Space-constrained high-dimensional parameter optimization algorithm for surface water body

Abstract

The application discloses a kind of high-dimensional parameter optimization algorithm of space constraint surface water body, specific processing steps are as follows: (1) water quality parameter number and range determination (2) parameter initial sampling.Through sensitivity analysis, low-sensitive parameters are screened out, and the optimal sampling space is determined to carry out SCE-UA sampling, to form initial sample group.(3) Dynamic dimension reduction.In each iteration space, sensitivity analysis is carried out, low-sensitive parameters are temporarily cooled, and the remaining parameters are optimized.(4) SCE-UA complex shape division and simplex generation.Set each complex shape reference sample point, and cluster and divide the remaining points by Euclidean distance.Find the sample point with the highest similarity in each complex shape, as simplex.(6) Track optimization space changes, if space diffusion occurs, activate the cooled parameter in time, and restore the dimensionality.(7) Convergence condition and output.The application is based on the space difference characteristics of parameters, uses multiple space constraint strategies to find the optimal parameter space, reduces the optimization difficulty, and improves the optimization efficiency.

Description

Technical Field

[0001] This invention belongs to the field of hydrological model parameter optimization algorithms, especially for calibration methods of hydrological models under high-dimensional conditions, and particularly a spatially constrained high-dimensional parameter optimization algorithm for surface water bodies. Background Technology

[0002] Water is one of the most fundamental natural resources upon which all life depends. However, water scarcity has long threatened people in various regions, and global water shortages are driven by both quantity and quality issues. Long-term water quality prediction modeling is a fundamental method for addressing water pollution, with parameter optimization being a crucial step in determining model parameters and improving simulation accuracy. However, when conducting large-scale, long-term 3D surface water model simulations, the high time cost required for optimization iterations due to the wide geographical area, small grid scale, and complex 3D computation of 3D surface water models has been a persistent challenge for researchers.

[0003] Currently, research on evolutionary parameter optimization algorithms is mainly applied to terrestrial surface water hydrological models (such as SWAT and SWMM). For three-dimensional surface water models with computationally intensive calculations and a large number of parameters, the optimization process is very time-consuming. Existing solutions to improve optimization efficiency can be broadly categorized into three types. The first type starts with the target hydrological model, utilizing the rapid learning and prediction capabilities of models such as machine learning as a substitute or surrogate model to simulate and predict the computational results of the hydrological model, and then uses these results as function values ​​to optimize parameters. Although this type of solution reduces simulation time, the optimization accuracy decreases due to the inherent uncertainties of machine learning.

[0004] The second approach focuses on the internal workings of the optimization algorithm. In high-dimensional cases, optimization algorithms unconsciously reduce dimensionality during the search and evolution process. Some researchers have observed changes in parameters during optimization and implemented weighting strategies. For example, through extensive prior experiments, different weight ratios are assigned to the parameters to be optimized, reducing the possibility of important parameters being overlooked. Alternatively, neglected dimensions can be extracted and considered separately during the optimization process. While these algorithms maintain optimization accuracy to some extent, their efficiency is significantly reduced. Finding a method that incorporates spatial constraints during optimization to achieve static or dynamic dimensionality reduction would effectively improve the optimization efficiency of 3D surface water models and reduce simulation difficulty.

[0005] To this end, this patent is based on a multi-spatial constraint strategy and incorporates current SCE-UA parameter optimization algorithms such as sensitivity analysis, spatial clustering, and similarity analysis to improve optimization efficiency and reduce model simulation difficulty while ensuring optimization accuracy. Summary of the Invention

[0006] Purpose of the invention: This invention addresses the problem of low efficiency in optimizing hydrological parameters of existing high-dimensional surface water models by researching and implementing a high-dimensional hydrological model parameter optimization strategy based on multiple spatial constraints.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A spatially constrained high-dimensional parameter optimization algorithm for surface water bodies includes the following steps:

[0009] (1) Determination of water quality parameters and range; Based on the environment of the study area (nutrient concentration of water bodies) and the hydrological model (the hydrological model case in the instruction manual is a surface water model simulation, using the environmental fluid dynamics model EFDC), determine the range of water quality parameters simulated by the hydrological model;

[0010] (2) Static dimensionality reduction; using the OAT method of sensitivity analysis, the global space is coarsely sampled, the number of trajectories is set to be the same as the parameter dimension n, the gradient of each parameter can be set to an integer, here it is set to 10, and sensitivity analysis is performed; based on the sensitivity analysis results, parameters with sensitivity results less than the custom rejection threshold are filtered out, and static dimensionality reduction is performed on the parameters; the remaining parameters (optimized parameters) are substituted into the subsequent optimization.

[0011] (3) SCE-UA dense sampling: Based on the sensitivity analysis process, the sampling space most likely to obtain the optimal solution is divided, and dense sampling is performed in this space;

[0012] (4) Dynamic dimensionality reduction; Determine the spatial range of each iteration. First, determine whether this range is the same as the range of the previous iteration. If they are the same, directly use the sensitivity analysis results of the previous iteration. If they are different, use the sensitivity analysis method again to freeze the parameters with sensitivity less than the custom cooling threshold in the current range and set them as cooling parameters. Prioritize the optimization of parameters with higher sensitivity in the current range; thus achieving dynamic dimensionality reduction.

[0013] (5) SCE-UA complex shape partitioning; The SCE-UA algorithm decomposes a complex shape (the spatial shape formed by the entire set of sample points) into multiple simple shapes; Based on the clustering idea, this algorithm partitions n+1 complex shapes and sets an optimal base point for each complex shape. That is, the sample point corresponding to the i-th function value of the objective function value calculated by the current hydrological model from smallest to largest is placed into the i-th complex shape as the base point of the complex shape; and the remaining points are placed into the complex shape in turn according to the Euclidean distance clustering idea until the number of points inside the complex shape reaches 2n, thus completing the determination of the complex shape;

[0014] (6) Determination of SCE-UA simplex and evolutionary parameters; In the SCE-UA algorithm, within each complex, sample points that can form the basic shape are searched to form a simplex as the minimum optimization unit, further reducing the optimization difficulty; In this algorithm, within each complex, the similarity analysis method is applied to identify the n+1 sample points with the highest similarity within the complex; These points are set as the simplex of the current iteration; At the same time, the evolutionary parameters α and β are determined according to the similarity coefficient of the worst point;

[0015] (7) Optimize spatial tracking and recovery; during the evolution of the simplex, track whether there is an outward expansion search in space. If so, immediately activate the cooling parameter and restore the dimension.

[0016] (8) SCE-UA convergence condition determination: Based on the results of each iteration, determine whether the convergence condition is met and output the convergence result.

[0017] As a further preferred option, step (2) includes:

[0018] (2-1) Sensitivity model construction; Input the range of parameter values ​​into the sensitivity model and use the OAT method, which is to sample by changing one dimension of the parameter at a time;

[0019] (2-2) Sensitivity model parameter settings; the number of trajectories is set to the parameter dimension n, and the gradient of the change of each dimension of the parameter can be set to an integer, which is set to 10 here; perform global sensitivity analysis on the sampling points (Morris algorithm);

[0020] (2-3) Sensitivity analysis results: Based on the sensitivity analysis results, parameters with a sensitivity coefficient of 0 are removed to achieve initial global dimensionality reduction.

[0021] As a further preferred option, step (3) includes:

[0022] (3-1) Sorting of sample points: Sort the target model function values ​​corresponding to the sample points obtained by OAT sampling in the sensitivity analysis process of step (2) in ascending order;

[0023] (3-2) Fine-grained sampling space determination: Statistically sum the spatial ranges of the top n sample points in the sorting, identify them as spaces more likely to produce better (smaller) solutions, and determine them as the next fine-grained sampling space;

[0024] (3-3) Fine-grained sampling; In the divided fine-grained sampling space, hypercubic Latin sampling is performed, with a sampling number of (n+1)×(2n-9); At this point, the initial sampling stage is completed.

[0025] As a further preferred option, step (4) includes:

[0026] (4-1) Determining the spatial range of each iteration: First, determine the geometric center point x of all sample points in this round of optimization. mean and parameter x i The maximum absolute value abs(x) for each dimension j in the matrix. i,j As shown in formula (1), the radius r of the iteration space is determined. range ;

[0027] r range ={max j＝1,…,n (abs(x i,j Formula (1) is given by: |i=1,…,(n+1)×(2n+1)}

[0028] And determine the upper limit (x) of the iteration space range according to formulas (2) and (3). up ) and lower limit (x) low ):

[0029] x low =x mean -x range Formula (2)

[0030] x up =x mean +x range Formula (3)

[0031] (4-2) Dynamic dimensionality reduction: First, determine whether the iteration space of this round is consistent with the previous iteration space. If it is consistent, the previous sensitivity analysis results are used directly. If it is inconsistent, a new round of sensitivity analysis is performed. Based on the sensitivity analysis results, the parameters with a sensitivity coefficient of 0 are dynamically cooled during this round of iteration.

[0032] As a further preferred option, step (5) includes:

[0033] (5-1) Selection of base points for the complex: Based on the sorting result of the objective function values ​​corresponding to all sample points from smallest to largest, the first n+1 sample points are placed into n+1 complexes as base points, that is, the first sample point is placed into the first complex, and the ith sample point is placed into the ith complex.

[0034] (5-2) Composite partitioning; the remaining sample points are clustered into the composite based on the minimum distance principle; according to formula (4), the dimensions (x) of each remaining sample point are calculated. m,j ) and the corresponding dimension (x) of each base point i,j The total distance is used to determine the complex with the smallest distance; if the complex is already full, the search proceeds sequentially from smallest to largest distance until a complex is found.

[0035] dm ={sum(abs(x)} m,j -x i,j ))|m=n+2,…,(n+1)×(2n+1); j=1,…,n}

[0036] Formula (4).

[0037] As a further preferred option, step (6) includes:

[0038] (6-1) Similarity matrix generation: Based on the Pearson correlation coefficient of each dimension between sample points, calculate the mean of the standard covariance to generate a similarity coefficient matrix of sample points. Where c ij This refers to the similarity coefficient between the i-th sample point and the j-th sample point;

[0039] (6-2) Simplex determination: Based on the similarity matrix results, find the n+1 sample points with the highest similarity among all sample points; determine these n+1 sample points as the simplex.

[0040] (6-3) Determine the SCE-UA algorithm parameters α and β; sort all sample points in the simplex according to their objective function values ​​from smallest to largest, and determine the similarity coefficient (c) corresponding to the worst (largest) value point. n+1 ), and random disturbance factor (δ), and according to formulas (5) and (6), determine the optimization parameters α and β;

[0041] α=c n+1 ×(δ+1) Formula (5)

[0042] δ=α×0.5 Formula (6).

[0043] Beneficial effects

[0044] This invention is based on a multi-space constraint strategy. Through sensitivity analysis, it sets screening and cooling thresholds to screen parameters (statically) and cool them (dynamically), reducing the parameter dimensionality and optimization burden during the optimization process. It utilizes spatial clustering and similarity analysis to perform complex form partitioning and simplex generation for the SCE-UA algorithm, constraining the optimization space and improving the optimization rate. Overall, it achieves the goal of maintaining optimization accuracy while reducing optimization difficulty and improving optimization efficiency in high-dimensional states. Attached Figure Description

[0045] Figure 1 This is the overall flowchart of the method of the present invention;

[0046] Figure 2 This refers to the location and extent of the study area in this embodiment;

[0047] Figure 3This embodiment uses the water depth data and spatial discrete grid partitioning data of Dianchi Lake.

[0048] Figure 4 This is a comparison diagram of the optimization algorithm process and the SCE-UA algorithm in this embodiment;

[0049] Figure 5 EFDC static parameter filtering results;

[0050] Figure 6 EFDC model KRO parameter optimization process;

[0051] Figure 7 This is a comparative analysis of the optimization algorithm on the benchmark test function in this embodiment. Detailed Implementation

[0052] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0053] The technical solution of the present invention will be further described in detail below. In this example, Dianchi Lake in Kunming City, Yunnan Province is selected. Figure 1 Data sources include nutrient concentration observations of the lake (organic nitrogen, organic phosphorus, ammonia nitrogen, and dissolved oxygen) with a time resolution of 4 hours, and basic geographic data (elevation data and underwater topographic data). Figure 2 Meteorological data (air pressure, wind field, temperature, precipitation, relative humidity, solar radiation, evaporation, and cloud cover) with a time resolution of 1 hour, and flow boundary ( Figure 3 The time resolution is 4 hours of data, etc. Model simulation and algorithm verification are performed based on the 3D hydrodynamic water quality model EFDC. This is further illustrated with the accompanying figures and a specific embodiment described below.

[0054] This embodiment provides a spatial constraint parameter optimization strategy for high-dimensional cases based on the SCE-UA algorithm, which specifically includes the following steps:

[0055] (1) Determination of water quality parameters and range. Based on the basic geographic data of the lake, a large spatial discrete rectangular grid unit of 600m×600m was divided using the Cartesian coordinate system, containing a total of 804 rectangular grids. In order to more accurately simulate the topography of the lake bottom, the σ coordinate was used to divide it vertically into 3 layers. At the same time, the dry water depth was set to 0.1m to accommodate changes in water level.

[0056] Typical data from the Dianchi Lake cyanobacterial bloom period from July 6 to July 11, 2022, were selected as the total simulation duration. Considering factors such as the temporal resolution of the measured data, the Courant number used in model construction, the grid size, model computational stability, and simulation accuracy, the simulation time step was set to 10 seconds.

[0057] Based on eight inflow data points and wind speed and direction data, the model's inflow and outflow boundary conditions, wind field boundary conditions, and water quality point source concentration data were set. Meteorological conditions were set based on meteorological data. Initial conditions represent the model's initial state, including initial water temperature and initial water quality concentration indicators. At this point, the Dianchi Lake water quality model was completed.

[0058] Based on the actual conditions of Dianchi Lake and existing research results, the EFDC water quality parameters were optimized, and the parameters and their calibration ranges are shown in the table below (Table 1).

[0059] Table 1. EFDC Model Optimization Parameter Selection and Calibration Range

[0060]

[0061]

[0062] (2) Static dimensionality reduction. Morris sensitivity analysis was used to quantify the uncertainty of 20 parameters. A parameter elimination threshold of 0 was set to filter out parameters with no impact (sensitivity coefficient less than 0), and the remaining parameters (optimization parameters) were substituted into the subsequent optimization. The sensitivity coefficient results are shown in the figure.

[0063] (3) Static dimensionality reduction using SCE-UA. Based on the sensitivity results, the parameter range most likely to produce the optimal sampling results is selected, and SCE-UA sampling is performed within this range. Here, parameter KRO is taken as an example. Figure 2 In the 200th to 400th iterations, it performs dense sampling in the space where better parameters are most likely to be generated, and the optimal KRO value obtained in the end is indeed within this optimal range.

[0064] (4) Dynamic dimensionality reduction. Before each round of optimization, the optimization range is determined, and sensitivity analysis is performed within this range. The cooling threshold is set to 0, and parameters with sensitivity less than or equal to 0 are cooled down. Parameters with sensitivity greater than 0 are optimized first.

[0065] (5) Complex shape segmentation and optimized spatial tracking: Based on the current parameter dimensions, determine the number of complexes n+1, set the first n+1 sample points as the base points of each complex, and perform complex shape clustering based on Euclidean distance. Within each complex, apply similarity analysis to identify the n+1 sample points with the highest similarity to form a simplex. Track changes in the shape of the complexes and restore the dimensions in a timely manner.

[0066] (6) Convergence conditions and algorithm parameter settings. Parameter settings for the multi-space constraint SCE-UA algorithm. The internal parameters of the optimization algorithm are set according to actual conditions, as shown in Table 2.

[0067] Table 2. Internal parameter design of the SCE-UA algorithm with multiple spatial constraints.

[0068]

[0069]

[0070] (7) EFDC Optimization Result Settings. In the EFDC model, observed data for organic nitrogen, organic phosphorus, ammonia nitrogen, and dissolved oxygen were used, with the root mean square error (RMSE) as the index function. At this point, the spatially constrained SCE-UA algorithm was completed. The changes in RMSE values ​​during the optimization process are shown in the figure.

[0071] Table 3. Comparison of simulation results for various parameters between the spatially constrained high-dimensional optimization algorithm for surface water and the Morris-SCEUA algorithm.

[0072]

[0073]

[0074] (8) Benchmark Function Optimization and Comparison. To further verify the effectiveness of the algorithm, multiple benchmark functions were used for comparative testing, as shown in Table 4. The test results show that, in the EFDC model case, when achieving the same accuracy, the algorithm extracted in this paper is 9.33% more efficient than the original SCE-UA algorithm, and 33% more efficient across multiple benchmark functions.

[0075] Table 4: Benchmark Function Categories and Parameter Ranges

[0076]

[0077]

[0078] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A spatially constrained method for optimizing high-dimensional parameters of surface water bodies, characterized in that, Includes the following steps: (1) Determination of water quality parameters and range; Based on the environment of the study area and the hydrological model, determine the range of water quality parameters simulated by the hydrological model; (2) Static dimensionality reduction; using the OAT method of sensitivity analysis, the global space is coarsely sampled, the number of trajectories is set to be the same as the parameter dimension n, the gradient of each parameter is set to an integer, and sensitivity analysis is performed; based on the sensitivity analysis results, parameters with sensitivity results less than the custom rejection threshold are filtered out, and static dimensionality reduction is performed on the parameters; the remaining parameters are substituted into subsequent optimization. (3) SCE-UA dense sampling; Based on the sensitivity analysis process, the sampling space most likely to obtain the optimal solution is divided, and dense sampling is performed in this space; (4) Dynamic dimensionality reduction; Determine the spatial range of each iteration. First, determine whether this range is the same as the range of the previous iteration. If they are the same, directly use the sensitivity analysis results of the previous iteration. If they are different, use the sensitivity analysis method again to freeze the parameters with sensitivity less than the custom cooling threshold in the current range and set them as cooling parameters. Prioritize the optimization of parameters with higher sensitivity in the current range. (5) SCE-UA complex partitioning: The step of decomposing the spatial shape formed by the entire set of sample points into multiple simple shapes; According to the clustering algorithm, n+1 complexes are partitioned, and an optimal base point is set for each complex. That is, the sample point corresponding to the i-th function value of the objective function value calculated by the current hydrological model is placed into the i-th complex as the base point of the complex; The remaining points are placed into the complexes in turn until the number of points inside the complex reaches 2n, and the complex is determined. (6) Determination of SCE-UA simplex and evolution parameters; In the SCE-UA algorithm, within each complex, sample points that can form the basic shape are searched to form a simplex as the minimum optimization unit, thereby reducing the optimization difficulty; In this method, within each complex, a similarity analysis method is applied to identify the n+1 sample points with the highest similarity within the complex. These points are set as the simplex of the current iteration; at the same time, the evolutionary parameters α and β are determined based on the similarity coefficient of the worst point; (7) Optimize spatial tracking and recovery; during the evolution of the simplex, track whether there is an outward expansion search in space. If so, immediately activate the cooling parameter and restore the dimension. (8) Determining the convergence condition of SCE-UA; Based on the results of each iteration, determine whether the convergence condition is met and output the convergence result.

2. The method for optimizing high-dimensional parameters of spatially constrained surface water bodies according to claim 1, characterized in that: Step (2) includes: (2-1) Sensitivity model construction; Input the range of parameter values ​​into the sensitivity model and use the OAT method, which is to sample by changing one dimension of the parameter at a time; (2-2) Sensitivity model parameter settings; the number of trajectories is set to the parameter dimension n, and the gradient of the change of each parameter dimension can be set to an integer; global sensitivity analysis is performed on the sampling points using the Morris algorithm; (2-3) Sensitivity analysis results: Based on the sensitivity analysis results, parameters with a sensitivity coefficient of 0 are removed to achieve initial global dimensionality reduction.

3. The method for optimizing high-dimensional parameters of spatially constrained surface water bodies according to claim 1, characterized in that: Step (3) includes: (3-1) Sorting of sample points: Sort the target model function values ​​corresponding to the sample points obtained by OAT sampling in the sensitivity analysis process of step (2) in ascending order; (3-2) Fine-grained sampling space determination: Statistically calculate the sum of the spatial ranges of the top n sample points in the sorting, identify them as the spaces more likely to produce better solutions, and determine them as the fine-grained sampling space for the next step; (3-3) Fine-grained sampling; In the divided fine-grained sampling space, hypercubic Latin sampling is performed, with a sampling number of (n+1)×(2n-9); At this point, the initial sampling stage is completed.

4. The method for optimizing high-dimensional parameters of spatially constrained surface water bodies according to claim 1, characterized in that: Step (4) includes: (4-1) Determining the spatial range of each iteration: First, determine the geometric center point x of all sample points in this round of optimization. mean and parameter x i The maximum absolute value abs(x) for each dimension j in the matrix. i,j As shown in formula (1), the radius r of the iteration space is determined. range ; r range ={max j＝1,…,n (abs(x i,j ))|i=1,…,(n+1)×(2n+1)} Formula (1) and determine the upper limit x of the iteration space range according to formulas (2) and (3). up and lower limit x low : x low =x mean -x range Formula (2) x up =x mean +x range Formula (3) (4-2) Dynamic dimensionality reduction: First, determine whether the iteration space of this round is consistent with the previous iteration space. If it is consistent, the previous sensitivity analysis results are used directly. If it is inconsistent, a new round of sensitivity analysis is performed. Based on the sensitivity analysis results, the parameters with a sensitivity coefficient of 0 are dynamically cooled during this round of iteration.

5. The method for optimizing high-dimensional parameters of spatially constrained surface water bodies according to claim 1, characterized in that: Step (5) includes: (5-1) Selection of base points for the complex: Based on the sorting result of the objective function values ​​corresponding to all sample points from smallest to largest, the first n+1 sample points are placed into n+1 complexes as base points, that is, the first sample point is placed into the first complex, and the ith sample point is placed into the ith complex. (5-2) Composite partitioning; the remaining sample points are clustered into the composite based on the minimum distance principle; according to formula (4), the dimensions x of each remaining sample point are calculated. m,j The corresponding dimension x of each base point i,j The total distance is used to determine the complex with the smallest distance; if the complex is already full, the search proceeds sequentially from smallest to largest distance until a complex is found. d m ={sum(abs(x m,j -x i,j ))|m=n+2,…,(n+1)×(2n+1);j=1,…,n} Formula (4).

6. The method for optimizing high-dimensional parameters of spatially constrained surface water bodies according to claim 1, characterized in that: Step (6) includes: (6-1) Similarity matrix generation: Based on the Pearson correlation coefficient of each dimension between sample points, calculate the mean of the standard covariance to generate a similarity coefficient matrix of sample points. Where c ij This refers to the similarity coefficient between the i-th sample point and the j-th sample point; (6-2) Simplex determination: Based on the similarity matrix results, find the n+1 sample points with the highest similarity among all sample points; determine these n+1 sample points as the simplex. (6-3) Determine the SCE-UA algorithm parameters α and β; sort all sample points in the simplex according to their objective function values ​​from smallest to largest, and determine the similarity coefficient c corresponding to the worst-case point. n+1 And the random disturbance factor δ, according to formulas (5) and (6), determine the optimization parameters α and β; α=c n+1 ×(δ+1) Formula (5) β=α×0.5 Formula (6).

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