Marine transportation network oscillation propagation process analysis method based on time-frequency disturbance signal

Abstract

The invention discloses a marine transportation network oscillation propagation process analysis method based on a time-frequency disturbance signal, and belongs to the field of geographic information intelligent prediction, and the method comprises the steps: calculating the monthly total transportation volume of original marine transportation network data, and forming multi-time-point marine transportation network time series data; clustering the entity import and export time sequences by adopting dynamic time warping to obtain a plurality of entity groups; in each entity group, extracting oscillation fluctuation characteristics of each entity by adopting a sliding standard deviation analysis method; the entity inlet and outlet time sequence is converted into a time-frequency space through short-time Fourier transform, and an oscillation type and oscillation outbreak time are obtained through calculation; and constructing a disturbance propagation map, and analyzing the ocean transportation network oscillation propagation process of each entity group in combination with the oscillation fluctuation characteristics. The research aims at disclosing a propagation mechanism of disturbance in a marine transportation network, and provides support for understanding network structure toughness, identifying key influence nodes and optimizing marine transportation network management.

Description

Technical Field

[0001] This invention belongs to the field of intelligent prediction of geographic information, and specifically relates to a method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals. Background Technology

[0002] Frequent occurrences of multi-source disturbances, such as port congestion, transportation delays, and natural disasters, cause the maritime network structure and function to undergo complex dynamic changes. These disturbances may not only lead to the failure of local nodes, but may also spread through the network structure, forming cascading failures or oscillating propagation, ultimately affecting the stability of the global trade chain.

[0003] Current research primarily focuses on static network topology, local vulnerability assessment, or single disturbance perspectives, making it difficult to comprehensively characterize the dynamic evolution mechanisms of maritime networks under multiple disturbances. Particularly in identifying disturbance propagation paths, analyzing oscillation processes, and capturing disturbance-induced structural failure chains, there are issues of lagging identification, unclear mechanisms, and insufficient quantification capabilities. These shortcomings severely restrict the improvement of maritime network risk early warning capabilities and the scientific formulation of resilience governance measures. Summary of the Invention

[0004] The purpose of this invention is to address the issue that disturbances between nodes in maritime networks caused by multi-source disturbances may exhibit oscillating fluctuations along the time axis (these oscillations not only reflect the stability of the nodes themselves but may also serve as indicators of upstream disturbances propagating downstream, possessing significant structural resilience indicative value). This invention provides a method for analyzing the propagation process of oscillations in maritime networks based on time-frequency disturbance signals. Based on raw maritime network data, the data is first aggregated by calendar month and the total monthly transport volume is calculated to form multi-time-point time series data of the maritime network. Then, based on Dynamic Time Warping (DTW) distance, the import and export time series of entities are clustered to obtain entity groups with similar dynamic trends. Subsequently, within each group, the moving standard deviation analysis method is used to extract the oscillation characteristics of each entity, including oscillation amplitude, duration, and intensity. Finally, a Short-Time Fourier Transform (SFT) is applied. The STFT (Sequential Transform) projects time series data into a time-frequency space, analyzes the energy distribution of frequency bands to identify oscillation types (low / medium / high frequency) and oscillation burst times. Finally, by combining oscillation types and burst times, a disturbance propagation map is constructed, enabling the identification of oscillation intensity, frequency characteristics, and burst times from time series data. Furthermore, it performs classification analysis at the dimension of entity grouping to capture the spatial diffusion patterns and path characteristics of disturbances.

[0005] According to one aspect of the present invention, a method for analyzing the propagation process of oscillations in maritime networks based on time-frequency disturbance signals is provided, comprising:

[0006] Based on the acquired raw maritime network data, the total monthly transport volume is collected according to the calendar and calculated to form multi-time point time series data of the maritime network;

[0007] Based on the import and export time series of entities in the multi-time point maritime network time series data, dynamic time warping is used to cluster the import and export time series of entities to obtain multiple groups of entities with similar dynamic change trends.

[0008] Within each group of entities with similar dynamic trends, the oscillation and fluctuation characteristics of each entity are extracted using the moving standard deviation analysis method.

[0009] The time series of entity import and export is converted to time-frequency space by short-time Fourier transform, and the energy intensity is calculated. The oscillation type and oscillation outbreak time are obtained based on the energy intensity.

[0010] Based on the oscillation type and oscillation outbreak time, a disturbance propagation map is constructed. Combined with the oscillation fluctuation characteristics of each entity, the oscillation propagation process of the shipping network of each entity group is analyzed.

[0011] Furthermore, the moving standard deviation analysis method is used to extract the oscillation characteristics of each entity, including:

[0012] For each entity's time series, calculate its moving standard deviation sequence;

[0013] The maximum value of the moving standard deviation sequence is taken as the oscillation amplitude;

[0014] The longest time period in which the oscillation condition is met continuously is taken as the oscillation duration; the oscillation condition is when the sliding standard deviation at a certain moment exceeds the overall mean of the sliding standard deviation of the time series.

[0015] The intensity of the oscillation is determined by the amplitude and duration of the oscillation.

[0016] Furthermore, the moving standard deviation sequence The expression is:

[0017]

[0018] in, Indicates the window length. , indicating that at a time node The endpoint is [point name], and the length is [length]. Within a given time window, the local average level of the entity's import and export volume. This represents the summation index used in the calculation of the moving standard deviation. Indicates a time point.

[0019] Furthermore, the entity's import and export time series are transformed to time-frequency space using short-time Fourier transform, and the energy intensity is calculated, including:

[0020] The time series of entity import and export is localized by using a sliding window function. Fourier transform is then performed on the data within each time window after localization to obtain the Fourier coefficients.

[0021] The square of the modulus of the Fourier coefficients is defined as the energy intensity, expressed as:

[0022] ,

[0023] in, For entities In time ,frequency Energy intensity at that location For entities In time ,frequency Fourier coefficients at the location.

[0024] Furthermore, the expression for calculating the Fourier coefficients is as follows:

[0025] ,

[0026] in, For entities In time ,frequency Fourier coefficients at the location; For entities The original time series signal; This is a sliding window function; For integration variables; The time corresponding to the center of the window; For frequency variables; These are the basis functions for the Fourier transform.

[0027] Furthermore, the oscillation type and oscillation burst time are obtained based on the energy intensity, including:

[0028] The type of oscillation is determined by analyzing the distribution pattern of energy intensity in the time-frequency space;

[0029] Find the time point corresponding to the maximum energy intensity and define it as the oscillation burst time. The expression is:

[0030] ,

[0031] in, For entities In time ,frequency The energy intensity at that location.

[0032] Furthermore, based on the acquired raw maritime network data, the total monthly transport volume is collected and calculated according to the calendar, including:

[0033] Based on the original maritime network data, all transport records between the same departure entity and arrival entity within each calendar month are summarized, and the total transport volume for the month is calculated.

[0034] Furthermore, dynamic time warping is used to cluster the import and export time series of the entities to obtain entity groups with similar dynamic trends, including:

[0035] The dynamic time warping algorithm is used to calculate the dynamic similarity between the import and export time series of any two entities.

[0036] Based on the dynamic similarity between the import and export time series of any two entities, agglomerative hierarchical clustering algorithm is used to cluster them on the distance matrix, dividing them into multiple groups of entities with similar dynamic changing trends.

[0037] According to one aspect of the present invention, a system for analyzing the propagation process of oscillations in maritime networks based on time-frequency disturbance signals is provided, comprising:

[0038] The data processing module is used to collect and calculate the total monthly transportation volume based on the acquired raw maritime network data according to the calendar, forming multi-time point time series data of the maritime network.

[0039] The clustering module is used to obtain the import and export time series of entities based on multi-time point maritime network time series data, and to cluster the import and export time series of entities using dynamic time warping to obtain multiple groups of entities with similar dynamic trends.

[0040] The oscillation and fluctuation feature extraction module is used to extract the oscillation and fluctuation features of each entity within each group of entities with similar dynamic trends using the moving standard deviation analysis method.

[0041] The short-time Fourier transform module is used to convert the time series of entity import and export to time-frequency space through short-time Fourier transform, calculate the energy intensity, and obtain the oscillation type and oscillation burst time based on the energy intensity;

[0042] The analysis module is used to construct disturbance propagation maps based on oscillation type and oscillation outbreak time, and analyze the oscillation propagation process of each entity group in the shipping network by combining the oscillation fluctuation characteristics of each entity.

[0043] According to one aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method for analyzing the propagation process of oscillations in maritime networks based on time-frequency disturbance signals.

[0044] Compared with the prior art, the beneficial effects of the present invention are:

[0045] 1. This invention uses dynamic time warping to cluster the import and export time series of entities to obtain entity groups with similar dynamic trends. It uses the sliding standard deviation analysis method to extract the oscillation and fluctuation characteristics of entities within each group. This solves the problem that current research often focuses on static network topology, local vulnerability assessment or single disturbance perspective, which makes it difficult to comprehensively characterize the dynamic evolution mechanism of maritime networks under multiple disturbance backgrounds.

[0046] 2. This invention projects the time series onto the time-frequency space through short-time Fourier transform to identify the oscillation type and oscillation burst time, thereby achieving accurate capture of the spatial diffusion mode and path characteristics of disturbance.

[0047] 3. This invention constructs a disturbance propagation map by combining oscillation type and oscillation outbreak time, and performs classification analysis on the entity group dimension, revealing the oscillation behavior and propagation mechanism caused by disturbance factors in the maritime network, providing support for understanding network structural resilience, identifying key influencing nodes, and optimizing global maritime network management. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 The flowchart of the method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals provided by the present invention is shown. Detailed Implementation

[0050] It should be noted that the entity proposed in the embodiments of the present invention can be an organization with maritime transport capabilities.

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] like Figure 1 As shown in the figure, this invention proposes a method for analyzing the oscillation propagation process of a maritime network based on time-frequency disturbance signals. The method includes: based on the original maritime network data, aggregating the data by calendar month and calculating the total monthly transport volume to form multi-time-point maritime network time series data; clustering the import and export time series of entities based on dynamic time warping to obtain entity groups with similar dynamic trends; extracting the oscillation characteristics of each entity within each group using the sliding standard deviation analysis method, including oscillation amplitude, duration, and intensity; projecting the time series onto the time-frequency space using short-time Fourier transform and analyzing the frequency band energy distribution to identify the oscillation type and oscillation outbreak time; constructing a disturbance propagation map by combining the oscillation type and oscillation outbreak time, and performing classification analysis on the entity grouping dimension.

[0053] Specifically, embodiments of the present invention provide specific steps for parameter initialization and data input:

[0054] The data used in this embodiment of the invention comes from a professional shipping big data platform (Elane Shipping Big Data Platform, https: / / www.elane.com / ), which covers actual transportation records of various maritime goods between major ports worldwide. The raw data includes departure entity (country_code1), arrival entity (country_code2), transport volume (dwt_split, in tons), and transport time (atd, recorded as actual departure time).

[0055] For ease of study, coal was selected as the research sample, as it is highly representative and can effectively reflect the response differences of various network types under disturbance conditions. It can serve as a vehicle for experimentally verifying the method for analyzing the oscillation propagation process of maritime transport networks—using the analysis of the coal maritime transport network to demonstrate the response differences of various network types under disturbance conditions, thereby supporting the effectiveness and applicability of the method. The raw data was aggregated by calendar month, and the total monthly transport volume was calculated to form multi-time-point time series data of the maritime transport network. This comprehensively reflects the dynamic changes in transport volume between different entities over time, providing a standardized data foundation for subsequent analysis.

[0056] Specifically, embodiments of the present invention provide specific steps for entity time series clustering based on DTW:

[0057] 1. In entity time series clustering based on dynamic time warping, the import and export transportation data of each entity are first processed into time series data. The import and export time series is not directly equivalent to the import and export transportation data, but rather the result obtained after processing the import and export transportation data of each entity into time series data (e.g., let the import and export time series of entity i be...). ,in This represents the import and export volume of entity i at time t.

[0058] Let entity The import and export time series are The DTW distance is used to measure the similarity between any two entity sequences, allowing for "stretching" and "compression" on the time axis to find the optimal matching path. Pairwise DTW distance calculations are performed on all entities to obtain a symmetric distance matrix. An agglomerative hierarchical clustering algorithm is then used to cluster entities on the distance matrix D, dividing entities with similar dynamic behaviors into K entity groups. This enhances the local correlation and dynamic consistency of subsequent oscillation propagation analysis, facilitating the identification of propagation patterns within each group. The expression for calculating the distance using dynamic time warping is:

[0059] (1)

[0060] in, This represents the distance between the import and export time series of two entities (corresponding to time series x and y) calculated using the Dynamic Time Warping (DTW) algorithm. It is used to measure the dynamic similarity between the two in terms of the trend and fluctuation rhythm of transportation volume changes. The smaller the value, the more similar the dynamic trend. P represents the set of all legal time alignment paths when calculating the DTW distance. These paths are used to "stretch" and "compress" different time series on the time axis to match their asynchronous dynamic changes. This indicates any specific regularized path selected. Representing a path The alignment point of two sequence elements. Then it is a sequence The Elements and sequences The The difference between elements is measured (usually using Euclidean distance). By calculating the pairwise DTW distance between the time series of all entities, a symmetric N*N distance matrix D (where N is the total number of entities involved in the analysis) can be obtained. The elements in the matrix... The smaller the value, the stronger the entity. With entity The more similar the dynamic trends of import and export time series, the better.

[0061] 2. Agglomerative clustering algorithm is used to cluster entities on D, dividing them into K entity groups. The significance of clustering is to group entities with similar dynamic behaviors into the same group, which facilitates the identification of propagation patterns within each group, rather than performing "unstructured" oscillation identification on the overall network. This step makes the subsequent oscillation propagation analysis more locally relevant and dynamically consistent.

[0062] Specifically, in the dynamic trend clustering based on the time series of entity import and export, the sample entities in the coal transportation network were divided into five groups with similar trends, as shown in Table 1. Overall, these groups exhibit different fluctuation characteristics and system behaviors.

[0063] Table 1 Information on the Fluctuation Process of Coal Transportation Network

[0064] serial number Amplitude (tons / month) Duration (months) strength Entity Count group_0 1587855 9.62 178884.4 13 group_1 370476.4 8.67 42053.26 6 group_2 101092.2 5.40 20551.04 47 group_3 458016 8 57252 4 group_4 393536.3 7.5 55728.03 2 group_5 487655.3 7 69665.04 1

[0065] Specifically, embodiments of the present invention provide specific steps for extracting oscillation characteristic indicators in the time domain by calculating the moving standard deviation sequence:

[0066] Sliding standard deviation analysis: extraction of time-domain oscillation characteristics.

[0067] For each entity i's time series, calculate the moving standard deviation series with a window length w=3. :

[0068] (2)

[0069] in, , indicating that at a time node The endpoint is [point name], and the length is [length]. Within a time window, the local average level of the entity's import and export volume is used as a benchmark value to measure the degree of fluctuation during that period, and is used to calculate the local mean of the sliding standard deviation; Indicates the window length (in this study, we take...). =3); Indicates the summation index in the process of calculating the moving standard deviation; Indicates a time point.

[0070] Three oscillation indicators were extracted from this sequence: oscillation amplitude. (Amplitude, i.e., the maximum value of the moving standard deviation series, is...) ), duration of oscillation (MaxDuration, i.e., the longest period of time during which the oscillation conditions are continuously met), Oscillation Intensity (Calculated based on oscillation amplitude and oscillation duration, the calculation method is as follows) ).

[0071] Specifically, as shown in Table 1, Group 0 exhibits the most pronounced oscillation characteristics. This group has an average amplitude of 1.58 million tons, several times that of the other groups, with a maximum value approaching 7 million tons. The duration and intensity of the oscillations are also the highest. While the dominant frequency is also low, the rhythm shows a multi-peak distribution, indicating strong periodic fluctuation characteristics.

[0072] Specifically, as shown in Table 1, Group 1 exhibits moderate oscillation intensity, with an average amplitude of approximately 370,000 tons and a maximum duration of nearly 9 months. The dominant frequency type is low frequency, and the overall fluctuation rhythm is stable. This group demonstrates a relatively slow response to disturbances and self-regulation ability, typically representing relatively robust, moderately dependent entities. Their fluctuations are significantly affected by upstream transmission, but they do not possess the ability to actively disturb or amplify them.

[0073] Specifically, as shown in Table 1, the second group has the largest number of entities, but its average oscillation amplitude is only about 100,000 tons, with the lowest intensity and shortest duration. The oscillation peaks occur at dispersed times, and the overall response mode is asynchronous, low-energy, and weakly structured. This group is characterized by being affected by disturbances early, but lacks sufficient system coupling capacity. It is located at the outer edge of the propagation structure, belonging to the initial perception and spillover response layer of the disturbance.

[0074] Specifically, as shown in Table 1, the fluctuation amplitude of Group 3 is at a moderate level, averaging 458,000 tons. The peak surge occurred in August 2016, with a dominant low frequency, exhibiting a clear rhythmic concentration and consistency within the group. Its structural characteristics are reflected in its ability to absorb, temporarily store, and mitigate disturbances.

[0075] Specifically, as shown in Table 1, Group 4 contains a few entities with similar structural characteristics, with an average oscillation amplitude of approximately 393,000. Its average intensity ranks second among all groups, second only to Group 5. The relatively small number of nodes, stable fluctuation rhythm, and clear frequency structure reflect its independent response mechanism within the global transportation system.

[0076] Specifically, as shown in Table 1, Group 5 has only one entity, and its oscillation process lasted for 7 months.

[0077] Specifically, this embodiment of the invention also provides specific steps for analyzing the frequency structure and time distribution of oscillations by converting time series fluctuation features extracted based on the sliding standard deviation method to the frequency domain space through short-time Fourier transform:

[0078] 1. Time-frequency domain oscillation feature identification based on STFT analysis

[0079] In the analysis of oscillation propagation in maritime transport networks, the previously used sliding standard deviation method, while effectively extracting indicators characterizing the degree of fluctuation such as oscillation amplitude and duration, only reflects the overall discreteness of the sequence and cannot reveal the distribution pattern of oscillations across different frequency dimensions (i.e., the speed of fluctuation). For example, for entities with periodic fluctuations in transport volume, the fluctuations may contain multi-scale components such as low-frequency (e.g., quarterly or annual cycles), medium-frequency (e.g., monthly fluctuations), or high-frequency (e.g., sudden short-term fluctuations). Standard deviation struggles to distinguish the contributions of these different frequency components, limiting the in-depth analysis of the essential characteristics of disturbances (e.g., whether the disturbance is a continuous low-frequency oscillation or a sudden high-frequency shock). Therefore, this study introduces the Short-Time Fourier Transform (STFT) to transform the time series from the time domain to the time-frequency space, enabling a refined characterization of the frequency structure of the oscillating signal and its dynamic distribution on the time axis. The core idea of ​​STFT is to localize the non-stationary time series using a sliding window function, performing a Fourier transform on the signal within each window, thereby simultaneously preserving the signal's time and frequency information. Its mathematical definition is:

[0080] (3)

[0081] in, For entities The original time series signal (i.e., the change of transportation volume over time). For sliding window functions (such as Hanning window, rectangular window, etc., used to control the precision of temporal localization); The variable is the integral variable, representing the time offset; The time corresponding to the center of the window; For frequency variables; These are the basis functions of the Fourier transform; For entities In time ,frequency The Fourier coefficients at a given time frequency point reflect the signal strength at that time frequency.

[0082] Specifically, to quantify the strength of the oscillations, the square of the magnitude of the Fourier coefficients is defined as the energy intensity:

[0083] (4)

[0084] in, For entities In time ,frequency The energy intensity at a given time and frequency is considered; higher energy indicates more significant oscillations at that time and frequency. Furthermore, by iterating through all times and frequencies, the energy intensity can be determined. The time point corresponding to the maximum value is defined as the oscillation outbreak time. :

[0085] (5)

[0086] This moment Entities were marked The key points where the oscillation energy is most concentrated throughout the time series can be regarded as the potential time when the disturbance begins to significantly affect the transport volume of the entity or when the oscillation intensity reaches its peak, providing an important time reference benchmark for subsequent tracking of the propagation starting point and diffusion path of the disturbance.

[0087] Specifically, the time series of each entity is projected into the time-frequency space using Short-Time Fourier Transform (STFT time-frequency analysis) to identify the oscillation type and oscillation outbreak time. By analyzing the distribution pattern of energy intensity in the time-frequency space, the oscillation type is determined, and finally, a disturbance propagation map is constructed and classified. A disturbance propagation map is constructed by combining the oscillation type and oscillation outbreak time of each entity. Furthermore, at the entity grouping dimension, the oscillation amplitude, duration, intensity, number of entities, and propagation characteristics (such as dual-period feedback type sectors and delayed accumulation type sectors in the coal transportation network) of each group are classified and analyzed to capture the spatial diffusion pattern and path characteristics of the disturbance. The construction of the disturbance propagation map involves sorting entities according to the oscillation outbreak time to form the entity oscillation sequence, i.e., the disturbance propagation map.

[0088] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a system for analyzing the propagation process of oscillations in maritime networks based on time-frequency disturbance signals. This system is used to execute a method for analyzing the propagation process of oscillations in maritime networks based on time-frequency disturbance signals from the above method embodiments.

[0089] The system includes: a data processing module for aggregating and calculating monthly total transport volume based on the acquired raw maritime network data according to a calendar, forming multi-time-point maritime network time series data; a clustering module for obtaining entity import and export time series based on the multi-time-point maritime network time series data, and clustering the entity import and export time series using dynamic time warping to obtain multiple entity groups with similar dynamic trends; an oscillation and fluctuation feature extraction module for extracting the oscillation and fluctuation features of each entity within each entity group with similar dynamic trends using the moving standard deviation analysis method; a short-time Fourier transform module for converting the entity import and export time series to time-frequency space using short-time Fourier transform, calculating the energy intensity, and obtaining the oscillation type and oscillation outbreak time based on the energy intensity; and an analysis module for constructing a disturbance propagation map based on the oscillation type and oscillation outbreak time, and analyzing the maritime network oscillation propagation process of each entity group in conjunction with the oscillation and fluctuation features of each entity.

[0090] The maritime network oscillation propagation analysis system based on time-frequency disturbance signals provided in this invention addresses the situation where disturbances between nodes in a maritime network caused by multi-source disturbances may exhibit oscillatory fluctuations along the time axis. It employs several modules to cluster the import and export time series of entities through dynamic time warping to obtain entity groups with similar dynamic trends. The system then uses sliding standard deviation analysis to extract the oscillation characteristics of entities within each group. This solves the problem that current research often focuses on static network topology, local vulnerability assessment, or single disturbance perspectives, making it difficult to comprehensively characterize the dynamic evolution mechanism of maritime networks under multi-disturbance backgrounds.

[0091] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides an electronic device, including a memory and a processor. The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize the method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals as proposed in the above embodiments.

[0092] In summary, the present invention proposes a method for analyzing the propagation process of maritime network oscillations based on time-frequency disturbance signals. First, data is collected by calendar month to calculate the total monthly transport volume, forming multi-time-point maritime network time series data. This comprehensively reflects the dynamic changes in transport volume between entities, providing a standardized basis for subsequent analysis. Second, the similarity of entity import and export time series is measured based on dynamic time warping distance (DTW allows for finding the optimal matching path through time axis "stretching" and "compression"). An agglomerative hierarchical clustering algorithm is then used to cluster the calculated symmetric distance matrix, dividing it into K groups of entities with similar dynamic trends. This makes the subsequent oscillation propagation analysis more locally correlated and dynamically consistent. Subsequently, within each group, the sliding standard deviation analysis method (with a window length of 3) is used to extract the oscillation characteristics of each entity: the maximum value of the sliding standard deviation sequence defines the oscillation amplitude; the maximum duration of continuously satisfying the oscillation condition defines the oscillation duration; and an amplitude-quantified index defines the oscillation intensity (the oscillation condition indicates that the sliding standard deviation at a certain moment exceeds the overall mean of the sliding standard deviation of the sequence). Next, the time series is projected into the time-frequency space using a short-time Fourier transform (sampling frequency 1 time / month, maximum window length 64 periods, overlap ratio 50%), and the energy intensity (squared Fourier coefficient modulus) is calculated. The dominant oscillation types (low-frequency, mid-frequency, and high-frequency) are identified through frequency band energy distribution, and the oscillation outbreak time is determined by the moment of maximum energy. Finally, a disturbance propagation map is constructed by integrating the oscillation types and outbreak times of each entity. The oscillation characteristics, propagation time series, and node behavior patterns of each group are categorized and analyzed at the entity grouping level, accurately capturing the spatial diffusion patterns and path characteristics of disturbances in the global maritime transport network.

[0093] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals, characterized in that, include: Based on the acquired raw maritime network data, the total monthly transport volume is collected according to the calendar and calculated to form multi-time point time series data of the maritime network; Based on the import and export time series of entities in the multi-time point maritime network time series data, dynamic time warping is used to cluster the import and export time series of entities to obtain multiple groups of entities with similar dynamic change trends. Within each group of entities with similar dynamic trends, the oscillation and fluctuation characteristics of each entity are extracted using the moving standard deviation analysis method. The time series of entity import and export is converted to time-frequency space by short-time Fourier transform, and the energy intensity is calculated. The oscillation type and oscillation outbreak time are obtained based on the energy intensity. Based on the oscillation type and oscillation outbreak time, a disturbance propagation map is constructed. Combined with the oscillation fluctuation characteristics of each entity, the oscillation propagation process of the shipping network of each entity group is analyzed.

2. The method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals according to claim 1, characterized in that, The oscillation characteristics of each entity are extracted using the moving standard deviation analysis method, including: For each entity's time series, calculate its moving standard deviation sequence; The maximum value of the moving standard deviation sequence is taken as the oscillation amplitude; The longest time period in which the oscillation condition is met continuously is taken as the oscillation duration; the oscillation condition is when the sliding standard deviation at a certain moment exceeds the overall mean of the sliding standard deviation of the time series. The intensity of the oscillation is determined by the amplitude and duration of the oscillation.

3. The method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals according to claim 2, characterized in that, The sliding standard deviation sequence The expression is: ， in, Indicates the window length. , indicating that at a time node The endpoint is [point name], and the length is [length]. Within a given time window, the local average level of the entity's import and export volume. This represents the summation index used in the calculation of the moving standard deviation. Indicates a time point.

4. The method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals according to claim 1, characterized in that, The energy intensity is calculated by converting the time series of the entity's import and export to the time-frequency space using short-time Fourier transform, including: The time series of entity import and export is localized by using a sliding window function. Fourier transform is then performed on the data within each time window after localization to obtain the Fourier coefficients. The square of the modulus of the Fourier coefficients is defined as the energy intensity, expressed as: ， in, For entities In time ,frequency Energy intensity at that location For entities In time ,frequency Fourier coefficients at the location.

5. The method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals according to claim 4, characterized in that, The Fourier coefficients are calculated as follows: ， in, For entities In time ,frequency Fourier coefficients at the location; For entities The original time series signal; This is a sliding window function; For integration variables; The time corresponding to the center of the window; For frequency variables; These are the basis functions for the Fourier transform.

6. The method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals according to claim 1, characterized in that, The oscillation type and oscillation burst time are determined based on energy intensity, including: The type of oscillation is determined by analyzing the distribution pattern of energy intensity in the time-frequency space; Find the time point corresponding to the maximum energy intensity and define it as the oscillation burst time. The expression is: ， in, For entities In time ,frequency The energy intensity at that location.

7. The method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals according to claim 1, characterized in that, Based on the acquired raw maritime network data, the total monthly transport volume is collected and calculated according to the calendar, including: Based on the original maritime network data, all transport records between the same departure entity and arrival entity within each calendar month are summarized, and the total transport volume for the month is calculated.

8. The method for analyzing the oscillation propagation process of maritime networks based on time-frequency disturbance signals according to claim 1, characterized in that, Dynamic time warping is used to cluster the import and export time series of the entities to obtain groups of entities with similar dynamic trends, including: The dynamic time warping algorithm is used to calculate the dynamic similarity between the import and export time series of any two entities. Based on the dynamic similarity between the import and export time series of any two entities, agglomerative hierarchical clustering algorithm is used to cluster them on the distance matrix, dividing them into multiple groups of entities with similar dynamic changing trends.

9. A system for analyzing the oscillation propagation process of a maritime network based on time-frequency disturbance signals, characterized in that, The method for analyzing the oscillation propagation process of a maritime network based on time-frequency disturbance signals, as described in claims 1-8, includes: The data processing module is used to collect and calculate the total monthly transportation volume based on the acquired raw maritime network data according to the calendar, forming multi-time point time series data of the maritime network. The clustering module is used to obtain the import and export time series of entities based on multi-time point maritime network time series data, and to cluster the import and export time series of entities using dynamic time warping to obtain multiple groups of entities with similar dynamic trends. The oscillation and fluctuation feature extraction module is used to extract the oscillation and fluctuation features of each entity within each group of entities with similar dynamic trends using the moving standard deviation analysis method. The short-time Fourier transform module is used to convert the time series of entity import and export to time-frequency space through short-time Fourier transform, calculate the energy intensity, and obtain the oscillation type and oscillation burst time based on the energy intensity; The analysis module is used to construct disturbance propagation maps based on oscillation type and oscillation outbreak time, and analyze the oscillation propagation process of each entity group in the shipping network by combining the oscillation fluctuation characteristics of each entity.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method for analyzing the propagation process of oscillations in maritime networks based on time-frequency disturbance signals as described in any one of claims 1 to 8.

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