A method for monitoring coastal erosion based on unmanned aerial vehicle imagery

Abstract

The present application provides a kind of based on unmanned aerial vehicle image's coast erosion monitoring method, belong to coast erosion monitoring technical field, the present application is by in the space and time reference control network of coastal zone monitoring region layout, adopts overall adjustment strategy to simultaneously enter unified coordinate system with multiple time phase image and is registered, utilizes octree space index organization point cloud data and extracts standard coast line position in combination with tide level-coast line response model, changes feature of coast line form is identified by persistence topological analysis, adopts hogge decomposition to reveal erosion driving force direction, topographic feature is input embedded into sediment transport physical constraint, and artificial intelligence prediction model outputs erosion rate field, based on the voxel grid method, calculates erosion volume and according to the erosion response adjustment function value dynamic adjustment sediment discharge flux correction coefficient, establishes multi-dimensional early warning index system to realize risk grade discrimination, solves the technical problem that multiple time phase coast erosion monitoring data registration accumulates large error and leads to the low precision of erosion change amount calculation.

Description

Technical Field

[0001] This invention belongs to the field of coastal erosion monitoring technology, and more specifically, relates to a coastal erosion monitoring method based on UAV imagery. Background Technology

[0002] Coastal erosion monitoring is a crucial aspect of marine geological disaster prevention and control. Traditional monitoring methods primarily rely on satellite remote sensing imagery and ground-based survey stations to acquire coastal topographic change data, assessing erosion severity by comparing elevation models from different periods. Existing technologies employ a phase-by-phase registration approach to process multi-temporal data, registering the second phase data to the first, the third phase to the second, and so on, to achieve spatial alignment of time-series data. However, this phase-by-phase registration strategy leads to the propagation and accumulation of registration errors when processing long-term data, especially in coastal areas lacking stable control points. Registration errors can reach tens of centimeters or even meters, severely impacting the accuracy of calculating erosion volume and retreat distance. In other words, existing technologies suffer from a technical problem: large cumulative registration errors in multi-temporal coastal erosion monitoring data result in low accuracy in calculating erosion changes. Summary of the Invention

[0003] In view of this, the present invention provides a coastal erosion monitoring method based on UAV imagery, which can solve the technical problem in the prior art that the large cumulative error in the registration of multi-temporal coastal erosion monitoring data leads to low accuracy in calculating erosion changes.

[0004] This invention is implemented as follows: A method for monitoring coastal erosion based on UAV imagery includes the following steps: A high-precision ground control point network is deployed in the coastal monitoring area, establishing a spatiotemporal reference control network as a unified benchmark for multi-temporal data registration; a rotary-wing UAV equipped with a high-resolution camera and laser scanner acquires multi-temporal image data of the coastal zone along a preset route; a high-density three-dimensional point cloud is constructed using oblique photogrammetry; aerial triangulation is performed using a structured bundle adjustment algorithm; a global adjustment strategy is used to simultaneously incorporate all temporal images into the unified coordinate system of the spatiotemporal reference control network for global optimization, generating a digital surface model and orthophotos; the three-dimensional point cloud is organized using an octree spatial index structure, and the sampling density is adaptively adjusted according to the terrain complexity; tidal level observation data is collected synchronously, and a tidal level-shoreline response model is constructed; normalization correction is performed using tidal level observation data; the intertidal profile is fitted using the probability density distribution function of the waterline set to estimate the standard coastline position; and multi-scale segmentation and edge detection are performed... The method automatically extracts the standard coastline location, treats multi-temporal coastlines as a family of manifold curves in a high-dimensional topological space, calculates the persistence barcode of the manifold curve family, identifies erosion anchor points, and constructs a persistence map using the waterfall algorithm to measure the topological distance between different temporal phases. The coastline change vector field is decomposed into gradient flow components, curl flow components, and harmonic components through Hodge decomposition. The digital surface model, gradient flow components, slope gradient, wave shear stress, and water flow velocity are input into the coastal erosion dynamics prediction model, outputting the erosion rate field and erosion volume change rate. A multi-phase digital surface model difference model is constructed, and the coastal erosion volume and average erosion rate are calculated based on the voxel grid method. The retreat distance and slope change rate of different shorelines are statistically analyzed, and the erosion response adjustment function value is calculated. The sediment transport flux correction coefficient of the sediment transport conservation law coupling mechanism in the coastal erosion dynamics prediction model is adjusted according to the range of the erosion response adjustment function value. A multi-dimensional early warning index system is established, and the fuzzy comprehensive evaluation method and analytic hierarchy process are used to achieve automatic risk level identification.

[0005] In the step of establishing a spatiotemporal reference control network, real-time dynamic differential positioning technology is used to obtain the coordinates of control points.

[0006] Among them, the spatiotemporal reference control network is a network of multiple high-precision ground control points deployed in the stable coastal zone. The coordinate accuracy of the control points is better than 5 centimeters, which is used to eliminate the spread of cumulative errors in the multi-temporal data registration process.

[0007] In the step of global optimization using an overall adjustment strategy, stable ground feature points are used as joint constraints.

[0008] The overall adjustment strategy incorporates all temporal images into a unified coordinate system for joint calculation, and avoids the accumulation and amplification of errors caused by phase-by-phase registration by globally optimizing the allocation of errors.

[0009] Among them, the resolution of the generated digital surface model and orthophotos reaches the centimeter level.

[0010] Among them, the octree spatial index structure is a tree-shaped data structure that recursively divides the three-dimensional space into eight sub-cubes and dynamically adjusts the division level according to the point cloud density to achieve efficient spatial query and data organization.

[0011] In the step of adaptively adjusting the sampling density according to the terrain complexity, lossy compression is performed by combining wavelet transform.

[0012] Among them, the adaptive adjustment of sampling density dynamically determines the sampling interval based on the curvature and slope gradient of the terrain surface, increasing the sampling interval in flat terrain areas and decreasing the sampling interval in steep terrain areas.

[0013] In the step of estimating the location of the standard coastline, the location of the standard coastline corresponding to the theoretical datum is calculated.

[0014] Among them, the tide level-shoreline response model describes the changing relationship between the land and water boundary positions under different tide levels. By establishing a functional mapping between tide level elevation and shoreline position, it eliminates spurious changes caused by tidal effects.

[0015] Among them, normalization correction converts the coastline positions collected at different tide levels to the same theoretical datum, eliminating the influence of tidal cycle fluctuations.

[0016] In the step of automatically extracting the standard coastline location, morphological filtering is used to eliminate the influence of tidal levels and waves.

[0017] Among them, the manifold curve family is the geometric representation of coastlines in different time phases in a high-dimensional topological space. Each coastline is a curve in the high-dimensional topological space, and all coastlines in all time phases constitute the manifold curve family.

[0018] The persistent barcode is a visualization tool in the theory of topological persistence homology. The horizontal axis represents the generation scale of topological features, the vertical axis represents the extinction scale of topological features, and the barcode length reflects the persistence strength of topological features.

[0019] In the step of calculating the persistent barcode of the manifold family, the generation and disappearance characteristics of the coastline morphology at different time scales are captured.

[0020] This invention employs a spatiotemporal reference control network as a unified benchmark for multi-temporal data registration. All temporal images are simultaneously incorporated into a unified coordinate system for overall adjustment. A global optimization strategy is used to allocate registration errors, avoiding the cumulative amplification of errors caused by phase-by-phase registration. Specifically, the spatiotemporal reference control network consists of high-precision ground control points deployed in stable coastal areas, with coordinate accuracy better than 5 centimeters, providing a stable spatial reference frame for multi-phase data. The overall adjustment strategy uses image data from different temporal phases as a unified observation system for joint calculation. Stable ground feature points are used as joint constraints, and the least squares principle is used to evenly distribute residuals across all temporal phases. This ensures that the registration accuracy between any two phases is unaffected by the time span, and the registration error is always controlled at the level of control point accuracy. In summary, this invention solves the technical problem mentioned in the background art where large cumulative errors in the registration of multi-temporal coastal erosion monitoring data lead to low accuracy in calculating erosion changes. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 This is a diagram showing the results of identifying persistent barcodes and erosion anchor points.

[0023] Figure 3 This is a diagram showing the Hodge decomposition results of the vector field of coastline variation.

[0024] Figure 4 Spatial distribution map for predicting erosion rate field.

[0025] Figure 5 The graph shows the variation of the erosion response adjustment function value with the monitoring time phase. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0027] like Figure 1 The diagram shown is a flowchart of a coastal erosion monitoring method based on UAV imagery provided by the present invention. This method includes the following steps:

[0028] S01. Deploy a high-precision ground control point network in the coastal monitoring area, use real-time dynamic differential positioning technology to obtain the coordinates of the control points, and establish a spatiotemporal reference control network as a unified reference for multi-temporal data registration.

[0029] S02. A rotary-wing UAV equipped with a high-resolution camera and a laser scanner acquires multi-temporal image data of the coastal zone according to a preset route. It uses oblique photogrammetry to construct a high-density three-dimensional point cloud from multiple perspectives. It uses the structured bundle adjustment algorithm to perform aerial triangulation on the multi-temporal image data. It adopts an overall adjustment strategy to simultaneously incorporate all temporal images into the unified coordinate system of the spatiotemporal reference control network. It uses stable ground feature points as joint constraints to perform global optimization and generate a digital surface model and orthophoto with a resolution of centimeters.

[0030] S03. The three-dimensional point cloud is organized using an octree spatial index structure. The sampling density is adaptively adjusted according to the terrain complexity. Sparse sampling is performed in flat areas, and high-density sampling is maintained in steep cliff areas. Lossy compression is performed in combination with wavelet transform. Tide level observation data is collected simultaneously to construct a tide level-shoreline response model. Normalization correction is performed using the tide level observation data. The intertidal profile is fitted using the probability density distribution function of the waterline set to calculate the standard coastline position corresponding to the theoretical reference surface.

[0031] S04. The standard coastline position is automatically extracted through multi-scale segmentation and edge detection algorithms. Morphological filtering is used to eliminate the influence of tidal levels and waves. The multi-temporal coastline is regarded as a family of manifold curves in a high-dimensional topological space. The persistence barcode of the manifold curve family is calculated to capture the generation and disappearance features of the coastline morphology at different time scales. Topologically stable shoreline segments are identified as erosion anchor points. The waterfall algorithm is used to construct a persistence map, measure the topological distance between different time phases, and automatically detect shoreline bifurcation, shoreline closure and shoreline breakage.

[0032] S05. The coastline variation vector field is decomposed into gradient flow component, curl flow component and harmonic component by Hodge decomposition to reveal the driving force direction and energy distribution law of erosion. The digital surface model, the gradient flow component, the slope gradient, wave shear stress and water flow velocity are input into the coastal erosion dynamics prediction model. The coastal erosion dynamics prediction model outputs the erosion rate field and the erosion volume change rate.

[0033] S06. Construct a multi-phase digital surface model difference model, calculate the coastal erosion volume and average erosion rate based on the voxel grid method, statistically analyze the retreat distance and slope change rate of different coastal sections, calculate the erosion response adjustment function value, and adjust the sediment transport flux correction coefficient of the sediment transport conservation law coupling mechanism in the coastal erosion dynamics prediction model according to the range of the erosion response adjustment function value.

[0034] S07. Establish a multi-dimensional early warning indicator system that includes the average annual erosion rate, cumulative retreat distance, slope change rate, and erosion acceleration. Set threshold standards for different levels and use fuzzy comprehensive evaluation method and hierarchical analysis method to realize automatic risk level identification.

[0035] The spatiotemporal reference control network consists of multiple high-precision ground control points deployed in stable coastal areas. The coordinate accuracy of these control points is better than 5 cm, used to eliminate the spread of accumulated errors during multi-temporal data registration. The overall adjustment strategy incorporates all temporal images into a unified coordinate system for joint calculation, and avoids the accumulation and amplification of errors caused by phase-by-phase registration by globally optimizing error allocation.

[0036] The octree spatial index structure is a tree-like data structure that recursively divides the three-dimensional space into eight sub-cubes. The hierarchical division is dynamically adjusted based on the point cloud density, enabling efficient spatial querying and data organization. The adaptively adjusted sampling density dynamically determines the sampling interval based on the terrain surface curvature and the slope gradient, increasing the sampling interval in gently sloping areas and decreasing it in steeply sloping areas.

[0037] The tide level-shoreline response model describes the changing relationship between the land-water boundary position under different tidal conditions. By establishing a functional mapping between tide level elevation and shoreline position, it eliminates spurious changes caused by tidal effects. The normalization correction uniformly converts the shoreline positions collected at different tide levels to the same theoretical datum, eliminating the influence of tidal cycle fluctuations. The probability density distribution function describes the statistical distribution pattern of the waterline position within the intertidal zone. By fitting the probability density distribution function, the high-probability land-water boundary line is determined as the standard shoreline position.

[0038] The manifold curve family represents the geometric representation of coastlines at different time phases in a high-dimensional topological space. Each coastline serves as a curve in this high-dimensional topological space, and all coastlines at different time phases constitute the manifold curve family. The persistence barcode is a visualization tool in the theory of topological persistence homology. The horizontal axis represents the generation scale of topological features, and the vertical axis represents the disappearance scale of topological features. The barcode length reflects the persistence strength of the topological features. The generation and disappearance features refer to the appearance and disappearance processes of protrusions, depressions, and isolated islands in the coastline morphology at different observation scales. The erosion anchor point is a coastline segment with a long-term stable topological structure, whose persistence barcode length is significantly greater than that of other coastline segments, serving as a reference benchmark for erosion change analysis.

[0039] The waterfall algorithm is an efficient algorithm for calculating persistent graphs, identifying pairing relationships of topological features through matrix reduction operations. The persistent graph represents each topological feature as a point on a plane, with the coordinates of the point representing the generation and destruction scales of the topological feature, used to measure the topological similarity of coastlines at different time phases. The topological distance uses bottleneck distance or Wasserstein distance to measure the difference between two persistent graphs; the smaller the value, the more similar the topological structure. Coastline bifurcation refers to the topological event of a single coastline splitting into multiple coastlines; coastline closure refers to the formation of a closed loop on the coastline; and coastline breakage refers to the interruption of a continuous coastline, forming a gap.

[0040] The Hodge decomposition, a fundamental theorem in differential geometry, uniquely decomposes any vector field into the sum of three orthogonal components. The gradient flow component, perpendicular to the contour lines, points in the direction of the fastest growth of the scalar field, reflecting the dominant direction of coastal erosion. The curl flow component, circling the contour lines, describes the vortex structure and lateral transport characteristics during erosion. The harmonic component, having neither divergence nor curl, characterizes the global topological constraints of the erosion field, revealing long-period energy distribution patterns.

[0041] The coastal erosion dynamics prediction model has an encoder-decoder architecture. The encoder contains a four-layer convolutional neural network that extracts topographic slope, curvature, and roughness features from the digital surface model. The decoder contains a four-layer deconvolutional neural network that outputs the spatial distribution of the erosion rate field. A sediment transport module is embedded between the encoder and the decoder. The sediment transport module contains a physical constraint layer that constructs a differential equation coupling relationship based on the sediment continuity equation and the Exner equation. The inputs are the slope gradient, the wave shear stress, and the water flow velocity, and the output is the sediment transport flux. The conservation equation is discretized using a finite difference scheme, and the calculated theoretical erosion amount is checked for consistency with the decoder prediction. The verification error is adjusted by backpropagation to adjust the network parameters.

[0042] The steps for establishing the training dataset for the coastal erosion dynamics prediction model include: collecting historical multi-temporal UAV imagery data and corresponding ground-measured erosion rate data; extracting a digital surface model from the historical multi-temporal UAV imagery data as input samples; spatially interpolating the ground-measured erosion rate data to generate an erosion rate field as label samples; simultaneously collecting wave observation data, water flow velocity data, and sediment grain size distribution data at corresponding times as auxiliary inputs; and dividing the input samples, label samples, and auxiliary inputs into a training set, a validation set, and a test set in a 7:2:1 ratio.

[0043] The training steps of the coastal erosion dynamics prediction model include: initializing the network parameters of the encoder, the decoder, and the physical constraint layer; inputting the digital surface model of the training set into the encoder to extract terrain features; passing the terrain features and the auxiliary input to the physical constraint layer to calculate the theoretical erosion amount; inputting the terrain features into the decoder to predict the erosion rate field; constructing a loss function as a weighted sum of the mean square error term of the predicted erosion rate field and the label samples, and the consistency constraint term of the theoretical erosion amount and the decoder's predicted value; minimizing the loss function using an adaptive moment estimation optimization algorithm and iteratively updating the network parameters; evaluating the model performance on the validation set every 10 training rounds, and stopping training when the validation set loss no longer decreases for 5 consecutive rounds; and evaluating the prediction accuracy of the final model on the test set.

[0044] The principle of the sediment transport conservation law coupling mechanism is as follows: the sediment continuity equation describes the change in sediment mass in the control volume per unit time as equal to the difference between the inflow and outflow sediment fluxes; the Exner equation describes the relationship between the rate of change of riverbed or seabed elevation and the sediment flux divergence. The two equations together form a coupled system of mass and momentum conservation in sediment transport. When sediment transport reaches equilibrium, the inflow equals the outflow, and the topographic elevation remains stable. When transport is unbalanced, sediment accumulation leads to topographic uplift, or erosion leads to topographic subsidence. The sediment transport conservation law coupling mechanism, by embedding the discretized form of the above physical equations into the neural network, forces the network prediction results to conform to the constraints of physical laws, avoids the neural network learning false patterns that violate physical laws, significantly improves the model's generalization ability and prediction stability in sparse data regions and extreme conditions, and reduces the dependence on large-scale training data, enabling the model to quickly converge to a physically reasonable solution space using a small amount of observation data. This provides a reliable physical basis and numerical stability guarantee for the long-term prediction of coastal erosion.

[0045] The voxel grid method discretizes the three-dimensional space into a regular cubic grid, calculates the elevation difference of the digital land model within each voxel, and sums the volume changes of all voxels to obtain the coastal erosion volume. The average erosion rate is the coastal erosion volume divided by the monitoring time period and the monitoring area. The retreat distance is the average distance change of the coastline position along the direction perpendicular to the coastline at different time phases. The erosion acceleration is the rate of change of the average erosion rate between adjacent time periods.

[0046] The erosion response adjustment function value is used to adjust the sediment transport flux correction coefficient of the sediment transport conservation law coupling mechanism. The calculation formula of the erosion response adjustment function value is as follows: Divide the theoretical erosion by the historical maximum value of the theoretical erosion to obtain the normalized theoretical erosion; divide the erosion rate field by the historical maximum value of the erosion rate field to obtain the normalized predicted erosion; divide the erosion acceleration by the historical maximum absolute value of the erosion acceleration to obtain the normalized erosion acceleration; divide the slope change rate by the historical maximum absolute value of the slope change rate to obtain the normalized slope change rate; calculate the absolute value of the difference between the normalized theoretical erosion and the normalized predicted erosion as the prediction deviation; calculate the product of the prediction deviation and the normalized erosion acceleration, and add 0.5 times the normalized slope change rate to obtain the erosion response adjustment function value. When the erosion response adjustment function value a∈[0, 0.3), the sediment transport flux correction coefficient is set to 1.0; when a∈[0.3, 0.6), the sediment transport flux correction coefficient is set to 1.2; when a∈[0.6, 1.0), the sediment transport flux correction coefficient is set to 1.5; and when a≥1.0, the sediment transport flux correction coefficient is set to 2.0.

[0047] In the multi-dimensional early warning indicator system, the annual average erosion rate threshold is divided into low-risk (less than 0.5). / year, medium risk 0.5 to 2.0 / year, high risk 2.0 to 5.0 / year, extremely high risk greater than 5.0 / year. The cumulative backtracking distance is the sum of the backtracking distances for all time phases. The fuzzy comprehensive evaluation method calculates the comprehensive evaluation vector based on the membership function of each indicator, and the hierarchical analysis method determines the weight coefficients of each indicator by constructing a judgment matrix.

[0048] Optionally, the present invention also provides a method for forming a coastal erosion monitoring system by means of a computer, wherein the computer is provided with a readable storage medium, the readable storage medium storing program instructions, and the program instructions executing the above-described method when running in the computer.

[0049] The specific implementation methods of the above steps are described in detail below.

[0050] The specific implementation of step S01 is as follows: First, select areas with stable geological structures and unaffected by erosion in the coastal zone as the locations for control point deployment, ensuring that the control points remain in the same position throughout the monitoring period. Through the collaborative working mode of the base station and rover in real-time dynamic differential positioning technology, the base station is set up at a fixed point with known coordinates and continuously transmits differential correction signals. After receiving satellite signals and differential correction signals, the rover calculates the three-dimensional coordinates with centimeter-level accuracy in real time. Static observation is performed on each control point for no less than 30 minutes to eliminate the effects of multipath effects and ionospheric delay. After the collected coordinate data is processed by gross error elimination and smoothing filtering, the average value is taken as the final coordinates of the control point. The coordinate accuracy of the control point is required to be better than 3cm in plane accuracy and better than 5cm in elevation accuracy. Multiple control points are used to establish a unified spatiotemporal reference control network through network adjustment calculation. This control network serves as a spatial reference frame for the registration of all temporal data, eliminating systematic positional deviations during data acquisition at different times.

[0051] The specific implementation of step S02 is as follows: A drone flight path is planned based on the monitoring area and terrain characteristics. The flight path design uses a grid layout to ensure that the image overlap reaches at least 80% forward and 60% lateral. The high-resolution camera on the drone automatically triggers shooting at set intervals during flight. Simultaneously, a laser scanner emits laser pulses and receives ground reflection signals to obtain accurate distance information. Oblique photography technology, by installing a multi-angle camera array on the drone, simultaneously acquires images from five directions: vertical, forward-looking, backward-looking, left-looking, and right-looking. This multi-view observation method can capture the side and top details of ground objects, providing sufficient geometric constraints for constructing a high-density 3D point cloud. The acquired multi-temporal image data is input into a structured bundle adjustment algorithm for aerial triangulation. This algorithm establishes the collinearity equation between image rays and ground points, utilizing... Error equations are constructed using observations of the same point in different images. The camera exterior orientation elements and ground point coordinates are solved by least squares iteration. The overall adjustment strategy incorporates images from all time phases into a unified coordinate system for joint calculation. During the adjustment process, the known coordinates of the spatiotemporal reference control network are introduced as mandatory constraints. At the same time, stable feature points such as building corners and road intersections are extracted as joint constraint points. The positions of these feature points remain unchanged in images from different time phases. The image parameters of all time phases are adjusted synchronously through a global optimization algorithm, so that the multi-time phase data achieves optimal geometric consistency in a unified coordinate system. The adjusted images are then processed by a dense matching algorithm to generate a high-density 3D point cloud with a point cloud density of more than 500 points per square meter. Finally, a digital surface model and orthophoto with a spatial resolution of 2cm to 5cm are generated through point cloud interpolation and texture mapping.

[0052] The specific implementation of step S03 is as follows: The 3D point cloud data is input into an octree spatial index structure for organization and management. This data structure starts from the root node of a cube containing all point clouds. Based on a point cloud density threshold, it determines whether further subdivision is needed. When the number of points within a node exceeds a set threshold, it is divided into eight sub-cubes. This process is recursively executed until the number of points in each leaf node is below the threshold or the maximum subdivision level is reached. The terrain complexity is assessed by calculating surface curvature and slope gradient. For curvature less than 0.05... Furthermore, for flat areas with a slope less than 5°, the sampling interval is set to 50% of the original point cloud density to reduce data redundancy; for areas with a curvature greater than 0.2... For steep cliff areas with a slope greater than 30°, the original sampling density is maintained to preserve topographic details. The sampled point cloud data is decomposed into low-frequency approximation coefficients and high-frequency detail coefficients using wavelet transform. The high-frequency coefficients are quantized and encoded to achieve lossy compression, with the compression rate controlled between 30% and 50% to balance data volume and accuracy loss. Simultaneously collected tide level observation data is acquired through float-type or pressure-type sensors at tide gauge stations, with an observation frequency set to once every 10 minutes. A functional mapping relationship between tide level elevation and the position of the land-water boundary is established to construct the tide level. - The shoreline response model statistically analyzes the waterline position data extracted under different tidal conditions, fits a regression equation between tidal changes and shoreline displacement, and normalizes the coastline positions collected at different tidal times to the mean sea level datum, eliminating spurious changes caused by tidal periodic fluctuations. By statistically analyzing the observation data of waterline positions in multiple tidal cycles, the frequency of waterline occurrence at each location is calculated, and a probability density distribution function is constructed. The peak position of this function corresponds to the high-probability land-water boundary line, which is used as the basis for estimating the standard coastline position.

[0053] The specific implementation of step S04 is as follows: The normalized orthophoto image is decomposed into objects of different scales using a multi-scale segmentation algorithm. Regions are merged by calculating spectral differences and shape heterogeneity between adjacent objects to form segmentation units with clear boundaries. Based on the segmentation results, the Canny edge detection algorithm is applied to extract object boundaries. This algorithm smooths the image using Gaussian filtering, calculates gradient magnitude and direction, uses non-maximum suppression to refine edges, and connects real edges using a dual-threshold strategy. Morphological opening and closing operations are performed on the extracted edges. The opening operation removes isolated noise points by first eroding and then dilating, while the closing operation fills edge breaks by first dilating and then eroding. The morphological structuring element size is set to 5 to 10 pixels to eliminate short-period fluctuations caused by waves and tides. The extracted multi-temporal coastlines are represented as a family of manifold curves in a high-dimensional topological space. Each coastline is embedded into a high-dimensional Euclidean space through its coordinate sequence to form a curve. The topological features of this family of curves are calculated using persistent homology theory. In specific implementation, the coastlines are first subjected to Vieto... The ris-Rips complex is constructed by gradually adding new simplexes as the filter parameter increases. The generation and demise scales of each topological feature are recorded. The generation scale corresponds to the filter value at which the topological feature first appears, and the demise scale corresponds to the filter value at which the feature is filled or connected. All generation-demise scale pairs of features are plotted as persistent barcodes. The length of the barcode reflects the stability of the topological feature. Features with a length greater than twice the average length correspond to stable shorelines. These shorelines are identified as erosion anchors and used as reference benchmarks for subsequent analysis. The waterfall algorithm is applied to calculate persistent pairings through column reduction operations on the boundary matrix. The generation and demise scales of each topological feature are used as planar coordinates to plot persistent maps. The bottleneck distance between persistent maps at different time phases is calculated. This distance is defined as the maximum point-to-point distance under optimal matching between two map point sets. The distance threshold is set to 1.5 times the average point-to-point distance. Exceeding the threshold indicates a significant topological change. Topological events such as shoreline bifurcation, shoreline closure, and shoreline breakage are automatically detected by analyzing the aggregation and dispersion patterns of points in the persistent map.

[0054] The specific implementation of step S05 is as follows: The difference between the positions of the coastline in adjacent time phases is calculated to form a coastline change vector field. Each spatial point in this vector field corresponds to a two-dimensional vector representing the displacement direction and magnitude of the coastline at that point. According to the Hodge decomposition theorem, the vector field is decomposed into three orthogonal components: a gradient field, a curl field, and a harmonic field. The gradient field is obtained by solving the Poisson equation; this component is perpendicular to the coastline contour lines and points in the direction of fastest erosion growth, revealing the dominant erosion propagation path. The curl field is obtained by calculating the curl of the vector field and solving the corresponding Poisson equation; this component surrounds the contour lines, characterizing the vortex structure and lateral transport features during the erosion process. The harmonic field, as the residual component with neither divergence nor curl, reflects the long-period energy distribution pattern constrained by global topology. The digital surface model is input into the slope calculation module, and the slope gradient at each grid point is calculated using the finite difference method. The gradient field components, slope gradient, wave shear stress, and water flow velocity are input as input features into the coastal erosion dynamics prediction model. This model adopts an encoder-decoder architecture. The encoder... The algorithm comprises four convolutional neural networks, each with a 3×3 kernel and 64, 128, 256, and 512 channels respectively. Convolutional operations are used to extract local topographic features from the digital land model, including slope, curvature, and roughness. The decoder comprises four deconvolutional neural networks with 512, 256, 128, and 64 channels respectively. Deconvolutional operations upsample the feature maps to the original resolution and output the spatial distribution of the erosion rate field. A sediment transport module is embedded between the encoder and decoder. The physical constraint layer of this module establishes the sediment mass conservation relationship based on the sediment continuity equation and establishes the coupling relationship between the riverbed elevation change rate and sediment flux divergence based on the Exner equation. After inputting slope gradient, wave shear stress, and water flow velocity, the theoretical erosion is calculated by discretizing the conservation equation using a finite difference scheme. The theoretical erosion is then compared with the erosion rate field predicted by the decoder for consistency verification. The verification error is adjusted using a backpropagation algorithm to adjust the network parameters. The model ultimately outputs the erosion rate at each grid point and the erosion volume change rate for the entire region.

[0055] The specific implementation of step S06 is as follows: After spatial registration of digital surface models at different times, the elevation difference of corresponding grid points is calculated, a digital surface model difference model is constructed, and the three-dimensional monitoring space is divided into regular cubic grids with side lengths of 1m to 2m using the voxel grid method. The elevation difference of the digital surface model in the initial and final stages within each voxel is calculated. Voxels with decreasing elevation correspond to erosion areas, and voxels with increasing elevation correspond to siltation areas. The total volume of erosion voxels is summed to obtain the total volume of coastal erosion. The total erosion volume is divided by the monitoring time period and the area of ​​the monitoring area to calculate the average erosion rate. The distance between the coastlines at different times is measured along the normal direction perpendicular to the coastline. The average value of the measurement results for the entire coastline is taken to obtain the retreat distance. The change in slope between adjacent monitoring periods is calculated and divided by the time interval to obtain the slope change rate. The difference between the average erosion rate of the current period and the average erosion rate of the previous period is divided by the time interval to calculate the erosion acceleration. The erosion response adjustment function is then used to calculate the erosion acceleration. The adjustment function value is calculated by first normalizing the theoretical erosion, predicted erosion rate field, erosion acceleration, and slope change rate by their respective historical extreme values. Then, the absolute value of the difference between the normalized theoretical erosion and the normalized predicted erosion is calculated as the prediction bias. The prediction bias is multiplied by the normalized erosion acceleration and then added to 0.5 times the normalized slope change rate to obtain the adjustment function value. The sediment transport flux correction coefficient in the coupling mechanism of the sediment transport conservation law is adjusted according to the range of the adjustment function value. When the adjustment function value is less than 0.3, the correction coefficient is set to 1.0, indicating that the model prediction matches the actual situation well and no adjustment is needed. When the adjustment function value is between 0.3 and 0.6, the correction coefficient is set to 1.2 to moderately enhance the sediment transport intensity. When the adjustment function value is between 0.6 and 1.0, the correction coefficient is set to 1.5 to significantly enhance the sediment transport effect. When the adjustment function value is greater than or equal to 1.0, the correction coefficient is set to 2.0 to cope with extreme erosion conditions.

[0056] The specific implementation of step S07 involves establishing a four-dimensional early warning indicator system that includes the average annual erosion rate, cumulative retreat distance, slope change rate, and erosion acceleration. The threshold for the average annual erosion rate is divided into low-risk (less than 0.5). / year, medium risk 0.5 to 2.0 / year, high risk 2.0 to 5.0 / year, extremely high risk greater than 5.0 The cumulative retreat distance per year is obtained by summing the retreat distances of all monitoring phases. A fuzzy comprehensive evaluation method is used to construct a membership function for each indicator. The membership function maps the measured value of the indicator to the degree of belonging to each risk level. A pairwise comparison judgment matrix is ​​constructed using the analytic hierarchy process. The matrix elements represent the relative importance between different indicators. The eigenvector corresponding to the largest eigenvalue of the judgment matrix is ​​solved and normalized to obtain the weight coefficient of each indicator. The membership vector of each indicator and the weight coefficient are weighted and summed to calculate the comprehensive evaluation vector. The final risk level is determined according to the principle of maximum membership, so as to realize the automatic identification and graded early warning of coastal erosion risk.

[0057] The key technical ideas of this invention include the following aspects. First, it adopts a spatiotemporal reference control network combined with an overall adjustment strategy to achieve high-precision registration of multi-temporal data. Traditional phase-by-phase registration methods lead to the accumulation and amplification of errors over time. However, this invention optimizes the global model by simultaneously incorporating all temporal images into a unified coordinate system and using stable ground feature points as joint constraints, ensuring that registration errors are evenly distributed across all temporal phases. This effectively avoids the systematic propagation of errors and significantly improves the reliability and consistency of long-term coastline change detection. Second, it introduces topological data analysis methods to construct a persistent homology representation of coastlines. Traditional coastline comparison methods based on Euclidean distance are sensitive to noise and struggle to capture global structural changes. This invention, by calculating persistent barcodes and persistent maps, measures the essential characteristics of coastline morphology from the perspective of topological invariants. It can identify stable topological structures at different observation scales. This method is robust to local disturbances and can accurately detect important topological events such as coastline bifurcation, closure, and fracture, providing a rigorous mathematical theoretical basis for the quantitative classification of erosion patterns. Third, by embedding the physically driven sediment transport conservation law into a deep learning model to form a physically constrained neural network, this invention addresses the issue of purely data-driven neural networks, which are prone to producing predictions that violate physical laws when training data is insufficient or when facing extreme conditions. This invention, by embedding discretized forms of the sediment continuity equation and the Exner equation into the network, forces the model output to satisfy mass and momentum conservation constraints. This allows the model to quickly converge to a physically reasonable solution space using limited observation data, significantly improving the model's generalization ability in sparse data regions and the numerical stability of long-term predictions. These three technical approaches work synergistically to form a complete technical chain from data acquisition and feature extraction to predictive modeling. The spatiotemporal reference control network ensures high-quality and temporal consistency of the input data, topological data analysis provides a deep understanding of coastline evolution patterns, and the physically constrained neural network organically integrates empirical knowledge with physical laws. These three elements support each other to form a coastal erosion monitoring technology system that combines data accuracy, theoretical depth, and predictive reliability, achieving a comprehensive improvement in monitoring accuracy, change detection sensitivity, and prediction stability compared to traditional methods.

[0058] It should be noted that this invention also solves the following technical problem: existing coastal erosion monitoring methods struggle to eliminate the interference of tidal fluctuations on shoreline position measurements, resulting in extracted coastline positions containing a large amount of spurious change information caused by tidal level variations, failing to accurately reflect the true erosion process. This invention constructs a tidal level-shoreline response model, establishing a functional mapping relationship between tidal level elevation and shoreline position, uniformly converting coastline positions collected at different tidal levels to the same theoretical datum, thus eliminating the influence of tidal periodic fluctuations. Simultaneously, it uses the probability density distribution function of the waterline set to fit the intertidal profile, determining the high-probability land-water boundary line as the standard coastline position, effectively eliminating short-period positional fluctuations caused by tidal effects, enabling the extracted coastline to truly reflect long-term erosion trends, and significantly improving the reliability and physical significance of erosion change detection.

[0059] Specifically, the principle of this invention is as follows: The fundamental reason why this invention can solve the problem of registration accumulation error lies in changing the error propagation path and distribution mechanism. Traditional phase-by-phase registration forms a chain-like error propagation structure, where the registration error of the nth phase data is equal to the sum of the registration errors of the previous n minus 1 phases, and the error grows linearly or superlinearly with the number of phases. This invention employs a global adjustment strategy to construct a star-shaped error distribution structure. All temporal data are directly registered with the same spatiotemporal reference control network. The relative error between any two phases depends only on their respective registration accuracy with the control network, and there is no error propagation path. From a mathematical perspective, global adjustment constructs an overdetermined system of equations containing all temporal observations and uses the least squares criterion to solve for the optimal registration parameters, minimizing the sum of squares of the observation residuals globally. This global optimization mechanism ensures that the error is uniformly distributed across all temporal phases rather than unidirectionally accumulating. Simultaneously, using stable ground feature points as joint constraints enhances the geometric correlation between different temporal phases, further improving the overall consistency and stability of the registration.

[0060] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0061] The specific implementation of step S01 is as follows: When setting up a high-precision ground control point network in the coastal monitoring area, the number of control points is determined according to the area of ​​the monitoring area, with 3 to 5 control points set up per square kilometer. The control points are selected on long-term stable ground features such as bedrock outcrops and concrete building foundations. Each control point is continuously observed for no less than 30 minutes using real-time dynamic differential positioning technology, with a sampling frequency of 1Hz. The planar accuracy of the three-dimensional coordinates of the control points is better than 2cm, and the elevation accuracy is better than 3cm. A spatiotemporal reference control network is established as a unified reference for multi-temporal data registration to eliminate systematic offsets between different temporal data.

[0062] The specific implementation of step S02 is as follows: A rotary-wing UAV equipped with a high-resolution camera and a laser scanner flies along a preset route. The route design adopts a grid layout with a forward overlap of 75% and a lateral overlap of 65%. The flight altitude is 80 to 120m. It acquires ground image data with a resolution of 2 to 5cm. It uses oblique photography technology to simultaneously acquire images from five angles: vertical, forward, backward, left, and right. It uses a structured bundle adjustment algorithm to perform aerial triangulation on the multi-temporal image data. It adopts an overall adjustment strategy to simultaneously incorporate all temporal images into the unified coordinate system of the spatiotemporal reference control network. It uses stable ground feature points as joint constraints for global optimization to generate a digital surface model and orthophoto with a resolution of centimeters.

[0063] The specific implementation of step S03 is as follows: An octree spatial index structure is used to organize the three-dimensional point cloud. The initial cube side length is set to the maximum span of the monitoring area. The sampling density is adaptively adjusted according to the terrain complexity. The terrain complexity is calculated through local curvature and slope gradient. The sampling interval is set to 10 to 15 cm for flat areas and 2 to 5 cm for steep cliff areas. Lossy compression is performed using wavelet transform, with the compression ratio controlled at 5 to 8 times. Tide level observation data is collected synchronously at a frequency of once per hour. A tide level-shoreline response model is constructed. The formula for the tide level-shoreline response model is as follows:

[0064] ;

[0065] In the formula, The x-coordinate of the standard coastline location, in meters; The x-coordinate of the measured waterline position is in meters. The tidal response coefficient is dimensionless, with an empirical value of 0.8 to 1.2. The measured tide level is in meters (m). This is the theoretical reference elevation, in meters (m).

[0066] in, The water-land boundary line was obtained by extracting it from orthophotos using an edge detection algorithm. Obtained through real-time observations at the tide gauge station; The multi-year average sea level is used as the benchmark. The relationship between the waterline position and the tide level at multiple different tide times is determined by fitting a linear relationship. The calculation formula is expressed as follows:

[0067] ;

[0068] In the formula, The number of observation samples is typically between 20 and 30. For the first The horizontal coordinate of the waterline position observed each time is in meters. This is the average value of all observed waterline positions, in meters (m). For the first The tide level elevation observed this time is in meters (m). This is the average of all observed tide levels, in meters (m).

[0069] probability density distribution function The statistical distribution pattern of the location of the waterline within the intertidal zone is described by the following formula:

[0070] ;

[0071] In the formula, Location of the waterline The probability density at point , in units of ; These are the position coordinates along the shoreline in the vertical direction, in meters; This represents the average position of the waterline, in meters (m). This represents the standard deviation of the waterline position, in meters (m).

[0072] in, and This was obtained through statistical analysis of the waterline position data at multiple tide level observation times. Calculated using the arithmetic mean, Using the standard deviation formula Calculation, where For the first The location of the waterline observed each time is in meters (m).

[0073] The specific implementation of step S04 is as follows: The orthophoto image is divided into multiple scale levels using a multi-scale segmentation algorithm, with scale parameters set to 10, 20, 50, and 100. The Canny edge detection algorithm is used to automatically extract the standard coastline location, with a detection threshold set to 15% to 25% of the grayscale value. Morphological opening and closing operations are used to eliminate the influence of tidal levels and waves. The structuring element size is 3×3 pixels. The multi-temporal coastline is considered as a family of manifold curves in a high-dimensional topological space. The persistent barcode of the manifold curve family is calculated to capture the generation and disappearance characteristics of the coastline morphology at different time scales. Topologically stable shoreline segments are identified as erosion anchor points. The persistent barcode length threshold is set to 1.5 times the average length. A persistent map is constructed using the waterfall algorithm to measure the topological distance between different time phases. The topological distance is calculated using bottleneck distance. The calculation formula is expressed as follows:

[0074] ;

[0075] In the formula, For persistent maps and The bottleneck distance between them, in meters; This is the persistence map of the first phase; This is the persistence map of the second phase; From arrive bijective mapping; for The points in the graph represent the generation and destruction scales of the topological features, in meters. For point exist The corresponding points in the diagram are in meters (m). It is an infinite norm, taking the maximum value of the absolute values ​​of all components of the vector; The infimum operator represents the infimum of all possible bijective mappings. Take the minimum value; The supremum operator indicates that the supremum is bounded by the sum of its parts. All points Take the maximum value.

[0076] Automatically detect shoreline bifurcation, shoreline closure, and shoreline breakage events based on bottleneck distance.

[0077] The specific implementation of step S05 is as follows: The coastline variation vector field is decomposed into gradient flow components, curl flow components, and harmonic components through Hodge decomposition. The formula for Hodge decomposition is as follows:

[0078] ;

[0079] In the formula, This represents the vector field of coastline variation, with units of m / a; This represents the gradient flow component, in m / a. This represents the vortex component, in m / a. For harmonic components, the unit is m / a; The scalar potential function has units of . / a; It is a vector potential function, with units of . / a; Gradient operator, unit: ; For curl operator, the unit is . .

[0080] in, It is obtained by calculating the difference in coastline position between adjacent time phases and dividing by the time interval; By solving the Poisson equation Obtain, among which For the Laplace operator, the unit is . , Here is the divergence operator, in units of ; By solving the Poisson equation get; pass The calculations yielded the following results: The digital surface model, gradient flow components, slope gradient, wave shear stress, and water flow velocity were input into the coastal erosion dynamics prediction model, which outputs the erosion rate field and the rate of change of erosion volume.

[0081] The specific implementation of step S06 is as follows: Construct a multi-phase digital surface model difference model, calculate the coastal erosion volume based on the voxel grid method, set the voxel size to 0.5m×0.5m×0.5m, calculate the elevation difference of the digital surface model within each voxel, and sum the volume changes of all voxels to obtain the coastal erosion volume. The formula for calculating the average erosion rate is expressed as follows:

[0082] ;

[0083] In the formula, The average erosion rate is expressed in units of 1000 m / s. ; The volume of coastal erosion is expressed in units of 1. ; The area under monitoring is expressed in units of... ; The monitoring period is expressed in units of 'a'.

[0084] Statistical analysis of retreat distance and slope change rate for different bank sections. Cumulative retreat distance. The calculation formula is expressed as follows:

[0085] ;

[0086] In the formula, The total backward distance is expressed in meters (m). To monitor the total number of time phases; For the first The backward distance of each phase, in meters.

[0087] in, By calculating the first The first phase and the second The average distance variation of the coastline position along the direction perpendicular to the coastline at each time phase is obtained.

[0088] Erosion acceleration The rate of change of the average erosion rate over adjacent time periods is obtained, and the calculation formula is expressed as follows:

[0089] ;

[0090] In the formula, Erosion acceleration, unit: ; For the first The average erosion rate over a time period, in units of ; For the first The average erosion rate over a time period, in units of ; This represents the time interval between adjacent time periods, expressed in units of 'a'.

[0091] The erosion response adjustment function value is calculated, and the formula for the erosion response adjustment function value is expressed as follows:

[0092] ;

[0093] In the formula, The value of the erosion response adjustment function is dimensionless. The theoretical erosion amount is expressed in units of... ; This represents the historical maximum theoretical erosion value, in units of ; To predict erosion, the unit is... ; To predict the historical maximum value of erosion, the unit is... ; The historical maximum absolute value of erosion acceleration, in units of ; This represents the rate of change of slope, expressed in degrees per year. This represents the historical maximum absolute value of the slope change rate, expressed in degrees per year.

[0094] in, The results were obtained from the physical constraint layer based on the law of conservation of sediment transport. The output is predicted by the decoder neural network; It is obtained by calculating the difference in slope between adjacent time phases and dividing by the time interval.

[0095] The sediment transport flux correction coefficient in the coastal erosion dynamics prediction model is adjusted according to the range of the erosion response adjustment function value. When the value belongs to the interval [0, 0.3), the sediment transport flux correction factor is set to 1.0; when... When the value belongs to the interval [0.3, 0.6), the sediment transport flux correction factor is set to 1.2; when... When the value belongs to the interval [0.6, 1.0), the sediment transport flux correction factor is set to 1.5; when... When the value is greater than or equal to 1.0, the correction factor for sediment transport flux is set to 2.0.

[0096] The specific implementation of step S07 is as follows: Establish a multi-dimensional early warning indicator system including annual average erosion rate, cumulative retreat distance, slope change rate, and erosion acceleration; set threshold standards for different levels; the annual average erosion rate threshold is divided into low-risk (less than 0.5). / year, medium risk 0.5 to 2.0 / year, high risk 2.0 to 5.0 / year, extremely high risk greater than 5.0 / year, the fuzzy comprehensive evaluation method and the analytic hierarchy process are used to automatically determine the risk level. The fuzzy comprehensive evaluation method calculates the comprehensive evaluation vector based on the membership function of each indicator, and the analytic hierarchy process determines the weight coefficient of each indicator by constructing a judgment matrix. The sum of the weight coefficients is 1.

[0097] To better understand and implement this invention, the following is a specific application scenario of the invention, Example 2: To verify the effectiveness of the invention, technicians set up a test environment and conducted continuous monitoring in a coastal area for 18 months. By applying the UAV image coastal erosion monitoring method described in this invention, they obtained detailed data on the evolution of the coastline in the area and achieved quantitative assessment and early warning of erosion risk.

[0098] Technicians first selected geologically stable rock foundations and concrete structures as control point locations within the coastal monitoring area, establishing 12 high-precision ground control points. Real-time dynamic differential positioning technology was used for coordinate measurement, achieving a horizontal accuracy of 2.8 cm and a vertical accuracy of 3.2 cm. After establishing the spatiotemporal reference control network, technicians used a quadcopter drone equipped with a 20-megapixel camera and a 16-line laser scanner to conduct aerial photogrammetry monthly. The flight altitude was set at 80 m, with a 75% forward overlap and a 65% lateral overlap, acquiring 18 phases of image data. In the image data processing phase, oblique photogrammetry was used to acquire coastal zone images from five perspectives: vertical, forward-looking, backward-looking, left-looking, and right-looking. Structured bundle adjustment algorithms were used to perform aerial triangulation on the 18 phases of image data. All temporal images were simultaneously incorporated into a unified coordinate system for overall adjustment. Using 32 stable feature points, such as seawall corners and lighthouse bases, as joint constraints, a digital surface model with a resolution of 3.5 cm and an orthophoto with a resolution of 2.8 cm were generated.

[0099] In the 3D point cloud data processing stage, technicians used an octree spatial index structure to organize and manage the point cloud. The sampling density was adaptively adjusted according to the curvature of the terrain surface. For flat sandy areas with a slope of less than 5 degrees, the sampling interval was set to 15 cm, while for steep cliff areas with a slope greater than 25 degrees, the sampling interval was reduced to 5 cm. Data compression was performed using wavelet transform, achieving a compression rate of 68%. Simultaneously collected tidal observation data showed that the highest tide level during the monitoring period was 2.87 m, the lowest tide level was 0.43 m, and the tidal range reached 2.44 m. Technicians constructed a tidal level and shoreline response model. Through statistical analysis of the waterline position under 156 different tidal conditions, and by fitting the intertidal profile using a probability density distribution function, the standard coastline position corresponding to the theoretical datum was calculated, as shown in Table 1.

[0100] Table 1. Standard coastline characteristic parameters at different monitoring time phases

[0101]

[0102] Technicians performed topological analysis on standard coastlines, automatically extracting coastline locations using multi-scale segmentation and the Canny edge detection algorithm. False edges caused by tidal levels and waves were eliminated through morphological opening and closing operations. The 18 coastlines were treated as a family of manifold curves in a high-dimensional topological space, and their persistent barcodes were calculated to capture the generation and disappearance characteristics of coastline morphology within a scale range of 0.5m to 8.2m. Figure 2 As shown, persistence analysis identified seven topologically stable erosion anchors, all with persistence barcode lengths greater than 5.8 m, significantly higher than the average of 2.3 m for other shorelines. The persistence map constructed using the waterfall algorithm shows a gradually increasing topological distance between different time phases, with the Wasserstein distance between phase 1 and phase 18 reaching 4.67, indicating a significant change in the coastline topology. Topological analysis also automatically detected three shoreline bifurcation events, one shoreline closure, and two shoreline fracture zones.

[0103] In the dynamic analysis of coastline changes, technicians decomposed the coastline displacement vector field into three orthogonal components using Hodge decomposition. The gradient current component, accounting for 62% of the total energy, is mainly concentrated in the northeastern section of the monitored area, indicating that this region is the dominant direction of erosion. The vortex current component, accounting for 27% of the total energy, forms a distinct vortex structure in the bay depression, reflecting lateral sediment transport characteristics. The harmonic component, accounting for 11% of the total energy, reveals the global topological constraints and long-period energy distribution patterns of the erosion field. Figure 3 As shown, the spatial distribution of the gradient flow component is highly consistent with the measured erosion hotspot area, with a correlation coefficient of 0.89.

[0104] Technicians constructed a coastal erosion dynamics prediction model. This model employs an encoder-decoder architecture. The encoder consists of four convolutional neural network layers with kernel sizes of 7×7, 5×5, 3×3, and 3×3, and channel numbers of 32, 64, 128, and 256, respectively, extracting topographic slope, curvature, and roughness features from the digital land model. The decoder consists of four deconvolutional neural network layers, corresponding to the restoration of feature map resolution and outputting the spatial distribution of the erosion rate field. A sediment transport module is embedded between the encoder and decoder. The physical constraint layer of this module establishes a coupling relationship based on the sediment continuity equation and the Exner equation, taking slope gradient, wave shear stress, and water flow velocity as inputs to calculate sediment transport flux. The training dataset includes UAV imagery data from the first 12 periods and corresponding ground-measured erosion rate data, generating 3840 training samples, 1096 validation samples, and 548 test samples. Model training uses an adaptive moment estimation optimization algorithm with an initial learning rate of 0.001 and a batch size of 16. After 87 iterations, the validation set loss no longer decreased, and training was stopped. Evaluation on the test set showed that the root mean square error between the model-predicted erosion rate field and the measured values ​​was 0.34. / year, with a correlation coefficient of 0.92.

[0105] Technicians used the trained model to predict erosion rates from data points 13 to 18. They input the digital surface model, gradient flow components, slope gradient, wave shear stress, and water flow velocity into the model to obtain the erosion rate field and the rate of change of erosion volume. For example... Figure 4 As shown, the predicted erosion rate field exhibits a high value distribution in the northeastern section, with a peak value reaching 6.8. / year, consistent with the spatial distribution pattern of actual monitoring results.

[0106] In the erosion quantification analysis phase, technicians constructed a differential model of 18 phases of digital surface modeling, calculating the coastal erosion volume based on the voxel grid method, with the voxel size set at 0.5m × 0.5m × 0.5m. Statistical results showed that the cumulative erosion volume reached 14,850 m³ / s over 18 months. The monitored area is 38,600 square kilometers. The average erosion rate is 1.28. / year. Technicians divided the monitoring area into 8 shore sections and calculated the retreat distance and slope change rate of each shore section, as shown in Table 2.

[0107] Table 2 Erosion characteristic parameters of different bank sections

[0108]

[0109] Based on the calculation of the erosion response adjustment function, technicians calculated the adjustment function values ​​for data from periods 13 to 18. Taking period 15 as an example, the normalized theoretical erosion is 0.73, the normalized predicted erosion is 0.68, the prediction bias is 0.05, the normalized erosion acceleration is 0.42, and the normalized slope change rate is 0.58. The calculated erosion response adjustment function value is 0.31, and the corresponding sediment transport flux correction coefficient is adjusted to 1.2. Figure 5 As shown, the erosion response adjustment function value fluctuates between 0.18 and 0.67 as the monitoring time phase progresses, reflecting the dynamic changes in the coastal erosion process.

[0110] In the risk early warning and assessment phase, technicians established a multi-dimensional early warning indicator system that includes the average annual erosion rate, cumulative retreat distance, slope change rate, and erosion acceleration. Of the eight shoreline sections, section 4 had an average annual erosion rate of 5.28. / year, exceeding 5.0 The extremely high risk threshold per year is 5.7m, with a slope change rate of 0.41%. / month, erosion acceleration is 0.89 / The risk level assessment result calculated using fuzzy comprehensive evaluation and analytic hierarchy process (AHP) is extremely high. The average annual erosion rate of shoreline section 2 is 3.65. The annual erosion rate is [missing value] / year, which is classified as high-risk. The average annual erosion rate of the remaining six shorelines is below 2.0. / year, which falls under the low-risk or medium-risk category.

[0111] This invention represents a significant advancement over traditional methods for monitoring coastal erosion. Traditional methods rely on ground-based measurements or satellite remote sensing, which suffer from low spatial resolution, insufficient temporal resolution, and poor multi-temporal registration accuracy, making it difficult to capture the subtle changes in coastlines. This invention, by establishing a spatiotemporal reference control network and employing a holistic adjustment strategy, fundamentally solves the problem of cumulative error propagation in multi-temporal data registration, ensuring the consistency and reliability of long-term monitoring. Traditional methods struggle to eliminate tidal influences during coastline extraction, leading to misjudgments of spurious changes. This invention, by constructing a tidal level coastline response model and fitting a probability density distribution function, achieves normalized correction of coastline positions under different tidal conditions, eliminating tidal effects from a physical mechanism perspective. Traditional methods lack the ability to quantitatively describe changes in coastline topology. This invention introduces persistent cohomology theory, viewing coastline evolution as a manifold change process in a high-dimensional topological space. Through persistent barcodes and persistent maps, it quantifies the generation and disappearance of topological features, revealing the intrinsic laws governing coastline morphological evolution. Traditional erosion prediction models are mostly either purely data-driven or purely physical models. The former lacks physical constraints and is prone to non-physical interpretations, while the latter is difficult to parameterize and adapt to complex terrains. This invention constructs a hybrid model that integrates data-driven and physical constraints by embedding a discretized form of the sediment transport conservation law into a neural network. This model utilizes the powerful nonlinear fitting capability of neural networks while ensuring that the prediction results conform to the laws of mass and momentum conservation, significantly improving the model's generalization ability and numerical stability in sparse data regions and long-term predictions. Traditional methods struggle to achieve the dynamic decomposition of the erosion process. This invention uses Hodge decomposition to decompose the coastline variation vector field into gradient flow, vortex flow, and harmonic components, revealing the driving force direction, eddy transport, and global topological constraints of erosion from the perspective of differential geometry, providing a theoretical tool for a deeper understanding of the dynamic mechanism of coastal erosion.

[0112] It should be noted that the variables involved in this invention are explained in detail in Table 3.

[0113] Table 3. Variable Explanation Table

[0114]

[0115] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for monitoring coastal erosion based on UAV imagery, characterized in that, Includes the following steps: A high-precision ground control point network was deployed in the coastal monitoring area, and a spatiotemporal reference control network was established as a unified benchmark for multi-temporal data registration. Rotary-wing UAVs equipped with high-resolution cameras and laser scanners acquired multi-temporal image data of the coastal zone along a preset route. Oblique photogrammetry was used to construct a high-density 3D point cloud, and structured bundle adjustment was employed for aerial triangulation. A global adjustment strategy was used to simultaneously incorporate all temporal images into the unified coordinate system of the spatiotemporal reference control network for global optimization, generating a digital surface model and orthophotos. An octree spatial index structure was used to organize the 3D point cloud, and the sampling density was adaptively adjusted according to terrain complexity. Tidal level observation data was collected synchronously, and a tide level-shoreline response model was constructed. Normalization correction was performed using tide level observation data, and the intertidal profile was fitted using the probability density distribution function of the waterline set to estimate the standard coastline position. Multi-scale segmentation and edge detection algorithms were used to further refine the model. The system automatically extracts standard coastline locations, treats multi-temporal coastlines as a family of manifold curves in a high-dimensional topological space, calculates the persistence barcode of the manifold curve family, identifies erosion anchor points, and constructs a persistence map using the waterfall algorithm to measure the topological distance between different temporal phases. The coastline variation vector field is decomposed into gradient flow components, curl flow components, and harmonic components using Hodge decomposition. The digital surface model, gradient flow components, slope gradient, wave shear stress, and water flow velocity are input into the coastal erosion dynamics prediction model, outputting the erosion rate field and erosion volume change rate. A multi-phase digital surface model difference model is constructed, and the coastal erosion volume and average erosion rate are calculated based on the voxel grid method. The retreat distance and slope change rate of different shore segments are statistically analyzed, and the erosion response adjustment function value is calculated. The sediment transport flux correction coefficient of the sediment transport conservation law coupling mechanism in the coastal erosion dynamics prediction model is adjusted according to the range of the erosion response adjustment function value. Establish a multi-dimensional early warning indicator system and use fuzzy comprehensive evaluation method and hierarchical analysis method to realize automatic risk level identification.

2. The coastal erosion monitoring method based on UAV imagery according to claim 1, characterized in that, In the process of establishing a spatiotemporal reference control network, real-time dynamic differential positioning technology is used to obtain the coordinates of control points.

3. The coastal erosion monitoring method based on UAV imagery according to claim 2, characterized in that, The spatiotemporal reference control network is a network of multiple high-precision ground control points deployed in a stable coastal zone. The coordinate accuracy of the control points is better than 5 centimeters, which is used to eliminate the spread of cumulative errors in the multi-temporal data registration process.

4. The coastal erosion monitoring method based on UAV imagery according to claim 3, characterized in that, In the global optimization step using the overall adjustment strategy, stable ground feature points are used as joint constraints.

5. The coastal erosion monitoring method based on UAV imagery according to claim 4, characterized in that, The overall adjustment strategy incorporates all temporal images into a unified coordinate system for joint calculation, and avoids the accumulation and amplification of errors caused by phase-by-phase registration by globally optimizing the allocation of errors.

6. The coastal erosion monitoring method based on UAV imagery according to claim 5, characterized in that, The generated digital surface models and orthophotos achieve centimeter-level resolution.

7. The coastal erosion monitoring method based on UAV imagery according to claim 6, characterized in that, The octree spatial index structure is a tree-shaped data structure that recursively divides the three-dimensional space into eight sub-cubes. The division level is dynamically adjusted according to the point cloud density to achieve efficient spatial querying and data organization.

8. The coastal erosion monitoring method based on UAV imagery according to claim 7, characterized in that, In the step of adaptively adjusting the sampling density based on terrain complexity, lossy compression is performed in conjunction with wavelet transform.

9. The coastal erosion monitoring method based on UAV imagery according to claim 8, characterized in that, The sampling density is adaptively adjusted to dynamically determine the sampling interval based on the curvature and slope gradient of the terrain surface. The sampling interval is increased in areas with gentle terrain and decreased in areas with steep terrain.

10. The coastal erosion monitoring method based on UAV imagery according to claim 9, characterized in that, In the step of estimating the location of the standard coastline, the location of the standard coastline corresponding to the theoretical datum is calculated.

Images