest amplitude in the spectrum. max As a major periodic feature of surface subsidence:

[0149] f max =argmaxH(f);

[0150] Among them, f max It represents the main periodic information of settlement data, used to analyze periodic settlement phenomena caused by geological structure, climate change or underground engineering construction factors;

[0151] S35. Based on the comprehensive calculations of surface subsidence rate characteristics, surface subsidence acceleration characteristics, nonlinear trend characteristics of surface subsidence, and periodic characteristics of surface subsidence, a feature matrix of surface subsidence measurement data is constructed:

[0152]

[0153] In this embodiment, S4 includes the following steps:

[0154] S41. Construct a radial basis function neural network model for fitting surface settlement measurement data. Define the input layer of the radial basis function neural network model, which receives the feature matrix F of the surface settlement measurement data. subsidence As input, let the number of neurons in the input layer be d, then the input layer neurons are represented as follows:

[0155] X = [x1, x2, ..., x d ];

[0156] Where X is the input neuron vector, x i The characteristic variables representing surface subsidence measurement data, where d=4 corresponds to the dimensions of velocity characteristics, acceleration characteristics, nonlinear trend characteristics, and periodic characteristics;

[0157] S42. Define the hidden layers of the radial basis function neural network model, using Gaussian radial basis functions as activation functions:

[0158]

[0159] Among them, H j Let X be the output of the j-th hidden layer neuron, and C be the input neuron vector. j Let σ be the j-th center vector. j Let be the scaling parameter of the j-th radial basis function, controlling the response range of the neuron, ∥XC j ∥ represents the Euclidean distance between the input neuron and the center vector. Let m be the total number of neurons in the hidden layer. The output vector of the hidden layer is represented as:

[0160] H = [H1,H2,...,H] j ];

[0161] S44. Define the output layer of the radial basis function neural network model. The output layer is used to calculate the fitting result of the surface subsidence measurement data and obtain the initial surface subsidence measurement data fitting function:

[0162]

[0163] Where y is the fitted output of the surface subsidence measurement data, W is the weight matrix from the hidden layer to the output layer, and b is the bias term of the output layer. This represents the fitted surface settlement height value at the i-th measurement point.

[0164] In this embodiment, S5 includes the following steps:

[0165] S51. Generate initial solutions for multiple fitting parameters to form an optimization population. Set the population size to P and initialize the population individuals Θ.0 :

[0166]

[0167] Among them, is the parameter vector of the p-th individual, including the weight matrix W, the bias term b, and the hidden layer center vector C of the radial basis function neural network, that is:

[0168]

[0169] S52. Combine the surface settlement measurement data feature matrix F subsidence and the sample dimension N to calculate the fitness evaluation sample size:

[0170] P = αN;

[0171] Among them, α is the population size coefficient;

[0172] S53. Use the mean square error and the model complexity penalty term as the optimization objective to calculate the fitness of the population individuals, and set the fitness function f(θ p ) to measure the fitting error of the individual:

[0173]

[0174] Among them, is the true surface settlement height value, is the fitting height value calculated using the parameters θ of the p-th individual p , λ∥θ p ∥ 2 is the regularization term;

[0175] S54. Use the alpha evolutionary algorithm for optimization, and adaptively adjust the evolutionary operator according to the evolutionary stage:

[0176] Global exploration stage (G < G1), use the alpha hybrid strategy to combine genetic algorithm and differential evolution for wide-area search:

[0177]

[0178] Among them, are randomly selected different individuals, and F is the scaling factor;

[0179] Use the elite retention mechanism to retain the current optimal individual:

[0180]

[0181] Local development stage (G1 ≤ G < G2), use the alpha adaptive mutation strategy to select the optimal individual for local fine-tuning:

[0182]

[0183] Where, p best,p For the individual optimal solution, g best For the global optimal solution of the population, c1 and c2 are adaptive weight coefficients, and r1 and r2 are random numbers;

[0184] Parameters are adjusted for the optimal individual using gradient descent optimization:

[0185]

[0186] Where η is the learning rate. The gradient of the fitness function;

[0187] S55. Optimize computational complexity using a dynamic weight adjustment strategy, setting a weight adjustment factor λ. g :

[0188]

[0189] Where, λ min and λ max These are the lower and upper limits of the weight adjustment factor, respectively;

[0190] S56. Determine whether the optimization has reached the convergence condition. If the convergence condition is met, output the optimal fitting parameters; otherwise, return to S53 to continue iterative optimization and finally obtain the optimized surface subsidence measurement data fitting function.

[0191] In this embodiment, S56 includes the following steps:

[0192] S561. Based on the optimization objective of the fitting function of the surface subsidence measurement data, calculate the mean fitness of the optimized population in the current generation g:

[0193]

[0194] in, This represents the average fitness value of the current population, where P is the number of individuals in the optimal population. Let be the fitness function value of the p-th individual in the g-th generation. The fitness function measures the degree of error in the fitting function of the surface subsidence measurement data.

[0195] S562. Calculate the fitness variance based on the current population fitness distribution. To measure the convergence of the population:

[0196]

[0197] in, The standard deviation of the fitness of the optimized population is represented by the standard deviation of ... fitness of the optimized population. The gradual convergence to the preset value indicates that the fitness of individuals in the population tends to be consistent;

[0198] S563. Determine if the convergence condition is met. Set a convergence threshold. If the following conditions are met, the optimization process is considered to have converged:

[0199] and

[0200] Wherein, ∈1 is the fitness convergence threshold, and ∈2 is the fitness variance threshold;

[0201] S564. Determine the optimal fitting parameters. When the convergence condition is met, select the best individual from the current generation as the optimal parameters for the final surface subsidence measurement data fitting function:

[0202]

[0203] Where, θ best The fitting parameters for the optimized surface subsidence measurement data include the weight matrix, bias term, and hidden layer center vector of the radial basis function neural network model, namely:

[0204] θ best ={W best ,b best C best};

[0205] S565. If the convergence condition is not met, continue the optimization iteration, return to S53 to recalculate the fitness of individual populations, and perform the next generation of iterative optimization based on the alpha evolution algorithm until the convergence condition is met.

[0206] S566. Obtain the optimized fitting function for the surface subsidence measurement data:

[0207]

[0208] in, W represents the fitted surface settlement height value for the i-th measurement point. best H is the optimal hidden-to-output layer weight matrix after optimization of the Alpha Evolutionary Algorithm. i Let b be the output vector of the hidden layer of the radial basis function neural network. best This is the optimal bias term after optimization by the Alpha Evolutionary Algorithm.

[0209] Example 1:

[0210] On April 15, 2024, during the construction of a tunnel section of Metro Line 10 in City A, the monitoring system detected an anomaly in the settlement data of GNSS monitoring point GNSS-045 at 03:20. The settlement rate at this point had increased significantly over the past 6 hours, accelerating from -0.0145 m / d to -0.0321 m / d, and the settlement acceleration had increased from 0.0008 m / d. 2 Increased to 0.0024 m / d 2 This indicates that there may be potential uneven subsidence in the area. At the same time, InSAR data at 03:45 also shows that the surface deformation in the area exceeds 15mm, which exceeds the normal safety threshold for subway tunnels.

[0211] At 04:00, the Alpha Evolutionary Algorithm begins real-time data fitting. The system automatically retrieves surface subsidence measurement data from the past 24 hours and combines it with a radial basis function neural network for data analysis.

[0212] The initial data input is shown in Table 1 below (data from some monitoring points):

[0213]

[0214] In the RBF-NN calculation, the data-based nonlinear feature system uses 10 radial basis functions. The alpha evolution algorithm randomly initializes 200 candidate parameter sets and begins optimization calculation. At 04:03:15, the system completes the 85th iteration and finds that the average fitness of the population has converged to the set threshold. Finally, the optimal fitting parameters are determined and the latest subsidence trend prediction is output.

[0215] Real-time fitting results:

[0216]

[0217] The fitted curve shows that the expected settlement of the monitoring point in the next 24 hours is -0.045m, which reaches the engineering warning value.

[0218] At 04:05, the system detected that the settlement trend exceeded the warning threshold, automatically generated a tunnel structure settlement warning report, and sent the report to the construction unit and the subway operation management center. The report included:

[0219] Warning time: 2024-04-15 04:05;

[0220] Monitoring point number: GNSS-045;

[0221] Settlement trend: The settlement is expected to be -0.045m in the next 24 hours, which exceeds the safety threshold;

[0222] Abnormal detection results: The settlement rate increased sharply, and the regional settlement variation range was 15 mm;

[0223] Recommended measures: Immediately investigate the surrounding groundwater drainage situation and check the stability of the tunnel structure;

[0224] At the same time, at 04:06, the A City Metro Operation and Dispatch Center received a system alarm and immediately dispatched engineering technicians to the site for inspection and suspended construction work on that section of the line.

[0225] To verify the effectiveness of this invention, the system simultaneously uses multinomial regression and MLP neural network for fitting, and compares the computational efficiency and prediction error. The data are shown in Table 2 below:

[0226]

[0227]

[0228] As shown in the table above, the present invention improves computational efficiency. This method completes fitting within 0.91 seconds, which is 3.1 times faster than the PR method and 1.95 times faster than the MLP method. The fitting error of this method is reduced, with a mean square error of only 0.0035, which is 65.3% lower than the PR method and 51.4% lower than the MLP method. The prediction error of this method is also reduced, with a 24-hour settlement prediction error of only 0.014m, which is 62.1% lower than the PR method and 51.7% lower than the MLP method, effectively improving the accuracy of long-term prediction.

[0229] At 04:40, technicians from the subway management center arrived at the scene and found that the groundwater level in the area had dropped by 1.2 meters in the past 12 hours, which could lead to further localized ground subsidence. Subsequently, at 05:15, the construction unit took measures to adjust the groundwater pumping rate, and at 06:30, the subsidence rate was remeasured, finding that the subsidence trend was stabilizing.

[0230] When a new round of data analysis was conducted at 04:00 on April 16, the deviation between the system's predicted 24-hour settlement trend and the actual measured value was less than 0.012m, which is 58% less than the deviation of the traditional method, proving the efficiency and reliability of this method in real-time fitting of surface settlement measurement data.

[0231] This embodiment successfully applied a radial basis function neural network optimized by the Alpha Evolutionary Algorithm in the construction area of ​​a subway tunnel in City A. Comparative experiments verified the advantages of this method in terms of computational speed, fitting accuracy, and prediction stability. Simultaneously, the system's real-time alarm function enabled the subway management to respond promptly, ultimately successfully avoiding the risk of tunnel structural settlement, demonstrating the practical value of this invention in the field of high-precision surface settlement monitoring.

[0232] This invention proposes an adaptive hybrid optimization strategy. During the evolutionary process, the algorithm can adjust the optimization operator according to the dynamic changes of land subsidence data. In the global search stage, it combines genetic algorithm and differential evolution for wide-area exploration. In the local optimization stage, it uses particle swarm optimization combined with gradient descent for fine-tuning and adopts an elite retention mechanism to ensure that the best individuals are retained. The alpha evolution algorithm can adaptively adjust the strategy according to the search stage, reduce unnecessary calculations, improve the convergence speed, and enable the fitting process to be optimized in a short time, thereby improving real-time computing capabilities.

[0233] This invention employs a radial basis function neural network as the fitting model for land subsidence measurement data, and optimizes the parameters of the neural network through the alpha evolution algorithm. By utilizing the local response characteristics of the Gaussian radial basis function, the model can more accurately capture the nonlinear characteristics of land subsidence and perform precise fitting at different time scales. In addition, an adaptive weight adjustment mechanism is combined to ensure that the optimal balance is found between computational complexity and fitting accuracy.

[0234] This invention proposes an adaptive convergence determination mechanism based on fitness mean and variance. In each generation of evolution, the fitness mean and fitness variance of the current optimization population are calculated to ensure that the optimization process searches in the global scope. When the fitness mean of the population reaches a preset threshold and the fitness variance converges, the algorithm automatically terminates the optimization to ensure the acquisition of the global optimum. The convergence strategy can reduce the computational cost and avoid getting trapped in local optima while ensuring global optima.

[0235] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A real-time fitting method for surface subsidence measurement data based on an evolutionary algorithm, characterized in that, Includes the following steps: S1. Obtain the surface subsidence measurement dataset; S2. Preprocess the surface subsidence measurement dataset to obtain a standardized surface subsidence measurement dataset; S3. Perform time-series analysis on standardized surface subsidence measurement data to generate a surface subsidence measurement data feature matrix; S4. Construct a radial basis function neural network model for fitting surface subsidence measurement data, and initialize the parameters of the radial basis function neural network model to obtain the initial surface subsidence measurement data fitting function; S5. The parameters of the fitting function for the initial surface subsidence measurement data are optimized using the Alpha Evolutionary Algorithm to obtain the optimized fitting function for the surface subsidence measurement data. S6. The optimized surface subsidence measurement data fitting function is used to predict the input surface subsidence measurement data, output the surface subsidence trend fitting curve, and calculate the fitting error, trend change rate, and prediction confidence interval index. S4 includes the following steps: S41. Construct a radial basis function neural network model for fitting surface subsidence measurement data, and define the input layer of the radial basis function neural network model, which receives the feature matrix of the surface subsidence measurement data. As input, let the number of neurons in the input layer be d, then the input layer neurons are represented as follows: ； Where X is the input neuron vector, The characteristic variables representing surface subsidence measurement data, d = 4, correspond to the dimensions of velocity characteristics, acceleration characteristics, nonlinear trend characteristics, and periodic characteristics; S42. Define the hidden layers of the radial basis function neural network model, using Gaussian radial basis functions as activation functions: ； in, Let X be the output of the j-th hidden layer neuron, and let X be the input neuron vector. Let j be the center vector. The scaling parameter of the j-th radial basis function controls the response range of the neuron. Let m represent the Euclidean distance between the input neuron and the center vector. The total number of neurons in the hidden layer is denoted as m. The output vector of the hidden layer is represented as: ； S44. Define the output layer of the radial basis function neural network model. The output layer is used to calculate the fitting result of the surface subsidence measurement data and obtain the initial surface subsidence measurement data fitting function: ； Where y is the fitted output of the surface subsidence measurement data, W is the weight matrix from the hidden layer to the output layer, and b is the bias term of the output layer. This represents the fitted surface settlement height value at the i-th measurement point.

2. The method for real-time fitting of surface subsidence measurement data based on evolutionary algorithm according to claim 1, characterized in that, S1 includes the following steps: S11. Obtain a surface subsidence measurement dataset, which includes global navigation satellite system measurement data, synthetic aperture radar measurement data, and lidar point cloud measurement data: ； ； ； Where x and y represent geographic coordinates, t represents a timestamp, and h represents the ground elevation. , , These represent the number of sampling points for Global Navigation Satellite System measurement data, Synthetic Aperture Radar measurement data, and LiDAR point cloud measurement data, respectively. S12. Perform spatial reference coordinate system transformation on the surface subsidence measurement dataset to unify the coordinate datum of the surface subsidence measurement dataset, resulting in a surface subsidence measurement dataset under a unified spatial reference coordinate system: ； in, , and These represent global navigation satellite system measurement data, synthetic aperture radar measurement data, and lidar point cloud measurement data, respectively, in a unified spatial reference coordinate system.

3. The method for real-time fitting of surface subsidence measurement data based on evolutionary algorithm according to claim 1, characterized in that, S2 includes the following steps: S21. Wavelet transform method is used to process the surface subsidence measurement dataset in a unified spatial reference coordinate system. Denoising is performed to remove random noise from the surface subsidence measurement data, resulting in a denoised surface subsidence measurement dataset. S22. The Mahalanobis distance analysis method is used to detect outliers in the denoised surface subsidence measurement dataset, and the anomaly degree of each data point is calculated: ； in, The Mahalanobis distance is the distance between the data points for surface subsidence measurement. This is the mean vector of the height of the surface subsidence measurement data. This is the covariance matrix of the elevation of the surface subsidence measurement data; Set threshold ,when When this happens, data points are identified as anomalous data points, and a set of anomalous data points is marked. S23. Perform interpolation correction on the set of abnormal data points. Use spline interpolation to calculate the correction value of the abnormal data points. Replace the original data points with the corrected abnormal data points to obtain the corrected surface settlement measurement dataset. S24. The corrected surface settlement measurement dataset was standardized using the mean-standard deviation normalization method to obtain the final standardized surface settlement measurement dataset. .

4. The method for real-time fitting of surface subsidence measurement data based on evolutionary algorithm according to claim 1, characterized in that, S3 includes the following steps: S31. Based on the changing trends of time series data, the time difference method is used to calculate the surface subsidence rate characteristics of each measurement point, which is used to reflect the degree of change in surface subsidence within different time intervals: ； in, Let represent the surface subsidence rate at time i. Let i be the standardized ground elevation value of the i-th measurement point. The time interval between two consecutive observations is used to calculate the instantaneous rate of surface subsidence. S32. By calculating the rate of change of subsidence rate, the characteristics of surface subsidence acceleration are captured, which can be used to reflect the intensification or deceleration of surface subsidence trends: ； in, This represents the surface subsidence acceleration at the i-th measurement point, reflecting the time change at that point. The trend of settlement rate change over time. Let be the surface subsidence rate at the i-th measurement point, representing the intensity of subsidence change at the current moment. For time intervals; S33. A polynomial fitting method is used to model the trend of surface subsidence data, characterizing the global trend of nonlinear changes in surface subsidence: ； in, Let be the fitted settlement trend value for the i-th measurement point. These are the fitting coefficients. For timestamps; S34. The settlement data is converted to the frequency domain using the Fast Fourier Transform method to identify potential periodic characteristics of surface settlement: ； Where H(f) represents the spectral amplitude of the surface subsidence data at the f-th frequency, reflecting the dominant frequency of periodic subsidence, and j is the imaginary unit, selecting the dominant frequency with the largest amplitude in the spectrum. As a major periodic feature of surface subsidence: ； in, It represents the main periodic information of settlement data, used to analyze periodic settlement phenomena caused by geological structure, climate change or underground engineering construction factors; S35. Based on the comprehensive calculations of surface subsidence rate characteristics, surface subsidence acceleration characteristics, nonlinear trend characteristics of surface subsidence, and periodic characteristics of surface subsidence, a feature matrix of surface subsidence measurement data is constructed: 。 5. The method for real-time fitting of surface subsidence measurement data based on evolutionary algorithm according to claim 1, characterized in that, S5 includes the following steps: S51. Generate initial solutions for multiple fitting parameters to form an optimization population. Set the population size to P and initialize the population individuals. : ； in, Let be the parameter vector of the p-th individual, containing the weight matrix W, bias term b, and hidden layer center vector C of the radial basis function neural network, i.e.: ； S52. Feature matrix combining surface subsidence measurement data The sample size N is used to calculate the fitness evaluation sample size. ； in, Population size coefficient; S53. Using mean squared error and model complexity penalty terms as optimization objectives, calculate the fitness of individuals in the population, and define the fitness function. Measuring the fit error of an individual: ； in, This represents the actual surface settlement height. To use the p-th individual parameter The calculated fitted height value, For regularization terms; S54. Optimization is performed using the Alpha Evolutionary Algorithm, adaptively adjusting the evolutionary operators according to the evolutionary stage: Global exploration phase A hybrid alpha strategy combining genetic algorithm and differential evolution is used for wide-area search: ； in, For each randomly selected individual, F is the scaling factor; The best individual is retained using an elite retention mechanism: ； Partial development phase An alpha adaptive mutation strategy is used to select the optimal individual for local fine-tuning. ； in, This is the optimal solution for the individual. This is the globally optimal solution for the population. For adaptive weighting coefficients, It is a random number; Parameters are adjusted for the optimal individual using gradient descent optimization: ； in, For learning rate, The gradient of the fitness function; S55. Optimize computational complexity using a dynamic weight adjustment strategy, and set a weight adjustment factor. : ； in, and These are the lower and upper limits of the weight adjustment factor, respectively; S56. Determine whether the optimization has reached the convergence condition. If the convergence condition is met, output the optimal fitting parameters; otherwise, return to S53 to continue iterative optimization and finally obtain the optimized surface subsidence measurement data fitting function.

6. The method for real-time fitting of surface subsidence measurement data based on evolutionary algorithm according to claim 5, characterized in that, S56 includes the following steps: S561. Based on the optimization objective of the fitting function of the surface subsidence measurement data, calculate the mean fitness of the optimized population for the current generation g: ； in, This represents the average fitness value of the current population, where P is the number of individuals in the optimal population. Let be the fitness function value of the p-th individual in the g-th generation. The fitness function measures the degree of error in the fitting function of the surface subsidence measurement data. S562. Calculate the fitness variance based on the current population fitness distribution. To measure the convergence of the population: ； in, The standard deviation of the fitness of the optimized population is represented by the standard deviation of ... fitness of the optimized population. The gradual convergence to the preset value indicates that the fitness of individuals in the population tends to be consistent; S563. Determine if the convergence condition is met. Set a convergence threshold. If the following conditions are met, the optimization process is considered to have converged: ； in, The fitness convergence threshold, The fitness variance threshold; S564. Determine the optimal fitting parameters. When the convergence condition is met, select the best individual from the current generation as the optimal parameters for the final surface subsidence measurement data fitting function: ； in, The fitting parameters for the optimized surface subsidence measurement data include the weight matrix, bias term, and hidden layer center vector of the radial basis function neural network model, namely: ； S565. If the convergence condition is not met, continue the optimization iteration, return to S53 to recalculate the fitness of individual populations, and perform the next generation of iterative optimization based on the alpha evolution algorithm until the convergence condition is met; S566. Obtain the optimized fitting function for the surface subsidence measurement data: ； in, Let be the fitted surface settlement height value for the i-th measurement point. This is the optimal hidden layer to output layer weight matrix after optimization of the Alpha Evolutionary Algorithm. This represents the output vector of the hidden layer in a radial basis function neural network. This is the optimal bias term after optimization by the Alpha Evolutionary Algorithm.

Images