Spatial constraint surface water body high-dimensional parameter optimization algorithm

Abstract

The invention discloses a spatial constraint surface water body high-dimensional parameter optimization algorithm. The algorithm comprises the following specific processing steps: (1) determining the number and range of water quality parameters; and (2) initially sampling the parameters. Screening out low-sensitivity parameters through sensitivity analysis, and determining an optimal sampling space for SCE-UA sampling to form an initial sample group; and (3) carrying out dynamic dimension reduction. And sensitivity analysis is carried out in the space of each iteration, low-sensitivity parameters are temporarily cooled, and residual parameters are optimized. And (4) carrying out SCE-UA complex shape division and simplex generation. And setting reference sample points of each complex, and clustering and dividing the remaining points through Euclidean distance. And searching a sample point with the highest similarity in each complex as a simplex. And (6) tracking and optimizing spatial changes, and if spatial diffusion occurs, activating cooling parameters in time to recover dimensions. And (7) condition convergence and output. According to the invention, based on the spatial difference characteristics of the parameters, the optimal parameter space is searched by using multiple spatial constraint strategies, the optimization difficulty is reduced, and the optimization efficiency is improved.

Description

Technical Field

[0001] The invention belongs to the field of hydrological model parameter optimization algorithms, in particular to a calibration method for a hydrological model in a high-dimensional state, and in particular to a spatially constrained high-dimensional parameter optimization algorithm for surface water bodies. Background Art

[0002] Water is one of the most basic natural resources that all life depends on. However, water shortage has always been a threat to people in different regions. The global water shortage is driven by both water quantity and water quality issues. Long-term water quality prediction modeling is one of the basic methods to solve water pollution problems. Parameter optimization is an important step in the modeling process to determine model parameters and improve simulation accuracy. However, when conducting large-scale, long-term three-dimensional surface water model simulation and prediction, due to the wide regional range, small grid scale, and complex three-dimensional calculations of the three-dimensional surface water model, the high time cost required for optimization iteration has always plagued researchers.

[0003] At present, the 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 intensive computation time and a large number of parameters, the time cost of the optimization process is very high. The existing solutions to improve optimization efficiency can be roughly divided into three types. The first is to start with the target hydrological model and use the rapid learning and prediction capabilities of models such as machine learning as an alternative model or proxy model of the hydrological model to simulate and predict the calculation results of the hydrological model and use this as the function value to optimize the parameters. Although this type of solution reduces the simulation time, the optimization accuracy is reduced due to factors such as the uncertainty of machine learning itself.

[0004] The second is from the internal perspective of the optimization algorithm. In the case of high dimensions, the optimization algorithm has an unconscious dimensionality reduction during the search and evolution process. Some scholars set weight ideas in the algorithm optimization process by observing the changes in parameters and other conditions during the algorithm optimization process. For example, through a large number of prior experiments, different weight ratios are given to the parameters to be optimized to reduce the possibility of important parameters being ignored. In addition, the dimensions that are ignored in the optimization process can be extracted, the optimization process can be increased, and these ignored dimensions can be considered separately. Although this type of algorithm guarantees the optimization accuracy to a certain extent, the optimization efficiency is greatly reduced. If a method can be found to perform spatial constraints during the optimization process to achieve static or dynamic dimensionality reduction, it will effectively improve the optimization efficiency of the three-dimensional surface water model and reduce the difficulty of simulation.

[0005] To this end, this patent is based on multiple spatial constraint strategies, and integrates algorithms such as sensitivity analysis, spatial clustering and similarity analysis into the current SCE-UA parameter optimization algorithm to achieve the goal of improving the optimization efficiency under high-dimensional surface water models while ensuring the optimization accuracy and reducing the difficulty of model simulation. Summary of the invention

[0006] Purpose of the invention: To address the problem of low efficiency in optimizing hydrological parameters of existing high-dimensional surface water models, the present invention studies and implements a high-dimensional hydrological model parameter optimization strategy based on multiple spatial constraint strategies.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[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 ranges: According to the study area environment (nutrient concentration in the water body) and the hydrological model (the hydrological model case in the 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 roughly 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, which is set to 10 here. A sensitivity analysis is then performed. Based on the sensitivity analysis results, the parameters whose sensitivity results are less than the custom screening threshold are screened out, and the parameters are statically reduced in dimension. The remaining parameters (optimization parameters) are then substituted into the post-optimization.

[0011] (3) SCE-UA intensive sampling: Based on the sensitivity analysis process, the sampling space that is most likely to obtain the optimal solution is divided, and intensive 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 previous iteration range, if the same, directly use the sensitivity analysis results of the previous order; if not, use the sensitivity analysis method again, freeze the parameters in the current range whose sensitivity is less than the custom cooling threshold, set them as cooling parameters, and give priority to optimizing the parameters with greater sensitivity in the current range; achieve dynamic dimensionality reduction;

[0013] (5) SCE-UA complex shape division: 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 divides n+1 complex shapes and sets an optimal base point for each complex shape. That is, the sample point corresponding to the ith function value of the target function value calculated by the current hydrological model is placed in the ith complex shape as the base point of the complex shape. Based on the Euclidean distance clustering idea, the remaining points are placed in the complex shape in sequence until the number of points inside the complex shape reaches 2n, and the complex shape is determined.

[0014] (6) Determination of SCE-UA simplex and evolution parameters: In the SCE-UA algorithm, sample points that can form the basic shape are found inside each composite shape to form a simplex as the minimum optimization unit, which further reduces the optimization difficulty; in this algorithm, similarity analysis methods are applied inside each composite shape to identify the n+1 sample points with the highest similarity inside the composite shape; these points are set as the simplex of the current iteration; at the same time, the evolution parameters α and β are determined according to the similarity coefficient of the worst point;

[0015] (7) Optimize space tracking and recovery: During the simplex evolution process, track whether there is any outward expansion search in the space. If so, immediately activate the cooling parameters and restore the dimension;

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

[0017] As a further preferred embodiment, step (2) comprises:

[0018] (2-1) Sensitivity model construction: the parameter value range is input into the sensitivity model, and the OAT method is used to perform sampling, that is, the method of changing one dimension of the parameter at a time;

[0019] (2-2) Sensitivity model parameter setting; the number of trajectories is set to parameter dimension n, and the gradient 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) Analysis of sensitivity results: Based on the results of the sensitivity analysis, the parameters with a sensitivity coefficient of 0 are removed to achieve initial global dimensionality reduction.

[0021] As a further preferred embodiment, step (3) comprises:

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

[0023] (3-2) Determine the fine-grained sampling space; Count the sum of the spatial ranges of the top n sample points in the ranking, identify them as spaces that are 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, hypercube Latin sampling is performed, and the number of samples is (n+1)×(2n-9); at this point, the initial sampling stage is completed.

[0025] As a further preferred embodiment, step (4) comprises:

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

[0027] r range ={max j＝1,…,n (abs(x i,j ))|i=1,…,(n+1)×(2n+1)} Formula (1) According to formulas (2) and (3), the upper limit of the iteration space range (x up ) and the 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, directly use the previous sensitivity analysis results; if it is inconsistent, conduct a new round of sensitivity analysis; and according to the sensitivity analysis results, dynamically cool the parameters with a sensitivity coefficient of 0 during this round of iteration.

[0032] As a further preferred embodiment, step (5) comprises:

[0033] (5-1) Selection of composite base points: According to the sorting results of the objective function values ​​corresponding to all sample points from small to large, the first n+1 sample points are sequentially placed in the n+1 composite shapes as base points, that is, the first sample point is placed in the first composite shape, and the i-th sample point is placed in the i-th composite shape;

[0034] (5-2) Composite division: cluster the remaining sample points according to the minimum distance principle and put them into the composite shape; calculate the dimensions (x m,j ) and the corresponding dimensions (x i,j ) The sum of the distances is used to determine the compound with the smallest distance; if the compound is full, search backwards in order from small to large distances until the compound is found;

[0035] d m= {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 embodiment, step (6) comprises:

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

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

[0040] (6-3) Determine the parameters α and β of the SCE-UA algorithm; sort all sample points in the simplex according to their objective function values ​​from small to large, and sort them according to the similarity coefficient (c n+1 ), and the random disturbance factor (δ), 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] The present invention is based on multiple spatial constraint strategies, sets screening thresholds and cooling thresholds through sensitivity analysis, screens out (static) and cools (dynamic) parameters, reduces the parameter dimension in the optimization process, reduces the optimization burden, and uses spatial clustering and similarity analysis to perform SCE-UA algorithm composite division and simplex generation, constrains the optimization space, and improves the optimization rate. The comprehensive realization ensures the optimization accuracy in a high-dimensional state, reduces the optimization difficulty, and improves the optimization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is the overall flow chart of the method of the present invention;

[0046] Figure 2 is the location and scope of the study area in this embodiment;

[0047] Figure 3The water depth data and spatial discrete grid subdivision data of the Dianchi Lake water body used in this embodiment;

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

[0049] Figure 5 EFDC static parameter screening results;

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

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

[0052] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0053] The technical solution of the present invention is further described in detail below. This example selects the Dianchi Lake in Kunming City, Yunnan Province ( Figure 1 The data sources include lake nutrient concentration (organic nitrogen, organic phosphorus, ammonia nitrogen and dissolved oxygen) observation data with a time resolution of 4 hours, basic geographic data (elevation data and underwater topography 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 boundaries ( Figure 3 ) The time resolution is 4 hours data, etc. Model simulation and algorithm verification are performed based on the three-dimensional hydrodynamic water quality model EFDC. Combined with the following figures, a specific embodiment is described to further illustrate.

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

[0055] (1) Determination of water quality parameters and ranges. Based on the basic geographic data of the lake, the Cartesian coordinate system was used to divide the larger spatial discrete rectangular grid unit into 600m×600m, which contained 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 three layers. At the same time, the dry water depth was set to 0.1m to adapt to the changes in water level.

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

[0057] The model's inflow and outflow boundary conditions, wind field boundary conditions, and water quality point source concentration data are set based on the eight inflow data and wind speed and direction data. Meteorological conditions are set based on meteorological data. The initial conditions represent the initial state of the model, including the initial water temperature and the initial water quality concentration index. At this point, the Dianchi Lake water quality model is completed.

[0058] According to the actual situation of Dianchi Lake and existing research results, the EFDC water quality parameters were optimized and the following table of parameters and their calibration ranges was given (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, and the parameter screening threshold was set to 0 to screen out parameters with no influence (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) SCE-UA static dimensionality reduction. According to the sensitivity results, the parameter range that is most likely to produce the optimal sampling result is selected, and SCE-UA sampling is performed within it. Here, the parameter KRO is taken as an example ( Figure 2 ), which performs dense sampling in the space most likely to produce better parameters in the 200th-400th iterations, and the optimal KRO value finally optimized is indeed within the optimal range.

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

[0065] (5) Complex shape division and optimization space tracking: According to the current parameter dimension, determine the number of complex shapes n+1, set the first n+1 sample points as the base points of each complex shape, and perform complex shape clustering division according to the Euclidean distance. In each complex shape, apply the similarity analysis method to identify the n+1 sample points with the highest similarity within the complex shape to form a simplex. And track the shape changes of the complex shape and restore the dimension in time.

[0066] (6) Convergence conditions and algorithm parameter settings. Multiple spatial constraint SCE-UA algorithm parameter settings. 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 SCE-UA algorithm with multiple spatial constraints

[0068]

[0069]

[0070] (7) EFDC optimization result setting. In the EFDC model, organic nitrogen, organic phosphorus, ammonia nitrogen and dissolved oxygen observation data are used, and the root mean square error (RMSE) is used as the indicator function. At this point, the spatial constraint SCE-UA algorithm is implemented. The change of RMSE value during the optimization process is shown in the figure.

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

[0072]

[0073]

[0074] (8) Benchmark function optimization comparison. In order to further verify the effectiveness of the algorithm, a multi-class benchmark function is used for comparative testing. The benchmark function is shown in Table 4. The test results show that in the EFDC model case, when the same accuracy is achieved, the algorithm extracted in this paper is 9.33% more efficient than the original SCE-UA algorithm. On the multi-class benchmark function, the efficiency is increased by 33%.

[0075] Table 4 Benchmark test function categories and parameter ranges:

[0076]

[0077]

[0078] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A spatially constrained high-dimensional parameter optimization algorithm for surface water bodies, characterized in that: The following steps are involved: (1) Determination of water quality parameters and ranges: Determine the range of water quality parameters simulated by the hydrological model based on the study area environment and hydrological model; (2) Static dimensionality reduction: Using the OAT method of sensitivity analysis, the global space is roughly 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, which is set to 10 here. A sensitivity analysis is then performed. Based on the sensitivity analysis results, the parameters whose sensitivity results are less than the custom screening threshold are screened out, and the parameters are statically reduced in dimension. The remaining parameters (optimization parameters) are then substituted into the post-optimization. (3) SCE-UA dense sampling; According to the sensitivity analysis process, the sampling space that is 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 previous iteration range, if the same, directly use the sensitivity analysis results of the previous order; if not, use the sensitivity analysis method again, freeze the parameters in the current range whose sensitivity is less than the custom cooling threshold, set them as cooling parameters, and give priority to optimizing the parameters with greater sensitivity in the current range; achieve dynamic dimensionality reduction; (5) SCE-UA complex shape division: 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 divides n+1 complex shapes and sets an optimal base point for each complex shape. That is, the sample point corresponding to the ith function value of the target function value calculated by the current hydrological model is placed in the ith complex shape as the base point of the complex shape. Based on the Euclidean distance clustering idea, the remaining points are placed in the complex shape in sequence until the number of points inside the complex shape reaches 2n, and the complex shape is determined. (6) Determination of SCE-UA simplex and evolution parameters; In the SCE-UA algorithm, sample points that can form the basic shape are found inside each composite shape to form a simplex as the minimum optimization unit, further reducing the optimization difficulty; In this algorithm, similarity analysis methods are applied inside each composite shape to identify the n+1 sample points with the highest similarity inside the composite shape; These points are set as the simplex of the current iteration; at the same time, the evolution parameters α and β are determined according to the similarity coefficient of the worst point; (7) Optimize space tracking and recovery: During the simplex evolution process, track whether there is any outward expansion search in the space. If so, immediately activate the cooling parameters and restore the dimension; (8) Determination of SCE-UA convergence conditions; According to the results of each round of iteration, determine whether the convergence conditions are met and output the convergence results.

2. The spatially constrained high-dimensional parameter optimization algorithm for surface water bodies according to claim 1, characterized in that: The step (2) comprises: (2-1) Sensitivity model construction: the parameter value range is input into the sensitivity model, and the OAT method is used to perform sampling, that is, the method of changing one dimension of the parameter at a time; (2-2) Sensitivity model parameter setting; the number of trajectories is set to parameter dimension n, and the gradient of each dimension of the parameter can be set to an integer, which is set to 10 here; global sensitivity analysis is performed on the sampling points using the Morris algorithm; (2-3) Analysis of sensitivity results: Based on the sensitivity analysis results, the parameters with a sensitivity coefficient of 0 are removed to achieve initial global dimensionality reduction.

3. The spatially constrained high-dimensional parameter optimization algorithm for surface water bodies according to claim 1, characterized in that: The step (3) comprises: (3-1) Sorting sample points: Sorting the target model function values ​​corresponding to the sample points obtained by OAT sampling in the sensitivity analysis process of step (2) from small to large; (3-2) Determine the fine-grained sampling space; Count the sum of the spatial ranges of the top n sample points in the ranking, identify them as spaces that are more likely to produce better (smaller) solutions, and determine them as the next fine-grained sampling space; (3-3) Fine-grained sampling: In the divided fine-grained sampling space, hypercube Latin sampling is performed, and the number of samples is (n+1)×(2n-9); at this point, the initial sampling stage is completed.

4. The spatially constrained high-dimensional parameter optimization algorithm for surface water bodies according to claim 1, characterized in that: The step (4) comprises: (4-1) The spatial range of each round of iteration is determined; first, the geometric center point x of all sample points in this round of optimization is determined. mean , and the parameter x i The maximum absolute value abs(x i,j ), as shown in formula (1), determine the radius r of the iteration space range range ; r range ={max j＝1，...，n (abs(x i，j ))|=i=1,...,(n+1)×(2n+1)} Formula (1) According to formulas (2) and (3), the upper limit of the iteration space range (x up ) and the 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, directly use the previous sensitivity analysis results; if it is inconsistent, conduct a new round of sensitivity analysis; and according to the sensitivity analysis results, dynamically cool the parameters with a sensitivity coefficient of 0 during this round of iteration.

5. The spatially constrained high-dimensional parameter optimization algorithm for surface water bodies according to claim 1, characterized in that: The step (5) comprises: (5-1) Selection of composite base points: According to the sorting results of the objective function values ​​corresponding to all sample points from small to large, the first n+1 sample points are sequentially placed in the n+1 composite shapes as base points, that is, the first sample point is placed in the first composite shape, and the i-th sample point is placed in the i-th composite shape; (5-2) Composite division: cluster the remaining sample points according to the minimum distance principle and put them into the composite shape; calculate the dimensions (x m,j ) and the corresponding dimensions (x i,j ) The sum of the distances is used to determine the compound with the smallest distance; if the compound is full, search backwards in order from small to large distances until the compound is found; <h2 style=";text-align:left;direction:ltr">d<h2 style=";text-align:left;direction:ltr"> m <h2 style=";text-align:left;direction:ltr"> ={sum(abs(x<h2 style=";text-align:left;direction:ltr"> m，j <h2 style=";text-align:left;direction:ltr"> -x<h2 style=";text-align:left;direction:ltr"> i，j <h2 style=";text-align:left;direction:ltr"> ))|m=n+2,....,(n+1)×(2n+1);j=1,...,n} Formula (4).

6. The spatially constrained high-dimensional parameter optimization algorithm for surface water bodies according to claim 1, characterized in that: The step (6) comprises: (6-1) Similarity matrix generation: Based on the Pearson correlation coefficient of each dimension between sample points, the mean of the standard covariance is calculated to generate the similarity coefficient matrix of the sample points. where c ij It means the similarity coefficient between the i-th sample point and the j-th sample point; (6-2) Simplex determination: According to the similarity matrix result, find the n+1 sample points with the highest similarity among all sample points; determine these n+1 sample points as simplex; (6-3) Determine the parameters α and β of the SCE-UA algorithm; sort all sample points in the simplex according to their objective function values ​​from small to large, and sort them according to the similarity coefficient (c 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×0.5Formula (6).

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