System and method for quantifying uncertainty of digital elevation model based on multi-model fusion and terrain analysis

Abstract

This invention discloses a system and method for uncertainty quantification and terrain analysis of digital elevation models (DEMs) based on multi-model fusion, comprising: a data management layer for reading, storing, and preprocessing raw DEM data; a graphical user interface layer for receiving user commands, configuring analysis parameters, and transmitting them to the core algorithm layer; a core algorithm layer integrating a Monte Carlo simulation module, an interval model analysis module, a surrogate model module, and a hybrid uncertainty analysis module for performing multi-paradigm uncertainty quantification and terrain factor calculation on DEM data; and a results display layer for visually outputting the calculation results of the core algorithm layer in a combination of text and graphics. This invention achieves a comprehensive and accurate assessment of DEM uncertainty, significantly improves the efficiency and feasibility of large-scale DEM data analysis, significantly reduces operational complexity, ensures the reliability of the analysis process, and greatly enhances the understandability and decision support capabilities of the analysis results.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of Geographic Information Systems (GIS), remote sensing, and surveying and mapping science and technology, and in particular to a system and method for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion. Specifically, it relates to an integrated system and method for uncertainty quantification, propagation analysis and visualization of digital elevation model (DEM) data, and on this basis, high-precision terrain factor calculation and sensitivity analysis. Background Technology

[0002] Digital Elevation Models (DEMs), as a digital and rasterized representation of the Earth's surface elevation information, serve as fundamental spatial data for numerous disciplines, including Geographic Information Systems (GIS), remote sensing, surveying and mapping, hydrology, geology, and ecology. They simulate continuous landforms using elevation values ​​on a regular grid, playing an irreplaceable role in applications such as flood simulation, landslide risk assessment, soil erosion prediction, military route planning, and communication base station site selection.

[0003] With the rapid development of technologies such as LiDAR, InSAR, and UAV photogrammetry, the ability to acquire high-precision, high-resolution DEM data has been greatly improved. However, regardless of the technology used, DEM data inevitably introduces various forms of errors and uncertainties throughout its entire lifecycle of acquisition, processing, and modeling. These uncertainties come from diverse sources, mainly including: 1) Observation noise: limitations in the measurement accuracy of the sensor itself; 2) Systematic bias: systematic errors caused by factors such as coordinate system transformation and atmospheric refraction; 3) Interpolation error: model errors generated when interpolating discrete sampling points into a continuous grid; 4) Data processing error: human or algorithmic errors introduced by post-processing steps such as filtering, denoising, and stitching.

[0004] These original elevation uncertainties do not exist in isolation. When DEMs are used as input data for secondary derivative analyses (such as calculating topographic factors like slope, aspect, curvature, and runoff accumulation), their uncertainties are significantly amplified and propagated through nonlinear mathematical models. This ultimately leads to a substantial reduction in the reliability of downstream applications (such as disaster early warning and engineering design). Therefore, how to scientifically and accurately quantify the uncertainties of DEMs and assess their propagation effects in subsequent analyses has become a core research hotspot and a key technological bottleneck in the field of geographic information science.

[0005] To address the uncertainty and propagation issues of DEMs, the academic community has proposed various analytical methods. However, current technologies in the field of DEM uncertainty quantification and terrain analysis have the following main drawbacks:

[0006] The methods are isolated and cannot fully characterize complex uncertainties: Existing analytical tools or research often focus only on a single uncertainty modeling paradigm. For example, Monte Carlo simulation can only handle aleatory uncertainty, while interval analysis can only handle epistemic uncertainty. In practical applications, the uncertainty of DEMs is often multi-source and mixed (such as the simultaneous presence of random observation noise and cognitive ambiguity caused by unclear data sources), and a single method cannot provide comprehensive and accurate assessment results. This leads to one-sided analytical conclusions that are difficult to support highly reliable decision-making.

[0007] Low computational efficiency makes it difficult to apply to large-scale data: Although probabilistic methods, such as Monte Carlo simulation, are highly versatile, their computational cost is directly proportional to the number of simulations. For high-resolution, large-scale DEM data, each terrain factor calculation is already quite time-consuming, and repeating simulations thousands or even tens of thousands of times is unacceptable in terms of time and computational resources, severely restricting its application in practical engineering and operational settings.

[0008] The workflow is fragmented, cumbersome, and prone to errors: Currently, from DEM loading, preprocessing, and terrain factor calculation to uncertainty analysis and result visualization, it typically requires the use of multiple independent software programs (such as ArcGIS, QGIS, MATLAB, Python scripts, etc.) or manually writing complex code processes. This fragmented workflow is not only inefficient but also highly susceptible to human error in data format conversion, parameter passing, and other stages, increasing the barrier to entry and technical risks.

[0009] The lack of an intuitive human-computer interaction interface makes result interpretation difficult: Most advanced uncertainty analysis methods (such as PCE and Sobol index) rely on command-line or programming environments, which are extremely unfriendly to non-professional users. At the same time, if the analysis results (such as high-dimensional uncertainty fields and sensitivity indices) are presented only in numerical tables, it is difficult to intuitively understand their spatial distribution characteristics and inherent laws, which is not conducive to rapid knowledge extraction and effective communication. Summary of the Invention

[0010] This invention addresses the problems of isolated methods, low efficiency, fragmented processes, and poor interactivity in existing technologies by proposing a system and method for uncertainty quantification and terrain analysis of digital elevation models (DEMs) based on multi-model fusion. This invention systematically integrates Monte Carlo methods, interval models, multinomial chaotic expansion, and hybrid uncertainty propagation algorithms to provide a comprehensive solution capable of handling complex, multi-source uncertainties. By introducing efficient surrogate models (such as PCE), this invention aims to overcome the performance bottlenecks of traditional Monte Carlo methods, making uncertainty analysis of large-scale DEMs practically feasible. This invention designs an integrated software architecture that tightly couples data management, core algorithms, result storage, and visualization modules, aiming to eliminate tool switching and manual intervention, providing a seamless end-to-end analysis experience. This invention develops a standardized GUI to present complex parameter configurations, computational process monitoring, and multi-dimensional results (spatial maps, statistical graphs, numerical reports) to users in a clear and consistent manner, allowing researchers and engineers to focus on the problem itself rather than technical details.

[0011] To achieve the above objectives, the present invention adopts the following technical solution:

[0012] This invention proposes a system for quantifying uncertainty in digital elevation models and analyzing terrain based on multi-model fusion, comprising:

[0013] The data management layer is used to read, store, and preprocess raw DEM data;

[0014] The graphical user interface layer is used to receive user commands, configure analysis parameters, and pass them to the core algorithm layer.

[0015] The core algorithm layer integrates a Monte Carlo simulation module, an interval model analysis module, a surrogate model module, and a hybrid uncertainty analysis module, which are used to perform multi-paradigm uncertainty quantification and terrain factor calculation on DEM data.

[0016] The results display layer is used to visualize the calculation results of the core algorithm layer in a combination of text and graphics.

[0017] Furthermore, the Monte Carlo simulation module is used for:

[0018] A random error matrix conforming to a set distribution is generated based on the original DEM data, and spatial correlation filtering is performed on the random error matrix.

[0019] Construct a perturbed DEM and calculate terrain factors;

[0020] The mean and standard deviation of multiple simulation results were statistically analyzed to quantify the impact of random observation errors on topographic factors.

[0021] Furthermore, the interval model analysis module is used for:

[0022] Based on the user-defined error interval radius, construct the lower and upper elevation boundaries of the DEM;

[0023] For the lower and upper bounds of the elevation of the DEM, the gradients in the X and Y directions and their truncation errors are calculated respectively. Using the gradients and their truncation errors, the lower and upper bounds of the gradient interval are calculated.

[0024] By using the lower and upper bounds of the gradient interval, the lower and upper bounds of the terrain factor and its interval length are derived to quantify the impact of cognitive uncertainty on the terrain analysis results.

[0025] Furthermore, the proxy model module is used for:

[0026] Experiments are designed based on the probability distribution of the input variables to generate sampling points;

[0027] The original complex terrain analysis model is invoked to obtain the output values;

[0028] A polynomial chaotic expansion proxy model is constructed, and the unknown coefficients in the PCE expansion are solved based on the sampling points and the corresponding output values, and then replaced with the original complex terrain analysis model.

[0029] By analyzing the coefficients of the polynomial chaotic expansion surrogate model, calculating the mean and variance of the output, and simultaneously outputting the Sobol sensitivity index, a single modeling and dual output of uncertainty quantification and sensitivity analysis is achieved.

[0030] Furthermore, the hybrid uncertainty analysis module is used for:

[0031] Simultaneously handle probability variables and interval variables;

[0032] Monte Carlo sampling is performed on the outer probability variables, and interval propagation is performed on the inner interval variables;

[0033] The output is a set of intervals, and its probability characteristics are statistically analyzed to realize the propagation of probability-interval mixed uncertainty.

[0034] Furthermore, the graphical user interface layer is built based on the Tkinter library and includes a file selection control, a method navigation tree, a parameter configuration panel, and a log output window. All computational tasks are executed in background threads to maintain interface responsiveness.

[0035] Furthermore, the result display layer is specifically used for:

[0036] A standardized visualization is presented using a 2x2 subplot layout, where: the top left subplot displays the spatial mean or upper limit of the core analysis results; the top right subplot displays the spatial distribution of uncertainty; the bottom left subplot displays details of the uncertainty distribution at representative locations; and the bottom right subplot displays global statistical information or sensitivity index comparisons.

[0037] The numerical statistics report is then output synchronously in the text box on the interface.

[0038] Another aspect of this invention proposes a method for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion, applied to the system described in any of the above, comprising the following steps:

[0039] The raw DEM data is loaded and preprocessed through the data management layer;

[0040] Select the analysis method and configure the parameters through the graphical user interface layer;

[0041] Call the corresponding analysis module in the core algorithm layer to perform uncertainty quantification and propagation calculations;

[0042] The results presentation layer outputs visual charts and numerical reports.

[0043] Furthermore, the core algorithm layer supports one or more combinations of the following analysis modes:

[0044] Monte Carlo simulation, interval analysis, polynomial chaotic expansion surrogate model, probability-interval hybrid analysis, probability-fuzzy hybrid analysis.

[0045] The present invention also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the aforementioned method for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] This invention achieves a comprehensive and accurate assessment of DEM uncertainty: Addressing the problem of existing technologies being "isolated and unable to fully characterize complex uncertainties," this invention employs a multi-model fusion framework and a hybrid uncertainty propagation mechanism. This allows for the flexible selection or combination of different analytical paradigms based on the sources of uncertainty in the actual problem. For example, when assessing slope error caused by both LiDAR measurement noise (randomness) and data source accuracy specifications (cognitive intervals), the system can automatically invoke a probability-interval hybrid model for analysis. This yields assessment results that are closer to reality than single Monte Carlo or single interval analyses, effectively solving the problem of one-sided analytical conclusions.

[0048] This invention significantly improves the efficiency and feasibility of large-scale DEM data analysis: Addressing the bottleneck of low computational efficiency in existing technologies, this invention fundamentally optimizes the computational process by employing efficient computational strategies and PCE-based sensitivity analysis. For scenarios requiring tens of thousands of simulations, the system prioritizes building a PCE surrogate model, reducing Monte Carlo simulations that originally took hours or even days to complete within minutes, while simultaneously outputting the Sobol sensitivity index. This makes it possible to move the uncertainty analysis of high-resolution, large-scale DEMs from theoretical research to practical engineering applications.

[0049] Significantly reducing operational complexity and ensuring the reliability of the analysis process: Addressing the shortcomings of existing technologies such as "fragmented workflows and cumbersome operations," this invention adopts a fully integrated approach, encapsulating data loading, calculation, analysis, and output into a coherent workflow. Users do not need to switch between different software or manually write scripts to connect them; all intermediate data is seamlessly transferred in memory, avoiding errors caused by format conversion or parameter mismatch. This not only improves work efficiency but also enhances the robustness and repeatability of the analysis process.

[0050] This invention significantly enhances the understandability and decision support capabilities of the analysis results: Addressing the pain points of existing technologies such as "lack of intuitive interaction and difficulty in interpreting results," this invention transforms complex uncertainty information into intuitive visual language through the synergistic effect of an integrated GUI and standardized visualization. Standardized 2×2 chart layouts (such as mean charts + standard deviation charts + histograms + statistical charts) coupled with synchronously generated detailed text reports enable users to quickly grasp the spatial distribution characteristics of uncertainty, its numerical statistical regularities, and the sensitivity of each factor, thereby providing clear and powerful data support for scientific decision-making. Attached Figure Description

[0051] Figure 1 This is a system architecture diagram of a digital elevation model uncertainty quantification and terrain analysis system based on multi-model fusion, according to an embodiment of the present invention.

[0052] Figure 2 A schematic diagram of a graphical user interface provided for an embodiment of the present invention;

[0053] Figure 3 This is a flowchart of the mixed uncertainty analysis module provided in an embodiment of the present invention;

[0054] Figure 4 This is a basic flowchart of a digital elevation model uncertainty quantification and terrain analysis method based on multi-model fusion, according to an embodiment of the present invention. Detailed Implementation

[0055] For ease of understanding, the following explanations are provided for some of the terms used in the specific embodiments of this invention:

[0056] Digital Elevation Model (DEM): A digital and rasterized representation of the Earth's surface elevation information. It is a basic spatial data that simulates continuous surface morphology using elevation values ​​on a regular grid.

[0057] Uncertainty Quantification (UQ) refers to the process of mathematically representing the uncertainties present in the model inputs, parameters, or structure, and assessing their impact on the model output. In this invention, it specifically refers to the scientific assessment of the reliability of DEM data and its derived terrain factors (such as slope).

[0058] Monte Carlo (MC) simulation is a numerical computation method based on probability and statistics theory. It generates input samples that conform to a specific distribution through a large number of random samplings, repeatedly executes model calculations, and uses the statistical properties of the output results (such as mean and variance) to quantify uncertainty.

[0059] Interval analysis is a non-probabilistic method for handling cognitive uncertainty. It represents an uncertain parameter as a defined numerical interval and derives the possible range of values ​​(i.e., upper and lower bounds) of the output result through interval operations.

[0060] Polynomial Chaos Expansion (PCE): An efficient surrogate model technique. It uses a linear combination of orthogonal polynomial basis functions to approximate complex computational models, enabling uncertainty propagation analysis at a low computational cost, and directly and analytically calculating the output statistical moments and global sensitivity index.

[0061] Global Sensitivity Analysis (GSA) is used to quantify the contribution of multiple input variables (and their interactions) to the overall variability of the output of a model. The Sobol index method is an important variance decomposition method.

[0062] Mixed uncertainty refers to the simultaneous existence of multiple types of uncertainty in the same problem, such as aleatory uncertainty caused by random observation noise and epistemic uncertainty caused by a lack of knowledge. This scheme uses strategies such as nested computation to jointly model and propagate these uncertainties.

[0063] Terrain Factor (Terrain Attribute): Quantitative indicators derived from DEM data that describe the geometric features of the land surface, such as slope, aspect, curvature, and flow accumulation.

[0064] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0065] like Figure 1 As shown, a digital elevation model uncertainty quantification and terrain analysis system based on multi-model fusion is presented. This system adopts a modular design concept and is mainly composed of four logical modules: data management layer, core algorithm layer, graphical user interface (GUI) layer, and result display layer. Each module exchanges data and calls functions through clear interfaces.

[0066] Data Management Layer: Responsible for reading raw DEM raster data, memory management, and basic preprocessing. This module uses the GDAL library to parse standard formats such as GeoTIFF and loads the data into memory for subsequent calculations.

[0067] The Graphical User Interface (GUI) layer, built on Python's Tkinter library (or using C++ with the Qt framework, Java with JavaFX, or C# with WPF to develop similar desktop applications), provides users with a visual interface. This layer includes components such as file selection controls, a method navigation tree (which can also be tabs (Notebook / Tabs), sidebar button groups, or top menu dropdown lists), parameter configuration panels, and log output windows, responsible for receiving user commands and passing them to the core algorithm layer. The graphical user interface is as follows: Figure 2 As shown.

[0068] Core Algorithm Layer: This is the core technology of the system, containing multiple algorithm implementations for uncertainty quantification, propagation, and sensitivity analysis. This layer is further subdivided into several independent sub-modules, each encapsulating a specific analysis method.

[0069] Results Presentation Layer: This layer is responsible for presenting the computational results of the core algorithm layer in a visually appealing format. It utilizes the matplotlib library to generate standardized (2×2) gridspec charts and simultaneously outputs detailed numerical statistical reports in text boxes.

[0070] The entire system runs in a single-machine environment, with all computational tasks executed in background threads to ensure the responsiveness of the GUI main thread and prevent the interface from freezing. As an alternative implementation, the CuPy library or Numba's CUDA backend can be used to offload highly parallelized tasks such as slope calculations and Monte Carlo loops to the GPU, further improving the efficiency of large-scale data processing.

[0071] The core innovation of this invention lies in its uncertainty analysis capability through multi-model fusion. The specific technical solutions for several key algorithm modules are described in detail below:

[0072] (1) Monte Carlo (MC) simulation module

[0073] Objective: To quantify the uncertainty of DEM derivatives (such as slope) caused by random observation errors.

[0074] Technical process:

[0075] Input: Original DEM data Z, number of simulations set by the user num_mc, standard deviation of elevation error σ, and slope calculation model (such as the Horn algorithm).

[0076] Error field generation: For each simulation i (i from 1 to num_mc), a random error matrix error_matrix of the same size as Z is generated, whose elements follow a normal distribution with mean 0 and standard deviation σ.

[0077] Spatial correlation processing: To make the error more consistent with reality, a 3×3 mean filter (uniform_filter) is applied to error_matrix to obtain an error matrix filtered_error with local spatial correlation.

[0078] Perturbation DEM Construction: The filtered error matrix is ​​added to the original DEM to obtain the perturbation DEMZ of the i-th simulation. err = Z + filtered_error.

[0079] Terrain factor calculation: Calculate Z using a specified slope model (such as the grad_24 function). err slope pre .

[0080] Cumulative statistics: slope pre Accumulated to slope mean and slope sq_sum In the (sum of squares) accumulator.

[0081] Result Synthesis: After completing all num_mc simulations, the final mean slope is calculated. mean / num_mc and standard deviation sqrt((slope) sq_sum / num_mc) - (slope mean / num_mc) 2 ).

[0082] It is worth noting that the method for generating the random error field in the Monte Carlo simulation module is not limited to the normal distribution. Depending on the actual data error characteristics, it can be replaced by a uniform distribution, log-normal distribution, or other empirical distributions. Furthermore, the filter introducing spatial correlation can be replaced by a Gaussian filter, an exponential covariance function model, or a more complex random field generation algorithm (such as the Cholesky decomposition method) instead of a 3×3 mean filter. Examples of Monte Carlo propagation steps and operational processing are shown in Table 1.

[0083] Table 1 Monte Carlo propagation steps and operational examples

[0084]

[0085] (2) Interval Model Analysis Module

[0086] Objective: To quantify the uncertainty boundary of DEM-derived products caused by insufficient knowledge (such as fixed accuracy range).

[0087] Technical process

[0088] Inputs: Original DEM data Z, user-defined interval radius interval_range, and slope calculation model.

[0089] 1. Interval DEM Construction:

[0090] Based on the user-defined interval radius (interval_range), the lower elevation DEM and upper elevation DEM are constructed using the original DEM data Z. The calculation formula is as follows:

[0091] Lower bound DEM elevation: Z_{lower} = Z - interval_range

[0092] Upper bound DEM: Z_{upper} = Z + interval_range

[0093] 2. Gradient interval calculation:

[0094] The custom gradient calculation function grad_24 of this invention is called on the lower bound DEM Z_{lower} and the upper bound DEM Z_{upper} respectively to obtain the gradient values ​​in the X and Y directions and their corresponding truncation errors. Subsequently, by combining the extreme values ​​of the gradients obtained above and incorporating the truncation errors for compensation calculation, the lower and upper bounds of the gradients in the X and Y directions are finally obtained.

[0095] It is worth noting that the grad_24 function is a key fundamental computational unit in this invention. It not only calculates the gradients in the X and Y directions, but also simultaneously estimates and returns the error term caused by truncation in the finite difference scheme. This characteristic is a technical prerequisite for realizing interval model analysis (especially considering the accurate interval propagation of truncation errors).

[0096] The gradient calculation function grad_24 aims to simultaneously obtain the directional gradient within the local window and the truncation error caused by discretization. Its specific processing flow is as follows:

[0097] Step 2.1 (Extracting Local Window): Traverse the input DEM data (Z_{lower} or Z_{upper}), and extract the neighborhood elevation matrix of the current target cell with a preset size (e.g., 3 times 3).

[0098] Step 2.2 (Calculate directional gradient): Based on the neighborhood elevation matrix, using a difference algorithm (such as second-order central difference) and combined with the grid resolution of the DEM, calculate the gradient Grad_X in the X direction and the gradient Grad_Y in the Y direction for the target pixel.

[0099] Step 2.3 (Calculate the truncation error): Based on the remainder term of the higher-order Taylor expansion (or higher-order difference), calculate the X-direction truncation error Err_X and the Y-direction truncation error Err_Y generated by the above difference algorithm in the discrete grid calculation process.

[0100] Step 2.4 (Result Output): Return the calculated directional gradient and the corresponding truncation error as the result to the main process.

[0101] The pseudocode for the gradient calculation function grad_24 is as follows:

[0102] Function grad_24(DEM_Grid_Window, resolution):

[0103] / / Input parameters:

[0104] / / DEM_Grid_Window: Local neighborhood elevation matrix centered on the target pixel

[0105] / / resolution: Grid resolution of DEM data (e.g., dx, dy)

[0106] / / Output parameters:

[0107] / / [Grad_X, Grad_Y, Err_X, Err_Y]: These represent the gradient in the X direction, the gradient in the Y direction, the truncation error in the X direction, and the truncation error in the Y direction, respectively.

[0108] / / 1. Obtain the elevation values ​​of the top, bottom, left, and right sides adjacent to the center pixel (taking a 3×3 window as an example)

[0109] Z_left = DEM_Grid_Window[row, col-1]

[0110] Z_right = DEM_Grid_Window[row, col+1]

[0111] Z_up = DEM_Grid_Window[row-1, col]

[0112] Z_down = DEM_Grid_Window[row+1, col]

[0113] / / 2. Calculate the gradients in the X and Y directions (Example: Second-order central difference method)

[0114] Grad_X = (Z_right - Z_left) / (2 * resolution)

[0115] Grad_Y = (Z_up - Z_down) / (2 * resolution)

[0116] / / 3. Calculate the corresponding truncation error (Example: Error evaluation model based on Taylor remainder or higher-order differences)

[0117] / / Note: This is a logical placeholder, representing the error evaluation formula in the actual patent.

[0118] Err_X = Evaluate_Truncation_Error(DEM_Grid_Window, "X_axis",resolution)

[0119] Err_Y = Evaluate_Truncation_Error(DEM_Grid_Window, "Y_axis",resolution)

[0120] / / 4. Return the calculation results

[0121] Return [Grad_X, Grad_Y, Err_X, Err_Y]

[0122] End Function

[0123] 3. Slope interval derivation: Using the upper and lower bounds of the gradient interval, the lower bound of the slope is calculated using the arctangent function. lower and the upper slope upper .

[0124] 4. Calculation of interval length: Calculate the slope interval length: slope_length = slope upper - slope lower This value directly reflects the magnitude of the uncertainty at that location.

[0125] (3) Proxy Model Module (Taking the Polynomial Chaos Expansion (PCE) Proxy Model as an Example)

[0126] Objective: To construct an efficient surrogate model for complex and computationally expensive terrain analysis models (such as the USLE soil erosion model and Monte Carlo simulation) to enable rapid uncertainty propagation and global sensitivity analysis.

[0127] Technical process:

[0128] Input: The complex model f to be replaced, the number of input variables n_inputs and their probability distribution, and the PCE order p.

[0129] Experimental Design: A Latin Hypercube Sampling (LHS) strategy was employed to generate a set of representative sampling points X within the joint probability space of the input variables. sample .

[0130] Truth calculation: For each sampling point x i ∈X sample The original complex model f is called to calculate its output y. i = f(x i ).

[0131] PCE coefficients are solved using the least squares method or pseudospectral method, based on the sampling points (X).sample ,Y sample Solve for the unknown coefficients in the PCE expansion.

[0132] Proxy model application: Once the PCE model is built, it can be used to replace the original model f. By analyzing the coefficients of the PCE, the mean, variance, and Sobol sensitivity index of the output can be calculated directly, eliminating the need for time-consuming repetitive simulations.

[0133] It is worth noting that in the surrogate model module, the polynomial chaotic expansion (PCE) can be replaced by other efficient surrogate models, such as Kriging interpolation models, support vector regression (SVR), random forests, or deep neural networks (DNNs). These models can also approximate complex terrain analysis models at a lower cost and be used for subsequent uncertainty propagation.

[0134] In global sensitivity analysis, in addition to the Sobol index method, Morris screening, EFAST method, or information theory-based mutual information method can also be integrated and used as alternatives to adapt to scenarios with different computational budgets and accuracy requirements.

[0135] (4) Mixed uncertainty analysis module (taking probability-interval mixed analysis as an example)

[0136] Objective: To handle complex scenarios that simultaneously include probabilistic variables (such as rainfall) and interval variables (such as DEM elevation).

[0137] Technical processes (such as) Figure 3 (as shown)

[0138] Input: Probability variables (and its distribution), interval variables (and its upper and lower bounds) and the target analysis model g.

[0139] Outer loop (probability sampling): sampling the probability variable Perform N Monte Carlo samplings to obtain .

[0140] Inner loop (interval propagation): For each probability sample ,fixed Then, taking the target analysis model g as the object, the interval variables are analyzed. Performing a complete interval analysis yields an interval of output Y. , ].

[0141] Result Synthesis: The final output uncertainty is represented by a set of intervals {[ , ],..., [ , The overall probabilistic characteristics can be described by statistically analyzing the center and radius of these intervals.

[0142] It is worth noting that the mixed uncertainty analysis module also includes probability-fuzzy mixed analysis.

[0143] Furthermore, to ensure the feasibility and ease of use of the technical solution, this invention designs a standardized result display process:

[0144] Visualization layout: All analysis results are displayed using a 2x2 subplot layout created by matplotlib.gridspec.

[0145] Content guidelines:

[0146] Top left image: Typically shows the spatial mean or upper limit of the core analysis results (such as mean slope or upper limit slope).

[0147] The top right image typically shows the spatial distribution of uncertainty (such as the standard deviation of slope and the length of slope intervals).

[0148] The bottom left image typically shows the details of the uncertainty distribution at a representative location (such as a histogram or scatter plot).

[0149] The bottom right image typically displays global statistical information (such as confidence interval width, sensitivity index comparison, and power spectrum).

[0150] Text Report: The GUI's text boxes synchronously output detailed numerical results, key statistics, and methodological descriptions corresponding to the charts, forming a complete report that complements the text and graphics.

[0151] It is worth noting that while this invention preferably uses a 2×2 gridspec layout for standardized display, this is not the only feasible solution. The arrangement of the visualized subplots can be replaced by a 1×4 horizontal layout, a 4×1 vertical layout, or an adaptive layout depending on the characteristics of the analysis method (e.g., a full-screen single plot can be used for methods that only need to display a single result). Furthermore, the chart types can be expanded; for example, a boxplot can be used instead of a histogram to display the distribution of point uncertainty, or a heatmap can be used to display the sensitivity index matrix.

[0152] It is worth noting that although this invention is primarily aimed at DEM terrain analysis, its underlying "multi-model uncertainty quantification framework" has universality. This framework can be seamlessly transferred to other raster data (such as remote sensing image classification results, meteorological raster fields) or any scientific computing field involving uncertainty in numerical model inputs (such as hydrological models, ecological models).

[0153] Based on the above embodiments, such as Figure 4 As shown, this invention also proposes a method for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion. This method is applied to the aforementioned system for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion, and includes the following steps:

[0154] The raw DEM data is loaded and preprocessed through the data management layer;

[0155] Select the analysis method and configure the parameters through the graphical user interface layer;

[0156] Call the corresponding analysis module in the core algorithm layer to perform uncertainty quantification and propagation calculations;

[0157] The results presentation layer outputs visual charts and numerical reports.

[0158] Based on the above embodiments, the present invention also proposes a computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the above-described method for quantifying uncertainty in digital elevation models and analyzing terrain based on multi-model fusion.

[0159] This invention has been validated on a real DEM dataset. The results show that, compared with the traditional pure Monte Carlo simulation method, the polynomial chaotic expansion surrogate model can reduce the computation time from several hours to a few minutes while ensuring the accuracy of the results (relative error <2%), and improve the efficiency by more than two orders of magnitude.

[0160] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-model fusion based digital elevation model uncertainty quantification and terrain analysis system, characterized in that, include: The data management layer is used to read, store, and preprocess raw DEM data; The graphical user interface layer is used to receive user commands, configure analysis parameters, and pass them to the core algorithm layer. The core algorithm layer integrates a Monte Carlo simulation module, an interval model analysis module, a surrogate model module, and a hybrid uncertainty analysis module, which are used to perform multi-paradigm uncertainty quantification and terrain factor calculation on DEM data. The results display layer is used to visualize the calculation results of the core algorithm layer in a combination of text and graphics.

2. The system for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion according to claim 1, characterized in that, The Monte Carlo simulation module is used for: A random error matrix conforming to a set distribution is generated based on the original DEM data, and spatial correlation filtering is performed on the random error matrix. Construct a perturbed DEM and calculate terrain factors; The mean and standard deviation of multiple simulation results were statistically analyzed to quantify the impact of random observation errors on topographic factors.

3. The system for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion according to claim 1, characterized in that, The interval model analysis module is used for: Based on the user-defined error interval radius, construct the lower and upper elevation boundaries of the DEM; For the lower and upper bounds of the elevation of the DEM, the gradients in the X and Y directions and their truncation errors are calculated respectively. Using the gradients and their truncation errors, the lower and upper bounds of the gradient interval are calculated. By using the lower and upper bounds of the gradient interval, the lower and upper bounds of the terrain factor and its interval length are derived to quantify the impact of cognitive uncertainty on the terrain analysis results.

4. The system for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion according to claim 1, characterized in that, The proxy model module is used for: Experiments are designed based on the probability distribution of the input variables to generate sampling points; The original complex terrain analysis model is invoked to obtain the output values; A polynomial chaotic expansion proxy model is constructed, and the unknown coefficients in the PCE expansion are solved based on the sampling points and the corresponding output values, and then replaced with the original complex terrain analysis model. By analyzing the coefficients of the polynomial chaotic expansion surrogate model, calculating the mean and variance of the output, and simultaneously outputting the Sobol sensitivity index, a single modeling and dual output of uncertainty quantification and sensitivity analysis is achieved.

5. The system for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion according to claim 1, characterized in that, The hybrid uncertainty analysis module is used for: Simultaneously handle probability variables and interval variables; Monte Carlo sampling is performed on the outer probability variables, and interval propagation is performed on the inner interval variables; The output is a set of intervals, and its probability characteristics are statistically analyzed. Achieve probability-interval mixed uncertainty propagation.

6. The system for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion according to claim 1, characterized in that, The graphical user interface layer is built on the Tkinter library and includes a file selection control, a method navigation tree, a parameter configuration panel, and a log output window. All computational tasks are executed in background threads to maintain interface responsiveness.

7. The system for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion according to claim 1, characterized in that, The results display layer is specifically used for: A standardized visualization is presented using a 2x2 subplot layout, where: the top left subplot displays the spatial mean or upper limit of the core analysis results; the top right subplot displays the spatial distribution of uncertainty; the bottom left subplot displays details of the uncertainty distribution at representative locations; and the bottom right subplot displays global statistical information or sensitivity index comparisons. The numerical statistics report is then output synchronously in the text box on the interface.

8. A method for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion, applied to the system described in any one of claims 1 to 7, characterized in that, Includes the following steps: The raw DEM data is loaded and preprocessed through the data management layer; Select the analysis method and configure the parameters through the graphical user interface layer; Call the corresponding analysis module in the core algorithm layer to perform uncertainty quantification and propagation calculations; The results presentation layer outputs visual charts and numerical reports.

9. The method for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion according to claim 8, characterized in that, The core algorithm layer supports one or more combinations of the following analysis modes: Monte Carlo simulation, interval analysis, polynomial chaotic expansion surrogate model, probability-interval hybrid analysis, probability-fuzzy hybrid analysis.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for uncertainty quantification and terrain analysis of digital elevation models based on multi-model fusion as described in claim 8 or 9.

Images