Method and device for estimating sequential deformation from horizontal coal seam to inclined coal seam based on Gaussian mixture

Abstract

The invention relates to the technical field of horizontal-to-inclined coal seam earth surface time sequence deformation, and provides a horizontal-to-inclined coal seam time sequence deformation estimation method and device based on Gaussian mixture, and the method comprises the steps: obtaining SAR images of a target coal seam region at N moments; obtaining a plurality of interferograms based on all the SAR images, and unwrapping all the interferograms to obtain an initial unwrapping phase; constructing a target Gaussian mixture model of the target coal seam area; optimizing the initial unwrapping phase according to the target Gaussian mixture model to obtain an optimized unwrapping phase; and constructing a mining area time sequence deformation model of the target coal seam area based on the optimized unwrapping phase, and resolving the mining area time sequence deformation model to obtain a time sequence deformation estimation result of the target coal seam area. According to the method, the estimation precision of the earth surface time sequence deformation result caused by horizontal to inclined coal seam mining can be improved.

Description

Technical Field

[0001] This application relates to the technical field of sequential deformation of coal seams, and particularly relates to a method and device for estimating sequential deformation of horizontal to inclined coal seams based on a mixture of Gaussians. Background Technique

[0002] Interferometric synthetic aperture radar (InSAR) technology is a satellite earth observation technology developed in recent years. By interpreting the phase difference from the satellite to the target, minute surface deformations can be obtained, which has the advantages of high efficiency, wide coverage area, and low cost. The sequential surface deformation caused by mining in mining areas has always been a problem worthy of attention, which may trigger disasters such as surface cracks, house collapses, and facility damage. Sequential deformation monitoring can effectively prevent the possibility of potential disasters in mining areas. However, mining activities in inclined coal seams are prone to cause asymmetric and irregular surface deformations, and it is difficult for traditional regular models to fit the position and scale of the deformation at the subsidence center. In order to accurately obtain the sequential surface deformation in mining areas, a general model needs to be established that can fit coal seam mining from horizontal to inclined, and continuously iteratively invert until the deformation at the surface subsidence center in the mining area is obtained.

[0003] Currently, most studies focus on monitoring the deformations caused by horizontal or nearly horizontal coal seam mining. The spatial shape of surface deformations usually follows a circle or an ellipse, and symmetric models such as the probability integral method model, the stochastic medium model, and the two-dimensional Gaussian model can be used for fitting. As the coal seam dip angle increases, when the coal seam dip angle is greater than 8°, the surface deformation no longer shows a symmetric circle or ellipse, but an asymmetric ellipse. At this time, using a symmetric model for modeling will introduce model errors, which will instead reduce the accuracy of surface deformation estimation in mining areas, and there are few studies on the deformation estimation of inclined coal seam mining. Thus, there is currently a problem of low accuracy in the deformation estimation of inclined coal seam mining. Summary of the Invention

[0004] This application provides a method and device for estimating sequential deformation of horizontal to inclined coal seams based on a mixture of Gaussians, which can solve the problem of low accuracy in deformation estimation caused by inclined coal seam mining.

[0005] In a first aspect, an embodiment of this application provides a method for estimating sequential deformation of horizontal to inclined coal seams based on a mixture of Gaussians. The method for estimating sequential deformation of horizontal to inclined coal seams includes: Obtain SAR images of the target coal seam area at N moments; the Nth moment is the current moment; Based on all SAR images, obtain multiple interferograms and unwrap all interferograms to obtain an initial unwrapped phase; Construct a target Gaussian mixture model for the target coal seam area; the target Gaussian mixture model is used to describe the deformation phase of the target coal seam area in the two-dimensional plane. Optimize the initial unwrapped phase according to the target Gaussian mixture model to obtain the optimized unwrapped phase. Construct a time-series deformation model for the mining area of the target coal seam area based on the optimized unwrapped phase, and solve the time-series deformation model for the mining area to obtain the time-series deformation estimation result of the target coal seam area; the time-series deformation model for the mining area is used to describe the relationship between the optimized unwrapped phase and the LOS-direction deformation displacement of the target coal seam area, and the time-series deformation estimation result is used to describe the LOS-direction deformation displacement of the target coal seam area under the time span of all SAR images.

[0006] Optionally, constructing a target Gaussian mixture model for the target coal seam area includes: Construct a two-dimensional rectangular coordinate system based on the target coal seam area. In the two-dimensional rectangular coordinate system, if the target coal seam area is stretched or compressed in the horizontal coordinate direction, use the first Gaussian mixture model as the target Gaussian mixture model; if the target coal seam area is stretched or compressed in the vertical coordinate direction, use the second Gaussian mixture model as the target Gaussian mixture model; if the target coal seam area is stretched or compressed in both the horizontal coordinate direction and the vertical coordinate direction, use the two-dimensional Gaussian mixture model as the target Gaussian mixture model.

[0007] Optionally, the first Gaussian mixture model is: ; Where represents the model phase that is stretched or compressed in the horizontal coordinate direction, represents the horizontal coordinate of the area in the target coal seam area in the two-dimensional rectangular coordinate system, represents the vertical coordinate of the area in the target coal seam area in the two-dimensional rectangular coordinate system, represents the parameter vector, , represents the compression or stretching parameter in the horizontal axis direction, represents the compression or stretching parameter in the vertical axis direction, represents the amplitude, represents the horizontal coordinate of the center point, represents the vertical coordinate of the center point, , , all represent intermediate parameters, represents the clockwise rotation angle, represents the standard deviation in the horizontal axis direction, represents the standard deviation in the vertical axis direction, represents the exponential function, represents the cosine function. represents the sine function, represents the transpose operation.

[0008] Optionally, the second Gaussian mixture model is: ; ; ; ; where, represents the model phase that is stretched or compressed in the vertical direction.

[0009] Optionally, the two-dimensional Gaussian mixture model is: ; where, represents the model phase that is stretched or compressed in both two-dimensional directions.

[0010] Optionally, the initial unwrapped phase is optimized according to the target Gaussian mixture model to obtain the optimized unwrapped phase, including: Inverting the target Gaussian mixture model using the nonlinear least squares method to obtain the model parameters of the target Gaussian mixture model; Substituting the model parameters into the target Gaussian mixture model, and using the model phase in the updated target Gaussian mixture model as the updated model phase; Calculating the difference between the initial unwrapped phase and the updated model phase to obtain the residual phase; Performing a wrapping operation on the updated target Gaussian mixture model to obtain a model interferogram, and subtracting the model interferogram from each interferogram to obtain the residual interferogram corresponding to each interferogram; Unwrapping all the residual interferograms to obtain the residual phase; Calculating the difference between the residual phase and the residual phase, and determining whether the root mean square of the difference is less than the root mean square preset value; If so, adding the updated model phase and the residual phase to obtain the optimized unwrapped phase; Otherwise, using the updated target Gaussian mixture model as the target Gaussian mixture model, and returning to the step of inverting the target Gaussian mixture model using the nonlinear least squares method to obtain the model parameters of the target Gaussian mixture model.

[0011] Optionally, the time-series deformation model of the mining area is: ; ; where, represents the optimized unwrapped phase, Indicates the deformation displacement in the LOS direction, Indicates the time list obtained from the image, Indicates the time list when the main image is obtained, Indicates the acquisition time of the Indicates the acquisition time of the Indicates the acquisition time of the th SAR image, When , is a preset value, Indicates pi, Indicates the wavelength of the radar, Indicates the deformation displacement in the LOS direction at time Indicates the deformation displacement in the LOS direction at time Indicates the deformation displacement in the LOS direction at time.

[0012] In a second aspect, an embodiment of the present application provides a device for estimating the time-series deformation of horizontal to inclined coal seams based on a mixture of Gaussians, including: An acquisition module for acquiring SAR images of the target coal seam area at N times; the N th time is the current time; An unwrapping module for obtaining multiple interferograms based on all SAR images and unwrapping all interferograms to obtain an initial unwrapped phase; A construction module for constructing a target mixture of Gaussians model for the target coal seam area; the target mixture of Gaussians model is used to describe the deformation phase of the target coal seam area in the two-dimensional plane; An optimization module for optimizing the initial unwrapped phase according to the target mixture of Gaussians model to obtain an optimized unwrapped phase; A solution module for constructing a mining area time-series deformation model of the target coal seam area based on the optimized unwrapped phase and solving the mining area degree time-series deformation model to obtain a time-series deformation estimation result of the target coal seam area; the mining area time-series deformation model is used to describe the relationship between the optimized unwrapped phase and the deformation displacement in the LOS direction of the target coal seam area, and the time-series deformation estimation result is used to describe the deformation displacement in the LOS direction of the target coal seam area under the time span of all SAR images.

[0013] In a third aspect, an embodiment of the present application provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the above-mentioned method for estimating the time-series deformation of horizontal to inclined coal seams based on a mixture of Gaussians is implemented.

[0014] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for estimating the time-series deformation of coal seams based on a mixture of Gaussians.

[0015] The above solution of the present application has the following beneficial effects: In the embodiment of the present application, by acquiring SAR images of the target coal seam area at N a plurality of moments, then obtaining a plurality of interferograms based on all the SAR images, and unwrapping all the interferograms to obtain an initial unwrapped phase, then constructing a target mixture of Gaussians model for the target coal seam area, and then optimizing the initial unwrapped phase according to the target mixture of Gaussians model to obtain an optimized unwrapped phase, and finally constructing a mining area time-series deformation model for the target coal seam area based on the optimized unwrapped phase, and solving the mining area time-series deformation model to obtain a time-series deformation estimation result of the target coal seam area. Among them, constructing the target mixture of Gaussians model can represent the deformation phase of the target coal seam area on a two-dimensional plane. Optimizing the initial unwrapped phase according to the target mixture of Gaussians model, by continuously optimizing the unwrapped phase of the mining area surface, the unwrapped phase of the settlement center of the target coal seam mining is inversely deduced, which can avoid the model fitting error under a wide range of various coal seam mining conditions and improve the accuracy of the unwrapped phase. The accuracy of the time-series deformation estimation result obtained based on the accurate unwrapped phase is improved.

[0016] Other beneficial effects of the present application will be described in detail in the subsequent specific implementation part. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] To more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for use in the embodiments or the description of the prior art. Obviously, the following drawings are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0018] Figure 1 It is a flowchart of the method for estimating the time-series deformation of horizontal to inclined coal seams based on a mixture of Gaussians provided by an embodiment of the present application; Figure 2 It is a specific flowchart block diagram of the method for estimating the time-series deformation of horizontal to inclined coal seams based on a mixture of Gaussians provided by an embodiment of the present application; Figure 3 Schematic diagram of an interference pattern provided by an embodiment of the present application; Figure 4 Schematic diagram of the model phase of a two-dimensional mixture Gaussian model provided by an embodiment of the present application; Figure 5 Schematic diagram of the residual phase provided by an embodiment of the present application; Figure 6 Schematic diagram of the unwrapped phase provided by an embodiment of the present application; Figure 7 Schematic diagram of the time-series deformation estimation result provided by an embodiment of the present application; Figure 8 Histogram of the mean value of the time-series deformation difference provided by an embodiment of the present application; Figure 9 Schematic diagram of the structure of a time-series deformation estimation device for horizontal to inclined coal seams based on a mixture Gaussian provided by an embodiment of the present application; Figure 10 Schematic diagram of the structure of a terminal device provided by an embodiment of the present application. Detailed implementation manners

[0019] In the following description, for the purpose of illustration rather than limitation, specific details such as specific system structures and technologies are presented to thoroughly understand the embodiments of the present application. However, those skilled in the art should clearly understand that the present application can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present application.

[0020] It should be understood that when used in the specification of the present application and the appended claims, the term "comprising" indicates the presence of the described features, wholes, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or their combinations.

[0021] It should also be understood that the term "and / or" as used in the specification of the present application and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0022] As used in the specification of the present application and the appended claims, the term "if" can be interpreted as "when", "once", "in response to determining", or "in response to detecting" according to the context. Similarly, the phrase "if determined" or "if [the described condition or event] is detected" can be interpreted as meaning "once determined", "in response to determining", "once [the described condition or event] is detected", or "in response to detecting [the described condition or event]" according to the context.

[0023] In addition, in the description of the specification and the appended claims of the present application, terms such as "first", "second", "third", etc. are only used for differential description and should not be construed as indicating or implying relative importance.

[0024] The reference to "one embodiment" or "some embodiments" etc. described in the specification of the present application means that specific features, structures or characteristics described in connection with the embodiment are included in one or more embodiments of the present application. Thus, statements such as "in one embodiment", "in some embodiments", "in other some embodiments", "in still other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "comprising", "including", "having" and their variants all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0025] Aiming at the existing problem of low accuracy of deformation estimation caused by the mining of inclined coal seams, the embodiment of the present application provides a method for horizontal-to-inclined coal seam time-series deformation estimation based on a mixture of Gaussians. The horizontal-to-inclined coal seam time-series deformation estimation method obtains SAR images of the target coal seam area at N a plurality of moments, then obtains a plurality of interferograms based on all the SAR images, unwraps all the interferograms to obtain an initial unwrapped phase, then constructs a target mixture of Gaussians model for the target coal seam area, then optimizes the initial unwrapped phase according to the target mixture of Gaussians model to obtain an optimized unwrapped phase, and finally constructs a mining area time-series deformation model for the target coal seam area based on the optimized unwrapped phase, and solves the mining area time-series deformation model to obtain a time-series deformation estimation result of the target coal seam area. Among them, constructing the target mixture of Gaussians model can represent the deformation phase of the target coal seam area on a two-dimensional plane. Optimizing the initial unwrapped phase according to the target mixture of Gaussians model, by continuously optimizing the unwrapped phase of the mining area surface, the unwrapped phase of the settlement center of the horizontal-to-inclined coal seam mining is inversely calculated, which can avoid the model fitting error under a large range of various coal seam mining conditions and improve the accuracy of the unwrapped phase, and obtain a time-series deformation estimation result with improved accuracy based on the accurate unwrapped phase.

[0026] Next, an exemplary description is made of the method for horizontal-to-inclined coal seam time-series deformation estimation based on a mixture of Gaussians provided by the present application.

[0027] As Figure 1 shown, the method for horizontal-to-inclined coal seam time-series deformation estimation based on a mixture of Gaussians provided by the present application includes the following steps: Step 11, obtain SAR images of the target coal seam area at N a plurality of moments.

[0028] The N th moment is the current moment. For example, if the current moment is July 1st and N = 6, then the N moments can be February 1st, March 1st, April 1st, May 1st, June 1st, July 1st. Assume that the imaging time of February 1st is used as a reference. The above target coal seam area is the area of gently inclined coal seam mining from horizontal to gentle inclination that needs to be subjected to deformation estimation.

[0029] In some embodiments of the present application, the SAR images of the target coal seam area can be obtained by using a satellite (such as the domestic Land Exploration-1) that collects SAR images.

[0030] Step 12: Obtain a plurality of interferograms based on all SAR images, and perform phase unwrapping on all interferograms to obtain an initial unwrapped phase.

[0031] The above initial unwrapped phase includes the unwrapping results of each interferogram.

[0032] Specifically, taking the SAR image at the 1st moment as a reference image, perform data registration on other SAR images, and use the SAR images corresponding to every two adjacent moments as an interference combination. For each interference combination, calculate the interference phase pixel by pixel to obtain an interferogram; then the minimum cost flow method can be used to perform phase unwrapping on all interferograms to obtain an initial unwrapped phase.

[0033] It should be noted that the expression of the initial unwrapped phase is: ; where represents the wavelength of the radar electromagnetic wave, represents the deformation in the upward direction of the radar line of sight (LOS, Line Of Sight). The negative sign indicates that the satellite is moving away from the surface object, and the surface deformation is manifested as subsidence, and vice versa.

[0034] Step 13: Construct a target mixture Gaussian model for the target coal seam area.

[0035] The above target mixture Gaussian model is used to describe the deformation phase of the target coal seam area in the two-dimensional plane.

[0036] In some embodiments of the present application, the steps of constructing the target mixture Gaussian model for the target coal seam area include:

[0037] The first step: Construct a two-dimensional rectangular coordinate system based on the target coal seam area.

[0038] Specifically, take the coal seam mining direction as the direction of one axis of the two-dimensional rectangular coordinate system, the direction of vertical deformation as the z-axis, determine the other axis according to the right-hand rule, and take the axis in the direction of vertical deformation and the axis determined by the right-hand rule to obtain the two-dimensional rectangular coordinate system, with the origin being the lower left corner that determines the boundary of the research area.

[0039] In the second step, in the two-dimensional rectangular coordinate system, if the target coal seam area is stretched or compressed in the horizontal coordinate direction, then use the first Gaussian mixture model as the target Gaussian mixture model; if the target coal seam area is stretched or compressed in the vertical coordinate direction, then use the second Gaussian mixture model as the target Gaussian mixture model; if the target coal seam area is stretched or compressed in both the horizontal coordinate direction and the vertical coordinate direction, then use the two-dimensional Gaussian mixture model as the target Gaussian mixture model.

[0040] Specifically, the first Gaussian mixture model is: ; where represents the model phase that only undergoes stretching or compression in the horizontal coordinate direction, and the shape remains symmetric in the vertical coordinate direction, represents the abscissa of the area in the target coal seam area in the two-dimensional rectangular coordinate system, represents the ordinate of the area in the target coal seam area in the two-dimensional rectangular coordinate system, represents the parameter vector, , represents the compression or stretching parameter in the horizontal axis direction, represents the compression or stretching parameter in the vertical axis direction, represents the amplitude, represents the abscissa of the center point, represents the ordinate of the center point, 、 、 all represent intermediate parameters, represents the clockwise rotation angle, represents the standard deviation in the horizontal axis direction, represents the standard deviation in the vertical axis direction, represents the exponential function, represents the cosine function, represents the sine function, represents the transpose operation.

[0041] The model phase is the deformation phase of the target coal seam area calculated by the Gaussian mixture model.

[0042] The second Gaussian mixture model is: ; ; ; ; Among them, represents the model phase that undergoes only stretching or compression in the vertical direction, and the shape remains symmetric in the horizontal direction.

[0043] Specifically, the two-dimensional mixture Gaussian model is: ; ; ; ; Among them, represents the model phase that undergoes stretching or compression in both two-dimensional directions.

[0044] It should be noted that by performing deformation analysis on all SAR images of the target coal seam area, it can be determined whether stretching or compression occurs in the horizontal and vertical directions. The above center point is the center point of the corresponding model (for example, in the first mixture Gaussian model, this center point is the center point of the first mixture Gaussian model).

[0045] Step 14: Optimize the initial unwrapped phase according to the target mixture Gaussian model to obtain the optimized unwrapped phase.

[0046] In some embodiments of the present application, the step of optimizing the initial unwrapped phase according to the target mixture Gaussian model to obtain the optimized unwrapped phase includes: The first step: Invert the target mixture Gaussian model using the nonlinear least squares method to obtain the model parameters of the target mixture Gaussian model.

[0047] The second step: Substitute the model parameters into the target mixture Gaussian model, and use the model phase in the updated target mixture Gaussian model as the updated model phase.

[0048] The third step: Calculate the difference between the initial unwrapped phase and the updated model phase to obtain the residual phase.

[0049] It should be noted that the relationship between the initial unwrapped phase and the updated model phase is: ; Among them, represents the initial unwrapped phase, represents the updated model phase, represents the residual phase.

[0050] In the fourth step, perform a winding operation on the updated target Gaussian mixture model to obtain a model interferogram, and subtract the model interferogram from each interferogram to obtain the residual interferogram corresponding to each interferogram.

[0051] In the fifth step, unwrap all the residual interferograms to obtain the residual phase.

[0052] Exemplarily, the minimum cost flow method can be used to perform unwrapping to obtain the residual phase.

[0053] In the sixth step, calculate the difference between the residual phase and the residual error phase, and determine whether the root mean square of the difference is less than the preset root mean square value.

[0054] Exemplarily, the residual phase and the residual error phase contain the phase at each position in the two-dimensional rectangular coordinate system, and the root mean square of the difference can be calculated using the calculation formula for the root mean square.

[0055] If so, add the updated deformation phase and the residual error phase to obtain the optimized unwrapped phase.

[0056] Otherwise, use the updated target Gaussian mixture model as the target Gaussian mixture model, and return to the step of using the nonlinear least squares method to invert the target Gaussian mixture model to obtain the model parameters of the target Gaussian mixture model.

[0057] It should be noted that the parameters are inverted by nonlinear least squares in each iteration, and through each iteration, the parameters of the target Gaussian mixture model become more and more accurate.

[0058] Step 15: Construct a mining area time-series deformation model for the target coal seam area based on the optimized unwrapped phase, and solve the mining area time-series deformation model to obtain the time-series deformation estimation result of the target coal seam area.

[0059] The above mining area time-series deformation model is used to describe the relationship between the optimized unwrapped phase and the LOS-direction deformation displacement of the target coal seam area, and the time-series deformation estimation result is used to describe the LOS-direction deformation displacement of the target coal seam area under the time span of the SAR data image. For example, it can be the value of the LOS-direction deformation displacement of the target coal seam area under the time span of 6 moments (February 1st, March 1st, April 1st, May 1st, June 1st, July 1st, and the time span is from February 1st to the current moment July 1st), where it is assumed that the time on February 1st is the reference and the LOS-direction deformation at this time is 0.

[0060] The above mining area surface time-series deformation model is as follows: ; ; Among them, represents the optimized unwrapped phase, Indicates the deformation displacement in the LOS direction, Indicates the time list obtained from the image, Indicates the time list for obtaining the master image, Indicates the acquisition time of the Indicates the acquisition time of the Indicates the acquisition time of the , when time, , is a preset value, Indicates pi, Indicates the wavelength of the radar, Indicates the deformation displacement in the LOS direction at Indicates the deformation displacement in the LOS direction at Indicates the deformation displacement in the LOS direction at

[0061] Exemplarily, the master image is usually the SAR image with the earliest acquisition time. The acquisition time of the above master image is February 1st, and the corresponding acquisition times of the slave images are March 1st and April 1st; the acquisition time of the master image is March 1st, and the corresponding acquisition times of the slave images are April 1st and May 1st; the acquisition time of the master image is April 1st, and the corresponding acquisition times of the slave images are May 1st and June 1st; the acquisition time of the master image is May 1st, and the corresponding acquisition time of the slave image is June 1st; the acquisition time of the master image is June 1st, and the corresponding acquisition time of the slave image is July 1st; a total of 8 groups of interferograms are simulated and combined.

[0062] In some embodiments of the present application, the steps of resolving the above large-gradient time-series deformation model of the mining area to obtain the time-series deformation estimation result of the target coal seam area include: Converting the above time-series deformation model of the mining area surface into an adjustment form , and then using Tikhonov regularization weighted least squares solution to obtain the time-series deformation parameters in the LOS direction , substituting the resolved parameters into to obtain the time-series deformation estimation result; where, Indicates the error, Indicates the coefficient matrix of the InSAR data observation, Indicates the coefficient matrix of the redundant observation, Indicates the observation vector, Indicates the normalized smoothing parameter, Denote the weight matrix: ; Wherein, denotes the weight matrix of the observation vector, denotes the weight matrix of the constraint.

[0063] Exemplarily, the overall process block diagram of the method of the present application is as shown in Figure 2 According to the SAR dataset, an interferogram sequence is obtained, and then the minimum cost flow method is used to obtain an initial phase sequence set (i.e., the initial unwrapped phase). At the same time, the horizontal to inclined coal seam mining research area is analyzed to determine the coal seam mining direction and angle, and the initial phase sequence set is fitted to establish a mixed two-dimensional Gaussian function and obtain the model phase. Then, it is judged whether the change value of the phase residual (i.e., the root mean square of the difference between the residual phase and the residual phase in the above text) obtained based on the model phase and the initial phase sequence set is less than 0.01 (i.e., the root mean square preset value). If so (YES), the residual unwrapped phase (i.e., the residual phase) is output. Otherwise (NO), the parameters of the two-dimensional Gaussian function are iterated; the output residual unwrapped phase is added to the model phase of the mixed two-dimensional Gaussian function (+) to obtain the optimized InSAR interferometric unwrapped phase, and a time-series deformation model of the mining area is established. Then, the Tikhonov regularization weighted least squares method is used to estimate the time-series deformation parameters of the mining area to obtain the fine time-series deformation result of the mining area surface (i.e., the time-series deformation estimation result).

[0064] It is worth mentioning that constructing the target mixed Gaussian model can represent the deformation phase of the target coal seam area on the two-dimensional plane. Optimize the initial unwrapped phase according to the target mixed Gaussian model. By continuously optimizing the unwrapped phase of the mining area surface, the unwrapped phase of the subsidence center of the horizontal to inclined coal seam mining is inversely calculated, which can avoid the model fitting error under a large range of various coal seam mining conditions, improve the accuracy of the unwrapped phase, and obtain a time-series deformation estimation result with improved accuracy based on the accurate unwrapped phase.

[0065] In addition, according to the characteristics of horizontal to inclined coal seam mining, the present application proposes a two-dimensional mixed Gaussian model, and uses an iterative method to continuously optimize the deformation phase of the mining area surface until the deformation phase of the subsidence center is inversely calculated. Then, by establishing a time-series deformation model of the mining area surface, the Tikhonov regularization weighted least squares method is used to solve the time-series deformation parameters. The present application significantly improves the estimation accuracy of mining area deformation and broadens the application prospect of InSAR in surface monitoring of different coal seams.

[0066] The method of the present application will be exemplarily described below with a specific example.

[0067] First, the three-dimensional temporal deformation phase (unit: rad) of the ground surface caused by the mining of two working faces at six time points was simulated using the probability integral method (a mathematical model for predicting mining subsidence). One of the working faces was for the non-uniform mining of an inclined coal seam, and the other was for the uniform mining of a nearly horizontal coal seam. According to the incident angle and heading angle of the domestic LUT-1 SAR satellite data, the three-dimensional deformation was projected onto the LOS direction to obtain the temporal deformation phase in the LOS direction. Then, pairwise combination and wrapping calculations were performed to obtain 8 interferograms with different deformation gradients. To make the simulation closer to the actual situation of mining in the mining area, an atmospheric phase (with a maximum phase change of 2 rad) and different noise levels (0.2 rad, 0.4 rad, 0.6 rad, and 0.8 rad) were added, as Figure 3 shown, Figure 3 where the horizontal and vertical axes represent the pixel positions, and different pixel values represent different phase changes in rad, Figure 3 (a) and Figure 3 (e) are the simulation results of the wrapped interferograms for the phase with a noise level of 0.8 rad, Figure 3 (b) and Figure 3 (f) are the simulation results of the wrapped interferograms for the phase with a noise level of 0.6 rad, Figure 3 (c) and Figure 3 (g) are the simulation results of the wrapped interferograms for the phase with a noise level of 0.4 rad, Figure 3 (d) and Figure 3 (h) are the simulation results of the wrapped interferograms for the phase with a noise level of 0.2 rad.

[0068] According to the mining characteristics and geological parameters of the mining area, the coal seam mining direction and dip angle were determined, a rectangular coordinate system was established, and the compression and stretching directions of the mining subsidence deformation were determined according to the mining progress, etc. Then, the minimum cost flow method was used to Figure 3 initially unwrap the simulated interferograms.

[0069] A two-dimensional mixed Gaussian model was constructed, and the initially unwrapped phase was optimized according to the two-dimensional mixed Gaussian model. The deformation phase of the two-dimensional mixed Gaussian model obtained from the last iterative calculation is as Figure 4 shown, Figure 4 where the horizontal and vertical axes represent the pixel positions, and different pixel values represent different phase changes in rad, Figure 4 (a)-(h) correspond one-to-one with Figure 3 (a)-(h), and the residual phase is as Figure 5 shown, Figure 5 where the horizontal and vertical axes represent the pixel positions, and different pixel values represent different phase changes in rad, Figure 5 (a)-(h) correspond one-to-one with Figure 3 (a)-(h).

[0070] The deformed phase and the residual phase of the two-dimensional Gaussian mixture model are added to obtain the optimized unwrapped phase as shown in Figure 6 (i)-(p) in Figure 6 where the horizontal axis and the vertical axis represent pixel positions, and different pixel values represent different phase changes in rad, Figure 6 (i)-(p) corresponds one-to-one with Figure 3 (a)-(h), Figure 6 (a)-(h) is the unwrapped phase obtained without parameter iteration. It can be seen from Figure 6 that as the noise level gradually increases, the method of the present application can obtain high-precision mining area interferogram phase unwrapping results for horizontal to inclined coal seams, which is beneficial to reducing errors. The results show that within a certain noise error level, the method of the present application can solve the problem of symmetric model errors introduced by different coal seam mining and obtain accurate phase unwrapping results.

[0071] Construct a large-gradient time-series deformation model for the target coal seam area in the mining area, and solve the time-series deformation model for the mining area to obtain the time-series deformation estimation results as shown in Figure 7 where the horizontal axis and the vertical axis represent pixel positions, and different pixel values represent the degree of deformation, with the unit of centimeter cm, Figure 7 (a) is the LOS direction zero value referenced on February 1st, Figure 7 (b) is the cumulative LOS direction displacement from February 1st to March 1st, Figure 7 (c) is the cumulative LOS direction displacement from February 1st to April 1st, Figure 7 (d) is the cumulative LOS direction displacement from February 1st to May 1st, Figure 7 (e) is the cumulative LOS direction displacement from February 1st to June 1st, Figure 7 (f) is the cumulative LOS direction displacement from February 1st to July 1st. Figure 7 (f) is the cumulative LOS direction displacement from February 1st to July 1st.

[0072] Subtract the time-series deformation estimation results from the simulated LOS direction time-series deformation results, and calculate the mean value of the six time-series deformation differences for histogram statistics, as shown in Figure 8 where the horizontal axis represents the mean value of the time-series residuals, with the unit of centimeter cm, and the vertical axis represents the statistical value, Figure 8 (a) is the difference statistics between the time-series deformation results obtained without model parameter optimization and the simulated LOS direction time-series results, Figure 8 (a) is the difference statistics between the time-series deformation results obtained without model parameter optimization and the simulated LOS direction time-series results, Figure 8 (b) is the difference statistics between the time-series deformation results obtained by the method of the present application and the simulated LOS direction time-series results.

[0073] It can be seen from this that the present application not only realizes the time-series deformation estimation caused by the mining of horizontal to inclined coal seams in the mining area, but also avoids the fitting error of the traditional symmetric model to the InSAR observed phase value, and improves the deformation estimation accuracy.

[0074] An exemplary description is given below for the device for estimating the time-series deformation of horizontal to inclined coal seams based on Gaussian mixture provided in this application.

[0075] As Figure 9 shown, an embodiment of this application provides a device for estimating the time-series deformation of horizontal to inclined coal seams based on Gaussian mixture. The device 900 for estimating the time-series deformation of horizontal to inclined coal seams based on Gaussian mixture includes: An acquisition module 901, configured to acquire SAR images of a target coal seam area at N a plurality of moments; the N last moment is the current moment; An unwrapping module 902, configured to obtain a plurality of interferograms based on all the SAR images and perform unwrapping on all the interferograms to obtain an initial unwrapped phase; A construction module 903, configured to construct a target Gaussian mixture model of the target coal seam area; the target Gaussian mixture model is used to describe the deformation phase of the target coal seam area in a two-dimensional plane; An optimization module 904, configured to optimize the initial unwrapped phase according to the target Gaussian mixture model to obtain an optimized unwrapped phase; A solution module 905, configured to construct a mining area time-series deformation model of the target coal seam area based on the optimized unwrapped phase and perform solution on the mining area time-series deformation model to obtain a time-series deformation estimation result of the target coal seam area; the mining area time-series deformation model is used to describe the relationship between the optimized unwrapped phase and the LOS-direction deformation displacement of the target coal seam area, and the time-series deformation estimation result is used to describe the LOS-direction deformation displacement of the target coal seam area under the time span of all the SAR images.

[0076] It should be noted that for the information interaction, execution process, etc. between the above-mentioned device / units, since they are based on the same concept as the method embodiment of this application, for their specific functions and the technical effects brought, reference can be specifically made to the method embodiment part, and details are not described herein again.

[0077] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the above-mentioned division of each functional unit and module is used as an example. In actual applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of each functional unit and module are only for the convenience of mutual distinction and do not limit the protection scope of this application. The specific working processes of the units and modules in the above system can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated here.

[0078] As Figure 10 shown, an embodiment of the present application provides a terminal device. The terminal device D10 in this embodiment includes: at least one processor D100 ( Figure 10 only one processor is shown in the figure), a memory D101, and a computer program D102 stored in the memory D101 and executable on the at least one processor D100. When the processor D100 executes the computer program D102, the steps in any of the foregoing method embodiments are implemented.

[0079] Specifically, when the processor D100 executes the computer program D102, by acquiring SAR images of the target coal seam area at N multiple moments, then obtaining multiple interferograms based on all the SAR images, and unwrapping all the interferograms to obtain an initial unwrapped phase, then constructing a target mixture Gaussian model of the target coal seam area, and then optimizing the initial unwrapped phase according to the target mixture Gaussian model to obtain an optimized unwrapped phase, and finally constructing a mining area time-series deformation model of the target coal seam area based on the optimized unwrapped phase, and solving the mining area time-series deformation model to obtain a time-series deformation estimation result of the target coal seam area. Among them, constructing a target mixture Gaussian model can represent the deformation phase of the target coal seam area on a two-dimensional plane. Optimizing the initial unwrapped phase according to the target mixture Gaussian model can avoid model fitting errors under a wide range of various coal seam mining conditions and improve the accuracy of the unwrapped phase. The accuracy of the time-series deformation estimation result obtained based on the accurate unwrapped phase is improved.

[0080] The so-called processor D100 may be a central processing unit (CPU), and this processor D100 may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or this processor may also be any conventional processor, etc.

[0081] In some embodiments, the memory D101 may be an internal storage unit of the terminal device D10, such as the hard disk or memory of the terminal device D10. In other embodiments, the memory D101 may also be an external storage device of the terminal device D10, such as a plug-in hard disk equipped on the terminal device D10, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. Further, the memory D101 may also include both the internal storage unit and the external storage device of the terminal device D10. The memory D101 is used to store an operating system, application programs, a boot loader, data, and other programs, such as the program code of the computer program, etc. The memory D101 may also be used to temporarily store data that has been output or will be output.

[0082] The embodiments of the present application also provide a computer-readable storage medium, and the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in the above various method embodiments can be implemented.

[0083] The embodiments of the present application provide a computer program product, and when the computer program product runs on a terminal device, the terminal device can be made to implement the steps in the above various method embodiments when executed.

[0084] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, to implement all or part of the processes in the above-described embodiment methods of this application, a computer program can be used to instruct relevant hardware to complete. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-described method embodiments can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file, or some intermediate form, etc. The computer-readable medium can at least include: any entity or device that can carry the computer program code to the device / terminal equipment for the time series deformation estimation method of horizontal to inclined coal seams based on a mixture of Gaussians, recording medium, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal, and software distribution medium. For example, a USB flash drive, a mobile hard disk, a magnetic disk, or an optical disc, etc.

[0085] In the above embodiments, the descriptions of the respective embodiments have their own focuses. For parts not detailed or recorded in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0086] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed in this document can be implemented by electronic hardware or a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. A professional technician can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of this application.

[0087] The above is the preferred implementation manner of this application. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle described in this application, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of this application.

Claims

1. A method for estimating the time - series deformation of horizontal to inclined coal seams based on a mixture of Gaussians, characterized in that, Including: Obtain SAR images of the target coal seam area at N moments; The N th moment is the current moment; Obtain multiple interferograms based on all SAR images, and unwrap all the interferograms to obtain the initial unwrapped phase; Construct the target mixture Gaussian model for the target coal seam area; the target mixture Gaussian model is used to describe the deformation phase of the target coal seam area in the two-dimensional plane; Optimize the initial unwrapped phase according to the target mixture Gaussian model to obtain the optimized unwrapped phase; Construct the mining area time-series deformation model for the target coal seam area based on the optimized unwrapped phase, and solve the mining area time-series deformation model to obtain the time-series deformation estimation result of the target coal seam area; The mining area time-series deformation model is used to describe the relationship between the optimized unwrapped phase and the LOS-direction deformation displacement of the target coal seam area, and the time-series deformation estimation result is used to describe the LOS-direction deformation displacement of the target coal seam area under the time span of all SAR images.

2. The sequential deformation estimation method for horizontal to inclined coal seams according to claim 1, characterized in that The constructing the target mixture Gaussian model for the target coal seam area includes: Construct a two-dimensional rectangular coordinate system based on the target coal seam area; Under the two-dimensional rectangular coordinate system, if the target coal seam area undergoes stretching or compression in the abscissa direction, use the first mixture Gaussian model as the target mixture Gaussian model; if the target coal seam area undergoes stretching or compression in the ordinate direction, use the second mixture Gaussian model as the target mixture Gaussian model; if the target coal seam area undergoes stretching or compression in both the abscissa direction and the ordinate direction, use the two-dimensional mixture Gaussian model as the target mixture Gaussian model.

3. The method for estimating the time-sequence deformation of horizontal to inclined coal seams according to claim 2, wherein, The first mixture Gaussian model is: ； Among them, represents the model phase with stretching or compression in the horizontal coordinate direction, represents the abscissa of the area in the target coal seam area under the two-dimensional rectangular coordinate system, represents the ordinate of the area in the target coal seam area under the two-dimensional rectangular coordinate system, represents the parameter vector, , represents the compression or stretching parameter in the horizontal axis direction, represents the compression or stretching parameter in the vertical axis direction, represents the amplitude, represents the abscissa of the center point, represents the ordinate of the center point, , , all represent intermediate parameters, represents the clockwise rotation angle, represents the standard deviation in the horizontal axis direction, represents the standard deviation in the vertical axis direction, represents the exponential function, represents the cosine function, represents the sine function, represents the transpose operation.

4. The method for estimating the sequential deformation of horizontal to inclined coal seams according to claim 3, characterized in that The second mixture Gaussian model is: ； ； ； ； Among them, represents the model phase with stretching or compression in the vertical coordinate direction.

5. The method for estimating the sequential deformation of horizontal to inclined coal seams according to claim 4, wherein The two-dimensional mixture Gaussian model is: ； Among them, represents the model phase where stretching or compression occurs in both two-dimensional directions.

6. The method for estimating the sequential deformation of horizontal to inclined coal seams according to claim 5, characterized in that, The optimizing the initial unwrapped phase according to the target mixture Gaussian model to obtain the optimized unwrapped phase includes: Use the nonlinear least squares method to invert the target mixture Gaussian model to obtain the model parameters of the target mixture Gaussian model; Substitute the model parameters into the target mixture Gaussian model, and use the model phase in the updated target mixture Gaussian model as the updated model phase; Calculate the difference between the initial unwrapped phase and the updated model phase to obtain the residual phase; Perform a wrapping operation on the updated target mixture Gaussian model to obtain a model interferogram, and subtract the model interferogram from each interferogram to obtain the residual interferogram corresponding to each interferogram; Unwrap all the residual interferograms to obtain the residual phase; Calculate the difference between the residual phase and the residual phase, and determine whether the root mean square of the difference is less than the root mean square preset value; If so, add the updated model phase and the residual phase to obtain the optimized unwrapped phase; Otherwise, use the updated target mixture Gaussian model as the target mixture Gaussian model, and return to the step of using the nonlinear least squares method to invert the target mixture Gaussian model to obtain the model parameters of the target mixture Gaussian model.

7. The method for estimating the sequential deformation of a horizontal to inclined coal seam according to claim 1, wherein The mining area time-series deformation model is: ； ； Among them, represents the optimized unwrapped phase, represents the LOS-direction deformation displacement, represents the time list obtained from the images, represents the time list of the master image acquisition, represents the acquisition time of the th SAR image, acquisition time of the th SAR image, acquisition time of the , when is satisfied, , are preset values, represents pi, represents the wavelength of the radar, represents the LOS-direction deformation displacement at time represents the LOS-direction deformation displacement at time represents the LOS-direction deformation displacement at time.

8. A time-series deformation estimation device for horizontal to inclined coal seams based on Gaussian mixture, characterized in that Including: An acquisition module for acquiring SAR images of a target coal seam area at N moments; The N th moment is the current moment; An unwrapping module, configured to obtain multiple interferograms based on all SAR images, and unwrap all the interferograms to obtain the initial unwrapped phase; A construction module for constructing a target Gaussian mixture model of the target coal seam area; the target Gaussian mixture model is used to describe the deformation phase of the target coal seam area in a two-dimensional plane; An optimization module for optimizing the initial unwrapped phase according to the target Gaussian mixture model to obtain an optimized unwrapped phase; A solution module for constructing a mining area time-series deformation model of the target coal seam area based on the optimized unwrapped phase and solving the mining area time-series deformation model to obtain a time-series deformation estimation result of the target coal seam area; The mining area time-series deformation model is used to describe the relationship between the optimized unwrapped phase and the LOS-direction deformation displacement of the target coal seam area, and the time-series deformation estimation result is used to describe the LOS-direction deformation displacement of the target coal seam area under the time span of all SAR images.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method for estimating the time-series deformation of horizontal to inclined coal seams based on Gaussian mixture according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method for estimating the time-series deformation of horizontal to inclined coal seams based on Gaussian mixture according to any one of claims 1 to 7.

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