A dynamic reference adjustment and deformation analysis method for multi-period deformation monitoring network

Abstract

The present application belongs to the field of engineering surveying and deformation monitoring, and discloses a dynamic reference adjustment and deformation analysis method for multi-period deformation monitoring network, which comprises the following steps: multi-period observation data acquisition and preprocessing; dynamic reference establishment and multi-period data unified adjustment; automatic identification of stable point group; real deformation calculation and output; deformation analysis and safety warning. The core of the method is to abandon the absolute dependence on the stability of a single reference point in the prior art, to automatically identify a relatively stable point group from the multi-period observation data through strict statistical testing, and to construct an optimal and unified dynamic reference, so as to accurately separate the reference point displacement and the real deformation of the monitoring point.

Description

Technical Field

[0001] This invention belongs to the field of engineering measurement and deformation monitoring technology, and in particular relates to a dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network, which is applicable to high-precision deformation monitoring and analysis of large-scale engineering structures such as hydropower stations, dams, and slopes. Background Technology

[0002] Currently, the most commonly used method for processing multi-period observation data of deformation monitoring networks is the classical adjustment method. The basic process of this method is as follows: when adjusting the observation data for each period, the coordinates of one or more reference points that are considered absolutely stable are fixed, thereby calculating the absolute coordinates of the monitoring points for that period; then, by directly subtracting the absolute coordinates calculated in the current period from the absolute coordinates calculated in the previous period, the deformation amount of each monitoring point in the current period is obtained.

[0003] This existing technology has the following inherent drawbacks: 1. Strong Dependency Assumption: The correctness of the results depends entirely on the strong assumption that "the fixed benchmark is absolutely stable." In actual engineering, especially in areas with complex geological conditions such as hydropower station reservoirs and mines, the benchmark itself may also shift due to crustal deformation or external environmental influences.

[0004] 2. Error Propagation and Masking: Once an unknown displacement occurs at the benchmark point, this displacement will be introduced into the entire adjustment result as a systematic error. This will lead to two serious consequences: first, the deformation of the actual deformation point will be underestimated or distorted; second, stable points may be misjudged as deformation points, thus seriously misleading the judgment of the engineering safety status.

[0005] 3. Distortion in deformation analysis: Since it is impossible to separate the displacement of the reference point from the actual deformation of the monitoring point, the reliability and accuracy of deformation analysis based on classical adjustment results cannot be guaranteed, making it difficult to meet the stringent requirements of precision engineering safety monitoring.

[0006] Therefore, there is an urgent need in this field for a new technological solution that can overcome the above-mentioned defects and automatically identify stable benchmarks to obtain the true deformation of monitoring points. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network.

[0008] The present invention is achieved through the following technical solutions.

[0009] This invention provides a dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network, comprising the following steps: Step S1, acquisition and preprocessing of multi-period observation data, including: acquiring observation data of continuous observation of the target monitoring area; detecting and eliminating gross errors in the observation values ​​of each period of observation data, normalizing the observation values, and generating an observation vector with a weight matrix and its weight matrix; Step S2, Dynamic Benchmark Establishment and Unified Adjustment of Multi-Period Data, includes: using the observation vectors and their weight matrices, through an overall quasi-stabilized adjustment scheme or a dynamically quasi-stabilized constrained adjustment scheme, to calculate the coordinates of each period under the unified benchmark, where the... The coordinate vector of all monitoring points during the period is The displacement time series of each monitoring point was obtained; Step S3: Identify stable point groups based on the displacement time series of each monitoring point: Step S4, Calculation and output of actual deformation, including: The stable point group identified in step S3 is used as the new pseudo-stable benchmark. The results of the dynamic pseudo-stable constraint adjustment scheme in step S2 are transformed into a benchmark or re-adjusted with constraints to obtain the optimized coordinates for each period. Based on the optimized coordinates for each period, the deformation of each monitoring point relative to the pseudo-stable benchmark in each observation period is calculated. The deformation of each monitoring point in all periods is arranged in chronological order to form the displacement time series of the monitoring point. The displacement time series of all monitoring points are collected to form a multi-period high-precision deformation time series. The multi-period high-precision deformation time series refers to a complete displacement time series that covers the entire spatial range of the monitoring network and the entire observation time range. S5. Deformation analysis and safety early warning, including: performing deformation trend analysis based on the multi-period high-precision deformation time series, obtaining deformation patterns through deformation trend analysis, calculating deformation rate based on deformation patterns, and then issuing safety threshold early warning based on the comparison between deformation rate and safety threshold; when the deformation amount or deformation rate exceeds the threshold, the system automatically triggers early warning information of different levels.

[0010] Preferably, the observation data obtained in step S1 includes the target monitoring area in a time series. N consecutive observation periods of data; For a leveling network, the observation data are elevation difference vectors. ( For planar networks, the observations are the side lengths, directions, or GNSS baseline vectors. The observation normalization includes converting observations of different precisions and dimensions into a unified form with weighted matrices. The observation vector; Among them, the observation vector To form an n×1 observation vector from all n observations in period i, we can represent it as: , Representing the period The nth observation; for the nth observation in the vector; Observations According to its prior variance The variance of the selected unit weight Calculate its weight ; Based on the assumption that all observations are independent, an n×n diagonal weight matrix is ​​constructed. Its diagonal elements are the weights of each observation. Off-diagonal elements are zero, represented as: The diagonal weight matrix Weights are used to control the influence of observations of different precisions on the final solution during the adjustment process.

[0011] Preferably, the overall pseudo-stabilization adjustment scheme in step S2 treats multi-period observation data as a whole, constructs a parameter system for one-time solution, and includes the following steps: A1. Parameterization: The coordinates or elevations of the monitoring points in each period are used as parameters to be estimated. Assume that each period has... Each monitoring point, The total parameter vector of the period data is ,in For the first The coordinate vectors of all monitoring points during the period; A2. Functional Model: Based on the principle of indirect adjustment, a unified expression for the N-period observation equation is established: in, It is the residual vector of the observed values. It is a design matrix with a clear block structure. It is a vector of observations for all periods; A3. Stochastic Model: Defining the Overall Weight Matrix ; A4. Baseline Constraint: A pseudo-stability constraint that minimizes the sum of squares of the total displacements at all monitoring points throughout the entire observation period, mathematically expressed as: In the formula, It is a scalar function to be minimized, defined as the sum of the squares of the displacements of all monitoring points from the first period to the last period. This indicates the total number of monitoring points. It's the last issue number. It is a coordinate vector; This constraint is achieved through a conditional indirect adjustment method; the constraint equation can be written as: in, As the baseline constraint matrix, Represents the transpose of a matrix. The parameter vector to be estimated; The specific form depends on the network type. For a one-dimensional leveling network, this condition is equivalent to minimizing the sum of the squares of the elevation changes of all points from the first period to the last period. A5. Adjustment Solution: Based on the least squares criterion, construct and solve the normal equations to directly obtain the coordinate estimates of all period data under a unified benchmark. This benchmark is to make the entire network... The optimal benchmark with the smallest overall change over a given period.

[0012] Preferably, the dynamic quasi-stabilized constraint adjustment scheme in step S2 adopts a recursive approach, unifying the data of subsequent periods onto the initial baseline established in the first period, including: B1. Definition of the benchmark period: For the first period Observational data Free network adjustment is performed using a centroid datum mathematical datum, with constraints applied. The initial coordinates of the monitoring network are obtained by solving the problem. This coordinate set defines the initial stable shape of the monitoring network; B2. Multi-period unified adjustment: For the first period... Expect( For observation data (e.g., 2, 3, ..., N), the coordinate estimates obtained from the first period adjustment are used in the adjustment model. As a quasi-stability constraint with extremely high weight, it is related to the first... Solving the observation equations for the first period together makes the first period... Solution coordinates of the period Approximately, provided that the observed values ​​for this period are met. This achieves a unified benchmark. The function model and the observation equation are as follows: In the formula, This is the design matrix for Phase 1, which has a clear block structure. The design matrix for period i has a clear block structure; Constraints: Coordinates obtained from the adjustment of the first period's observation data. As a pseudo-stable benchmark, the first requirement is... Coordinates of periodic observation data Compared to displacement vector The quadratic form is minimized, and its expression is: in, The weight matrix is ​​the weight matrix of the displacement vector, which is equivalent to... Introduced as a constraint with maximum weights in adjustment; B3. Adjustment Solution: Solve using the least squares method to obtain the... Coordinates of periodic observation data This coordinate is relative to the baseline of the first phase of observation data. Repeat this process until all period data has been processed, thus ensuring that all period data are unified under the same initial baseline.

[0013] Preferably, in step S3, the displacement time series of each monitoring point is obtained based on step S2. ,in For the displacement time series of the kth monitoring point in the Nth period, the stable point group is identified by the average gap method and the t-test method.

[0014] Preferably, the average gap method step includes: Calculate each monitoring point Average displacement over N periods and displacement standard deviation ; The confidence interval for the overall average displacement is calculated using the following formula: in, This represents the overall mean of the average displacement of all monitoring points; The overall standard deviation of the displacements at all points; Indicates the total number of monitoring points; The upper side of the standard normal distribution quantiles; This indicates the significance level, i.e., the confidence level. ; If a certain monitoring point average displacement If it falls within the confidence interval, and its displacement sequence If there is no significant trend, the monitoring point is identified as a relatively stable point.

[0015] Preferably, the t-test method includes: testing whether the mean of the displacement sequence of each monitoring point is significantly different from zero; if the test statistic does not reject the null hypothesis, then the point can be regarded as a stationary point.

[0016] Preferably, in step S4, when the overall pseudo-stabilized adjustment scheme is used in step S2, the adjustment result is... This is already the optimal state; the deformation between any two points and any two periods of observation data can be directly extracted as follows: in, Indicates the first Periodic observation, Indicates the first Period observation, representing the period number of the observation; Indicates the first The monitoring point number represents the number of a specific point in the monitoring network.

[0017] Preferably, in step S4, when a dynamic quasi-stabilized constraint adjustment scheme is used in step S2, the coordinates for each period are... The results are already relative to a unified benchmark. The deformation of the observation data between adjacent periods is as follows: In the formula, Indicates the first Periodic observation, express The previous observation in the previous period represents the period number of the observation; Indicates the first The monitoring point number represents the number of a specific point in the monitoring network.

[0018] Preferably, in step S5, the deformation rate of the monitoring point is calculated using the average rate method. : ,in For displacement, This represents the time interval between displacements.

[0019] The beneficial effects of this invention are as follows: The core of the method of this invention lies in abandoning the absolute dependence on the stability of a single benchmark point in the existing technology. It automatically identifies a group of relatively stable points from multiple observation data through rigorous statistical tests, and constructs an optimal and unified dynamic reference benchmark based on this, thereby accurately separating the displacement of the benchmark point from the actual deformation of the monitoring point. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0021] The technical solution of the present invention is further described below, but the scope of protection is not limited to what is described.

[0022] Example: like Figure 1As shown, a dynamic benchmark adjustment and deformation analysis method for a multi-period deformation monitoring network includes: performing unified adjustment on multi-period observation data to obtain a preliminary displacement sequence for each monitoring point; automatically identifying relatively stable point groups from the preliminary displacement sequence based on statistical tests; defining a dynamic reference benchmark using the stable point groups and calculating the actual deformation of each monitoring point relative to the dynamic reference benchmark; and performing deformation analysis and early warning based on the actual deformation. The method includes the following steps: Step S1, acquisition and preprocessing of multi-period observation data, including: acquiring observation data of continuous observation of the target monitoring area; detecting and eliminating gross errors in the observation values ​​of each period of observation data, normalizing the observation values, and generating an observation vector with a weight matrix and its weight matrix; Step S2, Dynamic Benchmark Establishment and Unified Adjustment of Multi-Period Data, includes: using the observation vectors and their weight matrices, through an overall quasi-stabilized adjustment scheme or a dynamically quasi-stabilized constrained adjustment scheme, to calculate the coordinates of each period under the unified benchmark, where the... The coordinate vector of all monitoring points during the period is The displacement time series of each monitoring point was obtained; Step S3: Identify stable point groups based on the displacement time series of each monitoring point: Step S4, Calculation and output of actual deformation, including: The stable point group identified in step S3 is used as a new pseudo-stable benchmark. The results of the dynamic pseudo-stable constraint adjustment scheme in step S2 are subjected to benchmark transformation or constraint re-adjustment to obtain the optimized coordinates for each period. Based on the optimized coordinates for each period, the deformation of each monitoring point relative to the pseudo-stable benchmark in each observation period is calculated. The deformation of each monitoring point in all periods is arranged in chronological order to form the displacement time series of the monitoring point. The displacement time series of all monitoring points are collected to form a multi-period high-precision deformation time series. This series is a pure series that reflects the true deformation state of the monitoring points because the systematic error introduced by the benchmark displacement has been eliminated by the dynamic benchmark adjustment method. The multi-period high-precision deformation time series refers to a complete displacement time series that covers the entire spatial range of the monitoring network and the entire observation time range. S5. Deformation analysis and safety early warning, including: performing deformation trend analysis based on the multi-period high-precision deformation time series, obtaining deformation patterns through deformation trend analysis, calculating deformation rate based on deformation patterns, and then issuing safety threshold early warning based on the comparison between deformation rate and safety threshold; when the deformation amount or deformation rate exceeds the threshold, the system automatically triggers early warning information of different levels to provide decision support for engineering safety management.

[0023] In step S1, the target monitoring area is obtained in a time series. The observation data consists of N periods (N≥3) of continuous observations. The observation data includes leveling observation data and plane observation data. The leveling points in the leveling observation data and the leveling routes connecting these points constitute a leveling network. The plane control points in the plane observation data constitute a plane network. Other contents related to the leveling network and plane network are known to those skilled in the art and will not be described in detail here. For a leveling network, the observed values ​​are the elevation difference vectors. ( For planar networks, the observations are the side lengths, directions, or GNSS baseline vectors. The gross error detection and removal adopts Criteria and data detection methods are used to remove gross errors from each period's observations to ensure the quality of the observation data; The Laida criterion, also known as the standard deviation criterion, is a simple outlier detection method based on the properties of normal distribution. Its core idea is that, under the assumption that observation errors follow a normal distribution, the probability of residuals exceeding three times the standard error is extremely small; therefore, such observations can be considered outliers and eliminated. Data probing is a more rigorous outlier detection and location method based on statistical hypothesis testing. It determines whether an observation contains outliers by performing a separate statistical significance test on the residuals of each observation.

[0024] The observation normalization includes: Observations of different precision and dimensions are uniformly transformed into values ​​with weighted matrices. The observation vector; the "different precision" refers to the different standard errors or variances of various observation values ​​due to differences in instruments, methods and environmental conditions; the "different dimensions" refers to the different physical units of the observation values, such as: elevation difference in meters, angle in radians.

[0025] Among them, the observation vector Let n be an n×1 observation vector formed by all n observations in the i-th period. , Representing the period For the nth observation value in the vector, Observations According to its prior variance The variance of the selected unit weight Based on the prior accuracy (mean error) of various observations ), calculate its weight ; Based on the assumption that all observations are independent, an n×n diagonal weight matrix is ​​constructed. Its diagonal elements are the weights of each observation. Off-diagonal elements are zero, represented as: The diagonal weight matrix The weights used in the adjustment process control the influence of observations of different accuracies on the final solution. The diagonal elements of the weight matrix represent the weights of each observation; a larger weight indicates a higher accuracy of the observation and a greater proportion in the adjustment solution. Conversely, zero off-diagonal elements reflect the assumption that the observations are independent of each other. This is used to control the influence weights of observations with different levels of precision on the final solution during the adjustment process. This unifies all observations into a dimensionless system that is measured by "weights" and can be computed collaboratively.

[0026] The overall pseudo-stabilization adjustment scheme in step S2 treats multi-period observation data as a whole, constructs a large parameter system, and performs a one-time solution. The steps include: A1. Parameterization: The coordinates or elevations of the monitoring points in each period are used as parameters to be estimated. Assume that each period has... Each monitoring point, The total parameter vector of the period data is ,in For the first The coordinate vectors of all monitoring points during the period; A2. Functional Model: Based on the principle of indirect adjustment, a unified expression for the N-period observation equation is established: in, It is the residual vector of the observed values. It is a design matrix with a clear block structure. It is a vector of observations for all periods; A3. Stochastic Model: Defining the Overall Weight Matrix ; A4. Baseline Constraint: Due to the rank deficiency in the network, a baseline constraint needs to be applied. This invention does not fix any point, but instead applies a pseudo-stability constraint that minimizes the sum of the squares of the total displacements of all monitoring points throughout the entire observation period. Its mathematical expression is as follows: In the formula, It is a scalar function to be minimized, defined as the sum of the squares of the displacements of all monitoring points from the first period to the last period (i.e., the entire observation period). This indicates the total number of monitoring points. It's the last issue number. It is a coordinate vector; This constraint is achieved through a conditional indirect adjustment method; the constraint equation can be written as: in, As the baseline constraint matrix, Represents the transpose of a matrix. The parameter vector to be estimated; The specific form depends on the network type. For a one-dimensional leveling network, this condition is equivalent to minimizing the sum of the squares of the elevation changes of all points from the first period to the last period. A5. Adjustment Solution: Based on the least squares criterion, construct and solve the normal equations to directly obtain the coordinate estimates of all period data under a unified benchmark. This benchmark is to make the entire network... The optimal benchmark with the smallest overall change over a given period.

[0027] The dynamic quasi-stable constraint adjustment model in step S2 adopts a recursive approach, unifying the data from subsequent periods onto the initial baseline established in the first period, which is easier to understand and implement in engineering. The steps include: B1. Definition of the benchmark period: For the first period Observational data Free network adjustment is performed using a centroid datum mathematical datum, with constraints applied. That is, the sum of the corrections for all point coordinates is zero, and the initial coordinates of the monitoring network are obtained by solving. This coordinate set defines the initial stable shape of the monitoring network; B2. Multi-period unified adjustment: For the first period... Expect( For observation data (e.g., 2, 3, ..., N), the coordinate estimates obtained from the first period adjustment are used in the adjustment model. As a quasi-stability constraint with extremely high weight, it is related to the first... Solving the observation equations for the first period together makes the first period... Solution coordinates of the period Approximately, provided that the observed values ​​for this period are met. This achieves a unified benchmark. The function model and the observation equation are as follows: Constraints: Coordinates obtained from the adjustment of the first period's observation data. As a pseudo-stable benchmark, the first requirement is... Coordinates of periodic observation data Compared to displacement vector The quadratic form is minimized, and its expression is: in, The weight matrix for the displacement vector can be set based on prior knowledge; this is equivalent to... Introduced as a constraint with maximum weights in adjustment; B3. Adjustment Solution: Solve using the least squares method to obtain the... Coordinates of periodic observation data This coordinate is relative to the baseline of the first phase of observation data. Repeat this process until all period data has been processed, thus ensuring that all period data are unified under the same initial baseline.

[0028] In step S3, the displacement time series of each monitoring point is obtained based on step S2. ,in For the displacement time series of the kth monitoring point in the Nth period, the stable point group is identified by the average gap method and the t-test method.

[0029] The average gap method includes the following steps: Calculate each monitoring point Average displacement over N periods and displacement standard deviation ; The confidence interval for the overall average displacement is calculated using the following formula: in, This represents the overall mean of the average displacement of all monitoring points; The overall standard deviation of the displacements at all points; Indicates the total number of monitoring points; The upper side of the standard normal distribution quantiles; This indicates the significance level, i.e., the confidence level. ; For example, the 95% confidence interval is: ; If a certain monitoring point average displacement If it falls within the confidence interval, and its displacement sequence If there is no significant trend, the monitoring point is identified as a relatively stable point.

[0030] The steps of the t-test method include: testing whether the mean of the displacement sequence of each monitoring point is significantly different from zero. If the test statistic does not reject the null hypothesis (i.e. the mean is equal to zero), then the point can be regarded as a stationary point.

[0031] In step S4, when the overall quasi-stable adjustment scheme is used in step S2, the adjustment result is... This is already the optimal state; the deformation between any two points and any two periods of observation data can be directly extracted as follows: in, Indicates the first Periodic observation, Indicates the first Period observation, representing the period number of the observation; Indicates the first The monitoring point number represents the number of a specific point in the monitoring network.

[0032] In step S4, when the dynamic quasi-stabilized constraint adjustment scheme is used in step S2, the coordinates of each period... The results are already relative to a unified benchmark. The deformation of the observation data between adjacent periods is as follows: In the formula, Indicates the first Periodic observation, express The previous observation in the previous period represents the period number of the observation; Indicates the first The monitoring point number represents the number of a specific point in the monitoring network.

[0033] In step S5, the deformation rate of the monitoring point is calculated using the average rate method. : ,in For displacement, This represents the time interval between displacements.

Claims

1. A dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network, characterized in that, Includes the following steps: Step S1, acquisition and preprocessing of multi-period observation data, including: acquiring observation data of continuous observation of the target monitoring area; detecting and eliminating gross errors in the observation values ​​of each period of observation data, normalizing the observation values, and generating an observation vector with a weight matrix and its weight matrix; Step S2, Dynamic Benchmark Establishment and Unified Adjustment of Multi-Period Data, includes: using the observation vectors and their weight matrices, through an overall quasi-stabilized adjustment scheme or a dynamically quasi-stabilized constrained adjustment scheme, to calculate the coordinates of each period under the unified benchmark, where the... The coordinate vector of all monitoring points during the period is The displacement time series of each monitoring point was obtained; Step S3: Identify stable point groups based on the displacement time series of each monitoring point; Step S4, Calculation and output of actual deformation, including: The stable point group identified in step S3 is used as the new pseudo-stable benchmark. The results of the dynamic pseudo-stable constraint adjustment scheme in step S2 are transformed into a benchmark or re-adjusted with constraints to obtain the optimized coordinates for each period. Based on the optimized coordinates for each period, the deformation of each monitoring point relative to the pseudo-stable benchmark in each observation period is calculated. The deformation of each monitoring point in all periods is arranged in chronological order to form the displacement time series of the monitoring point. The displacement time series of all monitoring points are collected to form a multi-period high-precision deformation time series. The multi-period high-precision deformation time series refers to a complete displacement time series that covers the entire spatial range of the monitoring network and the entire observation time range. S5. Deformation analysis and safety early warning, including: performing deformation trend analysis based on the multi-period high-precision deformation time series, obtaining deformation patterns through deformation trend analysis, calculating deformation rate based on deformation patterns, and then issuing safety threshold early warning based on the comparison between deformation rate and safety threshold; when the deformation amount or deformation rate exceeds the threshold, the system automatically triggers early warning information of different levels.

2. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 1, characterized in that: The observation data obtained in step S1 includes the target monitoring area in a time series. N consecutive observation periods of data; For a leveling network, the observation data are elevation difference vectors. ( For planar networks, the observations are the side lengths, directions, or GNSS baseline vectors. The observation normalization includes converting observations of different precisions and dimensions into a unified form with weighted matrices. The observation vector; Among them, the observation vector To form an n×1 observation vector from all n observations in period i, we can represent it as: , Representing the period The nth observation; for the nth observation in the vector; Observations According to its prior variance The variance of the selected unit weight Calculate its weight ; Based on the assumption that all observations are independent, an n×n diagonal weight matrix is ​​constructed. Its diagonal elements are the weights of each observation. Off-diagonal elements are zero, represented as: The diagonal weight matrix Weights are used to control the influence of observations of different precisions on the final solution during the adjustment process.

3. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 1, characterized in that: The overall pseudo-stabilization adjustment scheme in step S2 treats multi-period observation data as a whole, constructs a parameter system for one-time calculation, and includes the following steps: A1. Parameterization: The coordinates or elevations of the monitoring points in each period are used as parameters to be estimated. Assume that each period has... Each monitoring point, The total parameter vector of the period data is ; A2. Functional Model: Based on the principle of indirect adjustment, a unified expression for the N-period observation equation is established: in, It is the residual vector of the observed values. It is a design matrix with a clear block structure. It is a vector of observations for all periods; A3. Stochastic Model: Defining the Overall Weight Matrix ; A4. Baseline Constraint: A pseudo-stability constraint that minimizes the sum of squares of the total displacements at all monitoring points throughout the entire observation period, mathematically expressed as: In the formula, It is a scalar function to be minimized, defined as the sum of the squares of the displacements of all monitoring points from the first period to the last period. This indicates the total number of monitoring points. It's the last issue number. It is a coordinate vector; This constraint is achieved through a conditional indirect adjustment method; the constraint equation can be written as: in, As the baseline constraint matrix, Represents the transpose of a matrix. The parameter vector to be estimated; The specific form depends on the network type. For a one-dimensional leveling network, this condition is equivalent to minimizing the sum of the squares of the elevation changes of all points from the first period to the last period. A5. Adjustment Solution: Based on the least squares criterion, construct and solve the normal equations to directly obtain the coordinate estimates of all period data under a unified benchmark. This benchmark is to make the entire network... The optimal benchmark with the smallest overall change over a given period.

4. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 3, characterized in that: The dynamic quasi-stable constraint adjustment scheme in step S2 adopts a recursive approach, unifying the data from subsequent periods onto the initial baseline established in the first period, including: B1. Definition of the benchmark period: For the first period Observational data Free network adjustment is performed using a centroid datum mathematical datum, with constraints applied. The initial coordinates of the monitoring network are obtained by solving the problem. This coordinate set defines the initial stable shape of the monitoring network; B2. Multi-period unified adjustment: For the first period... Expect( For observation data (e.g., 2, 3, ..., N), the coordinate estimates obtained from the first period adjustment are used in the adjustment model. As a quasi-stability constraint with extremely high weight, it is related to the first... Solving the observation equations for the first period together makes the first period... Solution coordinates of the period Approximately, provided that the observed values ​​for this period are met. This achieves a unified benchmark; The function model and the observation equation are as follows: In the formula, This is the design matrix for Phase 1, which has a clear block structure. The design matrix for period i has a clear block structure; Constraints: Coordinates obtained from the adjustment of the first period's observation data. As a pseudo-stable benchmark, the first requirement is... Coordinates of periodic observation data Compared to displacement vector The quadratic form is minimized, and its expression is: in, The weight matrix is ​​the weight matrix of the displacement vector, which is equivalent to... Introduced as a constraint with maximum weights in adjustment; B3. Adjustment Solution: Solve using the least squares method to obtain the... Coordinates of periodic observation data This coordinate is relative to the baseline of the first phase of observation data. Repeat this process until all period data has been processed, thus ensuring that all period data are unified under the same initial baseline.

5. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 1, characterized in that: In step S3, the displacement time series of each monitoring point is obtained based on step S2. ,in For the displacement time series of the kth monitoring point in the Nth period, the stable point group is identified by the average gap method and the t-test method.

6. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 5, characterized in that: The average gap method includes the following steps: Calculate each monitoring point Average displacement over N periods and displacement standard deviation ; The confidence interval for the overall average displacement is calculated using the following formula: in, This represents the overall mean of the average displacement of all monitoring points. The overall standard deviation of the displacements at all points; Indicates the total number of monitoring points; The upper side of the standard normal distribution quantiles; This indicates the significance level, i.e., the confidence level. ; If a certain monitoring point average displacement If it falls within the confidence interval, and its displacement sequence If there is no significant trend, the monitoring point is identified as a relatively stable point.

7. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 5, characterized in that: The steps of the t-test method include: testing whether the mean of the displacement sequence of each monitoring point is significantly different from zero; if the test statistic does not reject the null hypothesis, then the point can be regarded as a stationary point.

8. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 1, characterized in that: In step S4, when the overall quasi-stable adjustment scheme is used in step S2, the adjustment result is... This is already the optimal state; the deformation between any two points and any two periods of observation data can be directly extracted as follows: in, Indicates the first Periodic observation, Indicates the first Period observation, representing the period number of the observation; Indicates the first The monitoring point number represents the number of a specific point in the monitoring network.

9. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 1, characterized in that: In step S4, when the dynamic quasi-stabilized constraint adjustment scheme is used in step S2, the coordinates of each period... The results are already relative to a unified benchmark. The deformation of the observation data between adjacent periods is as follows: In the formula, Indicates the first Periodic observation, express The previous observation in the previous period represents the period number of the observation; Indicates the first The monitoring point number represents the number of a specific point in the monitoring network.

10. The dynamic benchmark adjustment and deformation analysis method for a multi-stage deformation monitoring network as described in claim 1, characterized in that: In step S5, the deformation rate of the monitoring point is calculated using the average rate method. : ,in For displacement, This represents the time interval between displacements.

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