Method for optimizing land subsidence monitoring elevation control network

Abstract

The invention discloses a land subsidence monitoring elevation control network optimization method, which comprises the following steps: S1, carrying out bedrock mark stability evaluation by adopting a normal distribution theory to obtain a bedrock mark deformation stability evaluation index based on full historical time and space; s2: according to a multi-factor comprehensive analysis method, selecting a starting reference point to be added, optimizing the complex level network by adopting a Dijkstra algorithm, and carrying out overall consistency check and displacement significant point discrimination on the starting reference point to be added from a micro deformation detection perspective; and S3, according to result comparison of the target feature points in different adjustment systems, determining a new starting reference point of the land subsidence monitoring elevation control network. The method has the advantages that the stability evaluation effect and the datum point screening effect of the bed rock mark are good, and the method has certain practical significance in improving the ground elevation deformation monitoring precision in the later period, serving natural resource investigation, urban planning and construction and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of ground subsidence monitoring, in particular to a method for optimizing a ground subsidence monitoring elevation control network. Background Art

[0002] Bedrock mark is one of the important benchmarks for measuring ground elevation, settlement and other engineering elevation results. Periodic stability assessment has important practical significance. With the development of cities, the scope of ground settlement monitoring has expanded. Regular optimization of the starting reference point is of great significance to ensuring the reliability of elevation results and providing a stable benchmark for natural resource surveys and engineering construction.

[0003] Shanghai began monitoring ground subsidence in the last century, playing a crucial role in the city's economic development and its prevention and control efforts. The reference datum also transitioned from the Sheshan bedrock point to the Xiaozha Town bedrock point. To better describe the true extent of ground subsidence, Shanghai completed the transition from a single-datum free network to a four-datum attached network in 2008. After 2010, the construction of Shanghai's ground subsidence monitoring network accelerated. By 2024, 57 bedrock markers with a sufficient observation period were included in the city-wide ground subsidence monitoring network. The most recent stability assessment of the bedrock markers was completed in 2016, nearly 10 years ago. During this period, Shanghai not only added several new bedrock markers, but also accumulated sufficient periodic data for most of them. Stability assessments are urgently needed for these bedrock markers with extensive data.

[0004] The four reference datum points of the current land subsidence monitoring network were established in 2008 when the network transitioned from a free network to an attached network. At the time, they were fully capable of meeting the requirements of Shanghai's land subsidence monitoring work. However, with the acceleration of urban development, the continuous integration of satellite cities into the main area of ​​Shanghai, and the extension of major municipal projects such as rail transit and municipal elevated roads, the scope of Shanghai's land subsidence monitoring has been expanding year by year. The existing land subsidence leveling monitoring network has increasingly shown significant deficiencies in its reference datum. Taking Lingang New City as an example, the first-class attached leveling route is approximately 106 km away from the nearest starting datum, and the allowable deviation value of the round-trip height measurement difference is ±10.3 mm. This shows that the cumulative error effect caused by elevation transfer is very obvious, and the measured elevation values ​​have a large margin of error in deviating from the true values. Therefore, it is particularly urgent to select a suitable bedrock mark as the new starting reference point.

[0005] At present, domestic analysis and research on the stability of bedrock markers are mostly concentrated in the construction field. The verticality and other parameters of the bedrock marker during the construction period are ensured through the control of construction design and construction technology. For example, "Construction Technology of Bedrock Markers for Ground Subsidence Monitoring in Zhengzhou City" discussed by Wang Gang et al. and "Discussion on the Construction Technology of Kilometer-level Bedrock Markers in the Haihe River Basin Based on Geological Conditions" discussed by Liu Manjie et al. In the field of stability assessment of built bedrock markers, there are relatively few scholars, and the entry points vary significantly due to the geological environment, data accumulation, and the number of bedrock markers. For example, in "Analysis of the Impact of Temperature Change on the Bedrock Mark of Jinzhoutai Steel Pipe", Shang Guijia et al. discussed that based on the geographical conditions of Jinzhou, the depth of the bedrock marker they studied was within 30 meters, which is significantly different from the average bedrock depth of more than 200 meters in Shanghai, and its reference value is limited; in "Study on the Stability of Reference Benchmark of Ground Subsidence Level Monitoring Network in Beijing Plain Area", Lei Kunchao et al. changed the free network into the attached network to select the elevation control network benchmark, and used the average gap method to evaluate the stability of 7 bedrock markers in Beijing, but there is no precedent for conducting stability assessment of large-scale bedrock markers in Shanghai at the same time. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for optimizing the elevation control network for ground subsidence monitoring based on the above-mentioned deficiencies of the prior art. The method first adopts the normal distribution theory to carry out stability assessment of a large number of bedrock markers, proposes a bedrock marker deformation stability assessment index based on the entire historical time and space, and evaluates suspected unstable bedrock markers based on a macro perspective; secondly, the starting reference points to be added are selected according to the multi-factor comprehensive analysis method, the Dijkstra algorithm is used to optimize the complex leveling network, and then a statistical hypothesis testing model is established to carry out benchmark point stability assessment, and the overall consistency of the newly added starting reference points is tested from the perspective of micro-deformation; finally, the new starting reference points of the ground subsidence monitoring elevation control network are determined based on the comparison of the results of the target feature points in different adjustment systems, providing a more stable and reliable reference benchmark for subsequent natural resource surveys and research and urban planning and construction work.

[0007] The purpose of the present invention is achieved by the following technical solutions:

[0008] A method for optimizing a ground subsidence monitoring elevation control network, the method comprising:

[0009] S1: Use normal distribution theory to carry out bedrock marker stability assessment and obtain bedrock marker deformation stability assessment indicators based on the entire historical time and space;

[0010] S2: Select the proposed new reference points based on a multi-factor comprehensive analysis method, optimize the complex leveling network using the Dijkstra algorithm, and perform an overall consistency test and identify significant displacement points on the proposed new reference points from the perspective of micro-deformation detection.

[0011] S3: Determine the new starting reference point of the ground subsidence monitoring elevation control network based on the comparison of the results of the target feature points in different adjustment systems.

[0012] In step S1, the method for conducting bedrock target stability assessment using normal distribution theory is as follows:

[0013] The density function of the normal distribution is:

[0014]

[0015] Where ξ is the mean, representing the location parameter of the distribution, and σ is the standard deviation, representing the size parameter of the distribution. When ξ = 0 and σ = 1, the resulting density function is:

[0016]

[0017] The distribution with this density function is called the standard normal distribution. The random variable is recorded as X~N(0,1), and the distribution function is:

[0018]

[0019] Where x is a real number that can take any real value from -∞ to +∞, representing the possible values ​​of the standard normal random variable X. F(x) represents the probability that the random variable X is less than or equal to a certain value x, and its data meets the following four conditions:

[0020] (1) There are more errors with smaller absolute values ​​than errors with larger absolute values;

[0021] (2) The number of positive errors and negative errors with equal absolute values ​​is close;

[0022] (3) The absolute value of the error is subject to certain limits. Depending on the accuracy level required, the maximum value shall not exceed 2 or 3 times the mean error.

[0023] (4) The mathematical expectation of random error is zero;

[0024] When the annual deformation of the bedrock target meets the above four conditions at the same time, the indicators can be refined and its stability can be evaluated.

[0025] In step S1, the bedrock deformation stability evaluation index is as follows:

[0026] (1) The annual deformation amount in the past three years does not exceed 3 times the mean error of the annual deformation amount;

[0027] (2) The number of positive and negative values ​​of the annual deformation data is close, and the difference does not exceed 30%. For bedrock indicators with a small number of cycles, adjustments can be made based on other indicators, but not more than 45%;

[0028] (3) The mathematical expectation value of the deformation variable tends to zero and does not exceed 0.6 mm;

[0029] (4) The cumulative deformation in the past 10 years is within ±6 mm;

[0030] When the above four indicators are met at the same time, the bedrock mark can be considered stable.

[0031] In step S2, the multi-factor comprehensive analysis method is:

[0032] The three factors of geographical location, observation period and bedrock depth were selected, and weights of 0.5, 0.2 and 0.3 were assigned to the three factors respectively. The model was constructed, the comprehensive score was calculated, and some points with higher scores were selected according to needs.

[0033] In step S2, the Dijkstra algorithm is:

[0034] Assume that each point has a pair of labels: (d j ,p j ), where d j is the shortest path length from the origin point s to the point j, p j The shortest path algorithm from the origin point s to each point j is the point before the midpoint j in the shortest path from s to j. The basic process of solving the shortest path algorithm from the origin point s to each point j is as follows:

[0035] Step 1: Initialization:

[0036] The origin point is set to d s =0, p s is empty; label the origin point s, record k = s, and other points have not been processed;

[0037] Step 2: Check the distance from all marked points k to other directly connected unmarked points j and set:

[0038]

[0039] Where, l kj is the straight-line distance from point k to point j;

[0040] Step 3: Select the next point and select d from the node j , the lowest connection point i;

[0041]

[0042] Step 4: Find the previous point of point i, and find point j directly connected to point i from the marked points * ,set up:

[0043] i=j * As the previous point;

[0044] Step 5: Mark point i. If all points have been marked, the algorithm exits completely. Otherwise, k=i, and returns to step 2.

[0045] In step S2, the overall consistency check method is as follows:

[0046] Using the F test, after the same precision test, if the two-period sample observation data have the same precision, the overall consistency test of the two-period observation data can be performed, where the estimated unit weight variance of each period is:

[0047]

[0048]

[0049] The observation accuracy of the two periods is the same, and the common unit weight variance of the two periods is calculated:

[0050]

[0051] Null hypothesis: The point did not move during the two-week period, then the difference between the two periods d can be used to calculate another variance estimate:

[0052]

[0053] Where μ 2 and θ 2 Independent of each other; f d is the number of independent variables;

[0054] Use the F test to construct statistics:

[0055] F=θ 2 / μ 2 ;

[0056] Using F = θ 2 / μ 2 <F α (f d ,f1+f2), a right-tail test is performed with a given significance level α. When the low-probability event F>F α (f d ,f1+f2) occurs, the original hypothesis is rejected, indicating that there is an unstable starting point, otherwise it means that all points are stable points;

[0057] The F test method is used to carry out the overall consistency hypothesis test to determine whether there are significant displacement points in the network.

[0058] In step S2, the method for identifying significant displacement points is as follows:

[0059] When the overall consistency significance test fails and the F value falls into the rejection region, it is necessary to find the reference points that have moved. The block gap method, limit difference method and t test method can be used to eliminate the points with significant displacement;

[0060] The t-test method is used to eliminate unstable points:

[0061] t=d / σ d ;

[0062]

[0063] After selecting the significance level α, the test formula can be written as:

[0064]

[0065] Given a significance level α, we can get t by looking up the table. α / 2 , if t≤|t α / 2 |, the displacement is not significant and it is a stable point. Otherwise, it is a point with significant displacement and needs to be eliminated.

[0066] Based on the overall consistency calculation results, a t-test was performed on the years that failed the overall consistency test to identify unstable bedrock markers in the network.

[0067] The advantages of the present invention are: good effects on bedrock stability assessment and benchmark point screening, and certain practical significance for improving the accuracy of ground elevation deformation monitoring in the later stage, serving natural resource surveys, urban planning and construction, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A schematic diagram of the steps of the method for optimizing the elevation control network for monitoring land subsidence according to the present invention;

[0069] Figure 2 This is the bedrock map of Shanghai in 2024 according to the present invention;

[0070] Figure 3 This is a schematic diagram of the bedrock marker list for more than 7 consecutive observation periods of the present invention;

[0071] Figure 4 This is the annual deformation distribution curve of the present invention;

[0072] Figure 5 This is a schematic diagram of the statistical table of the annual positive and negative deformation variables, the difference ratio, and the cumulative deformation variables over a ten-year period of the present invention;

[0073] Figure 6 This is a schematic diagram of the annual deformation and tolerance statistics of each bedrock marker in the past three years;

[0074] Figure 7Schematic diagram of the statistical table of single-point stability assessment results of bedrock markers according to the present invention;

[0075] Figure 8 This is a schematic diagram of a multi-factor comprehensive analysis score sheet for selecting the newly added bedrock standard in the present invention;

[0076] Figure 9 This is a schematic diagram of the distance between bedrock markers and the height difference table after the entire network is simplified in the present invention;

[0077] Figure 10 Schematic diagram of the elevation difference correction table for each line in each period of the present invention;

[0078] Figure 11 Schematic diagram of the gap difference statistics table of each evaluation point of the present invention;

[0079] Figure 12 Schematic diagram of the overall consistency test statistics table of the present invention;

[0080] Figure 13 Schematic diagram of the t-test statistical table of the present invention;

[0081] Figure 14 This is a schematic diagram of the statistical table of the standard deviation and mean error of each bedrock mark in each year of the present invention;

[0082] Figure 15 Schematic diagram of the original free network adjustment calculation result table of the present invention;

[0083] Figure 16 Schematic diagram of the original attached network adjustment calculation result table of the present invention;

[0084] Figure 17 Schematic diagram of the new network adjustment calculation result table of the present invention;

[0085] Figure 18 This is the annual deformation curve of the characteristic point D8-048 in the Lingang area of ​​the present invention;

[0086] Figure 19 This is the annual deformation curve of the characteristic point D9-240 at Pudong Airport of the present invention;

[0087] Figure 20 This is the annual deformation curve of the characteristic point 9-521A Pudong Gu Road in the present invention;

[0088] Figure 21 This is the annual deformation curve of the characteristic point Jiading New Town 2-025A of the present invention;

[0089] Figure 22 This is the annual deformation curve of the characteristic point 5-042A in Sheshan area of ​​the present invention;

[0090] Figure 23This is the annual deformation curve of the characteristic point Fengxian area 7-030A of the present invention;

[0091] Figure 24 This is the deformation curve of the characteristic point Pudong Xinchang S16-07 of the present invention. DETAILED DESCRIPTION

[0092] The features of the present invention and other related features are further described in detail below through embodiments in conjunction with the accompanying drawings to facilitate understanding by those skilled in the art:

[0093] Example: Figure 1 As shown, this embodiment relates to a method for optimizing a ground subsidence monitoring elevation control network. Taking Shanghai as an example, the method mainly includes the following steps:

[0094] S1: Use normal distribution theory to carry out stability assessment of bedrock markers and obtain the bedrock marker deformation stability assessment index based on the entire historical time and space.

[0095] Among them, the burial depth in Songjiang, Sheshan, Jinshan, Qingpu and other areas is mostly between 160 and 220 meters; the burial depth in Pudong, Baoshan, Jiading and other riverside and coastal areas is mostly between 280 and 360 meters; the burial depth in the estuary sand island area is generally greater than 400 meters, and in some parts of Chongming Island it can reach nearly 500 meters.

[0096] As early as 1871, Shanghai began preparing for ground subsidence monitoring and leveling, establishing the Wusong zero point. Two more ground subsidence monitoring missions were conducted in 1910 and 1919. Due to the instability of the Wusong zero point, a bedrock benchmark was established at Sheshan in Songjiang in 1922. Between 1962 and 1964, five bedrock benchmarks were installed at Xiaozha Town, Wusong Middle School, No. 1 Jilin Road (Labor Park), Fuxing Island Park, and Luding Road, all continuing to use the Sheshan benchmark as the starting point. In September 1964, based on the recommendations of experts at the Shanghai Land Subsidence Conference, a new point was established on the hillside rock formations at the northern foot of Sheshan Mountain, adjacent to the Qingsong Highway, in accordance with national standards. This new point, designated the "Ning-Shanghai Sheshan Bedrock Mark," was incorporated into the national Shanghai-Nanjing First-Class Leveling Route. To improve the network structure, the Jiangjiaqiao Bedrock Mark (controlling the northern part of Shanghai) and the Pudong Tangqiao (controlling the Pudong area) were added, forming the initial Shanghai Land Subsidence Elevation Control Network. After 1965, the First-Class Leveling Network comprised three leveling rings from the Sheshan New Base Point to the bedrock marks in Puxi. In 1972, the Beixinjing-Labor Park leveling route was added. In 1975, the number of leveling rings increased to five with the completion of the Shanghai Flour Mill and the Bund Children's Park. Subsequently, the land subsidence monitoring leveling network underwent several expansions, with the completion of bedrock marks at Gaoqiao, the Academy of Agricultural Sciences, Taopu, and Wujing. After 1975, elevation transfer from Puxi to Pudong was accomplished through nighttime first-class leveling in cross-river tunnels. After 1980, to strengthen control over the northern corner of Pudong, surface leveling was added at Nenhui Road, transferring Puxi elevations to the Tangqiao bedrock mark and the Gaoqiao Chemical Plant bedrock mark. Later, to account for factors such as the error transfer caused by the distance between the Sheshan bedrock mark and the urban area, the 1983 "Report on Dynamic Analysis of Land Subsidence Using the Xiaozha Town Bedrock Mark as the Starting Point" was reviewed. Starting in 1984, the Shanghai Land Subsidence Monitoring Elevation Control Network was redesigned to use the Xiaozha bedrock mark as the starting point, relocating the starting point within the free network. In 2007, the "Feasibility Study Report on Converting the Shanghai Land Monitoring Leveling Network from a Free Network to a Coordinated Network" was reviewed. Since 2008, the Shanghai Land Subsidence Monitoring Elevation Control Network has replaced the single-reference free network with a coordinated network using Xiaozha, Beixinjing, Wusong, and Tangqiao as datum points, strengthening control over the northern, Pudong, and western parts of the city. By the end of 2024, Shanghai had built and applied a total of 66 bedrock markers for land subsidence, of which 57 were included in the annual area leveling survey. A land subsidence monitoring network covering most areas of the city has been basically formed. Figure 2 shown.

[0097] 43 bedrock marks (H1~H43) in Shanghai with 7 or more consecutive observation data as of the end of 2024 were selected, and their historical elevation difference data were recalculated through free network adjustment using a fixed bedrock mark as the starting point to ensure data continuity and reliability.

[0098] When sorting out past data, it was found that most of the bedrock markers with long historical observation data had large fluctuations in annual deformation between 1984 and 2000. After investigation and verification, the data was found to be authentic and reliable. In the decades of historical work on land subsidence monitoring in Shanghai, different observation equipment and technical methods were used at different historical stages. For example, before 1984, the optical level Zeiss 004 dual-point method was used for observation. From 1984 to 2000, a single-route round-trip observation was used. During this period, the annual deformation data fluctuations were the largest. After 2001, the electronic level was used for round-trip observation, and the data stability was significantly improved. Figure 3 shown.

[0099] According to measurement error theory and statistical theory, when a quantity is repeatedly measured with the same accuracy, the errors follow a normal distribution, meaning that the number of measurements with small errors is greater, and the number of measurements with large errors is smaller. Measurement theory also stipulates that when a quantity is repeatedly observed, the median of the observed values ​​is taken as the mean or average value, and the mean error is calculated based on this, with a tolerance of 2 or 3 times the mean error.

[0100] In the theory of measurement error, there is a test method for whether the error obeys the normal distribution. That is, when the difference between multiple observations of each bedrock mark conforms to the characteristics of the normal distribution, the error occurring at this point is dominated by accidental error, and the influence of gross error can be excluded.

[0101] The density function of the normal distribution is:

[0102]

[0103] Where ξ is the mean, representing the location parameter of the distribution; σ is the standard deviation, representing the size parameter of the distribution; when ξ = 0 and σ = 1, the resulting density function is:

[0104]

[0105] The distribution with this density function is called the standard normal distribution. The random variable is recorded as X~N(0,1), and the distribution function is:

[0106]

[0107] Where x is a real number that can take any real value from -∞ to +∞, representing the possible values ​​of the standard normal random variable X. F(x) represents the probability that the random variable X is less than or equal to a certain value x, and its data meets the following four conditions:

[0108] (1) There are more errors with smaller absolute values ​​than errors with larger absolute values;

[0109] (2) The number of positive errors and negative errors with equal absolute values ​​is close;

[0110] (3) The absolute value of the error is limited to a certain extent. According to the accuracy level requirements, the maximum value shall not exceed 2 or 3 times the mean error;

[0111] (4) The mathematical expectation of random error is zero;

[0112] When the annual deformation of the bedrock target meets the above four conditions at the same time, the indicators can be refined and its stability can be evaluated.

[0113] By obtaining the annual deformation data of dozens of bedrock marks over the years, the annual deformation data and cumulative deformation data of 43 bedrock marks in the past 10 periods (including less than 10 periods) were selected and counted. Figure 4 shown.

[0114] The number of positive and negative annual deformation variables and the percentage of the difference are statistically analyzed. The cumulative deformation variables of the 43 bedrock marks in the past 10 cycles (including less than 10) and the annual variables in the past 3 years and the mean error limit (3 times) are shown in the table. Figure 5 shown.

[0115] See also Figure 4 、 Figure 5 and Figure 6 As shown in the figure, the data of 43 bedrock benchmarks in the past ten years show that:

[0116] (1) The annual deformation distribution curve fully conforms to the normal distribution characteristics, and its mathematical expectation value is +0.29mm;

[0117] (2) After eliminating gross errors, the number of positive and negative signs of each bedrock standard of annual deformation variables is 35, accounting for 81.4%, with a difference ratio of ≤30%, 5, accounting for 11.6% (most of which are less than ten observation periods), and 3, accounting for 7.0%, with a difference ratio of ≥50%.

[0118] (3) After eliminating gross errors, the cumulative deformation has a mean error limit (twice the mean error) of ±8.46 mm; among them, 37 have an absolute value ≤6 mm, accounting for 86.1%, 1 has an absolute value between 6 mm and 9 mm, accounting for 2.3%, and 5 have an absolute value ≥9 mm, accounting for 11.6%.

[0119] Based on the measurement error theory and the normal distribution characteristics, the following bedrock deformation stability evaluation index is proposed from a macroscopic perspective:

[0120] (1) The annual deformation amount in the past three years does not exceed 3 times the mean error of the annual deformation amount;

[0121] (2) The number of positive and negative values ​​of the annual deformation data is close, and the difference does not exceed 30%. For bedrock indicators with a small number of cycles, adjustments can be made as appropriate based on other indicators, but shall not exceed 45%;

[0122] (3) The mathematical expectation value of the deformation variable tends to zero and does not exceed 0.6 mm;

[0123] (4) The cumulative deformation in the past 10 years is within ±6 mm;

[0124] If the above conditions are met at the same time, the bedrock mark is considered to be stable.

[0125] According to the above standards, the stability statistics of the 43 bedrock markers can be found in Figure 7 As shown, there are 7 bedrock markers suspected to be unstable.

[0126] S2: Select the proposed new starting reference points based on the multi-factor comprehensive analysis method, use the Dijkstra algorithm to optimize the complex leveling network, and conduct an overall consistency test and identification of significant displacement points on the proposed new starting reference points from the perspective of micro-deformation detection.

[0127] Among them, the multi-factor comprehensive analysis method is a method that combines manual experience with quantitative analysis. It selects the geographical location, observation period, and bedrock target depth, assigns different weights, builds a model, calculates the comprehensive score, and selects some points with higher scores according to needs. The weights of the above three factors are set to 0.5, 0.2, and 0.3 respectively, and the comprehensive score of each bedrock target is calculated. Figure 8 shown.

[0128] according to Figure 8 The calculation results show that in addition to the original bedrock point being directly included as the national origin, 6 additional bedrock points have been selected as new starting points, namely H22, H42, H21, H32, H20 and H15, a total of 7 bedrock marks.

[0129] The Dijkstra algorithm, proposed by EWDijkstra in 1959, generates shortest paths in ascending order of path length. It is widely considered the most classic and effective algorithm for solving this type of shortest path problem. The core idea is to select a node with the shortest distance from a node for which the shortest path has not yet been determined and update the shortest path from that node to the source node. Its advantages lie in its applicability to single-source shortest path problems on all graphs with non-negative weights. The algorithm is highly scalable and can easily handle graphs with large numbers of nodes and edges, offering excellent optimization performance.

[0130] Assume that each point has a pair of labels: (d j ,p j ), where d j is the shortest path length from the origin point s to the point j, p j The shortest path algorithm from the origin point s to each point j is the point before the midpoint j in the shortest path from s to j. The basic process of solving the shortest path algorithm from the origin point s to each point j is as follows:

[0131] Step 1: Initialization:

[0132] The origin point is set to d s =0, p s is empty; label the origin point s, record k = s, and other points have not been processed;

[0133] Step 2: Check the distance from all marked points k to other directly connected unmarked points j and set:

[0134]

[0135] Where, l kj is the straight-line distance from point k to point j;

[0136] Step 3: Select the next point and select d from the node j , the lowest connection point i;

[0137]

[0138] Step 4: Find the previous point of point i, and find point j directly connected to point i from the marked points * ,set up:

[0139] i=j * As the previous point;

[0140] Step 5: Mark point i. If all points have been marked, the algorithm exits completely. Otherwise, k=i, and returns to step 2.

[0141] In addition to the starting bedrock mark, the leveling route of Shanghai's annual area leveling survey also includes numerous other bedrock marks, depth marks, stratification marks and ground leveling points. Some of the intermediate points become nodes of the leveling network. According to statistical results, the average number of nodes from 2020 to 2024 is about 3,000 points per year, and the observed height difference is about 3,300. Such a complex leveling network must be simplified in a targeted manner in the later evaluation and calculation to obtain the distance and height difference between bedrock marks. There are multiple routes between two points in the entire network, and they must be selected to obtain the shortest distance and corresponding height difference data. For this purpose, the "Simplification Software for Complex Leveling Monitoring Networks of Ground Subsidence" was developed based on the Dijkstra algorithm to calculate the leveling route distance and height difference between each starting bedrock mark, complete the re-networking and apply it to later calculations. According to the needs, the simplified leveling network has 11 nodes and 23 height differences, see Figure 9 .

[0142] According to the principle of statistical hypothesis testing, the quasi-stable adjustment method is adopted and the bedrock elevation value of the small gate is assigned to perform adjustment calculation on the simplified leveling network. The adjustment results of each leveling network are obtained, including the height difference correction number, adjustment value and covariance matrix. The height difference correction number can be found in Figure 10 .

[0143] The overall consistency test is the F test. After the same precision test, if the two-period sample observation data have the same precision, the overall consistency test can be performed on the two-period observation data. The estimated unit weight variance of each period is:

[0144]

[0145] The observation accuracy of the two periods is the same, and the common unit weight variance of the two periods is calculated:

[0146]

[0147] Null hypothesis: The point did not move during the two-week period, then the difference between the two periods d can be used to calculate another variance estimate:

[0148]

[0149] Where μ 2 and θ 2 Independent of each other; f d is the number of independent variables;

[0150] Use the F test to construct statistics:

[0151] F=θ 2 / μ 2 ;

[0152] Using F = θ 2 / μ 2 <F α (f d ,f1+f2), a right-tail test is performed with a given significance level α (0.05). When the low-probability event F>F α (f d ,f1+f2) occurs, the original hypothesis is rejected, indicating that there is an unstable starting point, otherwise it means that all points are stable points;

[0153] The F test method is used to conduct the overall consistency hypothesis test to determine whether there are significant displacement points in the network. Figure 11 ;

[0154] Based on the gap difference, covariance and height difference correction number, the overall consistency test results for each year are calculated as follows. Figure 12 :

[0155] 2020~2021:

[0156]

[0157] F 0.05 (10,26)=2.3479;

[0158] F<F α , the inspection passed.

[0159] 2021~2022:

[0160]

[0161] F 0.05 (10,26)=2.3479;

[0162] F>F α , the test fails, indicating that there are significant displacement points in the 2021~2022 network.

[0163] 2022~2023:

[0164]

[0165] F 0.05 (10,26)=2.3479;

[0166] F<F α , the inspection passed.

[0167] 2023~2024:

[0168]

[0169] F 0.05 (10,26)=2.3479;

[0170] F>F α , the test fails, indicating that there are significant displacement points in the 2023~2024 network.

[0171] 2020~2023:

[0172]

[0173] F 0.05 (10,26)=2.3479;

[0174] F>F α , the test fails, indicating that there are significant displacement points in the 2020~2023 network.

[0175] 2020~2024:

[0176]

[0177] F 0.05 (10,26)=2.3479;

[0178] F>F α, the test passed, indicating that there is no significant displacement point in the 2020~2024 network.

[0179] When the overall consistency significance test fails and the F value falls in the rejection region, it is necessary to find the reference points that have moved. The block gap method, limit difference method and t test method can be used to eliminate the significant displacement points.

[0180] When using the t-test method to eliminate unstable points:

[0181] t=d / σ d ;

[0182]

[0183] After selecting the significance level α, the test formula can be written as:

[0184]

[0185] Given a significance level α, we can get t by looking up the table. α / 2 , if t≤|t α / 2 |, the displacement is not significant and it is a stable point. Otherwise, it is a point with significant displacement and needs to be eliminated.

[0186] According to the overall consistency calculation results, a t-test was performed on the years that failed the overall consistency test to identify unstable bedrock markers in the network. The calculation results showed that 2020-2021, 2022-2023, and 2020-2024 (even-numbered periods) passed the overall consistency test and no significant point identification was required. For other years, the theoretically constructed statistic t=d / σ was calculated based on the t-test method. d , see the data for details. Figure 13 .

[0187] According to the conclusion of the bedrock marker stability assessment, there are certain accidental errors in the field measurement process. The longer the distance, the greater the cumulative error and the unilateral nature of the error. However, there is a high probability that it will be corrected in subsequent years. Figure 13 The results indirectly confirmed this conclusion, and the overall consistency passed the test in the cross-year cycle (even cycle) from 2020 to 2024. Therefore, it is believed that based on the comprehensive evaluation of the annual and cross-year test results, the above bedrock marks are relatively stable and their geographical distribution is balanced, basically covering the current monitoring area of ​​Shanghai, and can be used as the starting point of Shanghai's ground elevation control network.

[0188] S3: Determine the new starting reference point of the ground subsidence monitoring elevation control network based on the comparison of the results of the target feature points in different adjustment systems.

[0189] Among them, the network adjustment calculation will be carried out based on 11 bedrock marks such as H0 as the starting points, but the source of the elevation value of the starting point and the time node need to be clarified.

[0190] First, the starting elevations of the original starting points H0, H3, H38, and H1 will not be adjusted. The starting elevations of other bedrock marks will be determined according to the following principles:

[0191] (1) Continuing the previous results system, that is, the elevation value system when the free network was converted to the attached network in 2008, the free network adjustment results with H0 as the starting point were adopted;

[0192] (2) Calculate the annual mean error of each bedrock marker between 2020 and 2024 The year with the smallest mean error is selected, and its bedrock elevation result is determined as the new starting point result of the Shanghai ground elevation control network.

[0193] according to Figure 14 According to the calculation results, the new starting elevation of the above bedrock mark in the Shanghai ground subsidence monitoring network is the result of the free network adjustment with H0 as the starting point in 2021.

[0194] According to the new starting point elevation, the attached network adjustment model is used to adjust the measurement results from 2020 to 2024. According to the geographical location of the starting point, characteristic leveling points are selected and compared with the original free network and attached network adjustment results to verify the reliability and superiority of the new starting point. The calculation results are shown in Figures 15-17 , the shape variable curves of different reference point systems are shown in Figures 18-24 .

[0195] according to Figures 15-17 and Figures 18-24 Among the annual variable mean error indicators calculated in different adjustment systems, the volatility of the Xinfuhe network is the smallest. In addition, from the perspective of the annual deformation variable mean error of a single point, the annual deformation variable mean error of a single point in the Xinfuhe network has dropped significantly, with the largest drop reaching 74%, located in Pudong Xinchang S16-07.

[0196] At the characteristic points far away from the original starting point, the deformation trends of the characteristic points of the original free network and the original attached network are basically the same, and the annual deformation fluctuation amplitude is large, but the deformation trend of the characteristic points in the new attached leveling network is obviously smoother.

[0197] This shows that the expansion of the ground subsidence monitoring scope, the continuous change of the network type, and the timely updating and supplementation of the starting reference point benchmark can effectively improve the monitoring accuracy, weaken the jumping phenomenon, and make the ground monitoring results more truly reflect the actual situation of ground subsidence and conform to the objective laws of ground subsidence.

[0198] In summary, this embodiment uses the classic free network adjustment to obtain the elevation deformation variables of all bedrock marks over the years as basic data, and based on the normal distribution theory, proposes a stability evaluation index for the deformation variables of bedrock marks in all historical time and space. Among the 43 bedrock marks, it is evaluated and determined that the stability of 7 bedrock marks is questionable. The multi-factor comprehensive analysis method is used to select 6 new starting reference points; based on the Dijkstra algorithm and the average gap method, the "Complex Leveling Network Line Simplification Software for Ground Subsidence Monitoring" and the "Stability Evaluation Program for Ground Subsidence Elevation Control Network" are developed. Through iterative calculations, the complex and huge leveling line network is simplified, and the overall consistency test and displacement significant points of the new starting reference points are identified from the perspective of micro-deformation detection. The error theory and indicators are used to determine the elevation time nodes and values ​​of the new starting reference points, and the adjustment results of different benchmark systems are compared and analyzed. 7 bedrock marks are proposed as the new starting reference points. The conclusions are as follows:

[0199] (1) Shanghai's land subsidence monitoring has adopted different observation equipment and technical methods in different historical stages, which has continuously improved the measurement accuracy, made the data more reliable, and better expressed the land subsidence situation;

[0200] (2) Based on the annual deformation of 43 bedrock markers in the past ten years, the distribution characteristics and regularity of the annual deformation variables were studied, and the conformity with the normal distribution was studied. Combined with the cumulative deformation over a period of time, four historical and spatiotemporal bedrock marker deformation stability assessment indicators were proposed, namely:

[0201] ① The annual deformation in the past three years does not exceed 3 times the mean error of the annual deformation;

[0202] ② The number of positive and negative values ​​in the annual deformation data is close, accounting for no more than 30%. Considering the relatively small number of observation cycles for some bedrock markers, some of them can be appropriately relaxed to 50% based on the situation of other indicators;

[0203] ③The mathematical expectation value of the deformation variable tends to zero, and the maximum does not exceed 0.6mm;

[0204] ④ The cumulative deformation in the past 10 years is within ±6mm;

[0205] (3) According to the assessment, the stability of 7 bedrock markers is questionable from a long-term historical and spatial macroscopic perspective, while 36 bedrock markers are relatively stable;

[0206] (4) Based on the multi-factor comprehensive analysis method, it is proposed to select six bedrock marks, H22, H15, H20, H21, H32 and H42, as the starting reference points;

[0207] (5) Based on the Dijkstra algorithm, the complex and large leveling network is simplified into a backbone network with 11 nodes and a total of 23 first-class leveling lines;

[0208] (6) Using the F test and t test methods in statistical hypothesis testing, we conducted an overall consistency test and identified significant displacement points, and concluded that all eleven bedrock markers were included in the reference points of the Shanghai land subsidence monitoring elevation control network;

[0209] (7) Using error theory to determine the elevation time nodes and values ​​of the newly added reference points, and comparing and analyzing the characteristic point results in different adjustment systems to clarify the superiority of the newly added points;

[0210] (8) In the stability analysis of benchmark points in a large-scale and long-distance control network, the average gap method should be used to analyze the results of a single year, and more importantly, the results of multiple years (even-numbered cycles) should be used to eliminate the impact of accidental errors in a single year;

[0211] (9) In the later stage, all technical indicators of field observation shall be strictly controlled to improve the accuracy of leveling observation. A layered assessment method shall be adopted for the stability assessment of bedrock markers, and assessment reports shall be issued regularly.

[0212] The beneficial technical effects of this embodiment are: good results in bedrock target stability assessment and benchmark point screening, and it has certain practical significance for improving the accuracy of ground elevation deformation monitoring, serving natural resource surveys, urban planning and construction, etc.

[0213] Although the above embodiments have described the concepts and embodiments of the present invention in detail with reference to the accompanying drawings, ordinary technicians in this field can recognize that various improvements and modifications can still be made to the present invention without departing from the scope of the claims, so they are not described in detail here.

Claims

1. A method for optimizing the elevation control network for land subsidence monitoring, characterized in that The method comprises: S1: Use normal distribution theory to carry out bedrock marker stability assessment and obtain bedrock marker deformation stability assessment indicators based on the entire historical time and space; S2: Select the proposed new reference points based on a multi-factor comprehensive analysis method, optimize the complex leveling network using the Dijkstra algorithm, and perform an overall consistency test and identify significant displacement points on the proposed new reference points from the perspective of micro-deformation detection. S3: Determine the new starting reference point of the ground subsidence monitoring elevation control network based on the comparison of the results of the target feature points in different adjustment systems.

2. A method for optimizing a ground subsidence monitoring elevation control network according to claim 1, characterized in that In step S1, the method for conducting bedrock target stability assessment using normal distribution theory is as follows: The density function of the normal distribution is: Where ξ is the mean, representing the location parameter of the distribution, and σ is the standard deviation, representing the size parameter of the distribution. When ξ = 0 and σ = 1, the resulting density function is: The distribution with this density function is called the standard normal distribution. The random variable is recorded as X~N(0,1), and the distribution function is: Where x is a real number that can take any real value from -∞ to +∞, representing the possible values ​​of the standard normal random variable X. F(x) represents the probability that the random variable X is less than or equal to a certain value x, and its data meets the following four conditions: (1) There are more errors with smaller absolute values ​​than errors with larger absolute values; (2) The number of positive errors and negative errors with equal absolute values ​​is close; (3) The absolute value of the error is subject to certain limits. Depending on the accuracy level required, the maximum value shall not exceed 2 or 3 times the mean error. (4) The mathematical expectation of random error is zero; When the annual deformation of the bedrock target meets the above four conditions at the same time, the indicators can be refined and its stability can be evaluated.

3. A method for optimizing a ground subsidence monitoring elevation control network according to claim 2, characterized in that In step S1, the bedrock deformation stability evaluation index is as follows: (1) The annual deformation amount in the past three years does not exceed 3 times the mean error of the annual deformation amount; (2) The number of positive and negative values ​​of the annual deformation data is close, and the difference does not exceed 30%. For bedrock indicators with a small number of cycles, adjustments can be made based on other indicators, but not more than 45%; (3) The mathematical expectation value of the deformation variable tends to zero and does not exceed 0.6 mm; (4) The cumulative deformation in the past 10 years is within ±6 mm; When the above four indicators are met at the same time, the bedrock mark is considered to be stable.

4. A method for optimizing a ground subsidence monitoring elevation control network according to claim 3, characterized in that In step S2, the multi-factor comprehensive analysis method is: The three factors of geographical location, observation period and bedrock depth were selected, and weights of 0.5, 0.2 and 0.3 were assigned to the three factors respectively. The model was constructed, the comprehensive score was calculated, and some points with higher scores were selected according to needs.

5. A method for optimizing a ground subsidence monitoring elevation control network according to claim 4, characterized in that In step S2, the Dijkstra algorithm is: Assume that each point has a pair of labels: (d j ,p j ), where d j is the shortest path length from the origin point s to the point j, p j The shortest path algorithm from the origin point s to each point j is the point before the midpoint j in the shortest path from s to j. The basic process of solving the shortest path algorithm from the origin point s to each point j is as follows: Step 1: Initialization: The origin point is set to d s =0, p s is empty; label the origin point s, record k = s, and other points have not been processed; Step 2: Check the distance from all marked points k to other directly connected unmarked points j and set: Where, l kj is the straight-line distance from point k to point j; Step 3: Select the next point and select d from the node j , the lowest connection point i; Step 4: Find the previous point of point i, and find point j directly connected to point i from the marked points * ,set up: i=j * As the previous point; Step 5: Mark point i. If all points have been marked, the algorithm exits completely. Otherwise, k=i, and returns to step 2.

6. A method for optimizing a ground subsidence monitoring elevation control network according to claim 5, characterized in that In step S2, the overall consistency check method is as follows: Using the F test, after the same precision test, if the two-period sample observation data have the same precision, the overall consistency test of the two-period observation data can be performed, where the estimated unit weight variance of each period is: The observation accuracy of the two periods is the same, and the common unit weight variance of the two periods is calculated: Null hypothesis: The point did not move during the two-week period, then the difference between the two periods d can be used to calculate another variance estimate: Where μ 2 and θ 2 Independent of each other; f d is the number of independent variables; Use the F test to construct statistics: F=θ 2 / m 2 ; Using F = θ 2 / μ 2 <F α (f d ,f1+f2), a right-tail test is performed with a given significance level α. When the low-probability event F>F α (f d ,f1+f2) occurs, the original hypothesis is rejected, indicating that there is an unstable starting point, otherwise it means that all points are stable points; The F test method is used to carry out the overall consistency hypothesis test to determine whether there are significant displacement points in the network.

7. A method for optimizing a ground subsidence monitoring elevation control network according to claim 6, characterized in that In step S2, the method for identifying significant displacement points is as follows: When the overall consistency significance test fails and the F value falls into the rejection region, it is necessary to find the reference points that have moved. The block gap method, limit difference method and t test method can be used to eliminate the points with significant displacement; The t-test method is used to eliminate unstable points: t=d / σ d ; After selecting the significance level α, the test formula can be written as: Given a significance level α, we can get t by looking up the table. α / 2 , if t≤|t α / 2 |, the displacement is not significant and it is a stable point. Otherwise, it is a point with significant displacement and needs to be eliminated. Based on the overall consistency calculation results, a t-test was performed on the years that failed the overall consistency test to identify unstable bedrock markers in the network.

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