Terrain change uncertainty analysis method based on time sequence sounding data

Abstract

The invention discloses a topographic change uncertainty analysis method based on time sequence sounding data, and relates to the technical field of marine surveying and mapping. According to the method, high-precision seabed deformation sequence data is acquired through time-space reference unification and data fusion correction processing based on multi-beam sounding data acquired by multiple periods and multiple platforms, and the influence of terrain gradient, seawater depth and the coupling effect of the terrain gradient and the seawater depth on the sounding uncertainty is systematically and quantitatively analyzed; comprehensively considering a coupling effect relationship between water depth and terrain gradient, combining horizontal uncertainty information obtained by the gradient-uncertainty statistical model with vertical uncertainty information obtained by the water depth-uncertainty statistical model based on an error propagation theory, and establishing a gradient-water depth joint probability statistical model under multi-period data constraint; the statistical separation capability of terrain deformation signals and measurement noise is remarkably improved, real and accurate seabed deformation information can be obtained, and precise detection and dynamic monitoring of seabed micro-landform changes in a complex deep sea environment are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of marine mapping technology, and particularly relates to a terrain change uncertainty analysis method based on time-series sounding data. BACKGROUND

[0002] Deep-sea terrain change information is of great significance for studying marine bottom geological structure, resource development and environmental monitoring. The progress of measurement technology makes it possible to obtain high-precision terrain data, but the accuracy of deep-sea terrain change information is affected by water depth, terrain slope, data registration error and other factors. At present, the uncertainty analysis of deformation information mainly focuses on the influence of a single factor-water depth, while ignoring the coupling effect of multiple factors. The systematic bias of sounding data caused by water depth change needs to be analyzed and processed, and the amplification effect of terrain slope on measurement noise cannot be ignored. Because the slope changes the reflection angle and propagation path of sound waves, leading to signal attenuation or distortion, the data uncertainty in steep terrain areas is usually high, especially in complex terrain areas such as seamounts, trenches and fault zones, where the terrain changes dramatically, and the measurement noise is significantly amplified, further reducing the reliability of the data.

[0003] Therefore, in order to more comprehensively evaluate the uncertainty of deep-sea terrain change, the coupling effect of water depth and terrain slope on the uncertainty of depth change needs to be considered, and the accuracy and reliability of deep-sea terrain change information need to be further improved. SUMMARY

[0004] In order to overcome the limitation of the existing method that only analyzes deep-sea deformation information based on a single factor, the present application proposes a terrain change uncertainty analysis method based on time-series sounding data, which comprehensively considers the coupling effect of terrain slope and water depth, quantifies the influence degree of terrain slope and water depth on the uncertainty of depth measurement change through the establishment of a multivariate statistical model, effectively reduces the error of single factor analysis, significantly improves the accuracy and reliability of deep-sea terrain change information, and provides more accurate scientific basis for terrain change monitoring and interpretation in complex deep-sea environment.

[0005] The present application specifically adopts the following technical solutions:

[0006] The terrain change uncertainty analysis method based on time-series sounding data uses the seabed terrain change quantity in time-series multibeam sounding data for uncertainty analysis, which specifically includes the following steps:

[0007] Step 1, obtain multibeam sounding data of multiple periods and multiple platforms, extract the overlapping area data of each period through spatial matching to obtain overlapping data, project the extracted overlapping data, grid the water depth data, and construct a unified spatial reference framework;

[0008] Step 2, using a robust terrain matching algorithm to correct the reference of multi-beam bathymetric data of each period and each platform, and extracting seafloor topographic deformation information;

[0009] Step 3, quantifying the uncertainty of bathymetric change detection based on slope factor;

[0010] Calculate the terrain slope value, determine the statistical relationship between the terrain slope and the depth change based on the robust statistical method, establish the slope-uncertainty statistical model, quantify the influence degree of slope on the uncertainty of depth change, and determine the global uncertainty of slope influence estimation combined with the water depth measurement error propagation theory and uncertainty analysis method, generate the relationship diagram considering the influence of slope factor on the uncertainty of depth change, and intuitively show the influence degree and spatial distribution characteristics of slope on the uncertainty of topographic deformation;

[0011] Step 4, quantifying the uncertainty of bathymetric change detection based on water depth factor;

[0012] Perform slope correction and noise processing on multi-beam bathymetric data, analyze the statistical relationship between water depth value and deformation information uncertainty using robust estimation method, establish a water depth-uncertainty statistical model, quantify the influence degree of water depth on the uncertainty of deformation information, establish the global uncertainty of water depth estimation combined with the water depth measurement error propagation theory and uncertainty analysis method, generate the relationship diagram considering the influence of water depth factor on the uncertainty of depth change, and intuitively show the influence degree and spatial distribution characteristics of water depth on the uncertainty of topographic deformation;

[0013] Step 5, considering the coupling effect relationship between water depth and terrain slope, combining the horizontal uncertainty information determined by the slope-uncertainty statistical model with the vertical uncertainty information determined by the water depth-uncertainty statistical model based on the error propagation theory, establishing a slope-water depth joint probability statistical model to determine the global uncertainty, and obtaining the real regional topographic change information combined with the preset confidence interval, completing the accurate detection of seafloor geomorphic change.

[0014] Preferably, in step 2, the multi-beam bathymetric data is corrected using a robust terrain matching algorithm, including the following sub-steps:

[0015] Step 2.1, calculating the difference h between multi-beam bathymetric data i , performing initial offset correction based on terrain matching algorithm, and obtaining the initial offset value between multi-beam bathymetric data by minimizing the absolute mean error of difference As shown in formula (1):

[0016]

[0017] Wherein,

[0018] h i = D n,i -D o,i (2)

[0019] where, is the initial offset value, abs(·) function is used to calculate the absolute value, median(·) function is used to calculate the median, and argmin(·) function is used to calculate the parameter that makes the objective function minimum;h i is the difference between multi-beam bathymetry data in different periods, D n,i and D o,i are the water depth values measured in different periods, respectively;

[0020] Step 2.2, after the initial offset correction, the difference v i between multi-beam bathymetry data in different periods is calculated, and the median absolute deviation method is used to estimate its standard deviation, as shown in equation (3):

[0021]

[0022] where,

[0023] v i = D cn,i -D co,i (4)

[0024] where, is the robust standard deviation estimation based on the median absolute deviation, used to measure the dispersion of data;v i is the multi-beam bathymetry data difference after the initial offset correction, D cni, and D co,i are the water depth values measured in different periods after correction, respectively;

[0025] The median μ of the depth change value is calculated, and the threshold value is set. ri The abnormal water depth change points are removed, and the effective data v i that meet the statistical confidence interval are selected.

[0026]

[0027] where,

[0028] μ = median(v i ) (6)

[0029] where, μ is the median of the depth change value;

[0030] Step 2.3, after removing the abnormal water depth change points, the deep sea terrain data is accurately matched using the least square error minimization criterion, the optimal offset is solved and corrected, and the multi-beam bathymetry data with unified reference is obtained.

[0031] Preferably, in step 2.3, the optimal offset is solved by minimizing the difference between the two periods of water depth data, and the optimal spatial offset Δ is calculated so that the corrected data satisfies:

[0032]

[0033] In the formula, Δ is the optimal spatial offset; i is the serial number, and N is the number of effective data points;

[0034] The optimal offset is applied to correct the multi-beam water depth data, and the reference-unified two-period water depth difference D is calculated after correction diff,i As shown in formula (8):

[0035] D diff,i = D' n,i - D' o,i (8)

[0036] In the formula, D' n,i and D' o,i are the multi-beam sounding data values of different periods after reference correction.

[0037] Preferably, in step 3, the following sub-steps are included:

[0038] Step 3.1, based on the multi-beam sounding data, an underwater depth model is constructed, a moving window is used to analyze and calculate the terrain slope value, a moving window with a size of 3x3 is set around each grid point, the elevation values of the center point and its eight adjacent grids are used in the moving window, and the terrain gradient value S t is calculated by using the finite difference method.

[0039]

[0040] In the formula,

[0041]

[0042] In the formula, S t is the terrain gradient value, arctan(·) is the inverse tangent function, f x is the gradient value in the x direction, and f y is the gradient value in the y direction; Z1, Z2, Z3, Z4, Z5, Z6, Z7, and Z8 are the water depth values of the adjacent grid elements of the center point, and d is the length of the grid element.

[0043] Step 3.2, in order to accurately quantify the influence of terrain slope on the uncertainty of depth change value, a stratified regression analysis method is used to eliminate the interference of water depth, the multibeam sounding data is divided into multiple intervals according to the size of water depth, the linear relationship between the standard deviation of depth change value and the tangent value of terrain slope is analyzed in each interval, a slope-uncertainty statistical model is established, the uncertainty of the whole slope is estimated by integrating the statistical relationship in each water depth interval, a relationship diagram considering the influence of slope on the uncertainty of depth change is generated, the influence degree and spatial distribution characteristics of slope on the uncertainty of terrain deformation are intuitively displayed, and the overall influence of slope on the uncertainty of depth change value is determined;

[0044] The slope-uncertainty statistical model is:

[0045] σ DoD =α0+α1·τ (12)

[0046] In the formula, α0 and α1 are to-be-determined adjustable coefficients, α0 is a first adjustable coefficient, α1 is a second adjustable coefficient, σ DoD is the standard deviation of depth change value, and τ is the tangent value of terrain slope.

[0047] Preferably, the to-be-determined adjustable coefficients α0 and α1 are determined by using a M-estimate robust regression method, and the specific steps are as follows:

[0048] Step 3.2.1, the to-be-determined adjustable coefficients α0 and α1 are taken as regression coefficients, the initial regression coefficients α0 and α1 are initialized, and the ordinary least squares algorithm is used to calculate the initial regression coefficients α0 and α1.

[0049] Step 3.2.2, the residual value u i is calculated according to the initial regression coefficients, as shown in formula (13):

[0050] u i =σ DoD,i -(α0+α1τ i ) (13)

[0051] In the formula, σ DoD,i is the i th standard deviation of depth change value, and τ i is the i th tangent value of terrain slope.

[0052] Step 3.2.3, according to the residual value u i , a weight function is used to calculate the weight ω h of each multibeam sounding data point in combination with a preset threshold c i , as shown in formula (14):

[0053]

[0054] Step 3.2.4, updating the regression coefficients a0 and a1 using the weighted least squares (WLS) method, as shown in equation (15):

[0055]

[0056] where n is the total number of multibeam sounding data points;

[0057] Step 3.2.5, repeating steps 3.2.2-3.2.4 until the change in the regression coefficients is less than a pre-set convergence threshold, and the regression coefficients a0 and a1 obtained at this time are determined as the adjustable coefficient values obtained by robust estimation of the statistical relationship;

[0058] Integrating the statistical relationship between the standard deviation of the depth difference and the tangent of the slope in each partition, the overall estimation result of the horizontal position random error of the seabed slope is obtained, and the uncertainty of the slope influence estimation global is determined as:

[0059] σ slope = a1 tan(S t ) + a0 (16)

[0060] where σ slope is the uncertainty of the slope influence estimation global.

[0061] Preferably, in step 4, the multibeam sounding data is slope corrected to reduce the amplification effect of the slope on the depth error, and the multibeam sounding data is first smoothed and denoised, the median filtering method is used to remove isolated outliers, and the median filtering is used to replace each data point in the multibeam sounding data with the median value in its neighborhood, so as to suppress noise and outliers without changing the overall trend of the data.

[0062] Based on the linear model proposed by the International Hydrographic Organization for describing the relationship between water depth and depth measurement uncertainty, the measurement error of water depth is decomposed into two parts, one part is related to the depth, and the other part is not related to the depth, and the measurement error of water depth value is obtained as:

[0063]

[0064] where TPU V (m) is the measurement error of water depth; a is an error constant not related to water depth, b is an error constant related to water depth, d is water depth, and bxd is an error related to water depth.

[0065] In order to flexibly capture the error characteristics of different water depth intervals, the multibeam sounding data error is statistically analyzed, and the uncertainty of the water depth influence estimation global is determined, as shown in equation (18):

[0066] σ depth= β1 · depth + β0 (18)

[0067] wherein σ depth is the uncertainty of the global water depth estimation, β1 and β0 are the estimated parameters, and depth is the water depth.

[0068] Preferably, in step 5, the uncertainty analysis is performed based on the differential terrain model, and a slope-water depth joint probability statistical model for determining the global uncertainty is established according to the horizontal uncertainty determined by the slope-uncertainty statistical model and the vertical uncertainty determined by the water depth-uncertainty statistical model, as shown in equation (19):

[0069]

[0070] wherein σ all is the global uncertainty.

[0071] According to the slope-water depth joint probability statistical model, a confidence interval is set, the real terrain change information D diff,true is obtained by using the minimum detection level to distinguish the real terrain change from the measurement noise.

[0072] D diff,true = {i∈DoD: |D diff | > median(D diff ) ± min LoD} (20)

[0073] wherein,

[0074] min LoD = k · σ all (21)

[0075] wherein D diff,true is the real regional terrain change information, DoD is the differential terrain model, D diff is the terrain change before quantization, min LoD is the minimum detection level, and k is the confidence coefficient.

[0076] The present application has the following beneficial effects:

[0077] The present application provides a topographic change uncertainty analysis method based on time-series sounding data, which innovatively registers multi-source time-series sounding data, organically combines the statistical relationship between topographic slope and seawater depth on depth change uncertainty based on error propagation theory, comprehensively considers the influence of topographic slope and seawater depth on submarine deformation uncertainty, overcomes the limitation of the prior art which is only based on water depth to analyze deep sea deformation information, effectively reduces the analysis error, significantly improves the accuracy and reliability of deep sea topographic change information, is beneficial to obtain more real and accurate submarine deformation information, realizes the topographic change monitoring and interpretation under complex deep sea environment, provides a new technical approach for deep sea topographic evolution analysis, and has important scientific significance and engineering application value in the fields of marine precision surveying and mapping, marine geological disaster monitoring and marine spatial information intelligent processing. BRIEF DESCRIPTION OF DRAWINGS

[0078] Figure 1 A flowchart of the topographic change uncertainty analysis method based on time-series sounding data of the present application.

[0079] Figure 2 The effect diagram of multi-beam sounding data before and after projection conversion and gridding in the example of the present application; in the diagram, (a) is the effect diagram of multi-beam sounding data before projection conversion and gridding, and (b) is the effect diagram of multi-beam sounding data after projection conversion and gridding.

[0080] Figure 3 The effect diagram of water depth difference change before and after registration in the example of the present application; in the diagram, (a) is the effect diagram of water depth difference change before registration, and (b) is the effect diagram of water depth difference change after registration.

[0081] Figure 4 The topographic slope calculation method and slope distribution relationship diagram in the example of the present application; in the diagram, (a) is a schematic diagram of a moving window, and (b) is a slope distribution relationship diagram.

[0082] Figure 5 The relationship diagram of slope factor on depth change uncertainty in the embodiment of the present application.

[0083] Figure 6 The relationship diagram of water depth factor on depth change uncertainty in the embodiment of the present application.

[0084] Figure 7 The relationship diagram of the coupling effect of slope and water depth on depth change uncertainty in the example of the present application. DETAILED DESCRIPTION

[0085] The specific embodiments of the present application will be further described below in combination with the drawings and specific embodiments:

[0086] Embodiment 1

[0087] The embodiment proposes a terrain change uncertainty analysis method based on time-series bathymetric data, as shown in Figure 1 The terrain change uncertainty analysis is performed using the seabed terrain change amount in time-series multi-beam bathymetric data, and specifically includes the following steps:

[0088] Step 1, obtain multi-period and multi-platform multi-beam bathymetric data, extract the overlapping data of each period data through spatial matching to ensure the consistency and comparability of the data, perform high-precision projection change on the extracted overlapping data, perform projection change by selecting appropriate projection coordinate system to reduce deformation error, and grid the water depth data to construct a unified spatial reference framework;

[0089] Step 2, use a robust terrain matching algorithm to correct the multi-beam bathymetric data of each period and each platform, and extract seabed terrain deformation information, which includes the following sub-steps:

[0090] Step 2.1, in order to reduce the interference of outliers in multi-beam bathymetric data, the difference h i between multi-beam bathymetric data is calculated, and initial offset correction is performed based on the terrain matching algorithm, and the initial offset value between multi-beam bathymetric data is obtained by minimizing the absolute mean error of the difference as shown in equation (1):

[0091]

[0092] wherein,

[0093] h i = D n,i -D o,i (2)

[0094] In the formula, is the initial offset value, the abs(·) function is used to calculate the absolute value, the median(·) function is used to calculate the median, and the argmin(·) function is used to calculate the parameter that makes the target function minimum; h i is the difference between multi-beam bathymetric data of different periods, D n,i and D o,i are the water depth values measured in different periods.

[0095] Step 2.2, after initial offset correction, calculate the difference v i between multi-beam bathymetric data of different periods, in order to improve robustness, the median absolute deviation method (MAD) is used to estimate the standard deviation, as shown in equation (3):

[0096]

[0097] wherein,

[0098] v i = D cn,i -D co,i (4)

[0099] wherein, is the robust standard deviation estimation based on median absolute deviation, used to measure the dispersion of data;v i is the difference of multi-beam bathymetry data after the initial offset correction, D cni, and D co,i are the water depth values measured in different periods after correction.

[0100] In order to maximize the elimination of outliers on the analysis results, improve the reliability of subsequent analysis, the median of depth change value μ is calculated, and the threshold value is set. ri The effective data v

[0101]

[0102] wherein,

[0103] μ = median(v i ) (6)

[0104] wherein, μ is the median of depth change value.

[0105] Step 2.3, after removing outliers, the deep sea terrain data is accurately matched by using the least square error minimization criterion, the optimal offset is solved and corrected, and the multi-beam bathymetry data of the reference uniform is obtained.

[0106] When solving the optimal offset, the optimal spatial offset Δ is calculated by minimizing the difference of two periods of water depth data, so that the corrected data satisfies:

[0107]

[0108] wherein, Δ is the optimal spatial offset; i is the serial number, and N is the number of effective data points.

[0109] Then, the reference correction and difference calculation are performed, the multi-beam bathymetry data is corrected by using the optimal offset, and the reference unified two-period water depth difference D diff,i is calculated after correction, as shown in formula (8):

[0110] D diff,i = D' n,i -D' o,i (8)

[0111] wherein, D' n,i , D' o,iare multi-beam sounding data values at different periods after the reference correction, respectively.

[0112] Step 3, slope factor-based sounding change uncertainty quantification;

[0113] The terrain slope value is calculated, the statistical relationship between the terrain slope and the depth change is determined based on a robust statistical method, a slope-uncertainty statistical model is established, the influence degree of the slope on the depth change uncertainty is quantified, the slope influence estimation global uncertainty is determined by combining the water depth measurement error propagation theory and the uncertainty analysis method, a relationship diagram considering the slope factor on the depth change uncertainty is generated, the influence degree of the slope on the terrain deformation uncertainty and the spatial distribution characteristics thereof are intuitively displayed, and the specific steps include the following sub-steps:

[0114] Step 3.1, an underwater depth model is constructed based on the multi-beam sounding data, a moving window is used to analyze and calculate the terrain slope value according to formula (9), a moving window with a size of 3*3 is set around each grid point, the elevation values of the center point and its eight neighboring grids are used, and the terrain gradient value S is calculated by using the finite difference method. t Thus, the local precision and spatial continuity of the slope calculation are ensured.

[0115] The terrain gradient value S t The calculation formula is as follows:

[0116]

[0117] Wherein,

[0118]

[0119] In the formula, S t is the terrain gradient value, arctan(·) is the inverse tangent function, f x is the gradient value in the x direction, and f y is the gradient value in the y direction; Z1, Z2, Z3, Z4, Z5, Z6, Z7, and Z8 are the water depth values of the grid elements adjacent to the center point, and d is the length of the grid element.

[0120] Step 3.2, in order to accurately quantify the influence of terrain slope on the uncertainty of depth change value, the hierarchical regression analysis method is adopted in this embodiment to eliminate the interference of water depth factor, that is, the multibeam sounding data is divided into multiple intervals according to the size of water depth, the linear relationship between the standard deviation of depth change value and the tangent value of terrain slope is analyzed in each interval, the slope-uncertainty statistical model is established, the influence of water depth factor on the depth change value is effectively isolated, so as to more accurately evaluate the influence of slope on the uncertainty of depth change value; then by integrating the statistical relationship in each water depth interval, the uncertainty of the global slope influence estimation is obtained, the relationship diagram considering the influence of slope factor on the uncertainty of depth change is generated, the influence degree and spatial distribution characteristics of slope on the uncertainty of terrain deformation are intuitively displayed, and the overall influence of slope on the uncertainty of depth change value is determined.

[0121] The slope-uncertainty statistical model is:

[0122] σ DoD =α0+α1·τ (12)

[0123] In the formula, α0 and α1 are to-be-determined adjustable coefficients, α0 is a first adjustable coefficient, α1 is a second adjustable coefficient, σ DoD is the standard deviation of depth change value, and τ is the tangent value of terrain slope.

[0124] In order to enhance the stability of data and reduce the influence of abnormal values on the regression result, the first adjustable coefficient α0 and the second adjustable coefficient α1 are used as the regression coefficients, and the M-estimate robust regression method is used to determine the regression coefficients. The M-estimate robust regression method estimates the regression coefficients by iterative reweighted least squares (IRLS), and the core idea is to dynamically adjust the weight of each data point according to the size of the regression residual. The specific steps are as follows:

[0125] Step 3.2.1, initialize the regression coefficients;

[0126] The to-be-determined adjustable coefficients α0 and α1 are used as the regression coefficients, the regression coefficients α0 and α1 are initialized, and the ordinary least squares algorithm is used to calculate the initial regression coefficients α0 and α1.

[0127] Step 3.2.2, calculate the residual;

[0128] According to the initial regression coefficients, the residual value u i is calculated, as shown in formula (13):

[0129] u i =σ DoD,i -(α0+α1τ i ) (13)

[0130] In the formula, σ DoD,i is the standard deviation of the i th depth change value, τi is the i-th terrain slope tangent value.

[0131] Step 3.2.3, calculating the weight;

[0132] According to the residual value u i , combining the preset threshold c h , the weight ω i of each multi-beam sounding data point is calculated using the weight function, as shown in formula (14):

[0133]

[0134] The threshold c h in this embodiment is 1.345.

[0135] Step 3.2.4, updating the regression coefficients;

[0136] The weighted least squares (WLS) is used to update the regression coefficients α0and α1, as shown in formula (15):

[0137]

[0138] In the formula, n is the total number of multi-beam sounding data points.

[0139] Step 3.2.5, iterative convergence;

[0140] Repeat steps 3.2.2-3.2.4 until the change of the regression coefficients is less than the preset convergence threshold, at which time the obtained regression coefficients α0and α1are the adjustable coefficient values obtained by the statistical relationship robust estimation.

[0141] Integrate the statistical relationship between the depth difference standard deviation and the slope tangent value in each partition to obtain the overall estimation result of the seabed slope and horizontal position random error, and determine the uncertainty of the slope influence estimation global as:

[0142] σ slope = α1· tan(S t ) + α0 (16)

[0143] In the formula, σ slope is the uncertainty of the slope influence estimation global.

[0144] Step 4, quantifying the uncertainty of the water depth factor sounding change detection;

[0145] The multi-beam bathymetric data were slope corrected and noise processed, and the robust estimation method was used to analyze the statistical relationship between water depth values ​​and deformation information uncertainty. A water depth-uncertainty statistical model was established to quantify the influence of water depth on the uncertainty of deformation information. Combining the water depth measurement error propagation theory and uncertainty analysis method, the global uncertainty of water depth estimation was established, and a relationship diagram considering the water depth factor and the uncertainty of depth change was generated, which intuitively demonstrated the influence of water depth on terrain deformation uncertainty and its spatial distribution characteristics.

[0146] In step 4, when analyzing the impact of water depth on deformation uncertainty, the influence of slope on depth (vertical) accuracy is a key factor. Research has shown that, given a given horizontal position error, the depth error generated on steep slopes is larger than on gentle slopes. This depth error is also propagated to the differential grid during the calculation process, affecting the accuracy of data analysis. Therefore, it is necessary to correct the slope of multibeam bathymetric data during data processing to reduce its amplification effect on depth error.

[0147] Slope correction is performed on the multi-beam bathymetry data to reduce the amplification effect of slope on depth error. The multi-beam bathymetry data is first smoothed and denoised, and the median filtering method is used to remove isolated outliers. The median filtering method is used to replace each data point in the multi-beam bathymetry data with the median of its neighborhood, thereby suppressing noise and outliers without significantly changing the overall trend of the data.

[0148] Based on the linear model proposed by the International Hydrographic Organization (IHO) to describe the relationship between water depth and depth measurement uncertainty, the water depth measurement error is decomposed into two parts, one part is related to the depth and the other part is not related to the depth. The measurement error of the water depth value is obtained as follows:

[0149]

[0150] Where, TPU V (m) is the measurement error of water depth; a is the error constant independent of water depth, b is the error constant related to water depth, d is the water depth, and b×d is the error related to water depth.

[0151] From formula (17), it can be seen that the uncertainty of water depth measurement mainly depends on the depth itself, and as the depth increases, the measurement error will usually increase.

[0152] Furthermore, in order to flexibly capture the error characteristics of different water depth intervals, the multi-beam bathymetric data errors are statistically analyzed, and the M-estimation robust regression method is used to estimate the most reasonable coefficient value to determine the global uncertainty of the water depth effect estimation, as shown in formula (18):

[0153] σ depth= β1 · depth + β0 (18)

[0154] where σ depth is the uncertainty of the water depth impact estimation, β1 and β0 are the estimated parameters, and depth is the water depth.

[0155] Step 5, considering the coupling effect relationship between water depth and terrain slope, based on the error propagation theory, the horizontal uncertainty information determined by the slope-uncertainty statistical model is combined with the vertical uncertainty information determined by the water depth-uncertainty statistical model to establish a slope-water depth joint probability statistical model, determine the global uncertainty, and obtain the real regional terrain change information by combining the preset confidence interval, complete the accurate detection of seafloor topographic change, the specific content is:

[0156] Based on the difference terrain model (DoD, Difference of DEMs) for uncertainty analysis, combining the error sources in the horizontal direction (slope related) and the vertical direction (water depth related) is a key step in uncertainty analysis. According to the horizontal uncertainty determined by the slope-uncertainty statistical model and the vertical uncertainty determined by the water depth-uncertainty statistical model, a slope-water depth joint probability statistical model for determining the global uncertainty is established, as shown in formula (19):

[0157]

[0158] where σ all is the global uncertainty.

[0159] At the same time, when using the difference terrain model to quantify the terrain change, the minimum detection level (min_LoD, Minimum Level of Detection) is a key threshold for distinguishing between real terrain change and measurement noise. The core idea is to use the slope-water depth joint probability statistical model σ all to set the confidence interval, only when the depth change value D diff,i exceeds the interval, it is considered as a statistically significant change.

[0160] In this embodiment, according to the slope-water depth joint probability statistical model, the confidence coefficient k is taken as 1.96, that is, the confidence degree is 95%, and the minimum detection level is used to distinguish between real terrain change and measurement noise to obtain the real regional terrain change information D diff,true :

[0161] D diff,true = {i∈DoD: |D diff |>median(D diff )±min LoD} (20)

[0162] in,

[0163] min LoD =k·σ all (twenty one)

[0164] Where D diff,true is the real regional terrain change information; DoD is the differential terrain model; D diff is the terrain change before quantification; min LoD is the minimum detection level; k is the confidence coefficient.

[0165] Example 2

[0166] This embodiment adopts the terrain change uncertainty analysis method based on time-series bathymetric data proposed in Example 1 to accurately extract the seabed terrain change information of a certain study area, specifically including the following steps:

[0167] Step 1: Obtain multi-beam bathymetric data from multiple periods, extract overlapping areas of data from each period through spatial matching to ensure data consistency and comparability, and perform high-precision projection changes and gridding on the extracted overlapping data, such as Figure 2 As shown, a unified spatial reference frame is constructed.

[0168] Step 2: Use a robust terrain matching algorithm to perform initial offset correction, calculate the initial plane offset between the two phases of multi-beam bathymetric data, correct the initial offset, and obtain the multi-beam bathymetric data after initial registration; based on the initial registration results of the multi-beam bathymetric data, calculate the water depth change value, use the mean absolute deviation as a robust estimator, and set a threshold to eliminate abnormal water depth change points to reduce the impact of noise and gross errors on the registration accuracy of the multi-beam bathymetric data. Furthermore, on this basis, use the root mean square error matching algorithm to iteratively calculate the optimal plane offset, perform accurate spatial translation transformation on the target data set, obtain the multi-beam bathymetric data after benchmark correction, and obtain the depth change value after benchmark correction, as shown in the following example. Figure 3 shown.

[0169] Step 3: Based on the high-resolution multi-beam bathymetric data after benchmark correction, use formula (9) and Figure 4 The slope value is calculated in the grid analysis window shown. The linear relationship between the standard deviation of depth change and the tangent value of terrain slope in each depth interval is analyzed and integrated by partition analysis method. The slope-uncertainty statistical model is established to derive the statistical relationship between the random error of horizontal position and terrain slope in the study area and generate Figure 5 The relationship diagram shown in the figure intuitively demonstrates the impact of slope on horizontal position error.

[0170] Step 4, after the slope correction of the multi-beam bathymetric data, a statistical relationship between the water depth value and the deformation information uncertainty is analyzed by using a robust estimation method, a water depth-uncertainty statistical model is established, the influence degree of the water depth on the deformation information uncertainty is quantified, and a relationship diagram considering the influence of the water depth factor on the depth change uncertainty is generated, as shown in FIG. 8, which intuitively displays the distribution characteristics of the deformation information uncertainty under different water depth intervals. Figure 6

[0171] Step 5, based on the error propagation theory, horizontal uncertainty information determined by the slope-uncertainty statistical model is combined with vertical uncertainty information determined by the water depth-uncertainty statistical model, a slope-water depth joint probability statistical model is established, and a statistical relationship diagram as shown in FIG. 9 is generated, and a suitable confidence interval is selected to obtain real regional terrain change information. Figure 7

[0172] Of course, the above description is not a limitation on the present application, and the present application is not limited to the above examples, and changes, modifications, additions or replacements made by those skilled in the art within the essential scope of the present application should also belong to the protection scope of the present application.​​

Claims

1. A terrain change uncertainty analysis method based on time series bathymetric data, characterized by: Uncertainty analysis of seabed topography changes in time-series multibeam bathymetry data is performed, which includes the following steps: Step 1: Acquire multi-beam bathymetric data from multiple periods and platforms, extract overlapping areas of data from each period through spatial matching to obtain overlapping data, project the extracted overlapping data, and grid the water depth data to build a unified spatial reference frame; Step 2: Use a robust terrain matching algorithm to benchmark the multibeam bathymetric data from each period and platform to extract seabed topographic deformation information; Step 3, quantification of uncertainty in bathymetric change detection based on slope factor; Calculate the terrain slope value, determine the statistical relationship between terrain slope and depth change based on robust statistical methods, establish a slope-uncertainty statistical model, quantify the impact of slope on depth change uncertainty, and then combine water depth measurement error propagation theory and uncertainty analysis methods to determine the global uncertainty of slope impact estimation. Generate a relationship diagram that considers the slope factor and depth change uncertainty, and intuitively display the impact of slope on terrain deformation uncertainty and its spatial distribution characteristics. Step 4: quantify the uncertainty of bathymetric change detection based on the water depth factor; Multibeam bathymetric data were slope-corrected and noise-processed. Robust estimation methods were used to analyze the statistical relationship between water depth values ​​and deformation uncertainty. A water depth-uncertainty statistical model was established to quantify the impact of water depth on deformation uncertainty. Combining water depth measurement error propagation theory with uncertainty analysis methods, a global uncertainty model for water depth estimation was established. A relationship diagram was generated that considers the effect of water depth on depth change uncertainty, visually demonstrating the impact of water depth on terrain deformation uncertainty and its spatial distribution characteristics. Step 5: Comprehensively consider the coupling effect relationship between water depth and terrain slope, and based on the error propagation theory, combine the horizontal uncertainty information determined by the slope-uncertainty statistical model with the vertical uncertainty information determined by the water depth-uncertainty statistical model to establish a slope-water depth joint probability statistical model, determine the global uncertainty, and combine the preset confidence interval to obtain the real regional terrain change information, thereby completing the accurate detection of seabed landform changes.

2. The terrain change uncertainty analysis method based on time series bathymetric data according to claim 1, characterized in that: In step 2, a robust terrain matching algorithm is used to perform a benchmark correction on the multi-beam bathymetric data, which includes the following sub-steps: Step 2.1, calculate the difference h between multi-beam bathymetric data i , based on the terrain matching algorithm, the initial offset correction is performed, and the initial offset value between the multi-beam bathymetric data is obtained by minimizing the absolute mean error of the difference As shown in formula (1): in, h i =D n,i -D o,i (2) In the formula, is the initial offset value, the abs(·) function is used to calculate the absolute value, the median(·) function is used to calculate the median, and the argmin(·) function is used to calculate the parameter that minimizes the objective function; h i is the difference between multi-beam bathymetric data at different times, D n,i and D o,i These are the water depth values ​​measured at different periods; Step 2.2: After the initial offset correction, calculate the difference v between the multibeam bathymetric data at different times. i , and the median absolute deviation method is used to estimate its standard deviation, as shown in formula (3): in, v i =D cn,i -D co,i (4) Where, is a robust standard deviation estimate based on the median absolute deviation, which is used to measure the degree of dispersion of the data; i is the difference of multi-beam bathymetric data after initial offset correction, D cni, and D co,i These are the water depth values ​​measured at different periods after correction; Calculate the median μ of the depth change value and set the threshold Eliminate abnormal water depth change points and filter out valid data that meet the statistical confidence interval v ri : in, μ=median(v i ) (6) Where μ is the median of the depth variation; In step 2.3, after eliminating abnormal water depth change points, the root mean square error minimization criterion is used to accurately match the deep-sea topography data, solve the optimal offset and perform correction to obtain the unified benchmark multi-beam water depth data.

3. The terrain change uncertainty analysis method based on time series bathymetric data according to claim 2, characterized in that: In step 2.3, when solving the optimal offset, the optimal spatial offset Δ is calculated by minimizing the difference between the two periods of water depth data, so that the corrected data satisfies: Where Δ is the optimal spatial offset; i is the sequence number, and N is the number of valid data points; Apply the optimal offset to correct the multi-beam water depth data, and calculate the water depth difference D between the two periods with the same benchmark after correction. diff,i , as shown in formula (8): D diif,i =D′ f,i -D′ o,i (8) Where D′ n,i , D′ o,i These are the multi-beam bathymetric data values ​​at different periods after benchmark correction.

4. The terrain change uncertainty analysis method based on time series bathymetric data according to claim 3, characterized in that: The step 3 includes the following sub-steps: Step 3.1: Build an underwater depth model based on multi-beam bathymetry data and calculate the terrain slope using a moving window analysis. A 3×3 moving window is set around each grid point. The elevation values ​​of the center point and its eight neighboring grids are used within the moving window to calculate the terrain gradient value S using the finite difference method. t , the calculation formula is: in, Where S t is the terrain gradient value, arctan(·) is the inverse tangent function, f x is the gradient value in the x direction, f y is the gradient value in the y direction; Z1, Z2, Z3, Z4, Z5, Z6, Z7, and Z8 are the water depth values ​​of the grid cells adjacent to the center point, and d is the length of the grid cell; Step 3.2: To accurately quantify the effect of terrain slope on the uncertainty of depth change, a hierarchical regression analysis method was used to eliminate the interference of water depth factors. The multibeam bathymetric data were divided into multiple intervals according to the water depth. The linear relationship between the standard deviation of the depth change value and the tangent value of the terrain slope was analyzed within each interval. A slope-uncertainty statistical model was established. By integrating the statistical relationships within each water depth interval, the global uncertainty of the slope effect was estimated. A relationship diagram considering the slope factor on the uncertainty of depth change was generated. This diagram intuitively shows the degree of influence of slope on the uncertainty of terrain deformation and its spatial distribution characteristics, and determines the overall impact of slope on the uncertainty of depth change. The slope-uncertainty statistical model is: s DoD =α0+α1·τ (12) In the formula, α0 and α1 are adjustable coefficients to be determined, α0 is the first adjustable coefficient, α1 is the second adjustable coefficient, σ DoD is the standard deviation of the depth variation, and τ is the tangent of the terrain slope.

5. The terrain change uncertainty analysis method based on time series bathymetric data according to claim 4, characterized in that: The adjustable coefficients α0 and α1 to be determined are determined using the M-estimation robust regression method, and the specific steps are as follows: Step 3.2.1, using the to-be-determined adjustable coefficients α0 and α1 as regression coefficients, initialize the regression coefficients α0 and α1, and calculate the initial regression coefficients α0 and α1 using the ordinary least squares algorithm; Step 3.2.2, calculate the residual value u based on the initial regression coefficient i , as shown in formula (13): u i =σ DoD,i -(α0+α1τ i ) (13) In the formula, σ DoD,i is the standard deviation of the i-th depth change value, τ i is the tangent value of the i-th terrain slope; Step 3.2.3, according to the residual value u i , combined with the preset threshold c h , use the weight function to calculate the weight ω of each multibeam bathymetric data point i , as shown in formula (14): In step 3.2.4, the regression coefficients α0 and α1 are updated using the weighted least squares (WLS) method, as shown in formula (15): Where n is the total number of multibeam bathymetric data points; Step 3.2.5: Repeat steps 3.2.2 to 3.2.4 until the change in the regression coefficient is less than the preset convergence threshold. The regression coefficients α0 and α1 obtained at this time are determined as the adjustable coefficient values ​​obtained by robust estimation of the statistical relationship. By integrating the statistical relationship between the standard deviation of the depth difference and the slope tangent value in each interval, the overall estimation result of the random error of the seabed slope and horizontal position is obtained, and the global uncertainty of the slope effect estimation is determined as: σ slope =α1·tan(S t )+α0 (16) where σ slope Estimate the global uncertainty for the slope effect.

6. The terrain change uncertainty analysis method based on time series bathymetric data according to claim 5, characterized in that: In step 4, the multi-beam bathymetric data is slope-corrected to reduce the amplification effect of the slope on the depth error. The multi-beam bathymetric data is first smoothed and denoised, and a median filter method is used to remove isolated outliers. The median filter is used to replace each data point in the multi-beam bathymetric data with the median value within its neighborhood, thereby suppressing noise and outliers without changing the overall trend of the data. Based on the linear model proposed by the International Hydrographic Organization to describe the relationship between water depth and depth measurement uncertainty, the water depth measurement error is decomposed into two parts, one part is related to the depth and the other part is not related to the depth. The measurement error of the water depth value is obtained as follows: Where, TPU V (m) is the measurement error of water depth; a is the error constant independent of water depth, b is the error constant related to water depth, d is the water depth, and b×d is the error related to water depth; In order to flexibly capture the error characteristics of different water depth intervals, the multi-beam bathymetric data error is statistically analyzed to determine the global uncertainty of the water depth effect estimation, as shown in formula (18): σ depth =β1·depth+β0 (18)In the formula, σ depth is the uncertainty of the global estimation caused by the water depth, β1 and β0 are estimation parameters, and depth is the water depth.

7. The terrain change uncertainty analysis method based on time series bathymetric data according to claim 6, characterized in that: In step 5, uncertainty analysis is performed based on the differential terrain model. According to the horizontal uncertainty determined by the slope-uncertainty statistical model and the vertical uncertainty determined by the water depth-uncertainty statistical model, a slope-water depth joint probability statistical model for determining the global uncertainty is established, as shown in formula (19): Where σ all is the global uncertainty; According to the slope-water depth joint probability statistical model, the confidence interval is set, and the minimum detection level is used to distinguish the real terrain changes from the measurement noise to obtain the real regional terrain change information D diff,true : D diff,true ={i∈DoD: |D diff |>median(D diff )±min LoD } (20) Among them, min LoD =k·σ all (twenty one) Where D diff,true is the real regional terrain change information; DoD is the differential terrain model; D diff is the terrain change before quantification; min LoD is the minimum detection level; k is the confidence coefficient.

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