CN114325693A - Goaf center deformation prediction method based on InSAR time sequence deformation result - Google Patents
Goaf center deformation prediction method based on InSAR time sequence deformation result Download PDFInfo
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Abstract
The invention discloses a goaf center deformation prediction method based on an InSAR time sequence deformation result, which comprises the following steps: acquiring a time sequence deformation result of an InSAR in the center of the goaf, and dividing a training sample and a prediction sample; determining an embedding dimension and a prediction step length, and establishing a prediction model based on Support Vector machine regression (SVR); training the model by using a Particle Swarm Optimization (PSO) according to training sample data to obtain optimal model parameters; and substituting the optimal parameters into the model, and inputting a prediction sample to obtain a model prediction result. Compared with the conventional method, the algorithm does not need to rely on the prior information of the mining area, and can quickly and accurately provide variable prediction for the center of the goaf.
Description
Technical Field
The invention belongs to the field of prediction of a synthetic aperture radar interferometry time sequence deformation result, and particularly relates to a goaf center deformation prediction method based on an InSAR time sequence deformation result.
Background
Since the end of the 20 th century, the mining order of China is disordered, and a large number of goafs are left in some mines and the periphery of the mines by illegal and disordered disorderly mining and abusing excavation, which is one of the main hazard sources influencing the safety production of the mines at present, poses serious threats to the safety production of mines, and causes environmental deterioration and serious waste of mineral resources. Mapping subsurface earth surface dynamic subsidence is critical to assessing geological hazards associated with mining and understanding the dynamics of mining subsidence. Over the past several decades, the on-board synthetic radar aperture interferometry (InSAR) technique has proven to be an effective remote sensing tool for mapping ground deformations caused by various natural causes or human activity. The application of InSAR technology in mining areas goes from first theoretical analysis to differential interference and then to time-series interference, the surface deformation measurement of InSAR is quite mature theoretically at present, and the application in mining area monitoring is more and more extensive.
However, the application of the InSAR in the mining area still has defects, relatively few researches are made on the aspect of prediction of central deformation of the mined-out area of the InSAR, most of the existing algorithms need a large number of prior parameters, mining area data are usually difficult to obtain, and time and labor are wasted when the mining area data are collected.
Therefore, the method which can quickly and accurately predict the time sequence deformation of the goaf center in the mining area and does not need to rely on the priori parameters of the mining area is provided, and the method is a problem which needs to be solved urgently.
Disclosure of Invention
In order to solve the problem of prediction of the goaf time sequence deformation, the invention provides a goaf center deformation prediction method based on an InSAR time sequence deformation result, which can quickly and reliably predict the goaf center deformation,
the purpose of the invention is realized as follows:
a goaf center deformation prediction method based on an InSAR time sequence deformation result is characterized by comprising the following steps:
acquiring the time sequence deformation of the center of the goaf by using a time sequence InSAR technology;
dividing a training sample and a prediction sample;
determining the embedding dimension and the prediction step length, and establishing an SVR prediction model by an SVR prediction method;
performing parameter optimization on the model by using a PSO algorithm according to the training sample to obtain optimal model parameters;
and step five, substituting the optimal parameters obtained in the step four into an SVR prediction model, inputting a prediction sample, and performing time sequence prediction.
Further, the SVR method in step three is:
assuming the allowable deviation is ω, the linear regression equation of the SVR is:
where C is a regularization constant, lεIs an epsilon insensitive loss function;
introducing relaxation variable xi to the above formulai,
The following can be obtained:
s.t f(xi)-yi≤ε+ξi
the above equation can be converted to a lagrange function by the lagrange multiplier method:
the Lagrange function
For omega, b and xi respectivelyi,
Calculating the partial derivative to make the value of 0, and converting the above formula into a dual problem:
the above process must satisfy the KKT condition (Karush-Kuhn-tuckercondition), in combination with the support vector machine model f (x) ═ ω @Tx + b, the model solution can be found as:
when in use
The sample is a support vector of the SVR;
in general, it is necessary to map the non-linear samples to a high-dimensional feature space, so that the sample model remains a linear regression model in the high-dimensional space, and such a hyperplane can be described as:
in the above equation, φ (x) is a mapping function of x; since the feature space may have a very high dimension, phi (x) is directly calculatedi)Tφ(xj) Often very difficult, so we assume:
κ(xi,xj)＝＜φ(xi),φ(xj)＞＝φ(xi)Tφ(xj)
this yields the SVR equation:
the complexity and generalization of the SVR model depend on the selection of three model parameters, namely a penalty factor, a kernel function and an insensitive loss function; the blind loss function and the penalty factor respectively determine whether the model is over-fitted or not, and the accuracy and the generalization capability of the model;
the PSO parameter optimization method in step four further includes:
firstly, generating an initial particle swarm, randomly searching and sharing respective information by each particle, identifying the particle closest to the optimal solution by using a fitness function, then, iteratively updating the position and the direction of the particle swarm according to the local optimal value and the global optimal value until the optimal solution is obtained, wherein the speed and position updating formula is as follows:
in the formula, n is the total number of particles, k is the kth iteration, and omega is an inertia factor, and the magnitude of the inertia factor determines the strength of the global optimization capability of the model;
is the velocity of the particle iteration, c1,c2Are an individual learning factor and a group learning factor, r1,r2Is a random number between 0 and 1,
gbestkrespectively an individual optimal value and a global optimal value in an iterative process; the new speed of the particles is determined by the speed of the particles at the previous moment, the current position, the distance between the particles and the optimal position of the group, and the next motion speed vector is calculated by the formula;
in the formula (I), the compound is shown in the specification,
is the position of the particle i at the kth iteration;
and calculating a new position of the particle by the formula until a final loop termination condition is reached, and finishing the iterative process.
Has the positive and beneficial effects that: the invention discloses a goaf center deformation prediction method based on an InSAR time sequence deformation result, which has the advantages of two aspects: on one hand, rapid and reliable deformation prediction can be carried out according to the InSAR time sequence deformation value of the center of the goaf of the mining area; on the other hand, the prior parameters of the mining area are not needed to be relied on, and manpower and material resources are saved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The present invention is further illustrated by the following detailed description of the invention, taken in conjunction with the accompanying drawings and the detailed description of the invention, it is to be understood that these examples are given solely for purposes of illustration and are not intended to limit the scope of the invention, which is defined by the claims appended hereto as modified by those skilled in the art upon reading the present disclosure in their various equivalent forms.
Examples
As shown in fig. 1, the method flow further clarifies the present invention by using "prediction of central deformation of gob in a certain mining area based on InSAR time series deformation" as an application example:
step one, acquiring an InSAR time sequence deformation result. The experiment adopts 61 scene rise orbit Sentine-1A data, the polarization mode is VV, the imaging mode is IW imaging mode, and the data coverage time is from 12 months 04 days in 2017 to 12 months 18 days in 2019. Solving an accumulated deformation graph from 12 months and 04 days in 2017 to 12 months and 18 days in 2019 of a goaf of a certain mine area by using a coherent point target analysis method (IPTA) and a small baseline set technology (SBAS), and selecting 6 goaf center sample points, wherein the time sequence deformation is as follows (unit: mm):
and step two, dividing the training sample and the prediction sample. Dividing the data in the first 44 stages into a training set and the data in the last 17 stages into a test set according to the proportion of the training set to the test set 7: 3;
and step three, determining the embedding dimension and the prediction step length, and establishing an SVR prediction model. Setting the embedding dimension as 3 and the prediction step length as 1, and further establishing an SVR prediction model;
and step four, selecting the optimal model parameters by using a PSO algorithm. Taking the data in the first 44 stages as training samples to be brought into the SVR model, and solving the parameters of the SVR optimal model;
and step five, inputting a prediction sample to perform time sequence prediction. And (4) substituting the data in the later 17 stages into the trained SVR model by using the optimal model parameters obtained in the third step, and performing time sequence prediction to obtain InSAR time sequence deformation predicted values of the central sample points of the 6 goafs.
And (4) checking the prediction result by using two factors of the root mean square error and the decision coefficient.
Root Mean Square Error (RMSE)
In the formula, yjDenotes the predicted value, y'jThe sample values are verified.
Determining the coefficient (R)2)
In the formula, a numerator represents the sum of squares of residual errors and represents the error magnitude of a predicted value, and a denominator is the sum of the total squares and represents the dispersion of a sample. The coefficient of determination is between 0 and 1, and the closer to 1, the more accurate the prediction.
The accuracy of the prediction is as follows:
| point number | Training sample RMSE/mm | Test specimen RMSE/mm | Training sample R2 | Test specimen R2 |
| 1 | 4 | 6 | 0.99 | 0.91 |
| 2 | 6 | 7 | 0.97 | 0.84 |
| 3 | 9 | 7 | 0.94 | 0.49 |
| 4 | 7 | 8 | 0.95 | 0.77 |
| 5 | 4 | 12 | 0.94 | 0.94 |
| 6 | 4 | 11 | 0.98 | 0.93 |
R of prediction results of 6 sample points in the center of goaf2All are greater than 0.4, minimum 0.49, RMSE maximum 11 mm. From the results, the algorithm can quickly provide accurate deformation prediction for the goaf center.
The invention has two advantages: on one hand, rapid and reliable deformation prediction can be carried out according to the InSAR time sequence deformation value of the center of the goaf of the mining area; on the other hand, the prior parameters of the mining area are not needed to be relied on, and manpower and material resources are saved.
Claims (3)
1. A goaf center deformation prediction method based on an InSAR time sequence deformation result is characterized by comprising the following steps:
step one, obtaining by utilizing a time sequence InSAR technology: taking out the time sequence deformation of the center of the goaf;
dividing a training sample and a prediction sample;
determining the embedding dimension and the prediction step length, and establishing an SVR prediction model by an SVR prediction method;
performing parameter optimization on the model by using a PSO algorithm according to the training sample to obtain optimal model parameters;
and step five, substituting the optimal parameters obtained in the step four into an SVR prediction model, inputting a prediction sample, and performing time sequence prediction to obtain a target point InSAR time sequence deformation prediction value.
2. The method for predicting the central deformation of the gob based on the InSAR time series deformation result as claimed in claim 1, wherein the SVR prediction method in the third step is as follows:
assuming the allowable deviation is ω, the linear regression equation of the SVR is:
where C is a regularization constant, lεIs an epsilon insensitive loss function;
introducing relaxation variable xi to the above formulai, 
The following can be obtained:
s.t f(xi)-yi≤ε+ξi
the above equation can be converted to a lagrange function by the lagrange multiplier method:
the Lagrange function
For omega, b and xi respectivelyi,
The partial derivative is calculated, the value is 0, and then the above formula is converted into a dual problem:
0≤αi,
the above process must satisfy the KKT condition (Karush-Kuhn-tuckercondition), in combination with the support vector machine model f (x) ═ ω @Tx + b, the model solution can be found as:
when in use
The sample is a support vector of the SVR;
in general, it is necessary to map the non-linear samples to a high-dimensional feature space, so that the sample model remains a linear regression model in the high-dimensional space, and such a hyperplane can be described as:
in the above equation, φ (x) is a mapping function of x; since the feature space may have a very high dimension, phi (x) is directly calculatedi)Tφ(xj) Often very difficult, so we assume:
κ(xi,xj)＝＜φ(xi),φ(xj)＞＝φ(xi)Tφ(xj)
this yields the SVR equation:
the complexity and generalization of the SVR model depend on the selection of three model parameters, namely a penalty factor, a kernel function and an insensitive loss function; the unknown loss function and the penalty factor respectively determine whether the model is over-fitted or not, and the accuracy and the generalization capability of the model.
3. The method for predicting the central deformation of the goaf based on the InSAR time series deformation result as claimed in claim 1, wherein the PSO optimization method in step four is as follows:
firstly, generating an initial particle swarm, randomly searching and sharing respective information by each particle, identifying the particle closest to the optimal solution by using a fitness function, then, iteratively updating the position and the direction of the particle swarm according to the local optimal value and the global optimal value until the optimal solution is obtained, wherein the speed and position updating formula is as follows:
in the formula, n is the total number of particles, k is the kth iteration, and omega is an inertia factor, and the magnitude of the inertia factor determines the strength of the global optimization capability of the model;
is the velocity of the particle iteration, c1,c2Are an individual learning factor and a group learning factor, r1,r2Is a random number between 0 and 1, pbestk i,gbestkRespectively an individual optimal value and a global optimal value in an iterative process; the new speed of the particles is determined by the speed of the particles at the previous moment, the current position, the distance between the particles and the optimal position of the group, and the next motion speed vector is calculated by the formula;
in the formula (I), the compound is shown in the specification,
is the position of the particle i at the kth iteration;
and calculating a new position of the particle by the formula until a final loop termination condition is reached, and finishing the iterative process.
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