An extreme wind field discrimination method based on non-equilibrium wasserstein distance

Abstract

This invention discloses an extreme wind field discrimination method based on non-equilibrium Wasserstein distance, belonging to the field of meteorological wind energy prediction technology. The method includes the following steps: obtaining a set of wind field samples in the study area during the target period to construct a reference field; calculating the non-equilibrium Wasserstein distance between each wind field sample and the reference field as an extremity index; fitting the statistical distribution of the extremity index; calculating an extreme discrimination threshold based on the fitted GEV distribution model; and comparing the extreme index with the extreme discrimination threshold to determine whether the wind field sample is an extreme event or a non-extreme event. This invention, employing the aforementioned extreme wind field discrimination method based on non-equilibrium Wasserstein distance, can provide a high-precision foundation for identifying typical extreme wind fields and constructing scenarios for research such as climate change scenario analysis, extreme scenario risk assessment, renewable energy uncertainty quantification, and energy system resilience optimization.

Description

Technical Field

[0001] This invention relates to the field of meteorological wind energy forecasting technology, and in particular to an extreme wind field discrimination method based on non-equilibrium Wasserstein distance. Background Technology

[0002] Traditional methods for identifying extreme wind fields typically follow a two-step paradigm: feature reduction followed by threshold determination. First, the two-dimensional wind field data is compressed into scalar extremeity indicators, commonly including extreme wind speeds (maximum / minimum), over-threshold coverage area, and regional statistics (mean, summation, etc.). Then, this indicator is compared with a threshold determined based on a historical reference period. When the indicator falls into the upper (or lower) tail of the distribution, it is determined to be an extreme high (or low) wind event. Threshold determination methods mainly fall into two categories: one is based on empirical quantiles (e.g., using the 98th percentile of the reference period as the extreme threshold); the other is based on tail modeling of extreme value theory (EVT), including the Block Maxima method (fitting a generalized extreme value distribution GEV to the block maximum to calculate the return period threshold) and the over-threshold peak method (fitting a generalized Pareto distribution GPD to the over-threshold excess).

[0003] However, the aforementioned dimensionality reduction strategies have limitations: the scaling process inevitably leads to the loss of spatial structural information, making it difficult to simultaneously characterize the intensity and spatial morphology of wind fields. Specifically, point-scale indicators such as extreme wind speeds are highly sensitive to local noise and completely ignore the spatial extent, geometric shape, and location variations of extreme events; while aggregate indicators such as regional mean can reflect overall intensity, they smooth out spatial heterogeneity, leading to wind fields with significantly different spatial distributions but similar statistical values ​​being misjudged as similar. Summary of the Invention

[0004] The purpose of this invention is to provide an extreme wind field discrimination method based on non-equilibrium Wasserstein distance, thereby solving the problems mentioned in the background art.

[0005] To achieve the above objectives, this invention provides a method for identifying extreme wind fields based on non-equilibrium Wasserstein distance, comprising the following steps: S1. Obtain a set of wind field samples in the study area during the target period and construct a reference field. The reference field is used to characterize the non-extreme wind field features in the study area. S2. Calculate the non-equilibrium Wasserstein distance between each wind field sample and the reference field, as an extreme indicator that simultaneously characterizes the differences in wind speed intensity and spatial distribution. S3. Using the generalized extreme value GEV distribution, the statistical distribution of the extreme index is fitted to obtain the fitted GEV distribution model. S4. Based on the fitted GEV distribution model, calculate the quantile corresponding to the target return period, or calculate the empirical threshold as the extreme discrimination threshold for the wind field sample. S5. Compare the extreme index of each wind field sample with the extreme discrimination threshold to determine whether the wind field sample is an extreme event or a non-extreme event.

[0006] Preferably, in step S1, the mean wind field of the wind field sample set is selected as the reference wind field.

[0007] Preferably, S2 uses the non-equilibrium Wasserstein distance as a metric to calculate the degree of deviation of each wind field sample relative to the reference wind field, and uses the quantified result of this deviation as an extreme index.

[0008] Preferably, the calculation of the unbalanced Wasserstein distance in S2 includes a source-side marginal distribution difference penalty term and a target-side marginal distribution difference penalty term, both of which are derived from the transmission scheme.

[0009] Preferably, the extreme index in S2 simultaneously measures the difference in wind speed intensity and spatial distribution between the wind field sample and the reference field, and this measurement method allows for situations where the total wind field volume of the wind field sample and the reference field are inconsistent.

[0010] Preferably, step S3 performs statistical modeling on the extreme index sequence, constructs the cumulative distribution function CDF of the extreme index using the generalized extreme value (GEV) distribution, fits the statistical distribution of the extreme index, and obtains the fitted GEV distribution model.

[0011] Preferably, S4 uses a quantile threshold to identify extreme events, and the quantile threshold satisfies a preset calculation formula.

[0012] Preferably, the discrimination rule in S5 is as follows: If the extreme index of a wind field sample is greater than or equal to the extreme event discrimination threshold, then the wind field sample is determined to be an extreme event; otherwise, the wind field sample is determined to be a non-extreme event.

[0013] Therefore, the present invention employs the above-mentioned extreme wind field discrimination method based on non-equilibrium Wasserstein distance, which has the following beneficial effects: (1) This invention can simultaneously characterize wind field intensity differences and spatial distribution differences. Compared with indicators based solely on point values ​​or regional summary statistics, this scheme uses non-equilibrium Wasserstein distance to measure the deviation of the wind field from the reference wind field, so that the extreme indicators simultaneously include information on wind speed amplitude changes and spatial morphological changes, which is suitable for identifying typical spatial pattern differences such as wind belt translation, range expansion and local enhancement.

[0014] (2) This invention is applicable to situations where the total amount of wind field is inconsistent, improving the comparability of samples and the stability of discrimination. By introducing marginal relaxation and KL penalty terms into the optimal transmission framework, this scheme does not require strict conservation of the total amount on the source side and the target side, and can maintain stable comparison even when the overall intensity level changes, reducing misjudgments caused by confusing the total amount change with spatial rearrangement.

[0015] (3) The discrimination threshold of the present invention is interpretable and adjustable. The extreme index sequence is modeled with a generalized extreme value distribution and discriminated using a quantile threshold, so that the extreme judgment directly corresponds to the tail probability level, which makes it easy to adjust the tail ratio according to risk preference or research needs and improve the reproducibility of the results.

[0016] (4) This invention can realize a unified identification framework for extreme high winds and extreme low winds. By unifying the construction of indicators and the tail discrimination method, extreme high winds and extreme low winds can be identified separately or simultaneously in the same process, reducing the scale inconsistency problem caused by using different empirical rules for the two types of events.

[0017] (5) This invention has strong applicability and is easy to migrate to different regions and different data sources. This scheme is designed for constructing extreme indexes and discrimination processes for two-dimensional nonnegative scalar fields defined on discrete grids, without relying on wind field-specific physical parameters or empirical thresholds.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating an embodiment of an extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to the present invention. Figure 2 These are five representative wind events from different periods in an embodiment of an extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to the present invention. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0022] Example Please see Figure 1-Figure 2 This invention provides a method for identifying extreme wind fields based on non-equilibrium Wasserstein distance. Addressing the limitations of existing technologies, it proposes an extremity measurement framework based on non-equilibrium optimal transport theory. The non-equilibrium Wasserstein distance (Wittstein distance) is introduced to measure the difference between the sample to be judged and the reference field, quantifying wind field extremity as a joint space-intensity cost under optimal transport. This metric maintains the spatial structure integrity of the field during comparison, simultaneously quantifying intensity and spatial displacement deviations. By combining extreme value theory with tail distribution modeling of the distance sequence, the sensitivity to identifying extreme spatial patterns can be significantly improved while maintaining the interpretability of the statistical framework. The method includes the following steps: S1. Obtain a set of wind field samples for the study area during the target period and construct a reference field to characterize non-extreme wind field features. In this embodiment, extreme wind scenarios are identified for four future periods: 2030-2040, 2040-2050, 2050-2060, and 2060-2070. A total of 14,610 diurnal near-surface wind speed samples from 2030 to 2070 are selected as the research object. The samples are derived from simulation data of the BCC-CSM2-MR climate model in CMIP6 under the SSP2-4.5 carbon emission scenario. The geographical range of the study area is 109° to 118° east longitude and 20° to 26° north latitude.

[0023] Obtain the wind field sample set for the region to be analyzed within a given time period. The wind field sample set is represented as follows: ; (1) in, Represents a wind field dataset; v n For the first nA two-dimensional wind field sample is defined as a non-negative scalar field on a discrete grid (x,y), representing the wind speed amplitude; n For sample number, n =1,2,…, N V ; N V The total number of samples.

[0024] Constructing a reference wind field v ∗ The sample mean wind field was selected as the reference wind field.

[0025] S2. Calculate the non-equilibrium Wasserstein distance between each wind field sample and the reference field, as an extreme indicator that simultaneously characterizes the differences in wind speed intensity and spatial distribution.

[0026] Wind field measured by nonequilibrium Wasserstein distance v n Relative reference wind field v ∗ The degree of deviation is used as an extreme indicator. , defined as formula (2): (2) in, Indicates the first n wind field sample v n Relative reference wind field v ∗ The unbalanced Wasserstein distance value is used as an indicator of extremes; From position ( x 1, y 1) To position ( x 2, y 2) Allocated transmission volume; The distance between the two positions; p To measure the order, the preferred choice is... p =2. Let be the penalty coefficient, satisfying... >0; This represents the Kullback-Leibler divergence, used to measure the difference between two nonnegative distributions; m , Indicates the transmission plan The induced marginal distributions correspond to the marginal totals on the source and target sides, respectively.

[0027] Source-side marginal distribution m With the original wind field v nThe difference penalty term at each grid point is defined by formula (3), and the target side marginal distribution Compared with reference wind field v ∗ The difference penalty term is defined by formula (4): (3) (4) in, Indicates wind field v n At grid points ( x 1, y 1) The value of ; Indicates reference wind field v ∗ At grid points ( x 2, y 2) The value of ; Indicates from position ( x 1, y 1) Total output data. Indicates the inflow location ( x 2, y 2) Total transmission volume.

[0028] The marginal distribution is derived from the transmission scheme and satisfies formulas (5)-(6): (5) (6) in, Indicates from the source point ( x 1, y 1) The total output transmission volume, which is the sum of the transmission plan at the source point and all destination points; Indicates the flow into the target point ( x 2, y 2) Total transmission volume, which is the sum of the transmission plan at the destination point and all source points.

[0029] Received It can simultaneously measure the intensity and spatial distribution differences of wind fields, and allows for inconsistent total wind field values.

[0030] S3. Use the generalized extreme value (GEV) distribution to fit the statistical distribution of the extreme value index.

[0031] For extreme index sequences Statistical modeling is performed, and the cumulative distribution function is constructed using the generalized extreme value distribution, as shown in formula (7): (7) in, The cumulative distribution function value of the GEV distribution is represented; Pr represents the probability operator. W As the independent variable, it can be understood as the value of the extreme index; W n Indicates the first n Extreme index of a single sample; t These are location parameters used for translational distribution; s For the scale parameter, satisfying s >0, used to control distribution scaling; x These are shape parameters used to control the tail shape; the parameters are preferably estimated using the maximum likelihood method.

[0032] S4. Based on the fitted GEV distribution, calculate the quantile corresponding to the target return period (such as the T-year return threshold), or calculate the empirical threshold (such as the 90th percentile) as the extreme discrimination threshold.

[0033] Quantile threshold To achieve extreme event discrimination, the threshold satisfies formula (8): (8) And it can be transformed into formula (9): (9) in, This represents the threshold for judging extreme events, corresponding to the quantile threshold. It is the inverse function of the cumulative distribution function, i.e., the quantile function; d This represents the tail probability level, satisfying 0 < d <1 is used to specify the upper tail ratio. This embodiment uses the 90th percentile empirically as the extreme discrimination threshold, i.e. δ= 0.9.

[0034] S5. Based on the obtained threshold, determine whether the sample is an extreme event or a non-extreme event.

[0035] when At that time, the first n The wind field was determined to be an extreme wind event; when At that time, it was determined to be a non-extreme event.

[0036] Based on threshold analysis, the total number of extreme wind events identified during 2030-2040 was 383, the total number of extreme wind events identified during 2040-2050 was 386, the total number of extreme wind events identified during 2050-2060 was 396, and the total number of extreme wind events identified during 2060-2070 was 356.

[0037] To facilitate a more intuitive demonstration of extreme wind events, this embodiment further employs a clustering method to extract representative wind events from different periods. The cluster center wind fields of various wind events are then used as corresponding representative wind scenes for display, thereby reflecting the typical spatial distribution characteristics of different extreme wind events. For example... Figure 2 As shown, five representative wind events from different periods are denoted as scenarios. s 1- s 5. The statistical characteristics of each representative wind scenario are shown in Table 1 below. The statistical characteristics include average wind speed, ten-year frequency of each representative wind event, and total frequency of events.

[0038] Table 1 Statistical characteristics of representative wind scenarios

[0039] Depend on Figure 2 As shown in Table 1, there are significant differences in both spatial distribution and statistical characteristics among the representative wind scenarios. s 1 represents an extremely low wind scenario. s 2- s 5 represents different types of extreme high-wind scenarios. The total number of extreme wind events will reach its maximum in 2050-2060, and will decline in 2060-2070. However, the average wind speed and frequency of some high-intensity wind scenarios are still on the rise, indicating that the dominant types and intensity characteristics of extreme wind events have changed significantly in different stages.

[0040] Therefore, the present invention employs the above-mentioned extreme wind field discrimination method based on non-equilibrium Wasserstein distance, which can provide a high-precision foundation for the identification of typical extreme wind fields and the construction of scenarios for climate change scenario analysis, extreme scenario risk assessment, renewable energy uncertainty quantification and energy system resilience optimization.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for identifying extreme wind fields based on non-equilibrium Wasserstein distance, characterized in that, Includes the following steps: S1. Obtain a set of wind field samples in the study area during the target period and construct a reference field. The reference field is used to characterize the non-extreme wind field features in the study area. S2. Calculate the non-equilibrium Wasserstein distance between each wind field sample and the reference field, as an extreme indicator that simultaneously characterizes the differences in wind speed intensity and spatial distribution. S3. Using the generalized extreme value GEV distribution, the statistical distribution of the extreme index is fitted to obtain the fitted GEV distribution model. S4. Based on the fitted GEV distribution model, calculate the quantile corresponding to the target return period, or calculate the empirical threshold as the extreme discrimination threshold for the wind field sample. S5. Compare the extreme index of each wind field sample with the extreme discrimination threshold to determine whether the wind field sample is an extreme event or a non-extreme event.

2. The extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to claim 1, characterized in that: S1 selects the sample mean wind field of the wind field sample set as the reference wind field.

3. The extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to claim 1, characterized in that: The S2 uses the non-equilibrium Wasserstein distance as a metric to calculate the degree of deviation of each wind field sample relative to the reference wind field, and uses the quantified result of this deviation as an extreme index.

4. The extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to claim 3, characterized in that: The calculation of the unbalanced Wasserstein distance in S2 includes a source-side marginal distribution difference penalty term and a target-side marginal distribution difference penalty term, both of which are derived from the transmission scheme.

5. The extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to claim 4, characterized in that: The extreme index in S2 measures both the difference in wind speed intensity and the difference in spatial distribution between the wind field sample and the reference field, and this measurement method allows for situations where the total wind field volume of the wind field sample and the reference field are inconsistent.

6. The extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to claim 1, characterized in that: S3 performs statistical modeling on the extreme index sequence, constructs the cumulative distribution function CDF of the extreme index using the generalized extreme value GEV distribution, fits the statistical distribution of the extreme index, and obtains the fitted GEV distribution model.

7. The extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to claim 1, characterized in that: The S4 uses a quantile threshold to identify extreme events, and the quantile threshold satisfies a preset calculation formula.

8. The extreme wind field discrimination method based on non-equilibrium Wasserstein distance according to claim 1, characterized in that, The specific discrimination rule in S5 is as follows: If the extreme index of a wind field sample is greater than or equal to the extreme event discrimination threshold, then the wind field sample is determined to be an extreme event; otherwise, the wind field sample is determined to be a non-extreme event.

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