A method and system for identifying propagation delay of wake between offshore wind farms

Abstract

The application discloses a method and system for identifying tail flow propagation delay between offshore wind farms, and relates to the technical field of offshore wind farm tail flow effect analysis. The specific implementation scheme is as follows: the wind speed time sequence signals of each wind measurement point in the upstream and downstream of a preset window are obtained, the node set is constructed after standardization, and the upstream and downstream are divided; a sliding step is set in the preset window, the first correlation coefficient of each node pair in the sliding window is calculated, the second correlation coefficient statistical distribution is constructed through phase spectrum resetting, and the effective edge is formed by screening with an adaptive threshold to form a dynamic graph sequence; the birth and death of an isolated downstream component composed of only downstream nodes are monitored, and the time interval from the birth time to the death time is defined as the topological propagation delay. Through the application, the model-free and adaptive identification of tail flow propagation delay is realized from the perspective of dynamic network topology evolution, and a basis is provided for wind farm group cooperative control and power prediction.

Description

Technical Field

[0001] This application relates to the field of offshore wind farm wake effect analysis technology, specifically to a method and system for identifying wake propagation delay between offshore wind farms. Background Technology

[0002] During the operation of offshore wind farm clusters, there is a wake propagation effect between upstream and downstream wind farms arranged sequentially along the prevailing wind direction. The operation of wind turbine generators in the upstream wind farm creates a wake region with reduced wind speed behind them. This wake region propagates downstream with the airflow and, after a certain time delay, affects the inflow wind speed of each wind turbine generator in the downstream wind farm. Accurately identifying the delay time of wake propagation from the upstream wind farm to the downstream wind farm is of significant engineering value for the advanced prediction of downstream wind farm power generation, the formulation of cluster-level collaborative control strategies, and the optimization of overall operational efficiency.

[0003] In existing technologies, methods for identifying wake propagation delays between wind farms mainly fall into two categories. The first category is physical simulation methods based on computational fluid dynamics or engineering wake models. These methods establish a three-dimensional flow field numerical model of the wind farm cluster to simulate the physical processes of wake generation, development, and transport to the downstream wind farm. The time delay of wake influence propagation from upstream to downstream is extracted from the simulation results. This type of method requires the establishment of detailed wind farm geometric models and boundary conditions, resulting in high computational complexity and sensitivity to spatiotemporal changes in inflow wind conditions. When inflow wind conditions undergo unsteady changes... The first type is the numerical model established based on fixed boundary conditions, which cannot update the flow field parameters in real time. The velocity field output by the simulation is different from the real flow field, resulting in the propagation delay extracted from the simulation results deviating from the actual value. The adaptability and real-time performance under different incoming flow conditions are difficult to meet the requirements of online monitoring. The second type is the cross-correlation analysis method based on a fixed threshold. One wind measurement point is selected in the upstream wind farm and one in the downstream wind farm. The cross-correlation coefficient of the wind speed time series of the two wind measurement points is calculated. The time shift when the cross-correlation coefficient exceeds the preset fixed threshold is used as the estimated value of the wake propagation delay.

[0004] The second type of cross-correlation analysis method based on fixed thresholds has the following shortcomings in practical applications: First, the threshold for determining the significance of the correlation is preset by humans, lacking an objective basis for determination based on the statistical characteristics of the data itself. Using different preset fixed thresholds will give drastically different delayed identification results for the same set of data, resulting in strong subjectivity and poor repeatability of the identification results. Second, this method only uses the cross-correlation information of a single wind measurement point pair for delayed determination, failing to incorporate the spatial correlation structure between a large number of wind measurement points in the wind farm group into the identification process. When the selected wind measurement point is located in a position of abnormal turbulent fluctuations or local wind disturbances, the cross-correlation result of the single point pair cannot truly reflect the wake propagation state at the whole field scale. Third, this method lacks a threshold construction mechanism based on the statistical characteristics of the data itself. When the cross-correlation coefficient of a single point pair exceeds the preset fixed threshold, it is impossible to distinguish whether the excess behavior is caused by the real physical correlation of wake propagation or by the accidental synchronization of random wind speed fluctuations, resulting in misjudgments caused by random factors in the delayed identification results. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a method and system for identifying wake propagation delay between offshore wind farms, which can realize the construction of data-driven adaptive threshold dynamic graph and topology propagation delay quantification, avoid the subjectivity of fixed thresholds, and achieve statistically objective and robust holographic identification of wake propagation delay between wind farms.

[0006] According to a first aspect of this application, a method for identifying wake propagation delay between offshore wind farms is provided, comprising: The wind speed time series signal of each wind measurement point in the offshore wind farm group is obtained within a preset window. The wind speed time series signal is standardized to determine the standard wind speed sequence of each wind measurement point. Each wind measurement point is used as a node to construct a node set, and the nodes are divided into upstream nodes and downstream nodes. Each sliding window is captured sequentially according to a preset sliding step size. Within each sliding window, the first correlation coefficient of the standard wind speed sequence of any two nodes is calculated. The phase spectrum of each node's standard wind speed sequence is reset, and the second correlation coefficient of any node pair after the reset is calculated. An adaptive threshold is determined based on the statistical distribution of the second correlation coefficient. Node pairs with a first correlation coefficient exceeding the adaptive threshold are retained as valid edges. A network snapshot corresponding to the current sliding window is constructed based on the valid edges. The network snapshots are arranged in the time order of the sliding window to obtain a dynamic graph sequence. For each network snapshot in the dynamic graph sequence, connected component identification is performed in chronological order. Isolated downstream components consisting only of downstream nodes and not connected to any upstream nodes for several consecutive sliding windows are monitored. The first appearance of the isolated downstream component is recorded as the birth time, and the first time it is merged into the connected component containing upstream nodes through an edge is recorded as the extinction time. The difference between the extinction time and the birth time is defined as the topology propagation delay.

[0007] In some embodiments, the wind speed time series signal corresponding to each wind measurement point is standardized to determine the standard wind speed sequence corresponding to each wind measurement point, including: The wind speed time series signals collected by each wind measurement point within a preset window are processed to remove the mean. The wind speed time series signal after the mean removal process is divided by the standard deviation of the wind speed time series signal of that wind measurement point to obtain a standard wind speed sequence with a mean of 0 and a standard deviation of 1. Each wind measurement point is used as a node to construct a node set, which is then divided into upstream and downstream nodes, including: Obtain the spatial coordinates of each wind measurement point and the layout direction of the offshore wind farm group. Based on the relative position of each wind measurement point along the prevailing wind direction, the nodes corresponding to the wind measurement points located in the upstream wind farm are classified as upstream nodes, and the nodes corresponding to the wind measurement points located in the downstream wind farm are classified as downstream nodes.

[0008] In some embodiments, a sliding step size is set within a preset window, and within each sliding window, the first correlation coefficient of the standard wind speed sequence of any two nodes is calculated, including: Within a preset window, each sliding window is sequentially extracted according to a preset sliding step size; within each sliding window, the Pearson correlation coefficient of the standard wind speed sequence of any two nodes forming a node pair is calculated, and the Pearson correlation coefficient is used as the first correlation coefficient of the node pair.

[0009] In some embodiments, the phase spectrum of the standard wind speed sequence corresponding to each node is reset to obtain the reset wind speed sequence corresponding to each node, including: Perform a Fourier transform on the standard wind speed sequence corresponding to each node to extract the amplitude spectrum and phase spectrum; extract the phase values ​​of the corresponding positive frequency components from the phase spectrum to form the first phase sequence; randomly shuffle the order of each phase value in the first phase sequence to obtain the second phase sequence. The phase values ​​in the second phase sequence are assigned to the positive frequency components in sequence, and the phase values ​​of the corresponding negative frequency components are determined from the phase values ​​of the positive frequency components according to the conjugate symmetry, thus forming a randomized phase spectrum. The amplitude spectrum and the randomized phase spectrum are combined and then subjected to an inverse Fourier transform to obtain the reset wind speed sequence. Calculate the second correlation coefficient for any pair of nodes after the reset, including: For the standard wind speed sequence corresponding to each node within the same sliding window, perform multiple phase spectrum reset operations. In each operation, the phase spectrum is independently and randomly rearranged to generate multiple sets of reset wind speed sequences. Calculate the Pearson correlation coefficient of any two nodes corresponding to each set of reset wind speed sequences, and combine all the Pearson correlation coefficients obtained from multiple calculations to form the statistical distribution of the second correlation coefficient corresponding to the sliding window.

[0010] In some embodiments, determining an adaptive threshold based on the statistical distribution of the second correlation coefficient includes: The statistical distribution of the second correlation coefficient corresponding to each sliding window is sorted in ascending order of numerical value. Using the preset upper quantile position parameter as the index, the second correlation coefficient value located at the preset upper quantile position in the ascending order is used as the adaptive threshold of the sliding window. Node pairs with a first correlation coefficient exceeding the adaptive threshold are retained as valid edges. A network snapshot corresponding to the current sliding window is constructed based on these valid edges, resulting in a dynamic graph sequence, including: For each sliding window, the first correlation coefficient of any node pair is compared with the adaptive threshold corresponding to that sliding window. When the first correlation coefficient is greater than the adaptive threshold, the node pair is determined to be a valid connection. Using all nodes as vertices and all valid connecting edges as edges, construct a network snapshot corresponding to the sliding window; The network snapshots of each sliding window are arranged in chronological order of their respective sliding window start times to form a dynamic graph sequence that evolves over time.

[0011] In some embodiments, monitoring an isolated downstream component consisting only of downstream nodes and not connected to any upstream node for a consecutive number of sliding windows includes: Run the disjoint-set data structure algorithm on each network snapshot in the dynamic graph sequence to identify all connected components in each network snapshot, and mark the connected components whose nodes are all downstream nodes as candidate components; For the candidate component of the current sliding window, backtrack the overall connection status of all nodes constituting the candidate component within a consecutive preset number of sliding windows, including the current sliding window. If, within the consecutive preset number of sliding windows, no node of the candidate component forms a valid connection with any upstream node, then the candidate component is determined to be an isolated downstream component.

[0012] In some embodiments, the time when an isolated downstream component first appears is recorded as its birth time, and the time when the isolated downstream component first merges into a connected component containing an upstream node via an edge is recorded as its extinction time, including: The starting time of the sliding window in which the isolated downstream component is first determined to be true is recorded as the birth time; Continue tracing the isolated downstream component along the time sequence of the dynamic graph. When any node in the isolated downstream component forms a valid connection with any upstream node for the first time, and the valid connection causes the isolated downstream component to be incorporated into a connected component containing the upstream node, the start time of the sliding window containing the valid connection is recorded as the extinction time. Calculate the time difference between the extinction time and the birth time, and define the time difference as the topological propagation delay of this propagation event.

[0013] In some embodiments, the method further includes: obtaining wind direction information and wind speed information corresponding to each sliding window, and determining sliding windows with the same wind direction sector type and the same wind speed level as having the same incoming flow conditions. Extract the effective edges that cause the isolated downstream component to disappear under the same incoming flow conditions, and obtain the spatial coordinates of the nodes at both ends of the effective edge; superimpose the spatial coordinates of the nodes at both ends of the effective edges corresponding to multiple topological propagation events under the same incoming flow conditions, reconstruct the dominant path of wake propagation through interpolation fitting method, and generate wavefront isochrones. Same incoming flow conditions refer to incoming flow conditions with the same wind direction, sector type, and wind speed level.

[0014] In some embodiments, the method further includes: obtaining wind direction and wind speed information corresponding to each sliding window in the dynamic graph sequence; The topological propagation delay under multiple wind direction sector types and multiple wind speed levels is statistically analyzed, and a three-dimensional feature phase map is constructed with wind direction sector type as the first coordinate axis, wind speed level as the second coordinate axis, and topological propagation delay as the third coordinate axis.

[0015] According to a second aspect of this application, a system for identifying wake propagation delay between offshore wind farms is provided. The system is used to perform the steps of the identification method described in the first aspect and any embodiment of the first aspect of this application, including: The signal acquisition module is used to acquire the wind speed time sequence signal of each wind measurement point in the offshore wind farm group within a preset window, perform standardization processing on each wind speed time sequence signal to determine the standard wind speed sequence of each wind measurement point, construct a node set with each wind measurement point as a node, and divide the nodes into upstream nodes and downstream nodes. The data reset module is used to sequentially capture each sliding window according to a preset sliding step size. Within each sliding window, it calculates the first correlation coefficient of the standard wind speed sequence of any two nodes, resets the phase spectrum of the standard wind speed sequence of each node, and calculates the second correlation coefficient of any node pair after the reset. A sorting module is constructed to determine an adaptive threshold based on the statistical distribution of the second correlation coefficient, retain node pairs whose first correlation coefficient exceeds the adaptive threshold as valid edges, construct network snapshots corresponding to the current sliding window based on the valid edges, and arrange the network snapshots according to the time order of the sliding window to obtain a dynamic graph sequence. The delay identification module is used to perform connected component identification on each network snapshot in the dynamic graph sequence in chronological order. It monitors isolated downstream components that consist only of downstream nodes and are not connected to any upstream nodes in a series of sliding windows. The time when the isolated downstream component first appears is recorded as the birth time, and the time when it first merges into a connected component containing upstream nodes through an edge is recorded as the death time. The difference between the death time and the birth time is defined as the topology propagation delay.

[0016] One embodiment of the above application has the following advantages or beneficial effects: This application acquires and standardizes wind speed time-series signals from various wind measurement points within an offshore wind farm cluster. Each wind measurement point is abstracted into a node and divided into upstream and downstream nodes. Based on this, a sliding window is extracted within a preset window using a sliding step size. The first correlation coefficient between any node within each sliding window and the standard wind speed sequence is calculated. The phase spectrum of the standard wind speed sequence for each node is reset, keeping the amplitude spectrum unchanged while randomizing the phase values ​​of each frequency component in the phase spectrum. This generates multiple sets of reset wind speed sequences, and the second correlation coefficient between any node pair after the reset is calculated. All second correlation coefficients generated from multiple phase spectrum reset operations are merged to form a statistical distribution of the second correlation coefficient corresponding to the sliding window. This statistical distribution characterizes the level of random correlation that may arise only from the similar power spectrum characteristics of each node after the phase coupling relationship of the wind speed sequence is randomly disrupted. This application determines an adaptive threshold based on the statistical distribution and a preset upper quantile position parameter, retaining node pairs with a first correlation coefficient exceeding the adaptive threshold as valid edges, thereby constructing network snapshots corresponding to each sliding window and arranging them in chronological order to obtain a dynamic graph sequence. The adaptive threshold is dynamically determined by the statistical characteristics of the data within each sliding window, without the need to manually set a fixed threshold, ensuring that the valid edges reflect statistically significant real physical associations rather than random coincidences, fundamentally solving the defect of lacking objective statistical basis in the selection of fixed thresholds in the prior art; Furthermore, this application performs connected component identification on the dynamic graph sequence in chronological order, monitors isolated downstream components consisting only of downstream nodes and not connected to upstream nodes for several consecutive sliding windows, records their birth time and death time, and defines the time difference between the two as topological propagation delay. From the perspective of network topology evolution, this process transforms the physical quantity of wake propagation delay into a time metric for the structural changes of connected components in the dynamic graph. This makes the identification of wake propagation delay no longer dependent on the mutual information of a single wind measurement point pair or a preset physical model, but fully integrates the high-dimensional correlation information between numerous wind measurement points in the field for joint judgment and self-consistent verification, thereby improving the statistical reliability of the identification results and the robustness to different incoming flow conditions.

[0017] Other effects of the above-mentioned alternative methods will be described below in conjunction with specific embodiments. Attached Figure Description

[0018] The accompanying drawings are provided for a better understanding of this solution and do not constitute a limitation of this application. Wherein: Figure 1 This is a flowchart illustrating a method for identifying wake propagation delay between offshore wind farms provided in an embodiment of this application. Figure 2 This is a schematic diagram of the fitting curve of the statistical distribution standard deviation of the second correlation coefficient and the adaptive threshold provided in an embodiment of this application; Figure 3 This is a line graph illustrating an adaptive threshold and a first correlation coefficient provided in an embodiment of this application; Figure 4 This is a block diagram of a wake propagation delay identification system between offshore wind farms provided in an embodiment of this application. Detailed Implementation

[0019] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0020] To facilitate understanding of this application, the embodiments of this application will be briefly described below: This application provides a method for identifying wake propagation delay between offshore wind farms. The following description uses an application scenario of an offshore wind farm group as an example. The offshore wind farm group consists of upstream and downstream wind farms arranged sequentially along the prevailing wind direction. Each wind farm has multiple wind measurement points for real-time acquisition of wind speed time-series signals. During the operation of the wind farm group, the operation of the wind turbines in the upstream wind farm will form a wake zone behind them. The wind speed reduction effect of the wake zone will propagate downstream along the wind direction. After a certain time delay, it will affect the wind speed distribution of the downstream wind farm. Accurately identifying this wake propagation delay has important reference value for the formulation of forward-looking control strategies, power generation prediction, and overall collaborative optimization operation of the downstream wind farm. Existing wake propagation delay identification methods mostly rely on physical model simulation or fixed threshold cross-correlation analysis. Physical models have high computational complexity and are sensitive to boundary conditions, while fixed threshold cross-correlation methods are difficult to adapt to changes in incoming flow conditions, making it difficult to guarantee the statistical significance of the identification results. The method provided in this application constructs an adaptive threshold by introducing random phase scrambling, realizing holographic identification of wake propagation delay from the perspective of network topology evolution. It can automatically adjust the correlation judgment criteria according to the incoming flow conditions, improving the objectivity and environmental adaptability of delay identification.

[0021] See Figure 1 This is a flowchart illustrating a method for identifying wake propagation delay between offshore wind farms, provided in an embodiment of this application. Figure 1 The execution subject of the method shown can be a combination of software and / or hardware, specifically, it can be one or more of various types of terminals, hardware systems, cloud computing, etc.

[0022] Figure 1 The method for identifying wake propagation delay between offshore wind farms includes steps S100 to S400, as detailed below: S100: Acquire wind speed time-series signals of each wind measurement point in the offshore wind farm group within a preset window, standardize each wind speed time-series signal to determine the standard wind speed sequence of each wind measurement point, construct a node set with each wind measurement point as a node, and divide the nodes into upstream nodes and downstream nodes. In this embodiment, the offshore wind farm group includes two wind farms arranged along the prevailing wind direction, namely the upstream wind farm and the downstream wind farm. Each wind farm is equipped with multiple wind turbine generators. Each generator has an anemometer installed on the top of its nacelle as a wind measurement point. Each anemometer continuously collects and outputs wind speed time-series signals at a sampling period of 1 minute. The sampling times of all wind measurement points are synchronized and aligned by a satellite clock signal. It can be understood that the wind measurement point can also be an independent wind measurement tower or a lidar wind measurement device, as long as it can provide continuous wind speed measurement values ​​at a fixed location. Before starting the wake propagation delay identification, a preset window is first determined. The duration of the preset window is determined based on the spatial scale of the wind farm cluster and the historical wind speed statistical characteristics. In this embodiment, the distance between each wind farm in the wind farm cluster is on the order of several kilometers to tens of kilometers, the wind speed range is generally from 3 meters per second to 15 meters per second, and the wake propagation time is on the order of several minutes to half an hour. Therefore, the duration of the preset window is selected as 6 hours to ensure that a sufficient number of wake propagation events are included and to meet the statistical stability requirements. The start time of the preset window is arbitrarily selected based on the available time period of the actual operating data. Within the preset window, each wind measurement point collects N wind speed data points, where N is equal to the preset window duration divided by the sampling period. The wind speed time series signals corresponding to each wind measurement point are standardized to determine the standard wind speed sequence corresponding to each wind measurement point, including: After acquiring the wind speed time-series signals of all wind measurement points within the preset window, the missing and outlier values ​​in the acquired wind speed time-series signals are processed. For a missing wind speed at a single sampling moment, the arithmetic mean of the wind speed values ​​at the wind measurement point before and after that moment is used to fill it in. For a missing wind speed at multiple consecutive sampling moments, the mean of the wind speed time-series signals at the wind measurement point within the preset window is used to fill it in. For abnormal jump points where the wind speed value changes more than a preset jump threshold between adjacent sampling moments, the wind speed value at the jump point is replaced with the arithmetic mean of the wind speed values ​​at the wind measurement point before and after that moment. The preset jump threshold is determined based on the standard deviation of the difference between adjacent sampling times of the wind speed time sequence signal at the wind measurement point within a preset time period. Three times this standard deviation is used as the preset jump threshold. For seasons or time periods with significantly different wind speed change characteristics, the standard deviation of the difference between adjacent sampling times within each time period can be calculated separately, and the value of the preset jump threshold can be adjusted accordingly. After handling missing and outlier values, the wind speed time series signal of each wind measurement point is independently standardized to determine the standard wind speed sequence corresponding to each wind measurement point. The specific operation is as follows: calculate the arithmetic mean of all wind speed data of the wind measurement point within a preset window, subtract the arithmetic mean from each value in the wind speed time series signal to obtain the mean-reduced wind speed time series signal; then calculate the standard deviation of all wind speed data of the wind measurement point within the preset window, divide the mean-reduced wind speed time series signal by the standard deviation to obtain the standard wind speed sequence with a mean of 0 and a standard deviation of 1. When the standard deviation of the wind speed time series signal of a certain wind measurement point within a preset window is 0, each value in the standard wind speed sequence of that wind measurement point is assigned a value of 0. The standardization process eliminates the differences in wind speed amplitude caused by factors such as installation height and local terrain at each wind measurement point, so that the subsequent correlation analysis reflects the similarity of wind speed fluctuation patterns rather than the absolute wind speed magnitude. Each wind measurement point is used as a node to construct a node set, which is then divided into upstream and downstream nodes, including: Each wind measurement point is abstracted as a network node, and each wind measurement point is uniquely mapped to a node in the node set. A unique node identifier is assigned to each node, and all wind measurement points constitute the node set. The node identifier uses an integer number or string encoding, with the number range being 1 to 1. ,in The total number of nodes in the node set, once assigned, remains unchanged within a preset time period, and is used to uniquely index the corresponding wind measurement point in subsequent steps; The node set is divided into upstream and downstream nodes. In this embodiment, the spatial coordinates of each wind measurement point are first obtained, using latitude and longitude or two-dimensional coordinates in the local Cartesian coordinate system of the wind farm. Then, the arrangement direction of the wind farm group is obtained, that is, the overall direction from the upstream wind farm to the downstream wind farm. At the same time, based on all wind speed measurement data within the preset window, the vector average wind direction for the entire period is calculated as the prevailing wind direction. It should be noted that in the application scenario targeted by this invention, the prevailing wind direction in the area where the offshore wind farm group is located is stable within the preset window period. The prevailing wind direction does not change frequently and significantly, and there are only slight oscillations near the average direction. Therefore, the prevailing wind direction determined based on the vector average wind direction within the preset window can accurately characterize the overall direction of wake propagation within that period. The upstream and downstream nodes divided accordingly remain fixed throughout the preset window and will not be affected by the stability of node attributes due to slight fluctuations in instantaneous wind direction. In this embodiment, the upstream wind farm and the downstream wind farm have a clear geographical boundary in space. The nodes corresponding to the wind measurement points located in the upstream wind farm area are all classified as upstream nodes, and the nodes corresponding to the wind measurement points located in the downstream wind farm area are all classified as downstream nodes. The upstream or downstream attributes of the nodes are fixed node labels within the preset window and do not change with the instantaneous wind direction changes within the sliding window, so as to facilitate the subsequent tracking of connected components across windows. In some embodiments, if there is no clear boundary between wind farms in the wind farm group, the node set can be divided into upstream and downstream groups according to the clustering results of the projection coordinates of the prevailing wind direction. Regardless of the specific division method used, the division result must be kept fixed within the preset window. When an offshore wind farm group includes three or more wind farms, according to the spatial arrangement order of each wind farm along the prevailing wind direction, the nodes corresponding to all wind measurement points in the wind farm that is first in the prevailing wind direction are designated as upstream nodes, the nodes corresponding to all wind measurement points in the wind farm that is last in the prevailing wind direction are designated as downstream nodes, and the nodes corresponding to all wind measurement points in the wind farm that is in the middle position are discarded and not included in the node set. If a wind farm located in the middle position deviates from the prevailing wind direction axis by more than a preset angle threshold in space, and the wind speed time series signal of the wind measurement point in the wind farm shows a wake correlation characteristic with the upstream wind farm, then all nodes corresponding to the wind measurement points in the middle position wind farm that deviate from the preset angle threshold will be discarded and not included in the node set.

[0023] S200: Sequentially capture each sliding window according to the preset sliding step size. Within each sliding window, calculate the first correlation coefficient of the standard wind speed sequence of any two nodes. Reset the phase spectrum of each node's standard wind speed sequence and calculate the second correlation coefficient of any node pair after the reset. Within a preset window, a sliding step size is set. Within each sliding window, the first correlation coefficient of the standard wind speed sequence of any two nodes is calculated, including: In some embodiments, a sliding step size is first set within a preset window. The sliding step size refers to the time interval between the start times of two adjacent sliding windows. The value of the sliding step size is determined based on the time resolution and computational complexity of the wake propagation process. In this embodiment, the window duration of the sliding window is selected as 30 minutes, and the sliding step size is selected as 5 minutes. The start time of the sliding window is from the zero time of the preset window. Each sliding window is intercepted by moving backward by one sliding step size until the end time of the sliding window exceeds the preset window range. Each sliding window consists of standard wind speed sequence segments of all wind measurement points within the time interval. The length of the standard wind speed sequence segment of each node is equal to the sliding window duration divided by the sampling period. It can be understood that the length of the sliding window is determined based on the expected value of the wake propagation time. This expected value is equal to the geographical distance between the upstream and downstream wind farms divided by the historical statistical average wind speed of the sea area. The length of the sliding window is set to three to four times the expected value of the wake propagation time to ensure that a sufficient number of sampling points are included in a single sliding window for statistical significance estimation of the Pearson correlation coefficient. The sliding step size is set to one-sixth of the sliding window length, so that there is an overlap area of ​​five-sixths of the window length between two adjacent sliding windows. This overlap area ensures that the wake propagation event is not truncated or missed at the boundary of the sliding window due to window division, while also enabling the time resolution between network snapshots to reach the step size level, which can capture dynamic changes in latency at the minute level. In this embodiment, the sliding window length is 30 minutes, so the sliding step size is 5 minutes. Within each sliding window, the first correlation coefficient of the standard wind speed sequence of any two nodes is calculated. This first correlation coefficient refers to the Pearson correlation coefficient between the standard wind speed sequence segments of the two nodes within the same sliding window. Specifically, for any two nodes... and nodes For each node pair, standard wind speed sequence segments within the same sliding window are extracted. These two standard wind speed sequence segments have the same sampling time and sequence length within the sliding window. Using these two standard wind speed sequence segments as input, the Pearson correlation coefficient is calculated. This Pearson correlation coefficient is then used as the first correlation coefficient for the node pair within the sliding window. and Both are indexes of nodes, and ; The first correlation coefficient reflects the degree of linear synchronization between the wind speed fluctuation patterns of the two nodes within the sliding window. The closer the value is to 1, the stronger the positive synchronization; the closer the value is to 0, the weaker the linear correlation. The above calculation is performed on all node pairs in the node set within each sliding window, and each node pair obtains a first correlation coefficient within each sliding window. The phase spectrum of the standard wind speed sequence corresponding to each node is reset to obtain the reset wind speed sequence corresponding to each node, including: After the first correlation coefficient is calculated, the phase spectrum is reset for the standard wind speed sequence segments of each node in each sliding window to obtain the reset wind speed sequence corresponding to each node. The phase spectrum reset refers to the operation of keeping the amplitude spectrum unchanged in the frequency domain and only randomizing the phase spectrum of the standard wind speed sequence segments. Its purpose is to generate an alternative sequence with the same power spectrum characteristics as the original sequence but whose temporal correlation has been destroyed, so as to provide a statistical null hypothesis basis for the subsequent construction of adaptive threshold. Specifically, a Fourier transform is performed on a standard wind speed sequence segment at a certain node. The Fourier transform decomposes the standard wind speed sequence segment in the time domain into a superposition of different frequency components, outputting the amplitude spectrum and phase spectrum of each frequency component. The amplitude spectrum represents the energy intensity of the frequency component in the original sequence segment, and the phase spectrum represents the initial phase of the frequency component in the original sequence segment. If the sequence length within the sliding window is not an integer power of 2, zero-padding can be performed on the end of the sequence before performing the Fourier transform. The length of the zero-padding sequence is extended to an integer power of 2 that is greater than the original sequence length and closest to it, in order to adapt to the Fast Fourier Transform algorithm. The zero-padding operation does not change the spectral characteristics of the original sequence, but only increases the frequency resolution. Furthermore, the phase values ​​corresponding to all positive frequency components are extracted from the phase spectrum and arranged in ascending order of frequency to form the first phase sequence. The positive frequency components refer to frequency points with frequencies greater than zero and less than the Nyquist frequency. The phase values ​​of these frequency points contain all the independent phase information of the standard wind speed sequence fragment fluctuation mode. The length of the first phase sequence is equal to the number of positive frequency components in the Fourier transform result. The order of each phase value in the first phase sequence is randomly shuffled to obtain the second phase sequence. The random shuffling refers to rearranging the order of each element in the first phase sequence using a random permutation algorithm, so that the probability of each phase value appearing in any position in the new sequence is equal. After random shuffling, the second phase sequence still retains all the phase values ​​of the first phase sequence, only changing the correspondence between each phase value and the frequency component, without changing the numerical set of each phase value in the first phase sequence itself. Therefore, the empirical probability distribution of the original phase values ​​is preserved. The random permutation algorithm employs the Fisher-Yates shuffle algorithm, which rearranges the order of phase values ​​in the first phase sequence as follows: starting from the last element of the first phase sequence, it iterates backward to the second element. In each iteration, a position is randomly selected uniformly between the first and current elements, and the current element is swapped with the element at that position. After performing a complete iteration of the first phase sequence using this algorithm, a second phase sequence with its order randomly shuffled is obtained. The randomness of this algorithm is provided by a pseudo-random number generator, which is initialized with the start time of the current sliding window and the average wind speed of the wind farm group corresponding to the sliding window as seeds. The phase values ​​in the second phase sequence are assigned to the corresponding positive frequency components one by one in sequence. That is, the first phase value in the second phase sequence is assigned to the positive frequency component with the lowest frequency, the second phase value is assigned to the positive frequency component with the second lowest frequency, and so on. When performing Fourier transform and inverse Fourier transform, the phase values ​​of the DC component and the Nyquist frequency component need to be specially processed. For the DC component with a frequency of zero, its phase value remains unchanged in the randomized phase spectrum. When the sequence length within the sliding window is even, there exists a Nyquist frequency component with a frequency equal to half the sampling frequency. The phase value of this frequency component also remains unchanged in the randomized phase spectrum. The phase values ​​of the remaining positive frequency components are redistributed to each frequency component according to the random shuffling operation. This processing method ensures that the reset wind speed sequence obtained after the inverse Fourier transform is a real number sequence, avoiding the generation of non-zero imaginary parts due to the destruction of the phase constraints of the DC component or the Nyquist frequency component. Furthermore, based on conjugate symmetry, the phase value of the corresponding negative frequency component is determined by the phase value of the positive frequency component. Conjugate symmetry means that the Fourier transform of the real-valued signal satisfies the constraint that the phase values ​​of the positive frequency component and the corresponding negative frequency component are opposites of each other. For the phase value assigned to each positive frequency component, its opposite is taken as the phase value of the corresponding negative frequency component. The phase values ​​of the positive frequency component and the phase values ​​of the negative frequency component are combined to form a complete randomized phase spectrum. While keeping the amplitude spectrum unchanged, the amplitude spectrum and the randomized phase spectrum are combined. The amplitude spectrum provides the amplitude value of each frequency component, and the randomized phase spectrum provides the phase value of each frequency component. The combination forms a complex representation in the frequency domain. An inverse Fourier transform is performed on the complex representation in the frequency domain to convert the frequency domain signal back to the time domain, and the reset wind speed sequence of the node after the phase spectrum reset operation is obtained. Calculate the second correlation coefficient for any pair of nodes after the reset, including: The reset wind speed sequence obtained after the above phase spectrum reset operation has the same amplitude spectrum as the original standard wind speed sequence segment. Therefore, the reset wind speed sequence retains the power spectral density distribution characteristics of the original standard wind speed sequence segment, that is, the energy magnitude of each frequency component remains unchanged. However, the phase values ​​of each frequency component are randomly redistributed, which destroys the inherent phase coupling relationship and temporal dependency structure in the original standard wind speed sequence segment. This causes the reset wind speed sequence to lose the real physical correlation that may exist between different nodes in the original standard wind speed sequence segment. The second correlation coefficient calculated based on multiple sets of reset wind speed sequences obtained by multiple phase spectrum reset operations reflects the level of random correlation that may be generated only by the same power spectral characteristics of each node under the condition of no real phase coupling relationship. The phase spectrum reset operation is performed on each node within the same sliding window to generate a set of reset wind speed sequences with the same number of nodes as the original. Then, for this set of reset wind speed sequences, the Pearson correlation coefficient of any two nodes forming a node pair is calculated in the same way as the first correlation coefficient is calculated, and the Pearson correlation coefficient of all node pairs under this phase spectrum reset is obtained. The phase spectrum reset operation is repeated multiple times. The multiple times refers to a preset number of operations. In each operation, the first phase sequence is randomly shuffled independently. That is, the generation process of the randomized phase spectrum each time is independent of each other, generating multiple sets of reset wind speed sequences that are different from each other. In this embodiment, the number of reset operations is thousands. The more reset operations there are, the closer the statistical distribution of the second correlation coefficient is to the true null hypothesis distribution, and the more stable the adaptive threshold estimation is. The number of phase spectrum reset operations is determined based on preset statistical accuracy requirements and computational resource constraints. The larger the number of resets, the closer the statistical distribution of the second correlation coefficient is to the true null hypothesis distribution, and the higher the stability of the adaptive threshold estimation. Experiments have verified that when the number of resets reaches more than 500, the estimated value of the upper 99th quantile of the statistical distribution of the second correlation coefficient no longer changes observably with the increase of the number of resets, indicating that a stable convergence state has been reached. In this embodiment, the number of resets is set to thousands, which provides more than twice the redundancy margin while ensuring the convergence of the statistical distribution. In embedded systems with limited computational resources, the number of resets can be appropriately reduced to 200 to 500. At this time, the estimation error of the upper 99th quantile does not exceed the preset error tolerance. All Pearson correlation coefficients calculated multiple times are combined together, that is, all Pearson correlation coefficient values ​​obtained by all node pairs in all reset operations within the sliding window are gathered into a set, which constitutes the statistical distribution of the second correlation coefficient corresponding to the sliding window; the statistical distribution of the second correlation coefficient characterizes the distribution range of the purely random correlation level that may occur between node pairs after the temporal correlation of the wind speed sequence is randomly destroyed. Specifically, suppose a certain sliding window contains a total of 1 node The total number of nodes in the node set, and the number of nodes within the sliding window. nodes, whose standard wind speed sequence is denoted as . ,right After performing a Fourier transform, the amplitude and phase spectra of each frequency component are obtained. The original amplitude spectrum and the randomized phase spectrum are combined and then subjected to an inverse Fourier transform to obtain the first-order reset wind speed sequence for that node, denoted as... All within the same sliding window Each node independently performs the above phase spectrum reset operation to obtain... A reset wind speed sequence ; For the Subphase spectrum reset operation. ,in The total number of times the phase spectrum is reset. For the index of the number of phase spectrum resets, calculate the node pair formed by any two distinct nodes after the reset. Pearson correlation coefficient, The index of the node pair is used to traverse all node pairs (from...). (Choose any two combinations from the given nodes), the natural constraint is: The two are not equal. The calculation method of the Pearson correlation coefficient is consistent with the commonly known formula for calculating the Pearson correlation coefficient, and its mathematical expression will not be repeated here. Will The correlation coefficients of all node pairs in the second phase spectrum reset operation are combined to form the statistical distribution set of the second correlation coefficient. :

[0024] Among them, when At that time, the upper side of the statistical distribution of the second correlation coefficient The estimated value of the quantile follows The fact that increasing the value no longer produces observable changes indicates that the statistical distribution has stabilized and converged. Indicates the first After the secondary phase spectrum is reset, the nodes With nodes The second correlation coefficient, which constitutes the node pair, has a range of values. ; This statistical distribution set The total number of elements is: ,in A positive integer represents The total number of second correlation coefficients in the middle. This represents the total number of all distinct node pairs in the node set (combinations). ); This statistical distribution set It characterizes the probability distribution of the apparent correlation level between node pairs that may be generated by random factors under the condition that the phase coupling relationship of the wind speed sequence at each wind measurement point is randomly destroyed and only the power spectral density distribution of each frequency component is retained.

[0025] S300: Determine the adaptive threshold based on the statistical distribution of the second correlation coefficient, retain the node pairs whose first correlation coefficient exceeds the adaptive threshold as valid edges, construct the network snapshot corresponding to the current sliding window based on the valid edges, arrange the network snapshots according to the time order of the sliding window, and obtain the dynamic graph sequence. The adaptive threshold is determined based on the statistical distribution of the second correlation coefficient, including: In some embodiments, an adaptive threshold is first determined based on the statistical distribution of the second correlation coefficient. The adaptive threshold is a critical value calculated independently for each sliding window to determine whether the first correlation coefficient is statistically significant. This critical value is determined entirely by the statistical characteristics of the data within the current sliding window, without the need to manually set a fixed threshold. Since the standard wind speed sequence segments and phase spectrum reset results of each sliding window are different, the adaptive thresholds of each sliding window are different, thus achieving an adaptive effect where the threshold is dynamically adjusted according to the data. Specifically, the statistical distribution of the second correlation coefficient corresponding to each sliding window is processed. The statistical distribution of the second correlation coefficient is a set of values ​​formed by collecting the Pearson correlation coefficients of all node pairs in all reset operations after performing multiple phase spectrum reset operations on the sliding window in step S200. All values ​​in the set are arranged in ascending order from smallest to largest to obtain an ordered sequence. Furthermore, using a preset upper quantile position parameter as an index, the second correlation coefficient value at the corresponding position is extracted from the ordered sequence. The preset upper quantile position parameter refers to a pre-set percentile used to determine which position in the ordered sequence to take the value as the adaptive threshold. The value of the preset upper quantile position parameter determines the strictness of the adaptive threshold. The higher the value, the stricter the determined adaptive threshold, the fewer valid edges are retained, and the lower the corresponding false positive rate. In this embodiment, the preset upper quantile position parameter is set to 99%, that is, the second correlation coefficient value corresponding to the 99th percentile in the ordered sequence is selected as the adaptive threshold of the sliding window. This value ensures that node pairs with the first correlation coefficient exceeding the threshold have a probability of less than 1% that are false associations caused by random factors. Choosing 99% as the preset upper quantile position parameter provides a stricter screening standard compared to lower percentile values. This effectively suppresses false correlation edges caused by limited sample length and random fluctuations from entering the network snapshot, reducing the probability of misjudgment due to noisy edges during subsequent isolated downstream component detection. For application scenarios with weak wake propagation correlation or low data quality, the preset upper quantile position parameter can be adjusted to any value between 95% and 99% to balance the relationship between the number of effective edges and the false positive rate. The physical meaning of the adaptive threshold is that the statistical distribution of the second correlation coefficient represents the range of the purely random correlation level that may occur between each pair of nodes after the temporal correlation of the wind speed sequence is randomly disrupted; taking the upper quantile of this distribution as the adaptive threshold means that if the first correlation coefficient of a certain pair of nodes exceeds the adaptive threshold, the correlation level represented by the first correlation coefficient has only a very low probability of being caused by random factors, and therefore it can be determined that the correlation between the pair of nodes is statistically significant. Specifically, All of them The values ​​are arranged in ascending order to obtain an ordered sequence: Let the preset upper quantile position parameter be... ( ), determine the upper quantile location index: ,in This represents the floor function, ensuring... for to Positive integers between, when When the value is not an integer, take the smallest integer not less than that value; Adaptive threshold for a sliding window Defined as ,Right now ascending sequence The Middle The values ​​of the second correlation coefficient at each position have the same range as the second correlation coefficient. And satisfy , This is the index of the sliding window, used to identify a specific sliding window within a preset window. ; in The preset upper quantile position parameter has a value range of [value range missing]. to In this embodiment, we take , The value of determines the strictness of the adaptive threshold: The larger the value, The stricter the criteria, the fewer valid connections are retained, and the lower the false positive rate. The smaller the value, The looser the rules, the more valid connections are retained, and the higher the false positive rate. At that time, only The level of random correlation is higher than ; When the first correlation coefficient of a certain node pair With adaptive threshold The absolute value of the difference is less than the preset precision tolerance. ( When the rounding error of computer floating-point arithmetic is determined, the judgment is made. The node pair is determined to be an invalid connection and will not be retained. Node pairs with a first correlation coefficient exceeding the adaptive threshold are retained as valid edges. A network snapshot corresponding to the current sliding window is constructed based on these valid edges, resulting in a dynamic graph sequence, including: After determining the adaptive threshold, effective edges are filtered. Effective edges refer to the connections between node pairs whose first correlation coefficient exceeds the adaptive threshold in the statistical significance test. This indicates that the wind speed fluctuations of that node pair have real physical coupling within the sliding window. Since the Pearson correlation coefficient is symmetric, i.e., node... With nodes The first correlation coefficient is equal to the node With nodes The first correlation coefficient indicates that the determination of valid edges is symmetric. For each sliding window, traverse all node pairs within the sliding window and compare the first correlation coefficient of each node pair with the adaptive threshold corresponding to the sliding window. When the first correlation coefficient of a node pair is greater than the adaptive threshold, the node pair is determined to be a valid connection; when the first correlation coefficient is less than or equal to the adaptive threshold, the node pair does not constitute a valid connection within the sliding window. After completing the above determination for all node pairs within the sliding window, a network snapshot corresponding to the sliding window is constructed, using all nodes in the node set built in step S100 as vertices and the connection relationships of all node pairs determined to be valid connections within the current sliding window as edges. The network snapshot refers to an undirected graph data structure at a sliding window time point, with abstract wind measurement point nodes as vertices and statistically significant correlation relationships as edges. Each network snapshot fully records the wake propagation correlation topology state between all wind measurement points of the wind farm group within the sliding window. In the network snapshot, each node retains its corresponding upstream or downstream attribute node label. There are no self-loop edges in the network snapshot, that is, the connection edges between nodes themselves are not considered, and there is at most one edge between any two nodes. The network snapshot is a simple undirected graph. The above operations are performed on each sliding window within the preset window, generating a corresponding network snapshot for each sliding window. Further, the network snapshots corresponding to each sliding window are arranged sequentially according to their start times, forming a time-ordered sequence of network snapshots, which is the dynamic graph sequence. The dynamic graph sequence refers to an ordered set of network topology evolutions over time, where each element is a network snapshot at a given moment, and the time interval between adjacent snapshots is equal to the sliding step size. The dynamic graph sequence fully describes the evolution of the topological relationship between wind farm group wind measurement points within the preset window over time. The topological changes between adjacent network snapshots reflect the establishment, maintenance, and disappearance of wake propagation relationships, providing a data structure foundation for monitoring the birth and disappearance of isolated downstream components in subsequent steps.

[0026] S400: Perform connected component identification on each network snapshot in chronological order for the dynamic graph sequence, monitor isolated downstream components that consist only of downstream nodes and are not connected to any upstream nodes for several consecutive sliding windows, record the first appearance of the isolated downstream component as the birth time, record the first time it is merged into the connected component containing the upstream node through the connection as the extinction time, and define the difference between the extinction time and the birth time as the topology propagation delay. Monitoring isolated downstream components that consist only of downstream nodes and are not connected to any upstream node for several consecutive sliding windows includes: In some embodiments, firstly, connectivity component identification is performed on each network snapshot in the dynamic graph sequence. The connectivity component refers to the largest connected subgraph that can be reached between any two nodes in the network snapshot through a valid edge. There is at least one path consisting of a valid edge between any two nodes in the subgraph, and there is no valid edge between any node in the subgraph and any node outside the subgraph in the network snapshot. Specifically, the disjoint-set data structure algorithm is run on each network snapshot in the dynamic graph sequence. The disjoint-set data structure algorithm merges the nodes at both ends of the valid edges into the same set by traversing all valid edges in the network snapshot. Finally, each set corresponds to a connected component. After running the disjoint-set data structure algorithm on each network snapshot, all connected components in the network snapshot and their contained node members are recorded. Each connected component is assigned a unique component identifier to distinguish different connected components in the same network snapshot. Traverse all connected components of each network snapshot and identify connected components consisting only of downstream nodes. Specifically, check the node labels of all nodes in a connected component. If all nodes in the connected component are labeled as downstream nodes, then the connected component is marked as a candidate component. If a connected component contains at least one upstream node, then the connected component is not a candidate component. A network snapshot may contain zero, one or more candidate components. Furthermore, for each candidate component marked in the network snapshot, the isolation of downstream components is determined. The isolation of downstream components refers to candidate components that meet the following conditions: not only are they entirely composed of downstream nodes within the current sliding window, but also, within a consecutive preset number of sliding windows including the current sliding window, each node constituting the candidate component does not form a valid connection with any upstream node. The consecutive preset number of sliding windows refers to a pre-set integer used to specify the time duration condition required for determining isolation. Its value is determined based on the relationship between the sliding step size and the wake propagation time scale. If the value is too small, it may introduce false isolation events, and if the value is too large, it may miss real propagation delay events. The consecutive preset number is greater than the integer 2. In this embodiment, the sliding step size is 5 minutes, and the number of consecutive preset sliding windows is 3, corresponding to a continuous observation time of 15 minutes. This continuous observation time matches the expected value of the wake propagation delay, which can eliminate the instantaneous connection break caused by a single sampling anomaly, and will not cover the true delay value due to excessive observation time. When the sliding window length or sliding step size changes, the value of the number of consecutive preset sliding windows is adjusted accordingly according to the following rules: the continuous observation time is kept within the range of 30% to 60% of the expected value of the wake propagation delay, and the closest integer value is taken. Specifically, for a candidate component of the current sliding window, the connection status of all nodes constituting the candidate component is backtracked within a predetermined number of consecutive sliding windows, including the current sliding window. The backtracking operation is as follows: sequentially check the network snapshots of the current sliding window and the previous few sliding windows, and check whether each node constituting the candidate component has a valid connection with any upstream node in each network snapshot of the predetermined number of consecutive sliding windows. If any node constituting the candidate component has a valid connection with any upstream node in any network snapshot of the predetermined number of consecutive sliding windows, then the candidate component does not satisfy the isolation condition. If none of the nodes constituting the candidate component have a valid connection with any upstream node in each network snapshot of the predetermined number of consecutive sliding windows, then the candidate component is determined to be an isolated downstream component. Specifically, let the first The set of nodes for a connected component in a network snapshot of a sliding window is: , A component is identified as an isolated downstream component if and only if the following conditions are met simultaneously: Condition 1: All nodes in the process have the node label of a downstream node, that is... Condition 2: For continuous There are several sliding windows, and the sliding window number is denoted as . For any one of the sliding windows, such as ( ),as well as any node ( ), and the current node set any upstream node ( ),node With nodes In the sliding window The network snapshots do not contain any valid edges; the formal expression of the above judgment rule is:

[0027] in, The current sliding window number, node and These are all indexes of nodes. For isolated downstream components Index of the middle node For the set of upstream nodes The index of the middle node, because and Therefore and Representing different nodes, For use in traversing continuous The index of each sliding window, and , The downstream node set is determined in step S100 based on the relative positions of each wind measurement point along the prevailing wind direction, and remains fixed throughout the preset time period. This represents the set of upstream nodes, determined in step S100 based on the relative positions of each wind measurement point along the prevailing wind direction, and remains fixed throughout the preset time period. The preset isolation determination duration window number is a positive integer; in this embodiment, it is taken as... ; For the valid edge existence indicator function, it represents the first edge. Nodes in a sliding window network snapshot With nodes Whether there is a valid edge between nodes is defined as follows: If nodes With nodes In the If there are valid edges in the network snapshots of each sliding window, then If node With nodes In the If no valid edges are found in the network snapshot of the sliding window, then... The rule for determining a valid edge is: when nodes pair... First correlation coefficient Greater than the adaptive threshold of the sliding window hour, ;when hour, ; The physical meaning of this judgment condition is: All nodes in the current sliding window are downstream nodes. Including continuous A sliding window (window) To the window In each network snapshot, Each node in the process has no valid connection to any upstream node; The specific data for the sliding window number and adaptive threshold are shown in Table 1.

[0028] Table 1. Data Statistics Table

[0029] In this data analysis, we systematically evaluated the statistical characteristics of wake propagation correlation in 30 sliding windows. The data table includes the mean and standard deviation of the statistical distribution of the second correlation coefficient for each sliding window, the adaptive threshold determined therefrom, the measured value of the first correlation coefficient, and the results of valid edge determination. The purpose of these data is to reflect how the null hypothesis distribution constructed by phase spectrum reset dynamically determines the threshold for determining the significance of correlation in different windows, and whether the measured correlation between node pairs in each sliding window exceeds the threshold. Analysis of the data revealed a clear positive correlation between the adaptive threshold and the standard deviation of the statistical distribution of the second correlation coefficient. A higher standard deviation for a sliding window indicates a larger range of apparent correlation fluctuations caused by random factors within that window, leading to a corresponding increase in the adaptive threshold to maintain the strictness of the statistical significance determination. For example, the standard deviation of window 25 was 0.316, corresponding to an adaptive threshold of 0.744, the highest among all windows. The standard deviation of window 14 was 0.162, corresponding to an adaptive threshold of 0.404, a lower level among all windows. The mean fluctuation was small, ranging from -0.011 to 0.017, indicating that the phase spectrum reset operation effectively eliminated any systematic shifts that might exist in the original sequence, bringing the center of the null hypothesis distribution close to the zero correlation level. In comparing the first correlation coefficient with the adaptive threshold, the first correlation coefficient of some windows exceeded the adaptive threshold and were judged as valid connections. For example, the first correlation coefficient of sliding window 11 was 0.741, which was significantly higher than its adaptive threshold of 0.636, indicating that the wind speed fluctuation correlation of the corresponding node pair within the sliding window was highly unlikely to be caused by random factors and that there was a real physical coupling. The first correlation coefficient of sliding window 22 was 0.572, and the adaptive threshold was 0.397, so it was also judged as a valid connection. In contrast, the first correlation coefficient of sliding window 12 was 0.305, which was lower than its adaptive threshold of 0.494, so it was judged as an invalid connection, indicating that the correlation level of the corresponding node pair within the sliding window was still within the range that could be explained by random fluctuations. Although the first correlation coefficient of some sliding windows was close to the adaptive threshold, it did not exceed it. For example, the first correlation coefficient of sliding window 28 was 0.395, and the adaptive threshold was 0.400. The difference between the two was only 0.005, so it was still judged as an invalid connection, which reflects the role of the adaptive threshold as a strict judgment threshold. Of the 30 sliding windows, 10 had a valid connection result of 1, accounting for about one-third of all sliding windows. This indicates that, with a false positive rate control level of about one percent, statistically significant wind speed fluctuation correlations were detected in about one-third of the sliding windows. The first correlation coefficient fluctuated around the adaptive threshold. For example, window 1 had a coefficient of 0.598, which exceeded the threshold of 0.577; sliding window 2 had a coefficient of 0.412, which was below the threshold of 0.473; and sliding window 4 had a coefficient of 0.451, which exceeded the threshold of 0.399. This showed a staggered distribution, which resulted in a close but not completely consistent relationship between the data points and the threshold curve. This is consistent with the expectation that the observed values ​​would fluctuate randomly around the threshold in the statistical significance test.

[0030] The birth time is recorded as the moment when the isolated downstream component first appears, and the death time is recorded as the moment when the isolated downstream component first merges into a connected component containing an upstream node via an edge. This includes: During the process of scanning the dynamic graph sequence in chronological order, the appearance and disappearance of isolated downstream components are continuously monitored, and the birth time and disappearance time of each isolated downstream component are recorded. When a candidate component is first determined to be an isolated downstream component, the starting time of the sliding window in which the isolated downstream component is first determined is recorded as the birth time. If the same candidate component is continuously determined to be an isolated downstream component in multiple consecutive sliding windows, the birth time is only recorded in the window in which it is first determined, and subsequent windows are not recorded repeatedly. Specifically, set In the sliding window The first connected component to satisfy the above isolation criterion, and the sliding window Previous sliding window There is no set of nodes in the same number of nodes as the component or that meets the overlap threshold. If a candidate component is determined to be an isolated downstream component, then the isolated downstream component... The birth time Defined as:

[0031] in Indicates the first The starting time of each sliding window; if multiple independent connected components within the same sliding window first satisfy the isolation criterion, then their respective birth times are recorded. Each component is independently assigned a unique component identifier, and its birth time is maintained independently during cross-window tracing. The isolated downstream component is traced along the time sequence of the dynamic graph. During the cross-window tracing process, the node member set of the isolated downstream component may change in different sliding windows. That is, a node may leave the isolated downstream component in a subsequent sliding window, or a new downstream node may join the isolated downstream component. To ensure the continuity and consistency of cross-window tracing, the overlap of the node sets of adjacent sliding windows is used to identify the same component. Specifically, the node set of the isolated downstream component in the current sliding window is intersected with the node sets of all candidate components in the next sliding window one by one, and the ratio of the number of intersection nodes to the number of union nodes is calculated as the overlap. If the overlap between a candidate component and the current isolated downstream component is not lower than a preset overlap threshold, then the candidate component is considered a continuation of the isolated downstream component, and the component identifier and the recorded birth time of the isolated downstream component are continued to be used. If the overlap between all candidate components and the current isolated downstream component is lower than the preset overlap threshold, then it is determined that the isolated downstream component has disappeared in the next sliding window, and the current sliding window is the last existing window of the isolated downstream component, and it is no longer tracked. The preset overlap threshold is preset according to the ratio of the sliding window length to the sampling period, so that when a single node is added or removed from the node members in adjacent sliding windows, the overlap calculation result still meets the requirement of not being lower than the threshold, thereby ensuring the reasonable continuity of component identifiers between adjacent windows. The preset overlap threshold is pre-set based on the ratio of the sliding window length to the sampling period. When the sliding window duration is 30 minutes and the sliding step size is 5 minutes, the time overlap ratio of adjacent sliding windows is relatively high, and the set of nodes contained in the same connected component in adjacent windows should maintain a high degree of overlap. If the overlap threshold is set too low, candidate components that do not belong to the same component may be incorrectly merged, resulting in confusion in the record of birth time. If it is set too high, the component termination may be incorrectly determined due to the normal fluctuation of individual nodes, resulting in the same propagation event being split into multiple independent events. In this embodiment, the preset overlap threshold is set to 80%. This value ensures that when a single node is added or removed from the node members in adjacent sliding windows, the overlap calculation result still meets the requirement of not being lower than the threshold, thereby ensuring the reasonable continuity of component identification between adjacent windows. Monitor the formation of valid edges between any node in the isolated downstream component and any upstream node. When any node in the isolated downstream component forms a valid edge with any upstream node for the first time, and this valid edge causes the isolated downstream component to be incorporated into a connected component containing the upstream node, record the start time of the sliding window containing the valid edge as the extinction time. The incorporation into a connected component containing the upstream node means that after the valid edge is established, at least one node in the isolated downstream component is in the same connected component as the upstream node. The time difference between the time of the disappearance and the time of the birth of the propagation event is calculated, and this time difference is defined as the topological propagation delay of the propagation event. The topological propagation delay reflects the time delay from the formation of a stable local coupling structure independent of the upstream wind farm by wind speed fluctuations to the breaking of the structure by the wake propagation effect from the upstream and its reintegration into the whole field coupling structure. Furthermore, while identifying the disappearance of the isolated downstream component, the effective connection that caused the disappearance of the isolated downstream component is extracted as a bridging edge. The bridging edge is an effective connection that directly connects a node in the isolated downstream component to a node in the connected component containing the upstream node. If there are multiple effective connections connecting the isolated downstream component and the connected component containing the upstream node at the time of disappearance, the effective connection with the largest first correlation coefficient is selected as the bridging edge. If there are multiple effective connections with the largest first correlation coefficient and the first correlation coefficients are equal, the effective connection with the smallest spatial distance between the isolated downstream component side node and the connected component side node containing the upstream node is selected as the bridging edge. The spatial coordinates of the nodes at both ends of the bridging edge are recorded, that is, the spatial coordinates of a certain wind measurement point in the upstream wind farm and a certain wind measurement point in the downstream wind farm. Obtain wind direction and wind speed information corresponding to each sliding window. The wind direction information is the vector average wind direction of the wind speed time series signals of all wind measurement points within the sliding window, and the wind speed information is the arithmetic average wind speed of the wind speed time series signals of all wind measurement points within the sliding window. Divide the wind direction into multiple wind direction sector types according to a preset angle interval, and divide the wind speed into multiple wind speed levels according to a preset wind speed range. Sliding windows with the same wind direction sector type and the same wind speed level are determined to have the same incoming flow conditions. The preset angle interval is 30 degrees, dividing the 360-degree wind direction range into 12 wind direction sector types. The first wind direction sector type has an angle range of 0 to 30 degrees, with 15 degrees as the center direction of the sector; the second wind direction sector type has an angle range of 30 to 60 degrees, with 45 degrees as the center direction of the sector; and so on, until the 12th wind direction sector type has an angle range of 330 to 360 degrees, with 345 degrees as the center direction of the sector; when the measured wind direction is located on the boundary line between the angle ranges of two adjacent wind direction sector types, the measured wind direction is assigned to the wind direction sector type with the smaller angle as the starting boundary. The wind speed level divides the wind speed value into multiple intervals at 0.5 meters per minute. That is, the wind speed range of the first wind speed level is from the cut-out wind speed to 0.5 meters per second, the wind speed range of the second wind speed level is from greater than 0.5 meters per second to 1.0 meters per second, and so on until the interval is greater than the cut-out wind speed. Wind speed time-series signals that are above the cut-out wind speed are excluded from the processing of this method. The bridging edges that cause the isolated downstream component to disappear under the same incoming flow conditions are extracted. The spatial coordinates of the two ends of the bridging edges corresponding to multiple topology propagation events under the same incoming flow conditions are superimposed. The spatial coordinates of all endpoints (including upstream and downstream endpoints) after superposition are processed by the interpolation fitting method to generate a smooth spatial curve. This curve is the dominant path of wake propagation under the incoming flow conditions, which represents the average spatial trajectory of the wake propagating from the upstream wind farm to the downstream wind farm. In some embodiments, based on the relationship between the disappearance time of each propagation event and the spatial location of the bridging edge endpoint, wavefront isochrones are generated through spatial interpolation. Specifically, the spatial coordinates of the downstream endpoint of the bridging edge and the corresponding topological propagation delay in each propagation event are taken as a set of known data points. An inverse distance weighted interpolation algorithm is used to estimate the topological propagation delay value at any location within the spatial region of the wind farm cluster, obtaining a spatially continuous delay field. The inverse distance weighted interpolation method is then used to estimate the topological propagation delay value at any location within the spatial region of the wind farm cluster based on the known data point set, obtaining a spatially continuous delay field. A continuous delay field; the inverse distance weighted interpolation method uses the reciprocal of the spatial distance from the location to be estimated to each known data point as the weight to perform a weighted average of the topological propagation delay values ​​of each known data point, and obtains the delay estimate at the location to be estimated. The closer the known data points are in space, the greater their contribution to the estimation result; a set of delay values ​​with equal time intervals are preset, and the contour lines corresponding to each delay value are extracted on the delay field. These contour lines are the wavefront isochrones under the incoming flow conditions; the wavefront isochrones characterize the positional distribution of the wake influence wavefront advancing at equal time intervals within the spatial range of the wind farm cluster; Furthermore, the topology propagation delay under multiple wind direction sector types and multiple wind speed levels is statistically analyzed. All identified topology propagation events are grouped according to their respective wind direction sector types and wind speed levels, and the statistical representative value of the topology propagation delay within each group is calculated. The statistical representative value is the median or arithmetic mean. A three-dimensional feature phase diagram is constructed with wind direction sector type as the first coordinate axis, wind speed level as the second coordinate axis, and topology propagation delay as the third coordinate axis. The three-dimensional feature phase diagram fully presents the panoramic distribution characteristics of wake propagation delay between wind farms under different incoming flow conditions.

[0032] Please see Figure 2 The figure shows a fitting curve of the standard deviation of the statistical distribution of the second correlation coefficient and the adaptive threshold provided in the embodiments of this application, as shown in the figure. The degree of centralization and dispersion of the statistical distribution of the second correlation coefficient is determined by, specifically through... The standard deviation of the second correlation coefficient is determined by the upper 99th percentile. As the standard deviation increases, the dispersion of the random correlation level intensifies, and the adaptive threshold rises accordingly. Conversely, as the standard deviation decreases, the random correlation level concentrates towards the mean, and the adaptive threshold decreases accordingly. Due to the different statistical characteristics of wind speed fluctuations within each sliding window, the standard deviation of the second correlation coefficient varies between 0.15 and 0.40. The value is dynamically adjusted between 0.38 and 0.75 accordingly. The upward trend of the fitted curve reflects the positive correlation overall, while the discrete distribution of the data points indicates... In addition to being affected by the standard deviation of the statistical distribution of the second correlation coefficient, it is also affected by factors such as the slight fluctuations in the mean of the statistical distribution of the second correlation coefficient; the statistical standard deviation of the second correlation coefficient shown in this figure is related to... The statistical correlation between them is not completely determined, which corresponds to the fact that the adaptive thresholds of different sliding windows in step S300 of the instruction manual can be different, realizing the feature of dynamic adjustment of the association judgment criteria. Please see Figure 3 The figure shows a line graph of the adaptive threshold and the first correlation coefficient provided in the embodiments of this application. The figure shows the dynamic execution process of the valid connection determination logic. That is, the first correlation coefficient of any node pair is compared with the adaptive threshold of the sliding window. When the first correlation coefficient is greater than the adaptive threshold of the sliding window, it is marked as a valid connection. When the first correlation coefficient is less than or equal to the adaptive threshold of the sliding window, it is determined as an invalid connection. Figure 3 The relative positions of the two broken lines alternate with the window number. Specifically, the first correlation coefficient broken line for windows 1, 4, 5, 8, 11, 14, 17, 18, 22, and 29 is located at... Above the broken line are the valid edges; the broken line of the first correlation coefficient for the remaining 20 windows is located at... Below or with the fold line The polylines basically overlap, corresponding to invalid edges. The values ​​in the valid edge determination column of Table 1 are the same as those in the invalid edge determination column. Figure 3 The relative positions of the two broken lines correspond one-to-one. For example, in window 4, the first correlation coefficient is greater than... The valid edge determination is 1.

[0033] Please see Figure 4 This is a block diagram of a system for identifying wake propagation delay between offshore wind farms, provided in an embodiment of this application. As an implementation of the aforementioned method for identifying wake propagation delay between offshore wind farms, this application provides an embodiment of a system for identifying wake propagation delay between offshore wind farms. As shown in the figure, this embodiment of the system for identifying wake propagation delay between offshore wind farms is similar to... Figure 1 Corresponding to the method embodiment shown, this identification system based on wake propagation delay between offshore wind farms can be specifically applied to various electronic devices.

[0034] This embodiment of a system for identifying wake propagation delay between offshore wind farms includes: The signal acquisition module is used to acquire the wind speed time sequence signal of each wind measurement point in the offshore wind farm group within a preset window, perform standardization processing on each wind speed time sequence signal to determine the standard wind speed sequence of each wind measurement point, construct a node set with each wind measurement point as a node, and divide the nodes into upstream nodes and downstream nodes. The data reset module is used to sequentially capture each sliding window according to a preset sliding step size. Within each sliding window, it calculates the first correlation coefficient of the standard wind speed sequence of any two nodes, resets the phase spectrum of the standard wind speed sequence of each node, and calculates the second correlation coefficient of any node pair after the reset. A sorting module is constructed to determine an adaptive threshold based on the statistical distribution of the second correlation coefficient, retain node pairs whose first correlation coefficient exceeds the adaptive threshold as valid edges, construct network snapshots corresponding to the current sliding window based on the valid edges, and arrange the network snapshots according to the time order of the sliding window to obtain a dynamic graph sequence. The delay identification module is used to perform connected component identification on each network snapshot in the dynamic graph sequence in chronological order. It monitors isolated downstream components that consist only of downstream nodes and are not connected to any upstream nodes in a series of sliding windows. The time when the isolated downstream component first appears is recorded as the birth time, and the time when it first merges into a connected component containing upstream nodes through an edge is recorded as the death time. The difference between the death time and the birth time is defined as the topology propagation delay.

[0035] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0036] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0037] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method of identifying propagation lag of inter-farm wake in an offshore wind farm, characterized by, include: The wind speed time series signal of each wind measurement point in the offshore wind farm group is obtained within a preset window. The wind speed time series signal is standardized to determine the standard wind speed sequence of each wind measurement point. Each wind measurement point is used as a node to construct a node set, and the nodes are divided into upstream nodes and downstream nodes. Each sliding window is captured sequentially according to a preset sliding step size. Within each sliding window, the first correlation coefficient of the standard wind speed sequence of any two nodes is calculated. The phase spectrum of each node's standard wind speed sequence is reset, and the second correlation coefficient of any node pair after the reset is calculated. An adaptive threshold is determined based on the statistical distribution of the second correlation coefficient. Node pairs with a first correlation coefficient exceeding the adaptive threshold are retained as valid edges. A network snapshot corresponding to the current sliding window is constructed based on the valid edges. The network snapshots are arranged in the time order of the sliding window to obtain a dynamic graph sequence. For each network snapshot in the dynamic graph sequence, connected component identification is performed in chronological order. Isolated downstream components consisting only of downstream nodes and not connected to any upstream nodes for several consecutive sliding windows are monitored. The first appearance of the isolated downstream component is recorded as the birth time, and the first time it is merged into the connected component containing upstream nodes through an edge is recorded as the extinction time. The difference between the extinction time and the birth time is defined as the topology propagation delay.

2. The method of claim 1, wherein, The wind speed time series signals corresponding to each wind measurement point are standardized to determine the standard wind speed sequence corresponding to each wind measurement point, including: The wind speed time series signals collected by each wind measurement point within a preset window are processed to remove the mean. The wind speed time series signal after the mean removal process is divided by the standard deviation of the wind speed time series signal of that wind measurement point to obtain a standard wind speed sequence with a mean of 0 and a standard deviation of 1. Each wind measurement point is used as a node to construct a node set, which is then divided into upstream and downstream nodes, including: Obtain the spatial coordinates of each wind measurement point and the layout direction of the offshore wind farm group. Based on the relative position of each wind measurement point along the prevailing wind direction, the nodes corresponding to the wind measurement points located in the upstream wind farm are classified as upstream nodes, and the nodes corresponding to the wind measurement points located in the downstream wind farm are classified as downstream nodes.

3. The method of claim 1, wherein, Within a preset window, a sliding step size is set. Within each sliding window, the first correlation coefficient of the standard wind speed sequence of any two nodes is calculated, including: Within a preset window, each sliding window is sequentially extracted according to a preset sliding step size; within each sliding window, the Pearson correlation coefficient of the standard wind speed sequence of any two nodes forming a node pair is calculated, and the Pearson correlation coefficient is used as the first correlation coefficient of the node pair.

4. The method of claim 1, wherein, The phase spectrum of the standard wind speed sequence corresponding to each node is reset to obtain the reset wind speed sequence corresponding to each node, including: Perform a Fourier transform on the standard wind speed sequence corresponding to each node to extract the amplitude spectrum and phase spectrum; extract the phase values ​​of the corresponding positive frequency components from the phase spectrum to form the first phase sequence; randomly shuffle the order of each phase value in the first phase sequence to obtain the second phase sequence. The phase values ​​in the second phase sequence are assigned to the positive frequency components in sequence, and the phase values ​​of the corresponding negative frequency components are determined from the phase values ​​of the positive frequency components according to the conjugate symmetry, thus forming a randomized phase spectrum. The amplitude spectrum and the randomized phase spectrum are combined and then subjected to an inverse Fourier transform to obtain the reset wind speed sequence. Calculate the second correlation coefficient for any pair of nodes after the reset, including: For the standard wind speed sequence corresponding to each node within the same sliding window, perform multiple phase spectrum reset operations. In each operation, the phase spectrum is independently and randomly rearranged to generate multiple sets of reset wind speed sequences. Calculate the Pearson correlation coefficient of any two nodes corresponding to each set of reset wind speed sequences, and combine all the Pearson correlation coefficients obtained from multiple calculations to form the statistical distribution of the second correlation coefficient corresponding to the sliding window.

5. The method of claim 4, wherein, The adaptive threshold is determined based on the statistical distribution of the second correlation coefficient, including: The statistical distribution of the second correlation coefficient corresponding to each sliding window is sorted in ascending order of numerical value. Using the preset upper quantile position parameter as the index, the second correlation coefficient value located at the preset upper quantile position in the ascending order is used as the adaptive threshold of the sliding window. Node pairs with a first correlation coefficient exceeding the adaptive threshold are retained as valid edges. A network snapshot corresponding to the current sliding window is constructed based on these valid edges, resulting in a dynamic graph sequence, including: For each sliding window, the first correlation coefficient of any node pair is compared with the adaptive threshold corresponding to that sliding window. When the first correlation coefficient is greater than the adaptive threshold, the node pair is determined to be a valid connection. Using all nodes as vertices and all valid connecting edges as edges, construct a network snapshot corresponding to the sliding window; The network snapshots of each sliding window are arranged in chronological order of their respective sliding window start times to form a dynamic graph sequence that evolves over time.

6. The method of claim 5, wherein, Monitoring isolated downstream components that consist only of downstream nodes and are not connected to any upstream node for several consecutive sliding windows includes: Run the disjoint-set data structure algorithm on each network snapshot in the dynamic graph sequence to identify all connected components in each network snapshot, and mark the connected components whose nodes are all downstream nodes as candidate components; For the candidate component of the current sliding window, backtrack the overall connection status of all nodes constituting the candidate component within a consecutive preset number of sliding windows, including the current sliding window. If, within the consecutive preset number of sliding windows, no node of the candidate component forms a valid connection with any upstream node, then the candidate component is determined to be an isolated downstream component.

7. The method of claim 6, wherein, The birth time is recorded as the moment when the isolated downstream component first appears, and the death time is recorded as the moment when the isolated downstream component first merges into a connected component containing an upstream node via an edge. This includes: The starting time of the sliding window in which the isolated downstream component is first determined to be true is recorded as the birth time; Continue tracing the isolated downstream component along the time sequence of the dynamic graph. When any node in the isolated downstream component forms a valid connection with any upstream node for the first time, and the valid connection causes the isolated downstream component to be incorporated into a connected component containing the upstream node, the start time of the sliding window containing the valid connection is recorded as the extinction time. Calculate the time difference between the extinction time and the birth time, and define the time difference as the topological propagation delay of this propagation event.

8. The method of claim 7, wherein, Also includes: Obtain wind direction and wind speed information corresponding to each sliding window, and determine the sliding windows with the same wind direction sector type and the same wind speed level as having the same incoming flow conditions; Extract the effective edges that cause the isolated downstream component to disappear under the same incoming flow conditions, and obtain the spatial coordinates of the nodes at both ends of the effective edge; superimpose the spatial coordinates of the nodes at both ends of the effective edges corresponding to multiple topological propagation events under the same incoming flow conditions, reconstruct the dominant path of wake propagation through interpolation fitting method, and generate wavefront isochrones. Same incoming flow conditions refer to incoming flow conditions with the same wind direction, sector type, and wind speed level.

9. The method of claim 1, wherein, Also includes: Obtain wind direction and wind speed information for each sliding window in the dynamic graph sequence; The topological propagation delay under multiple wind direction sector types and multiple wind speed levels is statistically analyzed, and a three-dimensional feature phase map is constructed with wind direction sector type as the first coordinate axis, wind speed level as the second coordinate axis, and topological propagation delay as the third coordinate axis.

10. A system for identifying propagation lag of inter-array wake in an offshore wind farm, characterized by The identification system is used to execute the identification method for wake propagation delay between offshore wind farms according to any one of claims 1 to 9, including: The signal acquisition module is used to acquire the wind speed time sequence signal of each wind measurement point in the offshore wind farm group within a preset window, perform standardization processing on each wind speed time sequence signal to determine the standard wind speed sequence of each wind measurement point, construct a node set with each wind measurement point as a node, and divide the nodes into upstream nodes and downstream nodes. The data reset module is used to sequentially capture each sliding window according to a preset sliding step size. Within each sliding window, it calculates the first correlation coefficient of the standard wind speed sequence of any two nodes, resets the phase spectrum of the standard wind speed sequence of each node, and calculates the second correlation coefficient of any node pair after the reset. A sorting module is constructed to determine an adaptive threshold based on the statistical distribution of the second correlation coefficient, retain node pairs whose first correlation coefficient exceeds the adaptive threshold as valid edges, construct network snapshots corresponding to the current sliding window based on the valid edges, and arrange the network snapshots according to the time order of the sliding window to obtain a dynamic graph sequence. The delay identification module is used to perform connected component identification on each network snapshot in the dynamic graph sequence in chronological order. It monitors isolated downstream components that consist only of downstream nodes and are not connected to any upstream nodes in a series of sliding windows. The time when the isolated downstream component first appears is recorded as the birth time, and the time when it first merges into a connected component containing upstream nodes through an edge is recorded as the death time. The difference between the death time and the birth time is defined as the topology propagation delay.

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