Application of Optimized Grey-Markov Model to Land Subsidence Monitoring With InSAR

Land subsidence prediction in mining areas is one of the most important applications of land deformation monitoring, which is significance for safe production. We used interferometric point target analysis (IPTA) timing series interferometry synthetic aperture radar (InSAR) processing technology to analyze the land subsidence results for the Xinfa mining area from 2017 to 2020; and compared them to global positioning system (GPS) static monitoring data. We proposed a residual correction theory based on deviation coefficient using the grey prediction and Markov models, and an optimized Grey-Markov model (RGM-M model) was established to predict the land subsidence of the mining area. Our results show that: (1) The maximum difference between InSAR timing processing results and GPS monitoring data in the same period is 10.91mm; they have roughly the same subsidence trend, indicating that IPTA timing series InSAR technology are strongly reliable in mining deformation. (2) Compared to the traditional Grey-Markov model, the improved residual correction and dynamic assignment of the Grey-Markov model improves the prediction accuracy. The optimized residual correction and dynamic empowerment of the Grey-Markov model prediction results are more suitable for the actual fluctuation of land subsidence value in the mining area. The maximum root mean square error of the prediction results is 0.751mm, and the maximum average absolute percentage error is 7.46%, which has a certain guiding significance for the work of monitoring, prediction and safety management of land deformation in the mining area.

on monitoring and predicting land subsidence in mining areas 23 has always been a prominent issue [1]. In the field of land  The need to establish monitoring stations along with the 30 mining deformation; through repeated field observation; is 31 The associate editor coordinating the review of this manuscript and approving it for publication was John Xun Yang . time-consuming; with input cost, especially since the labor 32 cost is also higher; furthermore, it is too complex for some 33 terrain, has inaccessible areas, and it is too difficult to estab-34 lish observation stations and measurement work. 35 In the past few decades, InSAR has become unanimously 36 recognized as important monitoring means in this field [2]. 37 InSAR technology is one of the most popular research fields. 38 With the development of commercial satellites in recent 39 years, more and more commercial SAR satellite data have 40 been applied to land subsidence monitoring, achieving the 41 expected results. The main advantage of using InSAR tech-42 nology for imaging is continuous no interval observation, 43 high accuracy and resolution, wide coverage, and low cost. 44 It has been used in various fields of national economic devel-45 opment; for example, InSAR technology is used for building 46 ground DEM models, land subsidence monitoring, volcano, 47 previously, namely that the evolutionary direction is not based 104 on past changes. This paper uses dynamic empowerment; 105 and data values after each Grey-Markov model prediction 106 was added to the calculated sample of the next evaluation 107 weight matrix. A dynamic Markov evaluation weight matrix 108 is established, more scientific in theory. Four typical subsi-109 dence points in the subsidence data of the new and spring 110 exploration areas were replaced with the traditional GM (1,1) 111 model, Grey-Markov combination prediction model with 112 optimized residual correction, and dynamic empowerment 113 of the Grey-Markov combination model. We compared and 114 analyzed the prediction results. The results showed the opti-115 mized Grey-Markov model predicts the trend and subsidence 116 value of land subsidence more accurately than the traditional 117 Grey-Markov combination model. These results have good 118 application prospects for mine land subsidence monitoring, 119 prediction, and safety management.

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A. STUDY AREA

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The main research area of this paper is the new exploration 123 area in the Wuzhong City, Ningxia Province, China. It is 124 located at 70km southeast of Wuzhong City. The exploration 125 area is about 4.17KM long from north to south and 2.22km 126 wide from east to west. The specific scope is shown in 127 Figure 1. The landform is mainly mountainous, with dry 128 climate and four distinct seasons.  The data used in this paper include SAR images captured 131 by the Sentinel-1A satellite. The Sentinel-1 satellite is a 132 C-band Earth observation satellite launched by ESA in the 133 Copernican Program. It consists of two satellites, A and B 134 satellite. Each satellite has a separate return period of 12 days 135 and a binary return period of 6 days. It's main working mode 136 is the interference wide amplitude (IW) scanning imaging 137 mode; the SAR image data width reaches 250km. The orbital data parameters are shown in Table 1.  solution parameters must be adjusted according to the actual 186 situation. Thus, the solution accuracy improves. At the same 187 time, IPTA timing processing technology also depends on 188 certain requirements related to the experience level of the data 189 processors.

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During timing processing, the interference phase in the 191 interference stripe diagram generated by any two images 192 mainly includes five parts, namely, the topographic phase, 193 land deformation phase, flat land phase, atmospheric delay 194 phase and noise phase. During IPTA processing: In the formula, ϕ is the interference phase of the target 197 point; ϕ top is the interference phase due to topographic ele-198 vation; ϕ f is the flat phase, which can be calculated from the 199 geometric relationship of image imaging; ϕ def is the line of 200 sight to radar ( LOS ); ϕ atm represents the noise phase caused 201 by the atmospheric delay; and ϕ n represents the system ther-202 mal noise phase.

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ϕ top and ϕ f can be removed after the differential interfer-204 ence treatment, to obtain the differential phase ϕ diff : ϕ tope is the elevation error phase. The required land defor-207 mation information can finally be extracted from the sepa-208 rated ϕ def : v represents the linear deformation rate of coherence points 211 relative to the reference point;t represents the time baseline; 212 and ϕ def_n is the nonlinear deformation phase.

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The IPTA method uses the two-dimensional linear phase 214 solution model, that is, through continuous regression iter-215 ative calculation; to complete the separation and removal of 216 various errors, obtaining the deformation rate. In this iteration 217 process, the Delaunay triangle network and Minimum cost 218 flow (MCF) algorithm can solve the phase disentanglement 219 of the target. The Grey system prediction refers to predicting the eigen-223 value changes of system behavior. It includes system predic-224 tions known and uncertain information. In other words, the 225 Grey process changes within a certain threshold range related 226 to the time series [20], [21]. The phenomena shown in the ash 227 process are random and fluctuating; however, they are also 228 orderly and bounded, so the data set has an underlying law. 229 The Grey system prediction model uses this potential law to 230 establish the Grey model, fulfilling the prediction of the Grey 231 system [17], [22], [23].

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The Grey model was established as follows:

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(1) The original data sequence that corresponds to time 234 is x (0) : (2) To reduce the dynamic randomness of the data, the raw 237 data sequence is accumulated: Adjacent to the mean is the whitening background value 243 y (1) (k).

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(4) Construction of the white-chemical differential 245 equation: By least squares, the following calculation is available:

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Test of mean variance ratio: the variance of the original 264 data, and variance of the residual columns are: where, x 0 (k) is the original data sequence;x (0) represents the 268 original data sequence mean; ε (0) (k) is the residual sequence; 269 andε (0) is the residual sequence mean.

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The Model is considered qualified if it meets these two 271 requirements.

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The Markov model divides the data into several different 281 state intervals (for both prediction accuracy and data com-282 plexity, generally divided into 3-4 data), and finds the optimal 283 state step by step using the state transfer matrix; to estimate 284 future changes. 285

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Using the ratio of the fitted predicted value of the GM (1,1) 287 model to the actual land subsidence monitoring data as a 288 reference, the fitted data of the GM (1,1) model is divided 289 into three state intervals according to this ratio, expressed by 290 S i ∈ [a i , b i ] , i = 1, 2, · · · n. The lower and upper limits of 291 the interval are a i , b i . The transfer probability from state S i to 292 state S j by k steps is expressed as: where k represents the steps from S i to S j ; P k ij indicates the 295 probability from state S i to S j after k steps; n i represents the 296 number of samples in S i ; and n k ij represents the number of 297 samples from state S i to S j after k steps. The state transition matrix consisting of state transition prob-300 ability is: where the final optimized prediction value is y (0) (i + 1), a i 309 is the lower limit value; b i is the upper limit value; and 310x (0) (i + 1) is the forecast of the Grey model.

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(4) The initial fitting data was optimized by the residual 332 correction value to obtain the optimization resultsx (1) (k): from January 2017 to December 2020 are shown in Figure 3.   From these figures, it can be seen that the settlement is 358 large from April 2017 to July 2017, and with the passage of 359 time, the settlement of each phase gradually tends to be stable. 360 This is because there is residual subsidence after mining in 361 the mining area. After mining, there will be subsidence on 362 the surface. At first, the subsidence is large, and then it tends 363 to be stable.

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The subsidence values of the four typical subsidence points 365 in the new exploration area were also compared to the mon-366 itoring values of the adjacent GPS monitoring points in the 367 same period. The GPS data was used as the ratio to obtain 368 InSAR monitoring accuracy, as shown in Table 3.      The original data sequence on timing had a roughly 376 exponential distribution of subsidence value prediction 377 VOLUME 10, 2022        is obviously insufficient. The Grey-Markov combined predic-419 tion model predicted the fluctuation changes more accurately 420 based on the Grey model; however, its prediction accuracy 421 must be improved. Compared with the traditional Grey-422 Markov model, the improved RGM-M model with resid-423 ual residue correction and dynamic assignment significantly 424 improved the prediction accuracy of the data sequence, which 425 is closest to the measured data sequence in the mining area. 426 According to the phase 14 data for points P1, P2, P3, 427 and P4 in the new exploration area of the Weizhou mining 428 VOLUME 10, 2022 area, the subsidence value of the following two periods was 429 predicted, and its accuracy compared to the measured value.

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The prediction results are shown in Tables 4-7.     (1) The RGM-M model proposes a new residual correction 449 method for the Grey model, which optimizes and improves 450 the residual weight. The data prediction accuracy is greatly 451 improved compared with the traditional Grey model. Previ-452 ous residual-corrected grey models; were mostly optimized 453 for residual sequence or used other model optimized resid-454 ual correction methods. However, in practice, its raw data 455 sequence may not satisfy the ideal exponential distribution 456 since some emergent, and uncontrollable factors can affect 457 land subsidence data. There is inevitable volatility in the raw 458 data of the time series. Therefore, its residual sequence is 459 not necessarily the ideal application situation for the Grey 460 model. Therefore, the grey model fit was optimized again. 461 In theory, there is a certain limit to its applicability. The resid-462 ual correction model was optimized according to the residual 463 weight and can theoretically be improved by the original 464 data sequence according to different original data sequence 465 conditions, improving the prediction accuracy of the Grey 466 model.

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(2) A weighted Markov model with dynamic empower-468 ment was developed for the mine land subsidence data volatil-469 ity. Compared to the traditional Markov model, its evaluation 470 weight matrix is determined from the initial sequence; and 471 remains fixed in the subsequent predictions; therefore, its 472 prediction inevitably deviates. Dynamic empowerment; and 473 data values after each Grey-Markov model prediction were 474 added to the calculated sample of the next evaluation weight 475 matrix; and a dynamic Markov evaluation weight matrix was 476 established; that was more scientific in theory. In previous 477 weighted Markov models, the prediction data was used in the 478 initial state; and predicted the row vector of the next proba-479 bility transition matrix based on the last transition probability 480 matrix. The first predication data produces an accumulation 481 of errors that negatively impact the subsequent prediction. 482 We propose a new dynamic empowerment method; to replace 483 the Markov optimization of the first data value in the data 484 sequence with the Markov initial data sequence and recal-485 culate the new Markov sequence, establishing a dynamic 486 Markov prediction model. Using this method, we would con-487 sistently update the evaluation weight matrix and transfer 488 the probability matrix, improving the scientific nature of the 489 model prediction.