CN114442094A - Surface deformation prediction method and system - Google Patents

Surface deformation prediction method and system Download PDF

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CN114442094A
CN114442094A CN202210126050.9A CN202210126050A CN114442094A CN 114442094 A CN114442094 A CN 114442094A CN 202210126050 A CN202210126050 A CN 202210126050A CN 114442094 A CN114442094 A CN 114442094A
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surface deformation
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deformation prediction
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程洋
王永
杨妍妨
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Institute of Karst Geology of CAGS
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    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9021SAR image post-processing techniques

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Abstract

The invention discloses a surface deformation prediction method and system based on InSAR technology and behavior characteristic deep learning, which are applied to the technical field of surface deformation monitoring of the InSAR technology, image data are obtained, a surface time sequence deformation prediction method based on the combination of the InSAR technology and a 3D-CNN network is combined with noise reduction processing, a prediction model is obtained, and surface deformation prediction is carried out. According to the method, the earth surface settlement is monitored in a large range and high precision through the InSAR technology, the economic investment of earth surface time sequence settlement monitoring can be effectively reduced, the 3D-CNN network is utilized to learn earth surface time sequence deformation characteristics, the future earth surface deformation trend is predicted, and auxiliary decision and technical support are provided for preventing earth surface settlement disasters; and after the null value and the abnormal value are removed, the image is subjected to statistical analysis operation without selecting the estimation deviation of the stable region on the regional scale, so that the strip noise can be globally and automatically corrected, and the useful information of the landslide deformation detection result can be retained to the greatest extent.

Description

Surface deformation prediction method and system
Technical Field
The invention relates to the technical field of surface deformation monitoring of InSAR technology, in particular to a surface deformation prediction method and system.
Background
The excessive exploitation of mineral resources easily damages underground geological structures of mining areas, causes accidents such as surface subsidence, landslide, collapse, debris flow, ground cracks, ground subsidence and surface water accumulation, even causes water permeation accidents of mining areas, and causes serious potential safety hazards and even casualties. Through long-term, dynamic settlement monitoring to the mining area, subside the law to the mining area and analyze, can in time master the destruction degree of mining area geological environment to corresponding emergency treatment scheme is formulated to actual conditions. Therefore, in the face of the problem of ground subsidence, there is an urgent need to monitor, analyze and predict the spatio-temporal changes in ground subsidence. Under the influence of shooting postures of the satellite sensor and the like, overall systematic deviation of deformation detection results often occurs in local areas, and strip noise appears in detection results in the whole image results, so that the precision and the efficiency of landslide deformation detection are directly influenced, and the application of the deformation detection technology in a large-range area is limited. In order to eliminate deformation detection deviation in local areas, previous researches are mostly carried out in non-landslide areas, stable areas are manually selected to evaluate the system deviation, and the strategy is difficult to be used for deviation elimination in large areas.
In recent years, Synthetic Aperture Radar (InSAR) technology is widely used for ground settlement monitoring. Compared with the defects of local single-point measurement, low spatial resolution, high cost and the like of the traditional geodetic measurement technology (GPS and level), the permanent Scatterer synthetic aperture radar technology (PS-InSAR) can realize observation with large range, high precision, high density and low cost. But there is no mature solution for the prediction of surface deformation.
Therefore, it is an urgent need for those skilled in the art to provide a method and system for predicting surface deformation to solve the problems of the prior art.
Disclosure of Invention
In view of the above, the invention provides a method and a system for predicting surface deformation, which are used for establishing a wind power prediction model for an actual wind power plant and realizing high-accuracy prediction of output power of the wind power plant according to the requirements of medium-short term prediction.
In order to achieve the purpose, the invention adopts the following technical scheme:
the earth surface deformation prediction method based on InSAR technology and behavior feature deep learning comprises the following steps:
s101: acquiring a synthetic aperture radar image of a target area and pixels of the synthetic aperture radar image of the target area;
s102: performing complex operation on the pixels to obtain an interference pattern of the target area, and performing noise reduction processing on the interference pattern to obtain an interference pattern with stripe noise removed;
s103: extracting a local deformation range from the interference image without the strip noise, and cutting all the interference images without the strip noise according to the local deformation range;
s104: processing the clipped interference image with the stripe noise removed by using a time series synthetic aperture radar interference measurement technology to obtain a local deformation time sequence result;
s105: forming a local deformation behavior matrix sequence by the local deformation time sequence result according to the geographical position, and dividing the local behavior matrix sequence into a training data set and a test data set;
s106: constructing a ground surface deformation prediction model based on behavior feature deep learning, inputting a quasi-training data set for training, and obtaining the trained ground surface deformation prediction model based on behavior feature deep learning;
s107: and inputting a test data set to the trained earth surface deformation prediction model based on the behavior characteristic deep learning, and outputting the earth surface deformation prediction value of each geographic position of the test data set.
Optionally, the obtaining the interferogram of the target region by performing complex operation on the pixels in step S102 includes: and acquiring the phase difference of the synthetic aperture radar image of the target area through the pixels, and performing gray scale calculation on the phase difference to acquire the interferogram.
Optionally, the performing noise reduction processing on the interferogram in step S102 to obtain an interferogram with stripe noise removed includes: and automatically correcting the stripe noise of the interference pattern by utilizing a noise removal method of column-by-column statistical analysis and correction to obtain the interference pattern with the stripe noise removed.
Optionally, the earth surface deformation prediction model based on the behavior feature deep learning in S106 includes a 3D-CNN network training step and a training end determination step;
the 3D-CNN network training step comprises: inputting the quasi-training data set, outputting a predicted value of the surface deformation of each geographic position of the sample matrix sequence, carrying out error analysis through a loss function according to the output predicted value and an actual value, and changing each weight value of the model;
the training end determination step: judging whether the error analysis reaches a preset threshold value, if not, returning to the step of selecting a simulated training data set; if so, ending the 3D-CNN network training step and outputting a surface deformation prediction model based on behavior feature deep learning.
Optionally, the 3D-CNN network is: the first layer is a convolutional layer C1, the second layer is a pooling layer P2, the third layer is a convolutional layer C3, and the fourth layer is a full-link layer F4.
Optionally, the synthetic aperture radar image of the target area obtained in S101 is a historical earth surface deformation image of the target area.
Optionally, in S105, the first 80% of the local behavior matrix sequence is the training data set, and the last 20% of the local behavior matrix sequence is the test data set.
The earth surface deformation prediction system based on InSAR technology and behavior feature deep learning comprises: the system comprises a data acquisition module, a preprocessing module, a cutting module time sequence processing module, a matrix construction and data division module, a 3D-CNN network training module and a behavior characteristic-based deep learning earth surface deformation prediction module;
the data acquisition module is connected with the input end of the preprocessing module and used for acquiring a synthetic aperture radar image of a target area and pixels of the synthetic aperture radar image of the target area;
the preprocessing module is connected with the input end of the cutting module and is used for carrying out complex operation on the pixels to obtain an interference pattern of the target area and carrying out noise reduction processing on the interference pattern to obtain an interference pattern with stripe noise removed;
the cutting module is connected with the input end of the time sequence processing module and is used for extracting the range of local deformation from the interference image without the strip noise and cutting all the interference images without the strip noise according to the range of the local deformation;
the time sequence processing module is connected with the input end of the matrix construction and data division module and is used for processing the cut interference pattern with the stripe noise removed by utilizing a time sequence synthetic aperture radar interferometry technology to obtain a local deformation time sequence result;
the 3D-CNN network training module is connected with the first output end of the matrix construction and data division module and used for inputting the data set to be trained, outputting a predicted value of the surface deformation of each geographic position of the sample matrix sequence, performing error analysis through a loss function according to the output predicted value and the output actual value, and changing each weight value of the model; judging whether the error analysis reaches a preset threshold value, if not, returning to the step of selecting a simulated training data set; if yes, ending the 3D-CNN network training step, and outputting a surface deformation prediction model based on behavior feature deep learning;
the output end of the 3D-CNN network training module and the output end of the matrix construction and data division module are connected with the input end of the earth surface deformation prediction module based on behavior characteristic deep learning, and are used for inputting the test data set to the trained earth surface deformation prediction model based on behavior characteristic deep learning and outputting earth surface deformation prediction values of all geographic positions of the test data set.
Optionally, the system further comprises a ground surface deformation prediction value output module connected to the output end of the behavior characteristic based deep learning ground surface deformation prediction module, and the ground surface deformation prediction value output module is used for outputting the obtained ground surface deformation prediction value.
Compared with the prior art, the technical scheme provided by the invention has the advantages that the method and the system for predicting the surface deformation are as follows: the earth surface time sequence deformation prediction method combining the InSAR technology and the 3D-CNN network monitors earth surface settlement in a large range and at high precision through the InSAR technology, can effectively reduce the economic investment of monitoring the earth surface time sequence settlement, learns the earth surface time sequence deformation characteristics by using the 3D-CNN network, predicts the future earth surface deformation trend, and provides auxiliary decision and technical support for preventing earth surface settlement disasters; the noise reduction processing method is adopted, stable region estimation deviation is not required to be selected on the regional scale, after null values and abnormal values are eliminated, statistical analysis operation is carried out on the image, strip noise can be globally and automatically corrected, and useful information of a landslide deformation detection result can be retained to the greatest extent.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flowchart of a surface deformation prediction method based on InSAR technology and behavior feature deep learning according to the present invention;
FIG. 2 is a flow chart of the construction of a surface deformation prediction model based on behavior feature deep learning according to the present invention;
fig. 3 is a structural block diagram of a surface deformation prediction system based on the InSAR technology and the behavior feature deep learning provided by the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, the invention discloses a surface deformation prediction method based on InSAR technology and behavior feature deep learning, which comprises the following steps:
s101: acquiring a synthetic aperture radar image of a target area and pixels of the synthetic aperture radar image of the target area;
s102: carrying out complex operation on the pixels to obtain an interference pattern of a target area, and carrying out noise reduction processing on the interference pattern to obtain an interference pattern with stripe noise removed;
s103: extracting a local deformation range from the interference image without the stripe noise, and cutting all the interference images without the stripe noise according to the local deformation range;
s104: processing the cut interference pattern with the stripe noise removed by using a time series synthetic aperture radar interference measurement technology to obtain a local deformation time sequence result;
s105: forming a local deformation behavior matrix sequence by the local deformation time sequence result according to the geographic position, and dividing the local behavior matrix sequence into a training data set and a test data set;
s106: constructing a ground surface deformation prediction model based on behavior feature deep learning, inputting a quasi-training data set for training, and obtaining the trained ground surface deformation prediction model based on behavior feature deep learning;
s107: and inputting a test data set to a trained earth surface deformation prediction model based on behavior characteristic deep learning, and outputting earth surface deformation prediction values of all geographic positions of the test data set.
Further, the step S102 of performing complex operation on the pixels to obtain the interferogram of the target area includes: and acquiring the phase difference of the synthetic aperture radar image of the target area through the pixels, and performing gray scale calculation on the phase difference to acquire an interference pattern.
Further, the step S102 of performing noise reduction processing on the interferogram to obtain an interferogram with stripe noise removed includes: and automatically correcting the stripe noise of the interference pattern by utilizing a noise removal method of column-by-column statistical analysis and correction to obtain the interference pattern with the stripe noise removed.
Further, step 1: selecting a plurality of interference pattern pairs Image before and after the detection time pointpair(ii) a Using deformation detection method based on interferogram ImagepairPerforming preliminary deformation detection calculation to obtain a preliminary deformation detection result Image of the detection area1Image (Image)1Including deformation direction vectors in east-west direction and south-north direction, and signal-to-noise ratio, wherein the deformation direction vector in east-west direction is represented by EW, and the deformation direction vector in south-north directionThe deformation direction vector is expressed by NS, and the signal-to-noise ratio is expressed by SNR;
step 2: removing Image based on cloud mask data of optical remote sensing Image1Obtaining the Image by the deformation detection result of the Image element of the middle cloud coverage area2
And step 3: acquiring Image2Rotating the Image to make the Image strip vertically intersect with the horizontal direction and obtaining the rotated Imagerotate1
And 4, step 4: image after rotationrotate1The EW and NS direction vector images in the image are preprocessed, pixels with the value of 0 are removed, the pixels are assigned to be null values, then EW and NS image pixel values corresponding to the pixel position with the signal-to-noise ratio value of less than 0.9 in the SNR image are assigned to be null values respectively, and preprocessed deformation detection result image Imagerotate2 is obtained;
and 5: for Imagerotate2The EW and NS direction vector images are respectively subjected to column-by-column statistical analysis and correction, and the specific calculation method is as follows: 1) acquiring a standard deviation stdcol and an average value Meancol column by column, 2) counting that the pixel value in each column is greater than Meancol-stdcol and less than the average value Meancol in the range of Meancol + stdcol, and 3) subtracting the mean value from the value of each pixel in the column; after the line-by-line statistical analysis and correction, the Image is obtainedrotate3
Step 6: the EW and NS direction vectors of the Image Imagerotate3 and the SNR Image are rotated according to the reverse direction-alpha angle to obtain the Image3Wherein, the EW and NS direction vector images are both subjected to stripe noise removal;
and 7: image-based Image3Vector synthesis is carried out on the EW and NS direction vector images to obtain Image4Thus, an interferogram from which the stripe noise is removed is obtained.
Further, referring to fig. 2, the earth surface deformation prediction model based on behavior feature deep learning in S106 includes a 3D-CNN network training step and a training end determination step;
3D-CNN network training step: inputting a quasi-training data set, outputting a predicted value of the surface deformation of each geographic position of the sample matrix sequence, carrying out error analysis through a loss function according to the output predicted value and an actual value, and changing each weight value of the model;
a training end judging step: judging whether the error analysis reaches a preset threshold value, if not, returning to the step of selecting the quasi-training data set; if yes, ending the 3D-CNN network training step, and outputting a surface deformation prediction model based on behavior feature deep learning.
Further, the 3D-CNN network is: the first layer is a convolutional layer C1, the second layer is a pooling layer P2, the third layer is a convolutional layer C3, and the fourth layer is a full-link layer F4.
Further, the length L of the history sequence is 10, and the CNN at the bottom adopts a 5-layer structure: the bottom layer is convolution layer C1, which directly faces the input wind power behavior matrix and adopts 2 convolution kernels of 2 x 3; the second layer is set as a pooling layer P2, the sampling pool size is set to 2 x 1 using max-pooling strategy; the third layer is convolutional layer C3, using 64 convolution kernels of 2 x 2; the fourth layer is a fully connected layer F4, which reconstructs the three-dimensional feature map output by C4 into a one-dimensional vector, whose dimension is set to 128. The RelU function is adopted as the convolutional layer activation function, SoftMax is adopted as the full connection layer activation function, and the initial learning rate is set to be 0.01.
Further, in S101, the synthetic aperture radar image of the target area is acquired as a historical earth surface deformation image of the target area.
Further, in S105, the first 80% of the local behavior matrix sequence is the training data set, and the last 20% of the local behavior matrix sequence is the testing data set.
Referring to fig. 3, the invention discloses an earth surface deformation prediction system based on InSAR technology and behavior feature deep learning, which comprises: the system comprises a data acquisition module, a preprocessing module, a cutting module time sequence processing module, a matrix construction and data division module, a 3D-CNN network training module and a behavior characteristic-based deep learning earth surface deformation prediction module;
the data acquisition module is connected with the input end of the preprocessing module and used for acquiring the synthetic aperture radar image of the target area and the pixels of the synthetic aperture radar image of the target area;
the preprocessing module is connected with the input end of the cutting module and used for carrying out complex operation on pixels to obtain an interference pattern of a target area and carrying out noise reduction processing on the interference pattern to obtain an interference pattern with stripe noise removed;
the cutting module is connected with the input end of the time sequence processing module and used for extracting the range of local deformation from the interference image without the stripe noise and cutting the interference image without the stripe noise according to the range of the local deformation;
the time sequence processing module is connected with the input end of the matrix construction and data division module and is used for processing the cut interference image without the strip noise by utilizing a time sequence synthetic aperture radar interferometry technology to obtain a local deformation time sequence result;
the 3D-CNN network training module is connected with the first output end of the matrix construction and data division module and used for inputting a training data set to be trained, outputting a predicted value of the surface deformation of each geographic position of the sample matrix sequence, performing error analysis through a loss function according to the output predicted value and an actual value, and changing each weight value of the model; judging whether the error analysis reaches a preset threshold value, if not, returning to the step of selecting the quasi-training data set; if so, finishing the 3D-CNN network training step, and outputting a ground surface deformation prediction model based on behavior feature deep learning;
the output end of the 3D-CNN network training module and the output end of the matrix construction and data division module are connected with the input end of the behavior characteristic deep learning-based earth surface deformation prediction module, and are used for inputting a test data set to a trained earth surface deformation prediction model based on behavior characteristic deep learning and outputting earth surface deformation prediction values of all geographic positions of the test data set.
And the earth surface deformation prediction value output module is connected with the output end of the earth surface deformation prediction module based on the behavior characteristic deep learning and is used for outputting the obtained earth surface deformation prediction value.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention in a progressive manner. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (9)

1. The earth surface deformation prediction method based on InSAR technology and behavior feature deep learning is characterized by comprising the following steps:
s101: acquiring a synthetic aperture radar image of a target area and pixels of the synthetic aperture radar image of the target area;
s102: performing complex operation on the pixels to obtain an interference pattern of the target area, and performing noise reduction processing on the interference pattern to obtain an interference pattern with stripe noise removed;
s103: extracting a local deformation range from the interference image without the strip noise, and cutting all the interference images without the strip noise according to the local deformation range;
s104: processing the clipped interference image with the stripe noise removed by using a time series synthetic aperture radar interference measurement technology to obtain a local deformation time sequence result;
s105: forming a local deformation behavior matrix sequence by the local deformation time sequence result according to the geographical position, and dividing the local behavior matrix sequence into a training data set and a test data set;
s106: constructing a ground surface deformation prediction model based on behavior feature deep learning, inputting the quasi-training data set for training, and obtaining the trained ground surface deformation prediction model based on behavior feature deep learning;
s107: and inputting the test data set to the trained earth surface deformation prediction model based on behavior characteristic deep learning, and outputting earth surface deformation prediction values of all geographic positions of the test data set.
2. The earth's surface deformation prediction method based on InSAR technology and behavior feature deep learning of claim 1,
the step S102 of performing complex operation on the pixels to obtain the interferogram of the target region includes: and acquiring the phase difference of the synthetic aperture radar image of the target area through the pixels, and performing gray scale calculation on the phase difference to acquire the interferogram.
3. The method of claim 1 for predicting surface deformation based on InSAR technology and deep learning of behavior features,
in step S102, performing noise reduction processing on the interferogram to obtain an interferogram with stripe noise removed includes: and automatically correcting the stripe noise of the interference pattern by utilizing a noise removal method of column-by-column statistical analysis and correction to obtain the interference pattern with the stripe noise removed.
4. The earth's surface deformation prediction method based on InSAR technology and behavior feature deep learning of claim 1,
the earth surface deformation prediction model based on the behavior feature deep learning in the S106 comprises a 3D-CNN network training step and a training end judging step;
the 3D-CNN network training step comprises: inputting the quasi-training data set, outputting a predicted value of the surface deformation of each geographic position of the sample matrix sequence, carrying out error analysis through a loss function according to the output predicted value and an actual value, and changing each weight value of the model;
the training end judging step: judging whether the error analysis reaches a preset threshold value, if not, returning to the step of selecting a simulated training data set; if so, ending the 3D-CNN network training step and outputting a surface deformation prediction model based on behavior feature deep learning.
5. The earth's surface deformation prediction method based on InSAR technology and behavior feature deep learning of claim 4,
the 3D-CNN network is as follows: the first layer is a convolutional layer C1, the second layer is a pooling layer P2, the third layer is a convolutional layer C3, and the fourth layer is a full-link layer F4.
6. The earth's surface deformation prediction method based on InSAR technology and behavior feature deep learning of claim 1,
and in the step S101, the synthetic aperture radar image of the target area is obtained as a historical earth surface deformation image of the target area.
7. The earth surface deformation prediction method based on InSAR technology and behavior feature deep learning according to any one of claims 1-6,
in S105, the first 80% of the local behavior matrix sequence is the training data set, and the last 20% of the local behavior matrix sequence is the test data set.
8. The earth's surface deformation prediction system based on InSAR technique and behavior feature deep learning is characterized by comprising: the system comprises a data acquisition module, a preprocessing module, a cutting module time sequence processing module, a matrix construction and data division module, a 3D-CNN network training module and a behavior characteristic-based deep learning earth surface deformation prediction module;
the data acquisition module is connected with the input end of the preprocessing module and used for acquiring a synthetic aperture radar image of a target area and pixels of the synthetic aperture radar image of the target area;
the preprocessing module is connected with the input end of the cutting module and is used for carrying out complex operation on the pixels to obtain an interference pattern of the target area and carrying out noise reduction processing on the interference pattern to obtain an interference pattern with stripe noise removed;
the cutting module is connected with the input end of the time sequence processing module and is used for extracting the range of local deformation from the interference image without the strip noise and cutting all the interference images without the strip noise according to the range of the local deformation;
the time sequence processing module is connected with the input end of the matrix construction and data division module and is used for processing the cut interference pattern with the stripe noise removed by utilizing a time sequence synthetic aperture radar interferometry technology to obtain a local deformation time sequence result;
the 3D-CNN network training module is connected with the first output end of the matrix construction and data division module and used for inputting the data set to be trained, outputting a predicted value of the surface deformation of each geographic position of the sample matrix sequence, performing error analysis through a loss function according to the output predicted value and the output actual value, and changing each weight value of the model; judging whether the error analysis reaches a preset threshold value, if not, returning to the step of selecting a simulated training data set; if so, ending the 3D-CNN network training step, and outputting a ground surface deformation prediction model based on behavior feature deep learning;
the output end of the 3D-CNN network training module and the output end of the matrix construction and data division module are connected with the input end of the earth surface deformation prediction module based on behavior characteristic deep learning, and are used for inputting the test data set to the trained earth surface deformation prediction model based on behavior characteristic deep learning and outputting earth surface deformation prediction values of all geographic positions of the test data set.
9. The InSAR technology and behavior feature deep learning based surface deformation prediction system of claim 8,
the earth surface deformation prediction value output module is connected with the output end of the earth surface deformation prediction module based on behavior characteristic deep learning and is used for outputting the obtained earth surface deformation prediction value.
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CN114859351A (en) * 2022-06-10 2022-08-05 重庆地质矿产研究院 Method for detecting surface deformation field abnormity based on neural network
CN116168304A (en) * 2023-02-02 2023-05-26 昆明理工大学 Surface deformation classification method, device and storage medium based on SAE and CNN models
CN117368920A (en) * 2023-12-06 2024-01-09 山东三矿地质勘查有限公司 D-insar-based coal mining area subsidence monitoring method and system
CN117368920B (en) * 2023-12-06 2024-02-27 山东三矿地质勘查有限公司 D-insar-based coal mining area subsidence monitoring method and system

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