Surface subsidence prediction method based on EOF-SSA-SVM spatiotemporal model

Abstract

The present invention provides a surface settlement prediction method based on EOF-SSA-SVM spatiotemporal model: the surface settlement time series of each monitoring point constitutes a settlement spatiotemporal matrix; the settlement spatiotemporal matrix is ​​decomposed into spatial mode and historical time series by using empirical orthogonal function, and the main settlement characteristics of surface settlement are screened out; the screened historical time series is divided into a training set and a test set; in combination with the training set data, the penalty parameter and the kernel function parameter of the support vector machine prediction model are optimized by using the sparrow search algorithm to obtain the optimized support vector machine prediction model; the optimized support vector machine prediction model is predicted according to the test set data to obtain the prediction time series; the screened spatial mode and the prediction time series are reconstructed and back-calculated by using the empirical orthogonal function to obtain the final surface settlement prediction result. The present invention fully considers the connection between time and space series, and the prediction result has high accuracy and reliability.

Description

Technical Field

[0001] The present invention relates to the technical field of surface subsidence prediction, and in particular to a surface subsidence prediction method based on an EOF-SSA-SVM spatiotemporal model. Background Art

[0002] With the development of urban rail transit, subway tunnel projects have also put forward higher requirements for their construction technology. Urban subway lines are generally busy with traffic, buildings and underground pipelines, and their construction environment is complex and changeable. The disturbance of the subway during the shield excavation process causes a certain degree of settlement of the surface near the tunnel line; in addition, in the shield tunnel environment, the total thickness of the soil aquifer is large and the water content is relatively rich, which also makes the surface settlement of the construction area more difficult to control. If the stratum has significant displacement, it will destroy the regional balance and threaten the safety of personnel. At this time, it is necessary to adjust and optimize the excavation parameters in time, strictly control the excavation volume and excavation speed, and balance the footage with the excavation volume to maintain the balance of the working face earth pressure and ensure the construction quality and safety. Therefore, surface settlement prediction is particularly important for tunnel construction safety, and domestic and foreign scholars have also carried out a lot of research.

[0003] According to the differences in the principles of surface settlement prediction, the prediction methods are mainly divided into: Peck formula method, analytical method, numerical simulation method, machine learning method, etc. Traditional surface settlement prediction methods have limitations such as low accuracy, complex calculation, and difficulty in practical application, and it is difficult to achieve accurate and efficient prediction. In recent years, artificial intelligence has developed rapidly, and machine learning has been widely used in various engineering fields, and has achieved many relevant results. However, the basic machine learning prediction model cannot capture the complete information of surface settlement. Considering that the settlement deformation caused by the shield excavation of subway tunnels is affected by many factors, and the complexity, nonlinearity, and multi-factor coupling of subway shield tunnel engineering problems have many characteristics, seeking efficient optimization algorithms has become one of the main research hotspots for surface settlement prediction.

[0004] In addition, the current surface subsidence prediction is mainly studied separately on time or space series. The model information obtained is one-sided and single, and cannot fully and accurately reflect the potential connections and changing patterns between monitoring data. Few scholars have explored the spatiotemporal correlation of surface subsidence. Therefore, the coupling application between different prediction dimensions is a general trend for more in-depth research on complex issues.

[0005] In summary, there is an urgent need for a surface subsidence prediction method based on the EOF-SSA-SVM spatiotemporal model to solve the problems existing in the existing technology. Summary of the invention

[0006] The present invention aims to provide a surface subsidence prediction method based on EOF-SSA-SVM spatiotemporal model, aiming to solve the problem that the existing technology does not consider the connection between time and space sequences for surface subsidence prediction, and the model information obtained is one-sided and single, resulting in low monitoring accuracy. The specific technical solution is as follows:

[0007] A surface subsidence prediction method based on EOF-SSA-SVM spatiotemporal model includes the following steps:

[0008] Step S1: The surface settlement time series of each monitoring point is used to form a settlement time-space matrix;

[0009] Step S2: Decompose the settlement space-time matrix into spatial modes and historical time series using empirical orthogonal functions, and screen out the main settlement characteristics of surface settlement according to the variance contribution rate; and divide the screened historical time series into a training set and a test set;

[0010] Step S3: combining the training set data, using the sparrow search algorithm to optimize the penalty parameters and kernel function parameters of the support vector machine prediction model to obtain an optimized support vector machine prediction model;

[0011] Step S4: The optimized support vector machine prediction model performs prediction based on the test set data to obtain a predicted time series;

[0012] Step S5: Use the empirical orthogonal function to reconstruct and back-calculate the screened spatial modes and predicted time series to obtain the final surface subsidence prediction results.

[0013] In the above technical solution, the step S1 is preferably as follows: m regional settlement monitoring points are set, and n historical time data of each monitoring point are used to form a settlement space-time matrix D m×n .

[0014] Preferably, in the above technical solution, step S2 is specifically:

[0015] The sedimentation space-time matrix D m×n After the anomaly processing, the data matrix X is obtained m×n ;

[0016] Calculate the data matrix X m×n The cross product of the matrix and its transposed matrix gives the cross product matrix C m×m , as shown in formula 1):

[0017]

[0018] Calculate C m×m The eigenvalue λ i and eigenvalue λ i The corresponding spatial eigenvector EOFm×m , where i=1, 2...m, and λ1>λ2>...>λ m ; and calculate the spatial eigenvector EOF according to formula 2) m×m The corresponding time coefficient PC m×n :

[0019] PC m×n =EOF T m×m ×X m×n 2),

[0020] Calculate the variance contribution rate of each eigenvalue, and select the main settlement characteristics according to the variance contribution rate; the variance contribution rate P i According to formula 3) calculation:

[0021]

[0022] In the above technical solution, it is preferred to retain the main sedimentation characteristics with a variance contribution rate greater than 0.001.

[0023] Preferably, in the above technical solution, step S3 specifically includes:

[0024] Step S3.1: Initialize parameters, including population size, ratio of discoverers to sentinels, maximum number of iterations, and upper and lower limits of optimization parameter targets;

[0025] Step S3.2: Calculate the fitness values ​​of the sparrows, sort them according to the fitness values, and select the current best and worst fitness values ​​and their corresponding position information;

[0026] Step S3.3: Update the location information of the discoverer, joiner and alerter;

[0027] Step S3.4: updating the position state of the sparrow population, and calculating the fitness value according to the current position state of the sparrow population;

[0028] Step S3.5: If the stopping condition is met, the training set data is used as input and the optimal parameter result is output;

[0029] If the stop condition is not met, return to step S3.2;

[0030] Step S3.6: Input the obtained optimal parameter results into the support vector machine prediction model to obtain the optimized support vector machine prediction model.

[0031] Preferably, in the above technical solution, in step S3.5, if the upper and lower limits of the optimization parameter targets or the maximum number of iterations are reached, the optimal parameter result is output.

[0032] Preferably, in the above technical solution, the optimal parameter results are penalty parameters and kernel function parameters.

[0033] The application of the technical solution of the present invention has the following beneficial effects:

[0034] The existing surface settlement prediction separates time and space characteristics for single research, which is somewhat one-sided. Under the conditions of subway shield tunnel engineering, the present invention proposes a space-time fusion method based on the time law and space characteristics of surface settlement. The empirical orthogonal function (EOF) decomposition can realize the coupling of time and space dimensions and the elimination of redundant information, thereby reducing the amount of calculation while improving accuracy; the traditional artificial intelligence prediction model has low stability and accuracy. The present invention uses a support vector machine prediction model optimized by a sparrow search algorithm. The SSA has good search and optimization effect and fast convergence speed. The foraging and predation behavior characteristics of sparrows are used to seek the best prediction parameters from a global perspective, thereby effectively improving the prediction performance of SVM; the shield construction surface settlement prediction method based on the EOF-SSA-SVM space-time model combines space-time characteristics, global optimization, and nonlinear prediction, overcomes the magnitude difference through data normalization, and fully mines data information to obtain higher accuracy, which can provide real-time control and early warning for surface settlement.

[0035] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0037] Figure 1 is a flow chart of the prediction method of the present invention;

[0038] Figure 2 is the prediction effect of monitoring point 1 in the test case in the four models;

[0039] Figure 3 It is the prediction effect of monitoring point 2 in the test case in the four models. DETAILED DESCRIPTION

[0040] In order to facilitate the understanding of the present invention, the present invention will be described more comprehensively below, and preferred embodiments of the present invention are provided. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive.

[0041] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0042] Embodiment 1:

[0043] See also Figure 1 A shield construction surface settlement prediction method based on EOF-SSA-SVM spatiotemporal model is proposed. This method combines spatiotemporal correlation characteristics and sparrow search optimization algorithm, and has the advantages of high accuracy, strong applicability, and ease of use. It specifically includes the following steps:

[0044] Step S1: The surface settlement time series of each monitoring point is used to form a settlement time-space matrix;

[0045] Preferably, the step S1 specifically includes: setting m regional settlement monitoring points, and forming a settlement space-time matrix D with n historical time data of each monitoring point m×n .

[0046] Step S2: Use the empirical orthogonal function (EOF) to decompose the settlement space-time matrix into spatial modes and historical time series, and screen out the main settlement characteristics of surface settlement according to the variance contribution rate; and divide the screened historical time series into a training set and a test set.

[0047] Preferably, the step S2 specifically includes:

[0048] The sedimentation space-time matrix D m×n After the anomaly processing, the data matrix X is obtained m×n ;

[0049] Calculate the data matrix X m×n The cross product of the matrix and its transposed matrix gives the cross product matrix C m×m , as shown in formula 1):

[0050]

[0051] Calculate C m×m The eigenvalue λ i and eigenvalue λ i The corresponding spatial eigenvector EOF m×m , where i = 1, 2, ..., m; and calculate the spatial eigenvector EOF according to formula 2) m×m The corresponding time coefficient PC m×n :

[0052] PC m×n =EOF T m×m ×X m×n2),

[0053] Among them, EOF T m×m EOF m×m The transposed matrix of m EOF m×m That is the m-order sedimentation field; the spatial eigenvector EOF m×m That is, the spatial mode, the time coefficient PC m×n That is, the historical time series;

[0054] Calculate the variance contribution rate of each eigenvalue, and screen out the main settlement features according to the variance contribution rate, thereby eliminating redundant data and simplifying the calculation; the variance contribution rate P i According to formula 3) calculation:

[0055]

[0056] In this embodiment, it is preferred to retain the variance contribution rate greater than 0.001 as the main sedimentation feature. Of course, those skilled in the art can also adjust it according to actual conditions.

[0057] Step S3: Combined with the training set data, the sparrow search algorithm (SSA) is used to optimize the penalty parameters and kernel function parameters of the support vector machine (SVM) prediction model to obtain the optimized support vector machine prediction model.

[0058] Preferably, the step S3 specifically includes:

[0059] Step S3.1: Initialize parameters, including population size, ratio of discoverers to sentinels, maximum number of iterations, and upper and lower limits of optimization parameter targets;

[0060] Step S3.2: Calculate the fitness values ​​of the sparrows, sort them according to the fitness values, select the current best and worst fitness values ​​and their corresponding position information (the position information corresponding to the best fitness value and the position information corresponding to the worst fitness value);

[0061] Step S3.3: Update the location information of the discoverer, joiner and alerter;

[0062] Specifically, the location information of the discoverer is updated according to formula 4), the location information of the joiner is updated according to formula 5), ​​and the location information of the alerter is updated according to formula 6):

[0063]

[0064] In formula 4): X i,jrepresents the position information of the i-th sparrow in the j-th dimension, t is the current iteration number, M is the maximum iteration number, the random number α∈(0,1], the random number Q follows a normal distribution, and L is a 1×d(d=j max ) matrix, warning value R2∈[0,1], safety value ST∈[0.5,1].

[0065]

[0066] In formula 5), ​​X P is the optimal position of the discoverer at present, X w is the current global worst position, A is a 1×d matrix with each element randomly assigned 1 or -1, where A + =A T (AA T ) -1 .

[0067]

[0068] In formula 6): X b is the current global optimal position, β is the step size control parameter (a random number that obeys the standard normal distribution), the random number K∈[-1,1], ε is the minimum constant to avoid the denominator being zero, and f i is the fitness value of the current sparrow individual, f g and f w are the optimal and worst fitness values ​​respectively.

[0069] Step S3.4: updating the position state of the sparrow population, and calculating the fitness value according to the current position state of the sparrow population;

[0070] Step S3.5: If the stopping condition is met, the training set data is used as input and the optimal parameter result is output;

[0071] If the stop condition is not met, return to step S3.2;

[0072] Specifically, in step S3.5, if the optimization parameter target upper and lower limits or the maximum number of iterations are reached, the optimal parameter result is output; if the optimization parameter target upper and lower limits or the maximum number of iterations are not reached, return to step S3.2;

[0073] Step S3.6: Input the obtained optimal parameter results into the support vector machine prediction model to obtain an optimized support vector machine prediction model. Specifically, the optimal parameter results are penalty parameters and kernel function parameters.

[0074] When using the sparrow search algorithm, discoverers, joiners and guards are introduced. Discoverers and joiners can be dynamically converted, but the number ratio of discoverers and joiners remains unchanged. At the same time, the positions of discoverers, joiners and guards are updated respectively according to the formula, and the optimal penalty parameter c and kernel function parameter g in SVM are sought from a global perspective.

[0075] Step S4: The optimized support vector machine prediction model performs prediction based on the test set data (the test set data needs to be processed before prediction, for details, please refer to the prior art) to obtain a predicted time series;

[0076] Step S5: Use the empirical orthogonal function to reconstruct and back-calculate the screened spatial modes and predicted time series to obtain the final surface subsidence prediction results.

[0077] Test case:

[0078] In this experimental case, taking a subway shield tunnel in the eastern coastal area of ​​China as an example, the monitoring values ​​of 15 surface settlement monitoring points around the buildings adjacent to the line were selected to form a settlement space-time matrix. The settlement data for a total of 244 days from January 6, 2020 to September 5, 2020 were used, with a collection frequency of once a day.

[0079] In order to investigate the changing characteristics of regional subsidence, the subsidence data set (i.e., the subsidence spatiotemporal matrix) was subjected to EOF decomposition. The variance contribution rates of the subsidence fields formed by the first six eigenvectors were all greater than 0.001, and their variance contributions were 0.967028, 0.013664, 0.010776, 0.002711, 0.001659, and 0.001147, respectively. The cumulative contribution rate of the first six subsidence fields was as high as 99.7%, which contained the main information of spatial subsidence and had the ability to accurately describe the characteristics of the subsidence field. The first six subsidence fields were selected for subsequent modeling.

[0080] In order to investigate the prediction effect of the SSA-SVM model combined with spatiotemporal characteristics, the single SVM, the SSA-SVM optimized by the sparrow search algorithm, and the EOF-SVM model were used to predict the settlement values ​​of each monitoring point. In order to facilitate the comparison of the prediction effects of each model and monitoring point, the mean absolute error (MAE), root mean square error (RMSE) and determination coefficient (R 2 ), where MAE and RMSE represent the error of the model, R 2 Reflects the accuracy of the model.

[0081] Finally, the settlement changes of each monitoring point are obtained by combining the back calculation and reconstruction of the settlement field and the predicted value of the time coefficient. Taking the prediction results of monitoring points 1 and 2 as an example, Figure 2 and Figure 3By comparison, the evaluation indicators of each monitoring point under the EOF-SSA-SVM model are significantly better than those of other models, followed by the EOF-SVM model. Among the four models, the prediction effect of SVM is the worst. It can be seen that the EOF and SSA processes in the method of this embodiment can effectively improve the accuracy of the surface subsidence prediction model.

[0082] See also Figure 2 and Figure 3 The average absolute error and root mean square error of the EOF-SSA-SVM model are reduced by 89.76% and 86.59% respectively compared with the SVM model, and its determination coefficient is increased by 4.66% at most. It can be seen that the method of this embodiment has high accuracy and reliability in surface subsidence prediction and can effectively predict the trend of surface subsidence.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A surface subsidence prediction method based on EOF-SSA-SVM spatiotemporal model, characterized in that: The following steps are involved: Step S1: The surface settlement time series of each monitoring point is used to form a settlement time-space matrix; Step S2: Decompose the settlement space-time matrix into spatial modes and historical time series using empirical orthogonal functions, and select the main settlement characteristics of surface settlement according to the variance contribution rate; And divide the filtered historical time series into training set and test set; Step S3: combining the training set data, using the sparrow search algorithm to optimize the penalty parameters and kernel function parameters of the support vector machine prediction model to obtain an optimized support vector machine prediction model; Step S4: The optimized support vector machine prediction model performs prediction based on the test set data to obtain a predicted time series; Step S5: Use the empirical orthogonal function to reconstruct and back-calculate the screened spatial modes and predicted time series to obtain the final surface subsidence prediction results; The step S1 specifically includes: setting The settlement monitoring points in each area are The historical time data constitutes the sedimentation space-time matrix ; The step S2 specifically comprises: The space-time matrix will be After anomaly processing, the data matrix is ​​obtained ; Calculate the data matrix The cross product of the matrix and its transposed matrix gives the cross product matrix , as shown in Formula 1): 1）， calculate The eigenvalue of and eigenvalues The corresponding spatial eigenvector ,in ,and ; and calculate the spatial eigenvector according to formula 2) The corresponding time coefficient : 2）， Calculate the variance contribution rate of each eigenvalue, and select the main settlement characteristics according to the variance contribution rate; According to formula 3) calculation: 3）。 2. The surface subsidence prediction method based on the EOF-SSA-SVM spatiotemporal model according to claim 1 is characterized in that: The variance contribution rate greater than 0.001 was retained as the main sedimentation characteristics.

3. The surface subsidence prediction method based on EOF-SSA-SVM spatiotemporal model according to claim 1 is characterized in that: The step S3 specifically includes: Step S3.1: Initialize parameters, including population size, ratio of discoverers to sentinels, maximum number of iterations, and upper and lower limits of optimization parameter targets; Step S3.2: Calculate the fitness values ​​of the sparrows, sort them according to the fitness values, and select the current best and worst fitness values ​​and their corresponding position information; Step S3.3: Update the location information of the discoverer, joiner and alerter; Step S3.4: updating the position state of the sparrow population, and calculating the fitness value according to the current position state of the sparrow population; Step S3.5: If the stopping condition is met, the training set data is used as input and the optimal parameter result is output; If the stop condition is not met, return to step S3.2; Step S3.6: Input the obtained optimal parameter results into the support vector machine prediction model to obtain the optimized support vector machine prediction model.

4. The surface subsidence prediction method based on EOF-SSA-SVM spatiotemporal model according to claim 3 is characterized in that: In step S3.5, if the upper and lower limits of the optimization parameter targets or the maximum number of iterations are reached, the optimal parameter results are output.

5. The surface subsidence prediction method based on EOF-SSA-SVM spatiotemporal model according to claim 3 is characterized in that: The optimal parameter results are penalty parameters and kernel function parameters.

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