A rainfall spatial uniformity analysis method and analysis system based on grey accumulation

Abstract

The present application relates to the technical field of hydrological simulation and hydraulic engineering, and particularly relates to a rainfall spatial uniformity analysis method and analysis system based on grey accumulation, which comprises the following steps: obtaining original rainfall of two-dimensional grid monitoring points to form an original data set, extracting an ordered rainfall sequence according to a spatial analysis direction, performing grey accumulation processing on the ordered rainfall sequence to obtain a cumulative sequence, performing multi-order trend fitting on the cumulative sequence, selecting a trend model according to fitting goodness, extracting a change rate and a trend inflection point from the trend model, calculating a rate variation coefficient and an inflection point influence degree, analyzing the fitting goodness, the rate variation coefficient and the inflection point influence degree one by one according to multi-dimensional evaluation indexes, obtaining uniformity analysis results of each direction, determining a judgment level of each direction, and determining an overall uniformity level and a non-uniform area position by comprehensively considering all direction results. The present application can quantize spatial ordered correlation, identify linear and nonlinear change trends, accurately locate non-uniform areas, and provide fine guidance.

Description

Technical Field

[0001] This invention relates to the field of hydrological simulation and water conservancy engineering technology, and in particular to a method and system for analyzing the spatial uniformity of rainfall based on gray accumulation. Background Technology

[0002] In artificial rainfall simulation systems, such as sprinkler system performance verification, soil erosion simulation experiments, and crop water requirement studies, the spatial uniformity of rainfall is a core indicator for evaluating system reliability and experimental validity. An ideal simulated rainfall device should provide a uniform and stable rainfall distribution throughout the entire test area, thereby ensuring the repeatability and scientific validity of experimental data. However, due to the combined effects of factors such as sprinkler layout, pipeline pressure fluctuations, environmental wind fields, and boundary effects, actual rainfall often exhibits a complex and uneven spatial distribution. How to accurately and quantitatively evaluate the degree of this uneven distribution and pinpoint its causes has always been a technical challenge that those skilled in the art have been striving to solve.

[0003] Currently, mainstream uniformity analysis methods generally adopt evaluation indicators based on statistical dispersion, such as the Christensen uniformity coefficient method and the Benamir-Hall method. These methods treat each monitoring point as a discrete sample that is independent and has no spatial order, and only calculate the standard deviation and coefficient of variation of the rainfall at each point relative to the overall average. These methods have three inherent defects: (1) They ignore spatial order, that is, they cannot distinguish between the gradual distribution of "more in the east and less in the west" and the disordered fluctuation of "random mottled". The two may obtain the same uniformity coefficient, but the actual physical meaning is completely different; (2) They cannot capture the change pattern, that is, they only output a general score between 0 and 1, and cannot answer detailed questions such as "from which direction does the unevenness start?" "Is the change trend linearly increasing or increasing first and then decreasing?" "How big is the change gradient?", which lacks guidance value for optimizing rain gauge design or locating faults; (3) They are sensitive to data characteristics, that is, in the case of a limited number of points (small sample) in simulated rainfall experiments, traditional methods are easily affected by random fluctuations and outliers, and the stability and reliability of the analysis results are insufficient.

[0004] In summary, the existing technology lacks a uniformity analysis method that can simultaneously take into account rainfall values, spatial order, and trend patterns, which has become a technical bottleneck restricting the refined development of this field. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for analyzing the spatial uniformity of rainfall based on gray accumulation, so as to solve the problems in the prior art that cannot quantify and simulate the ordered spatial correlation of rainfall, cannot identify nonlinear change trends, and have coarse analysis results lacking refined guidance information.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: This invention discloses a method for analyzing the spatial uniformity of rainfall based on gray accumulation, comprising: Based on multiple monitoring points pre-distributed in a two-dimensional grid within the simulated rainfall test area, the raw rainfall data collected at each monitoring point is obtained to obtain the raw dataset; At least one spatial analysis direction is set, and the original rainfall is extracted sequentially from the original dataset according to the position of each monitoring point along the spatial analysis direction to obtain an ordered rainfall sequence corresponding to each spatial analysis direction. Based on the location of each monitoring point along the spatial analysis direction, each original rainfall amount in the ordered rainfall sequence is processed by gray accumulation to obtain the cumulative sequence corresponding to each spatial analysis direction. For each of the cumulative sequences, at least two different orders of trend fitting are performed, and the goodness of fit of different orders is obtained. Based on the goodness of fit that meets the preset conditions, the trend model corresponding to each of the spatial analysis directions is selected. Based on the analysis of the trend model, the rate of change and trend inflection point of rainfall along the corresponding spatial analysis direction are extracted, and the rate of variation coefficient and inflection point influence are calculated. The goodness of fit of the trend model, the rate of variation coefficient and the inflection point influence are analyzed one by one according to the preset multidimensional evaluation index to obtain the analysis results of rainfall uniformity in each of the spatial analysis directions. Based on the analysis results, the determination level of rainfall uniformity in the corresponding spatial analysis direction is determined. Combining the analysis results and determination levels in all spatial analysis directions, the overall uniformity level and the location of non-uniform areas in the simulated rainfall test area are determined.

[0007] Optionally, obtaining the raw rainfall data collected at each of the monitoring points to obtain the raw dataset includes: The simulated rainfall intensity is controlled, and after the rainfall intensity reaches a stable state, the rainfall at each monitoring point is continuously collected within a preset time period to obtain the original rainfall at each monitoring point; Based on the row and column positions of each monitoring point in the two-dimensional grid, all the original rainfall data are arranged and labeled according to the distribution of the monitoring points to obtain the original dataset. The expression for the original dataset is:

[0008] In the formula, Represents the original dataset. Indicates the mark as the first Line number The original rainfall of the column, Indicates the row position index. Indicates the column position index.

[0009] Optionally, the step of setting at least one spatial analysis direction and sequentially extracting the original rainfall from the original dataset according to the position of each monitoring point along the spatial analysis direction to obtain an ordered rainfall sequence corresponding to each spatial analysis direction includes: Based on the form of the two-dimensional grid, several row analysis directions and several column analysis directions are defined; Based on the row labels of all the original rainfall amounts in the original dataset, multiple original rainfall amounts are extracted sequentially from the original dataset along each row analysis direction to obtain the ordered rainfall sequence corresponding to each row analysis direction. The functional expression for the ordered rainfall sequence corresponding to each row analysis direction is:

[0010] in, Indicates the first The ordered rainfall sequence corresponding to the direction of the strip analysis, Indicates the first The first line of analysis direction The original rainfall at each monitoring point Indicates the index of the monitoring point along the line analysis direction; Based on the column labels of all the original rainfall amounts in the original dataset, multiple original rainfall amounts are extracted sequentially from the original dataset along each column analysis direction to obtain the ordered rainfall sequence corresponding to each column analysis direction. The function expression for the ordered rainfall sequence corresponding to each column analysis direction is:

[0011] In the formula, Indicates the first The ordered rainfall sequence corresponding to the direction of the analysis is listed in the column. Indicates the first In the direction of list analysis, the first The original rainfall at each monitoring point This indicates the index of the monitoring point along the column analysis direction.

[0012] Optionally, the step of performing gray accumulation processing on each of the original rainfall amounts in the ordered rainfall sequence according to the positions of the monitoring points along the spatial analysis direction to obtain the cumulative sequence corresponding to each spatial analysis direction includes: Based on the row and column labels of all the original rainfall amounts in the ordered rainfall sequence, each original rainfall amount in the ordered rainfall sequence is gray-accumulated along the corresponding spatial analysis direction with all the preceding original rainfall amounts at the corresponding position, to obtain the cumulative sequence along the spatial analysis direction. The function expression for accumulating the original rainfall amounts is:

[0013] In the formula, Indicates the first The cumulative rainfall value of each monitoring point plus the previous monitoring point. Indicates the index of the monitoring point. Represents the first in an ordered rainfall sequence The original rainfall, This represents the total number of original rainfall amounts in an ordered rainfall sequence.

[0014] Optionally, the step of performing at least two different orders of trend fitting on each of the cumulative sequences and obtaining the goodness of fit of different orders, and selecting the trend model corresponding to each of the spatial analysis directions based on the goodness of fit that meets preset conditions, includes: A first-order polynomial model is established to linearly fit each of the cumulative sequences. The functional expression of the first-order polynomial model is as follows:

[0015] In the formula, Represents the first-order polynomial model for the th element in the cumulative sequence. The predicted value of the cumulative rainfall. Indicates linear slope. Represents a constant term; A second-order polynomial model and a third-order polynomial model are established to perform nonlinear fitting on each of the accumulated sequences, and the functional expressions of the second-order polynomial model and the third-order polynomial model are respectively:

[0016]

[0017] In the formula, This represents the second-order polynomial model for the cumulative sequence of the nth... The predicted value of the cumulative rainfall. The fitting coefficients represent the control coefficients for the curvature of the quadratic term. The fitting coefficient represents the control for the linear trend of the first-order term. Represents a constant term. This represents the third-order polynomial model for the cumulative sequence of the th... The predicted value of the cumulative rainfall. The fitting coefficients represent the control coefficients for the curvature of the cubic term. The fitting coefficient represents the control for the linear trend of the quadratic term. The fitting coefficient represents the control for the linear trend of the first-order term. Represents a constant term; The goodness of fit between the first-order polynomial model, the second-order polynomial model, and the third-order polynomial model and the cumulative sequence are calculated respectively. The polynomial model with the largest goodness of fit value that is greater than a preset goodness of fit threshold is selected as the trend model corresponding to each of the spatial analysis directions.

[0018] Optionally, the step of extracting the rate of change and trend inflection point of rainfall along the corresponding spatial analysis direction based on the analysis of the trend model includes: Taking the first derivative of each trend model yields the rate of change representation function corresponding to each spatial analysis direction. The expression for the rate of change representation function is as follows: In the formula, Indicates the first The rate of change at each monitoring point This indicates that the trend model applies to the th cumulative series. The predicted value of the cumulative rainfall. This indicates the trend model with respect to the independent variables. The first derivative; The first derivative of the function representing the rate of change is taken again, and the derivative is set to zero. The position of the trend inflection point corresponding to the spatial analysis direction is obtained. The functional expression of the function representing the rate of change after taking the first derivative and solving is as follows:

[0019]

[0020] In the formula, The representation function of the rate of change with respect to the independent variable The first derivative, Indicates the index of the trend inflection point.

[0021] Optionally, the calculation of the rate variation coefficient and the inflection point influence includes: Based on the characteristic function of the rate of change, the rate variation coefficient corresponding to the spatial analysis direction is calculated, and the functional expression for calculating the rate variation coefficient is:

[0022] In the formula, Represents the rate of variation coefficient. The standard deviation of the function representing the rate of change at each monitoring point location. The arithmetic mean of the values ​​of the function representing the rate of change at each monitoring point; If the solution of the first derivative of the rate of change characterization function has a trend inflection point, and the location of the trend inflection point is within the monitoring point location corresponding to the spatial analysis direction, then the inflection point influence degree is calculated according to the rate of change characterization function. The functional expression for calculating the inflection point influence degree is as follows:

[0023] In the formula, Indicates the degree of influence of the inflection point. Indicates the location of the trend inflection point. The average rate of change at each monitoring point previously, Indicates the location of the trend inflection point. The average rate of change at each monitoring point thereafter.

[0024] This invention also discloses an analysis system applied to the above-mentioned gray accumulation-based rainfall spatial evenness analysis method, the analysis system comprising: The data acquisition module is used to obtain the raw rainfall data collected by each of the multiple monitoring points pre-distributed in a two-dimensional grid within the simulated rainfall test area, thereby obtaining the raw dataset. The data extraction module is used to set at least one spatial analysis direction and extract the original rainfall from the original dataset in sequence according to the position of each monitoring point in the spatial analysis direction, so as to obtain an ordered rainfall sequence corresponding to each spatial analysis direction. The data processing module is used to perform gray accumulation processing on each of the original rainfall amounts in the ordered rainfall sequence according to the positions of the monitoring points in the spatial analysis direction, so as to obtain the cumulative sequence corresponding to each spatial analysis direction; The data fitting module is used to perform at least two different orders of trend fitting on each of the cumulative sequences, obtain the goodness of fit of different orders, and select the trend model corresponding to each of the spatial analysis directions according to the goodness of fit that meets the preset conditions. The feature parameter quantification module is used to extract the rate of change and trend inflection point of rainfall along the corresponding spatial analysis direction based on the analysis of the trend model, and to calculate and obtain the rate of variation coefficient and the inflection point influence. The uniformity evaluation module is used to analyze the goodness of fit of the trend model, the rate variation coefficient and the inflection point influence degree one by one according to the preset multidimensional evaluation index, so as to obtain the analysis results of rainfall uniformity in each spatial analysis direction. The rating module is used to determine the rating of rainfall uniformity in the corresponding spatial analysis direction based on the analysis results, and to determine the overall uniformity rating and the location of non-uniform areas in the simulated rainfall test area by combining the analysis results and ratings in all spatial analysis directions.

[0025] The present invention also discloses an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described method for analyzing the spatial uniformity of rainfall based on gray accumulation.

[0026] The present invention also discloses a storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described method for analyzing the spatial uniformity of rainfall based on gray accumulation.

[0027] Compared with the prior art, the beneficial effects of the rainfall spatial uniformity analysis method and analysis system based on gray accumulation provided by the embodiments of the present invention are as follows: By extracting ordered rainfall sequences from the original dataset according to the spatial analysis direction, the actual spatial arrangement of monitoring points is preserved, enabling subsequent analysis to distinguish between gradual distributions and random fluctuations. Gray accumulation processing is applied to the ordered rainfall sequences to obtain cumulative sequences. Utilizing the weakened randomness characteristics of accumulation, random fluctuations and outlier interference in the original rainfall under small sample conditions are effectively suppressed, improving the stability and reliability of the analysis results. Multi-order trend fitting is performed on the cumulative sequences, and a trend model is selected based on the goodness of fit. This automatically identifies whether rainfall exhibits linear or nonlinear variation patterns along the spatial analysis direction, avoiding subjective biases from manually pre-set models. Extracting the rate of change from the trend model quantitatively describes the speed of spatial changes in rainfall, and extracting trend inflection points pinpoints the transition points in the variation patterns. The coefficient of variation of the rate of change is calculated to evaluate the overall stability of the change, while the impact of inflection points is calculated to quantify the degree of abrupt change at the inflection points locally. By using multidimensional evaluation indicators to analyze the goodness of fit, rate coefficient of variation, and inflection point influence, the analysis results and judgment levels in each spatial analysis direction are obtained. By combining all directions, the overall uniformity level and the location of non-uniform areas in the simulated rainfall test area can be determined, thus providing clear and refined guidance for optimizing the simulated rainfall system. Attached Figure Description

[0028] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 A schematic flowchart illustrating the steps of the rainfall spatial uniformity analysis method provided in this embodiment of the invention. Detailed Implementation

[0029] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0030] This invention discloses a method for analyzing the spatial uniformity of rainfall based on gray accumulation, comprising: S1. Based on multiple monitoring points pre-distributed in a two-dimensional grid within the simulated rainfall test area, obtain the raw rainfall data collected at each monitoring point to obtain the raw dataset; S2. Set at least one spatial analysis direction, and extract the original rainfall data from the original dataset in sequence according to the location of each monitoring point in the spatial analysis direction to obtain the ordered rainfall sequence corresponding to each spatial analysis direction; S3. Based on the location of each monitoring point along the spatial analysis direction, perform gray accumulation processing on each original rainfall amount in the ordered rainfall sequence to obtain the cumulative sequence corresponding to each spatial analysis direction. S4. Perform at least two different orders of trend fitting on each cumulative sequence and obtain the goodness of fit for each order. Select the trend model corresponding to each spatial analysis direction based on the goodness of fit that meets the preset conditions. S5. Based on the analysis of the trend model, extract the rate of change and trend inflection point of rainfall along the corresponding spatial analysis direction, and calculate the rate of variation coefficient and the influence of the inflection point. S6. Based on the preset multidimensional evaluation indicators, the goodness of fit, rate variation coefficient and inflection point influence of the trend model are analyzed one by one to obtain the analysis results of rainfall uniformity in each spatial analysis direction. S7. Based on the analysis results, determine the judgment level of rainfall uniformity in the corresponding spatial analysis direction, and combine the analysis results and judgment levels in all spatial analysis directions to determine the overall uniformity level and the location of non-uniform areas within the simulated rainfall test area.

[0031] By implementing the above-mentioned method for analyzing the spatial uniformity of rainfall, the original rainfall data collected by multiple monitoring points pre-distributed in a two-dimensional grid within the simulated rainfall test area are first organized into an original dataset. The row and column position information of each monitoring point in the grid is preserved, laying a data foundation for subsequent spatially ordered analysis.

[0032] Secondly, a spatial analysis direction is defined, and the original rainfall data from the raw dataset is extracted sequentially based on the location of each monitoring point along that direction, constructing an ordered rainfall sequence. This process, for the first time, reorganizes the originally independent and disordered monitoring point data according to the actual spatial arrangement order, explicitly incorporating the spatial correlation between adjacent monitoring points into the mathematical model. This fundamentally solves the inherent defect of the traditional uniform coefficient method, which cannot distinguish between a gradual distribution of "more in the east and less in the west" and disordered fluctuations of "random mottled". Because the arrangement order of elements in the ordered rainfall sequence corresponds one-to-one with the actual spatial location of the monitoring points, subsequent accumulation processing can proceed along the real spatial path, ensuring that the analysis results have a clear spatial orientation.

[0033] The essence of grey cumulative generation processing is to smooth and weaken the irregular random fluctuations and outliers in the original sequence through item-by-item accumulation, while strengthening the deterministic information implicit in the spatial variation trend. In simulated rainfall experiments with limited sampling points, the original rainfall data is easily affected by instantaneous nozzle pressure fluctuations or local wind field interference, leading to random errors. Directly using the original data for analysis results in instability. Grey cumulative processing utilizes the positive transmission effect of the accumulation process, allowing random noise to cancel each other out during accumulation, while the actual increase or decrease trend of rainfall along the spatial direction is gradually amplified and presented as a monotonic variation of the cumulative sequence. This characteristic significantly improves the noise resistance and reliability of the analysis method.

[0034] Because different rainfall systems exhibit vastly different spatial distribution characteristics—some showing a linear decrease, while others show a non-linear distribution with an initial increase followed by a decrease—a single-order model cannot universally capture all patterns of change. By simultaneously fitting multiple orders of models and comparing their goodness of fit, the model order that best matches the actual distribution can be automatically identified from the data, avoiding subjective bias caused by pre-setting models. Goodness of fit quantitatively reflects the explanatory power of the selected trend model for the cumulative sequence. Only models that can describe the changing patterns of the cumulative sequence with sufficiently high accuracy are adopted as trend models. This ensures the statistical reliability of subsequently extracted rates of change and trend inflection points.

[0035] Extracting the rate of change quantitatively describes how quickly rainfall changes with spatial location, thus answering refined questions such as "from which direction does the change begin?" and "how fast does the change occur?" Extracting trend inflection points precisely pinpoints the spatial locations where rainfall change patterns shift, such as the point where rainfall changes from increasing to decreasing, providing crucial spatial coordinates for subsequent location of unevenly distributed areas. Calculating the coefficient of variation of the rate of change provides an overall assessment of the dispersion of the rate of change; a smaller coefficient indicates a more uniform and stable spatial variation in rainfall. Calculating the impact of inflection points measures the difference in the rate of change before and after the inflection point, quantifying the drastic change at the inflection point and helping to determine whether the inflection point belongs to a significant unevenly distributed location requiring attention. These four characteristic parameters together constitute a complete quantitative description of the spatial variation process of rainfall.

[0036] Multidimensional evaluation indicators comprehensively characterize the spatial distribution features of rainfall from three orthogonal dimensions: trend regularity, stability of change, and severity of abrupt changes. A single indicator cannot fully reflect uniformity. For example, a high goodness of fit but a large rate of variation coefficient means that although there is a clear trend, the changes are drastic, which is also considered uneven. Analyzing each direction provides clear indicator support for the uniformity conclusions, avoiding the information loss caused by relying on a single general coefficient in traditional methods. By integrating the analysis results from multiple directions such as rows and columns, it is possible to cross-locate which specific area in the two-dimensional plane has higher or lower rainfall, and which direction's inflection point causes the unevenness. This provides refined and quantifiable guidance for optimizing sprinkler layout, regulating pipeline pressure, or troubleshooting in simulated rainfall systems.

[0037] Furthermore, the raw rainfall data collected at each monitoring point is obtained to produce the raw dataset, which includes: The simulated rainfall intensity was controlled, and after the rainfall intensity reached a stable state, the rainfall at each monitoring point was continuously collected within a preset time period to obtain the original rainfall at each monitoring point. Based on the row and column positions of each monitoring point in the two-dimensional grid, all raw rainfall data are arranged and labeled according to the distribution of monitoring points, resulting in the raw dataset. The expression for the raw dataset is:

[0038] In the formula, Represents the original dataset. Indicates the mark as the first Line number The original rainfall of the column, Indicates the row position index. Indicates the column position index.

[0039] By implementing the above-described method for analyzing the spatial uniformity of rainfall, rainfall at each monitoring point is continuously collected over a preset time period. The core technical advantage of this process is that by waiting for the rainfall intensity to reach a stable state, it eliminates the unsteady fluctuations caused by pressure build-up or nozzle response delays during the startup phase of the simulated rainfall system. This ensures that the collected raw rainfall data accurately reflects the spatial distribution characteristics of the system under normal operating conditions, avoiding the contamination of data quality by dynamic interference. Continuously collecting cumulative rainfall over a preset time period, rather than instantaneous values, further smooths out high-frequency random fluctuations caused by instantaneous wind field disturbances or nozzle rotation cycles, improving the temporal representativeness of the raw rainfall data at each monitoring point.

[0040] All raw rainfall data were arranged and marked according to the distribution of monitoring points. This arrangement and marking followed a row-first, column-first order within the same row, with each raw rainfall element having an index (e.g., ...) In and This directly corresponds to the row and column position indices of the monitoring point in the two-dimensional grid, creating a one-to-one mapping between the spatial arrangement of the original dataset and the actual physical layout of the monitoring points. This structured organization avoids the overhead of maintaining an additional coordinate lookup table and provides a natural index path for subsequent sequential extraction of the original rainfall along the row or column direction. That is, when extracting by row, it is only necessary to continuously take the elements with increasing column positions within the same row; when extracting by column, it is necessary to take the elements with increasing row positions within the same column across rows, thus completely preserving the two-dimensional spatial location association information without increasing computational complexity.

[0041] Preferably, the monitoring points are evenly distributed in a two-dimensional grid with n rows and m columns, where n and m are both not less than three, forming a monitoring network covering the entire simulated rainfall test area. The collected raw rainfall data is the cumulative rainfall, expressed in millimeters.

[0042] Furthermore, at least one spatial analysis direction is defined, and based on the location of each monitoring point along the spatial analysis direction, the raw rainfall data in the original dataset is extracted sequentially to obtain an ordered rainfall sequence corresponding to each spatial analysis direction, including: Several row analysis directions and several column analysis directions are defined based on the form of a two-dimensional grid; Based on the row labels of all raw rainfall data in the original dataset, multiple raw rainfall data are extracted sequentially from the original dataset along each row analysis direction to obtain the ordered rainfall sequence corresponding to each row analysis direction. The function expression for the ordered rainfall sequence corresponding to each row analysis direction is as follows:

[0043] in, Indicates the first The ordered rainfall sequence corresponding to the direction of the strip analysis, Indicates the first The first line of analysis direction The original rainfall at each monitoring point Indicates the index of the monitoring point along the line analysis direction; Based on the column labels of all raw rainfall data in the original dataset, multiple raw rainfall data are extracted sequentially from the original dataset along each column analysis direction to obtain an ordered rainfall sequence corresponding to each column analysis direction. The function expression for the ordered rainfall sequence corresponding to each column analysis direction is as follows:

[0044] In the formula, Indicates the first The ordered rainfall sequence corresponding to the direction of the analysis is listed in the column. Indicates the first In the direction of list analysis, the first The original rainfall at each monitoring point This indicates the index of the monitoring point along the column analysis direction.

[0045] By implementing the above-mentioned method for analyzing the spatial uniformity of rainfall, several row analysis directions and several column analysis directions are set according to the form of a two-dimensional grid. This process decomposes the spatial structure of the simulated rainfall test area into ordered paths in two dimensions: horizontal and vertical, laying the foundation for subsequent evaluation of the spatial uniformity of rainfall in different directions.

[0046] The direction of the line analysis corresponds to the ordered rainfall sequence. Indicates the first The ordered rainfall sequence corresponding to the direction of the strip analysis, Indicates the first The first line of analysis direction The original rainfall at each monitoring point This represents the index of the monitoring point along the row analysis direction. Using this extraction rule, the original rainfall is extracted from the original dataset sequentially along each row analysis direction. The order of elements in each ordered rainfall sequence directly corresponds to the actual spatial position from left to right on that row, thus explicitly reorganizing the data that was originally stored continuously in row priority order in the original dataset into a sequence with a clear spatial direction.

[0047] Similarly, in the ordered rainfall sequences corresponding to the analysis directions, Indicates the first The ordered rainfall sequence corresponding to the direction of the analysis is listed in the column. Indicates the first In the direction of list analysis, the first The original rainfall at each monitoring point This represents the index of the monitoring point along the column analysis direction. When extracting along the column analysis direction, elements are arranged in spatial order from top to bottom, corresponding to the skip index stored in the original dataset in row-major order.

[0048] By establishing ordered rainfall sequences in both row and column analysis directions, the method of this invention decomposes the spatially ordered association on a two-dimensional plane into independent ordered associations in two one-dimensional directions. This allows the gradual trend or abrupt inflection point in each direction to be captured separately, thus avoiding the spatial pattern confusion problem caused by the traditional method of mixing statistics in all directions. This technical effect directly solves the deficiency in the prior art of being unable to distinguish between "more in the east and less in the west" and "random mottled patterns," because the monotonic change trend in the row analysis direction corresponds to east-west gradual change, while the monotonic change trend in the column analysis direction corresponds to north-south gradual change. Combining the two can accurately locate uneven spatial regions.

[0049] Preferably, the spatial analysis direction can also be along the diagonal direction or radial direction of the two-dimensional grid; the number of row analysis directions is equal to the number of rows of the two-dimensional grid, and the number of column analysis directions is equal to the number of columns of the two-dimensional grid.

[0050] Furthermore, based on the location of each monitoring point along the spatial analysis direction, each original rainfall amount in the ordered rainfall sequence is processed by grey accumulation to obtain the cumulative sequence corresponding to each spatial analysis direction, including: Based on the row and column labels of all raw rainfall amounts in the ordered rainfall sequence, each raw rainfall amount in the ordered rainfall sequence is gray-accumulated along the corresponding spatial analysis direction with all preceding raw rainfall amounts at the corresponding position, resulting in an accumulated sequence along the spatial analysis direction. The function expression for accumulating the raw rainfall amounts is:

[0051] In the formula, Indicates the first The cumulative rainfall value of each monitoring point plus the previous monitoring point. Indicates the index of the monitoring point. Represents the first in an ordered rainfall sequence The original rainfall, This represents the total number of original rainfall amounts in an ordered rainfall sequence.

[0052] Through the implementation of the above-described method for analyzing the spatial uniformity of rainfall, the core technical effect of gray accumulation lies in using the transitivity of the accumulation process to suppress random fluctuations. The functional expression for gray accumulation is: ,in By summing the original rainfall at each monitoring point with the original rainfall at all preceding monitoring points, the originally isolated and potentially transiently disturbed original values ​​are transformed into a gradually accumulating total. This accumulation process causes positive and negative random errors to cancel each other out along the accumulation path, while the actual increase or decrease trend of rainfall along the spatial analysis direction is significantly enhanced due to the same-direction superposition.

[0053] For small-sample conditions in simulated rainfall experiments, where the number of monitoring points is typically limited, this grey accumulation processing effectively solves the problems of traditional methods being sensitive to data characteristics and easily affected by outliers. Because an occasional deviation of a single monitoring point from the norm only produces minor local fluctuations in the accumulation sequence, it does not alter the overall monotonic trend, thus significantly improving the stability and noise resistance of the analysis results. Furthermore, since the accumulation processing is strictly performed along the spatial analysis direction according to the index order of the monitoring points, each... The values ​​all carry comprehensive information from the starting point to the current location of all monitoring points, enabling subsequent trend fitting to capture the cumulative change pattern of rainfall in the spatial direction from a global perspective, rather than relying solely on the discrete values ​​of each point.

[0054] Preferably, the gray accumulation processing is a single-step gray accumulation generation process, where each element in the accumulated sequence represents the previous... Cumulative rainfall values ​​at each monitoring point.

[0055] Furthermore, at least two different orders of trend fitting are performed on each cumulative sequence, and the goodness of fit for each order is obtained. Based on the goodness of fit that meets preset conditions, the trend model corresponding to each spatial analysis direction is selected, including: A first-order polynomial model is established to linearly fit each cumulative sequence. The functional expression of the first-order polynomial model is as follows:

[0056] In the formula, Represents the first-order polynomial model for the th element in the cumulative sequence. The predicted value of the cumulative rainfall. Indicates linear slope. Represents a constant term; A second-order polynomial model and a third-order polynomial model are established to perform nonlinear fitting on each cumulative sequence. The functional expressions of the second-order polynomial model and the third-order polynomial model are as follows:

[0057]

[0058] In the formula, This represents the second-order polynomial model for the cumulative sequence of the nth... The predicted value of the cumulative rainfall. The fitting coefficients represent the control coefficients for the curvature of the quadratic term. The fitting coefficient represents the control for the linear trend of the first-order term. Represents a constant term. This represents the third-order polynomial model for the cumulative sequence of the th... The predicted value of the cumulative rainfall. The fitting coefficients represent the control coefficients for the curvature of the cubic term. The fitting coefficient represents the control for the linear trend of the quadratic term. The fitting coefficient represents the control for the linear trend of the first-order term. Represents a constant term; The goodness of fit between the first-order polynomial model, the second-order polynomial model, and the third-order polynomial model and the cumulative sequence are calculated respectively. The polynomial model with the largest goodness of fit value that is greater than the preset goodness of fit threshold is selected as the trend model corresponding to each spatial analysis direction.

[0059] By implementing the above-mentioned method for analyzing the spatial uniformity of rainfall, first-order polynomial models, second-order polynomial models, and third-order polynomial models are established to fit each cumulative sequence. This process enables the automatic identification of different variation patterns of rainfall along the spatial analysis direction.

[0060] First-order polynomial models correspond to linear trends, second-order polynomial models to parabolic trends (such as increasing then decreasing or decreasing then increasing), and third-order polynomial models to more complex S-shaped or nonlinear trends with inflection points. In simulated rainfall experiments, the spatial distribution characteristics differ significantly under different conditions. Some exhibit linear decreases (such as wind field attenuation near the boundary), some show a symmetrical distribution with high values ​​in the middle and low values ​​on both sides, and some exhibit complex fluctuations. A single-order model cannot simultaneously adapt to all situations. However, by constructing three polynomial models of different orders, the method of this invention can adaptively identify the model form that best matches the actual distribution pattern from the data.

[0061] The goodness of fit of first-order, second-order, and third-order polynomial models to the cumulative sequence was calculated separately. Goodness of fit quantitatively reflects the explanatory power of each model for the cumulative sequence; a higher value indicates a more accurate description of the cumulative sequence's trajectory. The polynomial model with the highest goodness of fit exceeding a preset threshold was selected as the trend model for each spatial analysis direction. This selection mechanism ensures that the final trend model is both the best-fitting model and statistically significant, avoiding the misselection of low-quality models when data exhibits significant random fluctuations. Through this adaptive modeling process, the method of this invention can not only accurately identify whether the change in rainfall along the spatial analysis direction is linear or nonlinear, but also directly determine the complexity of the change pattern based on the order of the selected model. This provides an accurate mathematical basis for subsequently extracting the rate of change and trend inflection points, fundamentally overcoming the technical deficiency of traditional methods in failing to capture specific change patterns.

[0062] Preferably, the preset goodness-of-fit threshold is 0.95. If the goodness-of-fit of all models... If all three values ​​are below 0.95, the spatial trend of rainfall in this analysis direction is considered chaotic, requiring comprehensive judgment in conjunction with other analysis directions. The model with the highest goodness of fit among the three models... If the value is greater than or equal to 0.95, then the model is considered the optimal trend model.

[0063] More preferably, the goodness of fit can be calculated as follows: First, calculate the total sum of squares of deviations of all cumulative rainfall values ​​in the cumulative series around their arithmetic mean. This total sum of squares reflects the overall volatility of the cumulative series itself. Then, calculate the sum of squares of residuals between the predicted values ​​of each polynomial model and the actual cumulative rainfall values ​​in the cumulative series. This sum of squares of residuals reflects the volatility that the model failed to explain. Divide the sum of squares of residuals by the total sum of squares to obtain the unexplained proportion. Subtract this proportion from the value of 1 to obtain the goodness of fit value. The closer the goodness of fit is to 1, the smaller the proportion of the residual sum of squares predicted by the model to the total sum of squares, meaning that the model can explain most of the volatility information in the cumulative series.

[0064] Furthermore, based on the trend model analysis, the rate of change and trend inflection points of rainfall along the corresponding spatial analysis direction are extracted, including: Taking the first derivative of each trend model yields the rate of change representation function corresponding to each spatial analysis direction. The expression for the rate of change representation function is as follows: In the formula, Indicates the first The rate of change at each monitoring point This indicates that the trend model applies to the th cumulative series. The predicted value of the cumulative rainfall. This indicates the trend model with respect to the independent variables. The first derivative; Taking the first derivative of the function representing the rate of change again and setting it to zero, we can obtain the position of the trend inflection point in the corresponding spatial analysis direction. The functional expression for the first derivative and solution of the function representing the rate of change is as follows:

[0065]

[0066] In the formula, The representation function of the rate of change with respect to the independent variable The first derivative, Indicates the index of the trend inflection point.

[0067] By implementing the above-described method for analyzing the spatial uniformity of rainfall, the first derivative of each trend model is used to obtain the rate of change characteristic function corresponding to each spatial analysis direction. The differentiation operation transforms the original model describing the trend of cumulative changes into a function describing the instantaneous rate of change. The values ​​at any monitoring point directly and quantitatively reflect the rate at which rainfall changes with the monitoring point number at that location. When A positive value indicates that rainfall is increasing along the direction of spatial analysis, while a negative value indicates that it is decreasing. The larger the absolute value, the more drastic the change. This effect allows the method of the present invention to clearly answer the refined questions of "from which direction does the non-uniformity begin to change" and "how fast does the change occur," filling the gap in the traditional uniformity coefficient method, which can only provide a general score and cannot provide information on the direction of change.

[0068] By taking the first derivative of the function representing the rate of change and setting it to zero, the location of the trend inflection point in the corresponding spatial analysis direction is obtained. By solving for the extreme points of the rate of change function, the spatial location of the transition in rainfall change patterns is precisely pinpointed. For example, the turning point from increasing to decreasing or from decreasing to increasing. Because... It serves as the location index for trend inflection points, directly corresponding to the specific coordinates of a monitoring point in the original two-dimensional grid. Therefore, it provides a clear spatial location basis for uneven regions. By simultaneously obtaining the rate of change and the location of trend inflection points in each spatial analysis direction, a complete quantitative description of the spatial variation process of rainfall is achieved, providing a crucial mathematical foundation for subsequent assessment of the stability of changes and the location of uneven regions.

[0069] Preferably, the absolute value of the rate of change reflects the speed of spatial change of rainfall at the corresponding location; the gradient of change can also be obtained by calculating the rate difference between adjacent monitoring points, the sign of the gradient of change indicates the increasing or decreasing trend of the rate of change, and the absolute value indicates the steepness of the gradient of change; the inflection point of the trend corresponds to the turning point of the spatial change pattern of rainfall.

[0070] Furthermore, the coefficient of variation of the acquisition rate and the inflection point influence are calculated, including: Based on the characteristic function of the rate of change, the rate variation coefficient along the corresponding spatial analysis direction is calculated. The functional expression for calculating the rate variation coefficient is:

[0071] In the formula, Represents the rate of variation coefficient. The standard deviation of the function representing the rate of change at each monitoring point location. The arithmetic mean of the values ​​of the function representing the rate of change at each monitoring point; If the solution of the first derivative of the rate of change characterization function has a trend inflection point, and the location of the trend inflection point is within the monitoring point location along the corresponding spatial analysis direction, then the inflection point influence degree can be calculated based on the rate of change characterization function. The functional expression for calculating the inflection point influence degree is as follows:

[0072] In the formula, Indicates the degree of influence of the inflection point. Indicates the location of the trend inflection point. The average rate of change at each monitoring point previously, Indicates the location of the trend inflection point. The average rate of change at each monitoring point thereafter.

[0073] By implementing the above-described method for analyzing the spatial uniformity of rainfall, the rate variation coefficient is essentially the ratio of the standard deviation to the mean of the rate of change, a dimensionless measure of dispersion. This calculation normalizes the overall fluctuation range of the rate of change sequence relative to its average level, eliminating the influence of the absolute value of the rate of change under different rainfall intensities or spatial spans on the dispersion evaluation. A small rate variation coefficient indicates a high concentration of rate of change values ​​at each monitoring point along the spatial analysis direction, meaning that the rate of change of rainfall with location remains basically consistent throughout the entire path, reflecting a uniform and stable gradual change in the spatial distribution of rainfall. Conversely, a large rate variation coefficient indicates significant differences in the rate of change at different locations, with localized sharp fluctuations or non-uniform acceleration / deceleration phenomena. This effect allows the method of this embodiment to quantitatively evaluate the stability of spatial changes in rainfall as a whole, overcoming the shortcomings of traditional uniformity coefficient methods that only focus on the dispersion of rainfall while ignoring the consistency of the rate of change.

[0074] The inflection point impact, by comparing the average difference in the rate of change between the two stages before and after the inflection point, quantitatively characterizes the severity of the shift in rainfall change patterns at the trend inflection point. When the average rate of change before and after the inflection point differs greatly, the absolute value of the inflection point impact is large, indicating a sudden change in the spatial trend of rainfall near the inflection point, such as a sharp shift from rapid increase to rapid decrease. This sudden change often corresponds to physical fault locations such as the boundary of sprinkler overlap areas or abnormal pipe pressure points. Conversely, if the inflection point impact is close to zero, it indicates that although there is an inflection point in the trend, the transition is gradual, and the impact on overall uniformity is small. This effect allows the method of this invention to not only locate the spatial position of the trend inflection point but also assess the actual impact of the inflection point on the spatial distribution of rainfall. This helps to distinguish between significantly uneven locations that require special attention and acceptable minor fluctuations, providing a quantitative basis for prioritizing the optimization and adjustment of simulated rainfall systems.

[0075] As mentioned above, the goodness of fit reflects the explanatory power of the trend model for the cumulative sequence. The higher the value, the more definite the spatial variation of rainfall along that direction is, rather than random fluctuations. The rate of variation coefficient reflects the dispersion of the rate of change at each monitoring point. The smaller the value, the more consistent the speed of rainfall change with location along the entire path, and the more stable the spatial distribution. The inflection point influence reflects the degree of difference in the average level of the rate of change before and after the trend inflection point. The smaller the value, the smoother the change pattern transition, and vice versa, there are local abrupt changes.

[0076] By analyzing the goodness of fit, rate coefficient of variation, and inflection point influence of the trend model through pre-set multi-dimensional evaluation indicators, the rainfall evenness in each spatial analysis direction no longer relies on a single general coefficient, but instead obtains quantitative conclusions from three independent dimensions: trend regularity, stability of change, and severity of abrupt changes. The process of analyzing each value compares the goodness of fit, rate coefficient of variation, and inflection point influence with their respective pre-set threshold ranges. Only when all three dimensions simultaneously meet all the threshold conditions for a certain level is that level determined as the judgment level of rainfall evenness in that spatial analysis direction.

[0077] For example: in the uniformity rating criteria calibrated based on a large amount of simulated rainfall test data, when the goodness of fit... ≥0.98, rate variation coefficient ≤0.05 and inflection point influence A goodness of fit of <0.1 is considered excellent, indicating uniform spatial distribution and stable trend in rainfall; when the goodness of fit is 0.95 ≤ <0.98, the rate variation coefficient satisfies 0.05 < ≤0.10 and A value ≤ 0.2 is considered good, indicating a relatively uniform spatial distribution of rainfall with only slight ordered variations; the goodness of fit satisfies 0.90 ≤ <0.95, the rate variation coefficient satisfies 0.10 < ≤0.15 and A value ≤0.3 is considered acceptable, indicating that the spatial distribution of rainfall basically meets the experimental requirements and exhibits acceptable orderly variation. If the goodness of fit... <0.90, or rate variation coefficient >0.15, or the degree of influence at the inflection point If the goodness of fit is greater than 0.3 and the proportion of significant inflection points to the total number of inflection points is ≥30%, it is judged as unqualified. In this case, the spatial distribution of rainfall is uneven and there are significant disordered fluctuations or drastic changes. When the goodness of fit of all trend models in a certain spatial analysis direction is <0.90, the spatial trend of rainfall in that direction is judged to be chaotic, and it is necessary to make a comprehensive judgment in combination with other analysis directions.

[0078] Based on the analysis results of rainfall uniformity in each spatial analysis direction, the corresponding judgment level is determined. Then, by integrating the analysis results and judgment levels from all spatial analysis directions, the overall uniformity level and the location of non-uniform areas within the simulated rainfall test area can be determined. The integration process utilizes the spatial orthogonality of row and column directions: if an ordered rainfall sequence in a certain row direction shows a trend inflection point at a specific monitoring point index, and the corresponding column direction also exhibits abnormal changes near the same spatial coordinates, then the spatial intersection of the inflection points in both directions can accurately pinpoint the monitoring point area in the two-dimensional grid where rainfall abruptly changes. The final output of the overall uniformity level and the location of non-uniform areas directly answers refined questions such as "where exactly is the non-uniformity manifested?", "from which direction does the change begin?", and "is the trend linear or non-linear?", providing clear quantitative guidance for nozzle layout optimization, pipeline pressure regulation, or fault diagnosis in simulated rainfall systems.

[0079] This invention also discloses an analysis system applied to the above-mentioned gray accumulation-based rainfall spatial evenness analysis method. The analysis system includes: The data acquisition module is used to obtain the raw rainfall data collected by each monitoring point from multiple monitoring points pre-distributed in a two-dimensional grid within the simulated rainfall test area, thus obtaining the raw dataset. The data extraction module is used to set at least one spatial analysis direction and extract the original rainfall data in the original dataset in sequence according to the location of each monitoring point in the spatial analysis direction, so as to obtain the ordered rainfall sequence corresponding to each spatial analysis direction. The data processing module is used to perform gray accumulation processing on each raw rainfall amount in the ordered rainfall sequence according to the location of each monitoring point in the spatial analysis direction, so as to obtain the cumulative sequence corresponding to each spatial analysis direction. The data fitting module is used to perform trend fitting on each cumulative sequence at least two different orders and obtain the goodness of fit of different orders. Based on the goodness of fit that meets the preset conditions, the trend model corresponding to each spatial analysis direction is selected. The feature parameter quantification module is used to extract the rate of change and trend inflection point of rainfall along the corresponding spatial analysis direction based on the trend model analysis, and to calculate and obtain the rate of variation coefficient and the inflection point influence. The uniformity evaluation module is used to analyze the goodness of fit, rate coefficient of variation and inflection point influence of the trend model one by one according to the preset multidimensional evaluation indicators, and obtain the analysis results of rainfall uniformity in each spatial analysis direction. The rating module is used to determine the rating of rainfall uniformity in the corresponding spatial analysis direction based on the analysis results, and to determine the overall uniformity rating and the location of non-uniform areas in the simulated rainfall test area by combining the analysis results and ratings in all spatial analysis directions.

[0080] The present invention also discloses an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-mentioned method for analyzing the spatial uniformity of rainfall based on gray accumulation.

[0081] The present invention also discloses a storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described method for analyzing the spatial uniformity of rainfall based on gray accumulation.

[0082] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0083] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0084] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0085] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of processing steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0086] It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Those skilled in the art can modify the technical solutions described in the above embodiments, or make equivalent substitutions for some of the technical features; and all such modifications and substitutions should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for analyzing the spatial uniformity of rainfall based on grey accumulation, characterized in that: The method for analyzing the spatial uniformity of rainfall includes: Based on multiple monitoring points pre-distributed in a two-dimensional grid within the simulated rainfall test area, the raw rainfall data collected at each monitoring point is obtained to obtain the raw dataset; At least one spatial analysis direction is set, and the original rainfall in the original dataset is extracted sequentially according to the position of each monitoring point along the spatial analysis direction to obtain an ordered rainfall sequence corresponding to each spatial analysis direction. Based on the location of each monitoring point along the spatial analysis direction, gray accumulation processing is performed on each original rainfall amount in the ordered rainfall sequence to obtain the cumulative sequence corresponding to each spatial analysis direction. For each of the cumulative sequences, at least two different orders of trend fitting are performed, and the goodness of fit of different orders is obtained. Based on the goodness of fit that meets the preset conditions, the trend model corresponding to each of the spatial analysis directions is selected. Based on the analysis of the trend model, the rate of change and trend inflection point of rainfall along the corresponding spatial analysis direction are extracted, and the rate of variation coefficient and inflection point influence are calculated. The goodness of fit of the trend model, the rate of variation coefficient and the inflection point influence are analyzed one by one according to the preset multidimensional evaluation index to obtain the analysis results of rainfall uniformity in each of the spatial analysis directions. Based on the analysis results, the determination level of rainfall uniformity in the corresponding spatial analysis direction is determined. Combining the analysis results and determination levels in all spatial analysis directions, the overall uniformity level and the location of non-uniform areas in the simulated rainfall test area are determined.

2. The method for analyzing the spatial uniformity of rainfall based on gray accumulation according to claim 1, characterized in that, The process of obtaining the raw rainfall data collected at each monitoring point to obtain the raw dataset includes: The simulated rainfall intensity is controlled, and after the rainfall intensity reaches a stable state, the rainfall at each monitoring point is continuously collected within a preset time period to obtain the original rainfall at each monitoring point; Based on the row and column positions of each monitoring point in the two-dimensional grid, all the original rainfall data are arranged and labeled according to the distribution of the monitoring points to obtain the original dataset. The expression for the original dataset is: In the formula, Represents the original dataset. Indicates the mark as the first Line 1 The original rainfall of the column, Indicates the row position index. Indicates the column position index.

3. The method for analyzing the spatial uniformity of rainfall based on gray accumulation according to claim 2, characterized in that, The step of setting at least one spatial analysis direction and, based on the location of each monitoring point along the spatial analysis direction, sequentially extracting the original rainfall data from the original dataset to obtain an ordered rainfall sequence corresponding to each spatial analysis direction includes: Based on the form of the two-dimensional grid, several row analysis directions and several column analysis directions are defined; Based on the row labels of all the original rainfall amounts in the original dataset, multiple original rainfall amounts are extracted sequentially from the original dataset along each row analysis direction to obtain the ordered rainfall sequence corresponding to each row analysis direction. The functional expression for the ordered rainfall sequence corresponding to each row analysis direction is: in, Indicates the first The ordered rainfall sequence corresponding to the direction of the strip analysis, Indicates the first The first line of analysis direction The original rainfall at each monitoring point Indicates the index of the monitoring point along the line analysis direction; Based on the column labels of all the original rainfall amounts in the original dataset, multiple original rainfall amounts are extracted sequentially from the original dataset along each column analysis direction to obtain the ordered rainfall sequence corresponding to each column analysis direction. The function expression for the ordered rainfall sequence corresponding to each column analysis direction is: In the formula, Indicates the first The ordered rainfall sequence corresponding to the direction of the analysis is listed in the column. Indicates the first In the direction of list analysis, the first The original rainfall at each monitoring point This indicates the index of the monitoring point along the column analysis direction.

4. The method for analyzing the spatial uniformity of rainfall based on gray accumulation according to claim 3, characterized in that, The step of performing gray accumulation processing on each of the original rainfall amounts in the ordered rainfall sequence according to the positions of the monitoring points along the spatial analysis direction to obtain the cumulative sequence corresponding to each spatial analysis direction includes: Based on the row and column labels of all the original rainfall amounts in the ordered rainfall sequence, each original rainfall amount in the ordered rainfall sequence is gray-accumulated along the corresponding spatial analysis direction with all the preceding original rainfall amounts at the corresponding position, to obtain the cumulative sequence along the spatial analysis direction. The function expression for accumulating the original rainfall amounts is: In the formula, Indicates the first The cumulative rainfall value of each monitoring point plus the previous monitoring point. Indicates the index of the monitoring point. Represents the first in an ordered rainfall sequence The original rainfall, This represents the total number of original rainfall amounts in an ordered rainfall sequence.

5. The method for analyzing the spatial uniformity of rainfall based on gray accumulation according to claim 4, characterized in that, The process of performing at least two different orders of trend fitting on each of the cumulative sequences and obtaining the goodness of fit for each order, and selecting the trend model corresponding to each of the spatial analysis directions based on the goodness of fit that meets preset conditions, includes: A first-order polynomial model is established to linearly fit each of the cumulative sequences. The functional expression of the first-order polynomial model is as follows: In the formula, Represents the first-order polynomial model for the cumulative sequence of the nth... The predicted value of the cumulative rainfall. Indicates linear slope, Represents a constant term; A second-order polynomial model and a third-order polynomial model are established to perform nonlinear fitting on each of the accumulated sequences, and the functional expressions of the second-order polynomial model and the third-order polynomial model are respectively: In the formula, This represents the second-order polynomial model for the cumulative sequence of the nth... The predicted value of the cumulative rainfall. The fitting coefficients represent the control coefficients for the curvature of the quadratic term. The fitting coefficient represents the control for the linear trend of the first-order term. Represents a constant term. This represents the third-order polynomial model for the cumulative sequence of the th... The predicted value of the cumulative rainfall. The fitting coefficients represent the control coefficients for the curvature of the cubic term. The fitting coefficient represents the control for the linear trend of the quadratic term. The fitting coefficient represents the control for the linear trend of the first-order term. Represents a constant term; The goodness of fit between the first-order polynomial model, the second-order polynomial model, and the third-order polynomial model and the cumulative sequence are calculated respectively. The polynomial model with the largest goodness of fit value that is greater than a preset goodness of fit threshold is selected as the trend model corresponding to each of the spatial analysis directions.

6. The method for analyzing the spatial uniformity of rainfall based on gray accumulation according to claim 1, characterized in that, The step of extracting the rate of change and trend inflection point of rainfall along the corresponding spatial analysis direction based on the trend model analysis includes: Taking the first derivative of each trend model yields the rate of change representation function corresponding to each spatial analysis direction. The expression for the rate of change representation function is as follows: In the formula, Indicates the first The rate of change at each monitoring point This indicates that the trend model applies to the th cumulative series. The predicted value of the cumulative rainfall. This indicates the trend model with respect to the independent variables. The first derivative; The first derivative of the function representing the rate of change is taken again, and the derivative is set to zero. The position of the trend inflection point corresponding to the spatial analysis direction is obtained. The functional expression of the function representing the rate of change after taking the first derivative and solving is as follows: In the formula, The representation function of the rate of change with respect to the independent variable The first derivative, Indicates the index of the trend inflection point.

7. The method for analyzing the spatial uniformity of rainfall based on gray accumulation according to claim 1, characterized in that, The calculation of the rate of variation coefficient and the inflection point influence includes: Based on the characteristic function of the rate of change, the rate variation coefficient corresponding to the spatial analysis direction is calculated, and the functional expression for calculating the rate variation coefficient is: In the formula, Represents the rate of variation coefficient. The standard deviation of the function representing the rate of change at each monitoring point location. The arithmetic mean of the values ​​of the function representing the rate of change at each monitoring point; If the solution of the first derivative of the rate of change characterization function has a trend inflection point, and the location of the trend inflection point is within the monitoring point location corresponding to the spatial analysis direction, then the inflection point influence degree is calculated according to the rate of change characterization function. The functional expression for calculating the inflection point influence degree is as follows: In the formula, Indicates the degree of influence of the inflection point. Indicates the location of the trend inflection point. The average rate of change at each monitoring point previously, Indicates the location of the trend inflection point. The average rate of change at each monitoring point thereafter.

8. An analysis system, characterized in that, The analysis system, applied to the gray-accumulation-based rainfall spatial uniformity analysis method according to any one of claims 1-7, comprises: The data acquisition module is used to obtain the raw rainfall data collected by each of the multiple monitoring points pre-distributed in a two-dimensional grid within the simulated rainfall test area, thereby obtaining the raw dataset. The data extraction module is used to set at least one spatial analysis direction and extract the original rainfall from the original dataset in sequence according to the position of each monitoring point in the spatial analysis direction, so as to obtain an ordered rainfall sequence corresponding to each spatial analysis direction. The data processing module is used to perform gray accumulation processing on each of the original rainfall amounts in the ordered rainfall sequence according to the positions of the monitoring points in the spatial analysis direction, so as to obtain the cumulative sequence corresponding to each spatial analysis direction; The data fitting module is used to perform at least two different orders of trend fitting on each of the cumulative sequences, obtain the goodness of fit of different orders, and select the trend model corresponding to each of the spatial analysis directions according to the goodness of fit that meets the preset conditions. The feature parameter quantification module is used to extract the rate of change and trend inflection point of rainfall along the corresponding spatial analysis direction based on the analysis of the trend model, and to calculate and obtain the rate of variation coefficient and the inflection point influence. The uniformity evaluation module is used to analyze the goodness of fit of the trend model, the rate variation coefficient and the inflection point influence degree one by one according to the preset multidimensional evaluation index, so as to obtain the analysis results of rainfall uniformity in each spatial analysis direction. The rating module is used to determine the rating of rainfall uniformity in the corresponding spatial analysis direction based on the analysis results, and to determine the overall uniformity rating and the location of non-uniform areas in the simulated rainfall test area by combining the analysis results and ratings in all spatial analysis directions.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method for analyzing the spatial uniformity of rainfall based on gray accumulation as described in any one of claims 1-7.

10. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the gray accumulation-based rainfall spatial uniformity analysis method as described in any one of claims 1-7.

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