A traffic super network construction and resilience evaluation method considering cross-modal coupling

Abstract

The application relates to the technical field of transportation planning, and discloses a traffic super-network construction and resilience evaluation method considering cross-mode coupling, which comprises the following steps: obtaining a road network topology, traffic demand and disaster conditions from a basic traffic database, establishing a single-layer physical network topology model of each traffic mode, and configuring an equivalent energy storage buffer component at an intersection node; calculating dynamic passing impedance based on the buffer component storage capacity and converting the dynamic passing impedance into transient equivalent admittance parameters to assemble a global phasor admittance matrix; converting the traffic demand and disaster conditions into an equivalent current vector, combining the global phasor admittance matrix to solve a state space equation, obtaining an equivalent pressure distribution and an actual conduction flow, reconstructing the matrix when a capacity boundary is triggered, and performing evolution calculation to a steady state; and calculating a time integral value of instantaneous effective power based on the evolution result. The application can quantitatively simulate congestion transient conduction and overflow cutoff, and accurately locate key vulnerable nodes of the network.

Description

Technical Field

[0001] This invention relates to the field of transportation planning technology, specifically to a method for constructing and assessing the resilience of a transportation hypernetwork that considers cross-modal coupling. Background Technology

[0002] With the construction of integrated three-dimensional transportation systems, regional transportation systems are gradually evolving into complex hypernetworks interwoven with multiple modes of transportation, such as highways, railways, civil aviation, and waterways. When faced with external disturbances such as natural disasters or emergencies, the transportation network may experience localized physical disconnections and passenger congestion, which can then spread across a single mode of transport, causing global congestion. Therefore, constructing a transportation hypernetwork model that reflects the physical characteristics of multi-modal coupling and accurately assessing its resilience to disturbances is of guiding significance for transportation system planning and emergency resource allocation.

[0003] Existing multi-layer transportation network assessment methods are typically limited to static topology analysis of a single mode of transportation. When dealing with multi-network integration, they often use simple edge weight combinations to construct virtual transfer channels. This conventional modeling approach lacks the ability to dynamically map the actual transfer impedance and spatial capacity constraints at the intersection of cross-modal physical nodes, making it difficult to objectively reflect the real-world bottlenecks in flow storage and buffering within physical hubs, as well as the nonlinear abrupt changes in traffic impedance caused by passenger flow aggregation. Furthermore, under external disaster disturbance scenarios, existing solutions struggle to quantify and simulate the transient transmission process of congestion potential energy over time, especially accurately characterizing the local overflow and transmission interruption phenomena caused by passenger flow accumulation triggering hard physical capacity boundaries within nodes. Due to the lack of a fundamental mathematical description of the aforementioned spatiotemporal dynamic evolution and flow conservation constraints, conventional calculation models result in a static assessment process, making it difficult to accurately calculate the effective traffic power continuously output by the entire network during disturbances. Consequently, it becomes difficult to objectively quantify the entire process of the system's comprehensive dynamic resilience evolution and to accurately locate the key vulnerable entities causing a decline in the overall system's transport efficiency. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for constructing and assessing the resilience of a transportation hypernetwork that considers cross-modal coupling. This method solves the problems of difficulty in objectively quantifying the entire process of the comprehensive dynamic resilience evolution of the system and difficulty in accurately locating key vulnerable entities that cause a decline in the overall transportation efficiency of the system.

[0005] To achieve the above objectives, the first aspect of this invention provides a method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling, comprising the following steps: Obtain road network topology, traffic demand, and disaster disturbance conditions from the basic traffic database; establish single-layer physical network topology models for each mode of transportation based on the road network topology; configure equivalent energy storage buffer components at the intersection nodes of the models and set the flow input model; Based on the storage capacity of the buffer component, an asymmetric variable-weight impedance function is constructed, which transforms the dynamic passage impedance into transient equivalent admittance parameters and assembles them to generate a global phasor admittance matrix. Traffic demand and disaster disturbance conditions are transformed into equivalent current vectors of corresponding nodes; the state space equations are solved by combining the global phasor admittance matrix and the equivalent current vectors to obtain the equivalent pressure distribution and actual conduction flow; when the residence of the buffer component triggers the capacity boundary, the global phasor admittance matrix is ​​reconstructed and iteratively evolved to the steady state; Instantaneous effective power is calculated based on the actual conduction flow and equivalent pressure distribution after evolution calculation; the time integral value of instantaneous effective power under disturbance and baseline conditions is compared to generate a system resilience quantification index; and the physical node or line that causes the index to decrease the most is output based on the node isolation mechanism.

[0006] Preferably, when establishing single-layer physical network topology models for each mode of transportation and configuring equivalent energy storage buffer components, the physical node set and physical line set are extracted, and a single-layer topology model is generated by combining the upper limit of the line design capacity. Based on the spatial distance matching threshold and topological connectivity, the intersection boundary is delineated to generate a cross-modal coupling hub node set. The maximum physical current storage capacity of the equivalent energy storage buffer component is calibrated based on the weighted sum of the products of the actual effective transfer area and the safe space density threshold parameter.

[0007] Preferably, when constructing the asymmetric variable-weight impedance function, the absolute physical time required for cross-modal transfer streamlines under congestion-free free-flow conditions is extracted to generate a static asymmetric transfer impedance matrix. The ratio of the current buffer storage capacity to the maximum physical storage capacity is calculated, and this ratio is processed using upper and lower bound truncation functions. Dynamic amplification calculations are then performed using the nonlinear sensitivity index and impedance amplification penalty coefficient to obtain the dynamic passage impedance of the cross-level transfer channel. The reciprocal of the dynamic passage impedance is calculated and converted into a transient equivalent admittance parameter characterizing the smoothness of network flow. When assembling the global phasor admittance matrix, the transient equivalent admittance parameter is filled with off-diagonal coordinates according to inflow and outflow rules, the sum of the out-degree transient equivalent admittances of the nodes is filled with main diagonal coordinates, and regularized grounding conductance parameters are injected to ensure the matrix satisfies the diagonal dominance condition.

[0008] Preferably, when transforming traffic demand and external disturbance conditions into equivalent current vectors for topological nodes, the flow difference of the target node is calculated based on the dynamic start-point and end-point demand matrix as the nominal equivalent injected current component; the transient abnormal surge current component is calculated by combining the passenger flow release coefficient and the accumulated amount of stranded passenger flow; the nominal equivalent injected current component and the transient abnormal surge current component are algebraically superimposed to assemble an equivalent current vector, and when it is determined that the absolute value of the global initial current scalar residual is greater than the tolerance threshold, the global amortized compensation logic is triggered to perform flow conservation verification.

[0009] Preferably, when solving the system state-space linear equations to calculate the equivalent pressure and conduction flow, the inverse matrix of the global phasor admittance matrix is ​​calculated and multiplied by the verified equivalent current vector to obtain the current transient equivalent congestion potential energy distribution of all network nodes. The difference between the equivalent congestion potential energy at the starting and ending points of the connection is extracted and multiplied by the corresponding admittance parameters to obtain the conduction flow. When the potential energy at the starting point is not greater than that at the ending point, a directional cutoff protection mechanism is triggered to force the conduction flow at the connection to zero and to compensate the obstructed residual in the reverse direction to the equivalent energy storage buffer component inside the starting point, thus maintaining global flow conservation.

[0010] Preferably, when the ratio of the actual cumulative physical dwell time of the equivalent energy storage buffer component to the configured physical capacity hard boundary threshold is greater than the preset critical capacity saturation threshold, and the instantaneous net inflow shear difference is greater than zero, the node is determined to have experienced overflow paralysis. Physical blocking logic is triggered, forcibly overwriting the input connection admittance parameters pointing to this node in the global network to zero, retaining and amplifying the self-admittance elements of the node's main diagonal, and reconstructing the global phasor admittance matrix for the next time step based on the updated parameters.

[0011] Preferably, a set of legitimate destination nodes with net reception attributes and no overflow is selected. The actual aggregated passenger flow of each legitimate destination node is multiplied by the corresponding reception pressure variable and summed algebraically to obtain the instantaneous effective traffic power characterizing the transport efficiency of the system in the current time slice. A definite integral is performed on the instantaneous effective traffic power along the disturbance time axis to obtain the actual total work done during the disturbance period. This is divided by the definite integral of the undisturbed baseline effective power over time to output a resilience quantification index. The index difference before and after entity stripping is obtained through a node isolation traversal mechanism to calculate the relative gradient descent rate of comprehensive resilience. Combined with the resource intervention occupancy cost, a comprehensive intervention value index is generated, and a set of physical entities above the dynamic identification threshold range is output.

[0012] A second aspect of the present invention provides a system for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling, for implementing the method provided in the first aspect above. The system includes: The data acquisition module is used to obtain static road network topology data of highways, railways, civil aviation and waterways from the basic transportation database, as well as historical passenger and freight flow operation data of the corresponding modes of transportation; The hypernetwork mapping module is used to construct a traffic hypernetwork topology model that considers cross-modal coupling and extract network nodes and directed edges. The transient evolution calculation module is used to acquire multi-source heterogeneous traffic flow data, align the multi-source heterogeneous traffic flow data with the time axis, calculate the instantaneous total input flow rate of network nodes within a time step, and calculate the instantaneous total output flow rate in combination with the downstream node status; calculate the equivalent net flow source term vector of network nodes based on the dynamic start-point and end-point demand matrices and external sudden disturbance data; calculate the actual transmission flow on directed edges based on the congestion potential energy gradient between network nodes, and perform reverse compensation of obstructed flow residuals when one-way flow truncation is triggered; calculate the cumulative dwell volume of network nodes based on the actual transmission flow, determine the overflow state in combination with the preset node capacity threshold, and reconstruct the equivalent admittance matrix of the traffic supernetwork topology model when the overflow state is determined; The system evaluation module is used to calculate the instantaneous effective traffic power of the entire network by combining the absolute congestion potential energy of the endpoint nodes with the actual arrival flow in the combined traffic hypernetwork topology model.

[0013] This invention provides a method for constructing and assessing the resilience of a transportation hypernetwork that considers cross-modal coupling. It offers the following advantages: 1. This invention configures equivalent energy storage buffer components at the intersection nodes of single-layer physical network topology models of different transportation modes, and constructs an asymmetric variable-weight impedance function based on the storage capacity of the buffer components, transforming the dynamic passage impedance of cross-layer transfer channels into transient equivalent admittance parameters. This technical feature overcomes the shortcomings of existing multi-layer transportation network evaluation methods, which are mostly limited to static topology analysis of a single transportation mode. It realizes the dynamic calculation and mapping of transfer impedance and capacity constraints at the intersection of cross-mode physical nodes, improving the objectivity and accuracy of transportation supernetwork construction.

[0014] 2. This invention transforms traffic demand and disaster disturbance conditions into equivalent current vectors of topological nodes. It then uses the global phasor admittance matrix to solve the state-space equations to obtain the equivalent pressure distribution and actual conduction flow. Furthermore, it performs local admittance truncation and reconstructs the phasor admittance matrix when the dwell time of the equivalent energy storage buffer component triggers the capacity boundary. This technical feature can quantitatively simulate the transient conduction of congestion potential energy in the network and the overflow truncation phenomenon caused by passenger flow accumulation at nodes, solving the problem that the spread and evolution of traffic network congestion under external disaster disturbance scenarios is difficult to solve numerically.

[0015] 3. This invention calculates instantaneous effective traffic power based on the actual conduction flow of physical connections and the equivalent pressure distribution of corresponding nodes. It generates a system resilience quantification index by comparing the time integral value of this power under disturbance and baseline conditions, and outputs the physical set that causes the maximum decrease in this index by combining a node isolation traversal mechanism. This technical feature establishes a time-dimensional quantitative evaluation standard from transient power to overall system resilience, and can directly output key vulnerable nodes or lines that cause a decline in system efficiency, providing a clear decision-making basis for traffic network disaster intervention and resource allocation. Attached Figure Description

[0016] Figure 1 This is a flowchart of the toughness assessment method of the present invention; Figure 2 This is a schematic diagram of the toughness assessment system of the present invention; Figure 3 This is a curve showing the evolution of sudden disturbances during the morning rush hour in urban rail transit, as presented in this invention. Detailed Implementation

[0017] The technical solutions in 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.

[0018] Please see the appendix Figure 1 and attached Figure 2 This invention provides a system for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling. The system is deployed in a computer device. The computer device includes a processor and a memory. The memory stores a computer program, and the processor executes the computer program to implement the method provided by this invention. The system may include: a data acquisition module, a hypernetwork mapping module, a transient evolution calculation module, and a resilience assessment and output module.

[0019] The data acquisition module is used to obtain static road network topology data for highways, railways, civil aviation, and waterways from the basic transportation database, as well as historical passenger and freight flow data for the corresponding modes of transportation. The static road network topology data includes the physical node and route location information for each mode of transportation. The historical passenger and freight flow data includes train and flight timetable data, as well as continuous traffic flow data for highways.

[0020] The hypernetwork mapping module is connected to the data acquisition module. The hypernetwork mapping module is used to establish a single-layer physical network topology model based on static road network topology data. It also establishes equivalent energy storage buffer components at the intersections of physical nodes of different transportation modes to characterize the physical flow storage capacity of the integrated transportation hub. The hypernetwork mapping module converts the extracted timetable data into a discrete pulse flow input model and the continuous flow data into a continuous wave conduction flow input model.

[0021] The transient evolution calculation module is connected to the hypernetwork mapping module. The transient evolution calculation module calculates the state-dependent variable-weight impedance of the cross-layer transfer channel based on the instantaneous current storage state of the equivalent energy storage buffer components. It converts the physical line impedances and state-dependent variable-weight impedances of each layer into admittance values ​​and assembles them to generate a global node admittance matrix. The transient evolution calculation module also receives externally input disaster disturbance conditions, iteratively solves the discrete-time state-space equations, calculates the network node pressure and actual flow distribution, and performs cascaded evolution calculations for local admittance decay and matrix reconstruction.

[0022] The resilience assessment and output module is connected to the transient evolution calculation module. The resilience assessment and output module calculates the instantaneous effective traffic power based on the actual flow rate reaching the destination node and the equivalent node pressure within a set time period. It compares the integral value of the instantaneous effective traffic power under disturbance conditions with the theoretical integral value under undisturbed conditions, generates a comprehensive system resilience assessment index, and outputs the set of physical nodes or lines that cause the largest decrease in the resilience quantification index.

[0023] Please see the appendix Figure 1 The present invention provides a method for constructing and assessing the resilience of a transportation hypernetwork that considers cross-modal coupling, which may include the following steps.

[0024] In step S100, the data acquisition module extracts the physical nodes and routes of each mode of transportation and constructs a single-layer physical network topology model. The hypernetwork mapping module configures equivalent energy storage buffer components at cross-mode coupling nodes and sets discrete pulse input flow equations and continuous wave conduction flow equations according to the attributes of the transportation modes.

[0025] In step S200, the transient evolution calculation module sets the storage capacity update logic of the equivalent energy storage buffer component and constructs an asymmetric variable-weight impedance function with the storage capacity as the independent variable. The transient evolution calculation module calculates the initial admittance of each branch of the entire network and assembles it to generate the initial global node admittance matrix.

[0026] In step S300, the transient evolution calculation module transforms travel demand into node injection current vectors and solves the state-space equations at each discrete time step. When the current storage capacity of the buffer component reaches the set upper limit, local admittance truncation is triggered and the global node admittance matrix is ​​reconstructed. This process is repeated until the system reaches a new steady state.

[0027] In step S400, the resilience assessment and output module calculates the instantaneous effective traffic power within the evolution cycle and obtains the system resilience quantification index under disturbance scenarios through integration. The resilience assessment and output module compares the system resilience quantification index under different disturbance conditions, locates weak nodes or lines in the network that are coupled across modes, and outputs the identification results to the display terminal.

[0028] In this embodiment, the system provided by the present invention obtains static road network topology data from a basic transportation database and performs primitive definition of a single-layer physical road network. In order to accurately characterize the operating carriers of different modes of transportation in the computing environment, the system divides the integrated transportation network into multiple independent physical network layers according to the spatial distribution attributes and operating characteristics of transportation modes, and constructs a single-layer topology model for each.

[0029] The system defines a set of physical network layers in memory. The elements of this set include highway, railway, civil aviation, and waterway network layers. For any mode of transportation within this set, the data acquisition module extracts basic road network data and transmits it to the hypernetwork mapping module. As a preferred implementation, due to differences in acquisition frequency and spatial precision among multi-source traffic data, the system performs spatiotemporal alignment processing on the road network data based on a unified timestamp and a unified spatial coordinate reference system before constructing the topology model, in order to eliminate data heterogeneity between different transportation systems. The hypernetwork mapping module performs the following steps to complete the primitive definition.

[0030] In step S111, based on the spatial aggregation characteristics of multi-source traffic data, the system establishes a single-layer directed graph to map the actual physical network and extracts the spatial coordinates of traffic nodes in each physical network layer, generating a set of physical nodes. It should be noted that each node within the set of physical nodes in the single-layer directed graph has a strict mapping relationship with an actual spatial entity. For example, in the highway network layer, physical nodes include highway toll stations, interchanges, and arterial road intersections; while in the railway network layer, physical nodes include passenger railway stations and freight marshalling yards. The physical nodes in the civil aviation network layer are civil airports, and the physical nodes in the waterway network layer are passenger ports and freight terminals. For the specific spatial data transformation process of extracting coordinate data from the geographic information system and vectorizing it into nodes, those skilled in the art can use standard coordinate mapping and projection transformation algorithms. The coordinate system transformation is a well-known technique in this field and will not be elaborated upon here.

[0031] Step S112: Extract the trajectory data of the lines connecting adjacent physical nodes to generate a set of physical lines. Based on the generated set of physical nodes, the system establishes topological connections between nodes. The physical lines in the highway network layer are actual road segments. The physical lines in the railway network layer are railway track sections. The physical lines in the civil aviation network layer are defined air routes. The physical lines in the waterway network layer are fixed waterways. The system extracts the permissible travel direction parameters for each line and assigns directed edge attributes to each physical line.

[0032] Step S113: Obtain the upper limit of the design capacity for each physical route and generate the route capacity attribute. For any route in the set of physical routes, the system queries its corresponding upper limit of design capacity from the basic database. The upper limit of design capacity indicates the maximum number of traffic entities or the maximum load equivalent that the physical route can pass through per unit time. The upper limit of design capacity is chosen as the benchmark parameter for network capacity because this parameter directly reflects the ultimate carrying capacity of the physical channel and constitutes the physical causal boundary for traffic flow congestion and cascading failure. Considering the operational differences of various modes of transportation, the calculation of the upper limit of design capacity adopts a multi-dimensional quantitative logic. For the highway network layer, the upper limit of capacity is reflected as the maximum equivalent number of passenger cars passing through per unit time. For the railway network layer, the upper limit of capacity is reflected as the product of the maximum number of train departures per unit time and the train formation capacity. In this embodiment, the value range of the above-mentioned upper limit of capacity is a real number greater than 0, and its specific value is determined by reducing the theoretical capacity in the current national traffic design specifications, combined with the actual number of lanes in the road network and the design speed.

[0033] The system combines the set of physical nodes, the set of physical routes, and the upper limit of the designed traffic capacity to generate a single-layer physical network topology model for each mode of transportation. The mathematical expression of this topology model is given by the following formula: ; In the formula, Indicates mode of transportation The corresponding single-layer physical network graph model, subscript Indicates different modes of transportation. Indicates mode of transportation The set of physical nodes, index Representative node elements. Indicates mode of transportation The set of physical lines, subscript Representative elements of the route. This represents the set of capacity parameters that include the upper limit of the designed capacity of all physical routes for this mode of transportation. The purpose of establishing this topology model is to transform the complex macroscopic physical transportation network into a standard mathematical graph structure that can be used for subsequent matrix operations.

[0034] After generating the topology models of each single-layer physical network, the system adds time scheduling attributes to them based on the operational mechanisms of different transportation modes. The railway and civil aviation network layers have predetermined departure or takeoff timetables, and the system marks these two network layers as discrete scheduling layers. The highway network layer lacks a globally unified departure timetable control, and the time distribution of vehicles entering the highway network exhibits a continuous arrival state; the system marks this as a continuous transmission layer. The system writes the above-mentioned layer marking results as metadata into the corresponding single-layer physical network topology model. This metadata is used to trigger the calculation of heterogeneous traffic flow inputs from different transportation layers. This logic of dividing discrete and continuous attributes based on operational mechanisms aims to accurately reflect the heterogeneity of multimodal transportation systems in spatiotemporal distribution, avoiding computational biases caused by using a single homogeneous flow model.

[0035] In this embodiment, after constructing the topology models of each single-layer physical network and marking the hierarchical attributes, the system needs to inject initial traffic flow loads that conform to the physical operating laws of different modes of transportation. In order to accurately capture the transient impacts and cascading failure mechanisms in the cross-modal coupling process in the computing environment, the hypernetwork mapping module performs a mathematical extraction step of heterogeneous traffic flows based on the metadata scheduling attributes recorded in the single-layer physical network topology models.

[0036] For the transportation network layer labeled as the discrete scheduling layer, the hypernetwork mapping module executes step S121 to construct a discrete pulse flow input model based on timetables. Due to the high-capacity and concentrated arrival / departure physical characteristics of high-speed rail or civil aviation systems, the distribution of passenger or freight flow arriving at specific nodes is not uniformly spread across the time axis, but rather forms a highly concentrated flow injection within a short time window. Based on this physical causal relationship, the system retrieves historical passenger and freight flow operation data from the basic transportation database, parses out train timetables or flight arrival / departure timetables containing specific train numbers and flight numbers, and extracts them as discrete pulse signals on the time axis. The mathematical expression of the discrete pulse signal extraction process is as follows: ; In the formula, This represents the traffic mode tagged as a discrete scheduling layer. At the corresponding time Discrete pulse input flow rate. This represents the total size of the set of operational shifts that arrive at the target physical node within the set research time period, and its value is a positive integer. This refers to the discrete index values ​​for traversing the above set of shifts. Indicates the first The actual carrying capacity of each shift at the target physical node. This indicates the physical arrival time of the train in the timetable record. This represents the unit step impulse function. The purpose of establishing the discrete pulse flow input model is to accurately reproduce the impact load effect on the hub when a large-capacity vehicle arrives in the time domain through mathematical abstraction.

[0037] The system provides explicit lower-level features for calculating the specific variables involved in the above formulas. This is crucial for determining the actual carrying capacity equivalent. In such cases, priority is given to extracting actual settlement data from historical ticketing or freight dispatching systems. In situations lacking access to underlying ticketing data, the system uses an equivalent method: multiplying the designed passenger capacity of the vehicle by its historical average occupancy rate coefficient. The historical average occupancy rate data ranges from 0 to 1 (real numbers). As a preferred approach, this method considers that computer equipment inevitably relies on discrete time steps when performing dynamic numerical simulations. Directly using the impulse function can lead to dimensional mismatch and numerical overflow. Therefore, when the physical time reaches... When the time interval falls within a certain discrete computation time interval, the system calculates the actual carrying capacity of that shift. Divide by discrete time step This converts the total load into the equivalent average input flow rate within that time step. When performing this division operation, the system has a preset minimum overflow protection logic: when the configured minimum overflow is determined... When the value approaches 0 (below the preset minimum tolerance threshold), the system automatically intercepts the calculation and outputs a step size reset command to ensure the stability of the calculation process and the uniformity of heterogeneous flow dimensions.

[0038] For the traffic network layer, designated as a continuous conduction layer, the hypernetwork mapping module executes step S122 to construct a continuous wave conduction flow input model without mandatory timetable constraints. Vehicles in the highway system are primarily driven spontaneously by individual travelers, resulting in highly spatiotemporally dispersed travel decisions. This difference in underlying behavior leads to the arrival status of vehicles at highway network nodes exhibiting a continuous flow that evolves smoothly over time. To faithfully reproduce this pattern at the model level, the system extracts historical continuous flow monitoring data from highway physical cross-sections, specifically including continuous flow records generated by highway electronic toll collection gantries or video-recognized flow sequences generated by image monitoring equipment at urban arterial road intersections.

[0039] Based on the extracted historical continuous flow monitoring data, the system performs a time series smoothing transformation and constructs the continuous wave conduction flow equation: ; In the formula, Indicates the mode of transportation marked as a continuous transmission layer. At the specified time The continuous wave conduction rate. The physical dimension of this variable is expressed as the equivalent number of traffic entities per unit time. This represents the set of raw monitoring sample data extracted within the corresponding time window. This represents the time series smoothing kernel function used to eliminate high-frequency data jitter. In real-world business scenarios, due to the unreliability of monitoring hardware, signal loss or abnormal spikes often occur during multi-source data extraction. Therefore, before executing the smoothing function calculation, the system first uses linear interpolation to... Null records are filled using calculations. Then, based on the clock synchronization configuration of each transportation system, the multi-source data is time-axis aligned with a set minimum common time granularity. After alignment, those skilled in the art can use a moving average statistical algorithm with a fixed time window width or an extended Kalman filter algorithm for denoising and continuous transformation.

[0040] The discrete pulse flow and the continuous wave conducted flow extracted separately together constitute the source-end load boundary conditions for the hypernetwork to perform transient cascade failure calculations. These two traffic demand flows, which have fundamental differences in form, will eventually converge in time and space within the specific physical space of the integrated transportation hub. This convergence mechanism of heterogeneous flows necessitates that the hub system possess the buffering capacity to absorb peak transient pulses and gradually convert them into continuous wave conducted flows.

[0041] In this embodiment, after establishing a single-layer physical network topology model, the independently operating single-layer networks need to exchange traffic across layers through specific physical entities. The physical carrier for traffic exchange is defined in the system as a cross-modal coupled integrated transportation hub.

[0042] To achieve effective connectivity between different network layers, the hypernetwork mapping module executes step S131, delineating the spatial boundaries of the integrated transportation hub and generating a set of coupled nodes. The system calls the node coordinate data in each single-layer physical network topology model, traversing the physical node sets of different transportation modes. To avoid relying solely on a single distance extreme value, which could lead to the erroneous fragmentation of complex hubs (such as air-rail intermodal hubs), the system adopts a multi-dimensional weighted judgment logic that integrates spatial proximity and topological connectivity. Specifically, the system performs weighted clustering matching on nodes across layers. When two or more physical nodes belonging to different network layers have a relative distance between their geographical coordinates that is less than a preset spatial distance matching threshold, or when they have a dedicated internal rapid transit physical connection edge in their topological structure, the system determines that these nodes belong to the same integrated passenger or freight hub entity in physical space. Based on the above multi-dimensional matching logic, the system extracts a set of cross-mode coupled hub nodes between single-layer topologies, which is denoted as […] in the model. .

[0043] As a preferred approach, the spatial distance matching threshold is typically set between 500 meters and 2000 meters, with the specific value determined based on the planning red line range of the physical hub building complex provided by the local urban planning department.

[0044] After extracting the set of cross-modal coupling hub nodes, the system executes step S132 for each element in the set, configuring an equivalent energy storage buffer component for the hub node and calibrating its maximum physical storage capacity. The technical purpose of constructing this component is to provide a confined container for the spatiotemporal convergence of heterogeneous flows by equivalently replacing the physical transfer space within the hub for passenger or cargo walking, waiting, and security check distribution in the mathematical model.

[0045] For the configured equivalent energy storage buffer components, the system further calculates and calibrates their maximum physical capacity boundary. The calibration process for this capacity parameter is as follows: ; In the formula, Represents a set Any target hub node The corresponding maximum physical storage capacity indicates the limit of the total equivalent traffic volume that the hub can accommodate before reaching physical saturation. This represents the total number of core functional sub-areas within the hub that participate in intermodal transfers, and its value is a positive integer. The traversal index number for the functional sub-region represents specific spatial entities such as the arrival hall, security check waiting area, or underground passage in front of the station. Indicates the target hub node Inner The actual effective transfer area of ​​each sub-area. Indicates the first The safety space density threshold parameter corresponding to each sub-region is physically defined as the minimum area required for a single person or vehicle to be in a safe and mobile state.

[0046] When the system executes the above formula calculations, the acquisition of specific parameters follows strict engineering constraints. Actual effective transfer area. The data is automatically extracted from the system's building information model database or the hub's construction drawings system, excluding non-pedestrian access areas such as shops and equipment rooms. This is taken into account the varying passenger flow evacuation requirements across different areas within the hub. The value ranges from 0.5 to 2.0 square meters per person, and its specific calibration strictly follows the current national design specifications for fire protection and passenger flow distribution in transportation hub buildings. During the automatic execution of the above division and addition operations by the computer equipment, the system has built-in denominator exception protection logic. When the basic database returns a certain sub-region... When a value is missing or abnormally close to 0 (less than the set minimum tolerance), the system will perform a division operation on the abnormal sub-region and set its equivalent capacity to zero by default to ensure that the overall summation process will not cause computational overflow or matrix singularity errors.

[0047] Through the calibration and calculation of the physical capacity boundary described above, the equivalent energy storage buffer component in the model obtained definite state boundary parameters. The technical purpose of setting this step is that when the upstream discrete pulse flow is injected instantaneously due to the concentrated arrival and departure of trains, the buffer component can absorb the stranded passenger flow by virtue of the capacity boundary, and gradually release the flow outward by being limited by the continuous admittance of the downstream receiving layer.

[0048] In this embodiment, after establishing the physical capacity boundaries of the hub nodes, the system needs to construct a dynamic mathematical mapping relationship to characterize the flow accumulation and evolution process when heterogeneous traffic flows converge within the hub. In a real integrated transportation hub, there is a spatiotemporal mismatch between the discrete pulse passenger flow brought by high-speed trains and the continuous wave transmission passenger flow provided by the urban public transport system. This transient supply-demand imbalance requires the model to have the ability to track states between discrete and continuous boundaries. Based on the above requirements, the transient evolution calculation module executes the following state update logic.

[0049] To unify the computational dimensions of heterogeneous flows and establish a globally consistent evolutionary environment, the transient evolution calculation module executes step S141 to construct the instantaneous synthetic input-output flow rates of the hub node. The system obtains the flow input models of all physical network layers associated with the target hub from the hypernetwork mapping module. When calculating the instantaneous total input flow rate, due to the heterogeneity of the data sampling frequencies of discrete pulse flow and continuous wave conduction flow, the system first strictly aligns the independent timestamps of the multi-source flow input models based on a set global absolute time reference. Specifically, the system uses a zero-order hold or linear interpolation algorithm to map asynchronous flow data onto a unified discrete computation time axis. After time alignment is completed, the target hub node... At any moment Instantaneous total input flow rate The flow rate is obtained by adding the equivalent flow rate of all pulses flowing into the node at the current moment to the continuous wave conduction flow rate. Similarly, based on the real-time admittance state of the downstream receiving network layer and the expected evacuation requirements of the hub itself, the system uses multi-dimensional controlled constraint logic that takes the minimum of the two values ​​to calculate the instantaneous total output flow rate of the hub's outward evacuation. The instantaneous total input flow rate and instantaneous total output flow rate obtained based on time axis alignment and multidimensional controlled logic together constitute the rigorous input-output fluid dynamic boundary conditions of the hub node at a specific moment in the mathematical model.

[0050] After establishing unified input-output fluid dynamics boundary conditions, the system executes step S142 to calculate the updated state of the equivalent energy storage buffer component based on the macroscopic traffic fluid mass conservation law. When performing dynamic simulation, the computer equipment relies on a discrete time-progression mechanism; the system accumulates the traffic entities trapped within the hub by calculating the flow difference within adjacent time steps. To prevent non-physical states caused by computer rounding errors or extreme large flow impacts, the system forcibly introduces upper and lower bound cutoff functions into the state equations. The mathematical expression for the updated state of the buffer component is: ; In the formula, Indicates the target hub node The actual storage volume at the next moment after a calculation step is represented by the physical dimension of the equivalent number of traffic entities that are stuck. Indicates the current time The initial storage capacity. and Representing time respectively The instantaneous total input flow rate and the instantaneous total output flow rate. This represents the discrete time step set when the computer solves the model. This indicates the maximum physical storage capacity of the hub as specified in the preceding steps. and These represent the minimum and maximum values, respectively. The technical purpose of establishing a buffer flow state update is to accurately reconstruct the dynamic process of passenger flow accumulation or dissipation within the hub through differential iteration with strict physical boundaries.

[0051] Key parameters during buffer storage state update The choice of time step has a decisive impact on the stability and physical realism of the algorithm. As a preferred approach, the system does not use arbitrary fixed empirical values, but rather dynamically calibrates the time step based on physical causal relationships. Specifically, the system extracts the physical spatial length of various transfer paths within the hub and, combined with the average walking speed of pedestrians, calculates the shortest physical transfer time. The system will... It is strictly limited to less than or equal to one-third of the shortest physical transfer time.

[0052] By implementing buffer storage status updates, the system completed the transformation of intermodal transfer hubs from static physical attributes to dynamic evolutionary components. The nested extreme value truncation logic in the formula not only avoids the error of negative storage flow rates, which violates physical principles, but also establishes hub overflow (overflow state, i.e., storage flow rate reaching...). The precise judgment of triggering conditions. This storage state parameter. The real-time output provides a direct and reliable data input source for the subsequent system to transform the local passenger flow physical backlog into the nonlinear weighted calculation of the network node passage impedance.

[0053] In this embodiment, after obtaining the real-time physical flow rate within the hub by executing the buffer flow state update logic, the system needs to transform the macroscopic physical state into mathematical impedance parameters on the network graph model to drive subsequent traffic flow redistribution. In traditional static network topology modeling theory, the connectivity cost between nodes is often simplified to a fixed symmetric constant, or simply a linear mapping with spatial distance. However, cross-level transfer behavior within a physical hub has strong directional constraints and asymmetric properties. For example, transferring from a regular urban road layer to a civil aviation network layer usually requires routine security checks and long walks, while the reverse flow is relatively smooth. To accurately reflect this real heterogeneity based on spatial structure and management mechanisms at the model's underlying level, the transient evolution calculation module performs dynamic impedance update calculations based on an asymmetric weighting mechanism.

[0054] The transient evolution calculation module executes step S151 to establish the static baseline boundary of the evolution algorithm and extract the initial static impedance parameters of the cross-modal transfer streamlines. The system retrieves the internal topology streamline diagram within the target hub from the basic building information database. For any given origin and destination network layers, it calculates the absolute physical time required for traffic entities to complete the transfer in a congestion-free free-flow state. This absolute physical time includes spatial walking time, vertical elevator waiting time, and mandatory security check time. Based on the weighted superposition of the above physical components, the system generates a static asymmetric transfer impedance matrix. In the static asymmetric transfer impedance matrix, even if the absolute spatial height difference between the two network layers is fixed, the basic cost parameters for forward and reverse transfers are strictly separated. During the extraction and construction of the static asymmetric transfer impedance matrix, to ensure the completeness of the subsequent graph search algorithm based on this matrix, the system defaults to setting the initial static impedance of network layer node pairs that are completely non-adjacent in physical space and have no feasible connecting channels to the maximum floating-point value (i.e., equivalent to infinity) set by the system. This initialization protection logic for matrix elements can effectively prevent the pathfinding algorithm from throwing singularity exceptions or falling into infinite loops due to graph structure breakage.

[0055] After establishing the static baseline boundary, the system executes step S152 to construct a nonlinear dynamic variable-weight impedance function coupled with real-time traffic flow. As the equivalent of congested traffic entities within the hub continues to increase, the actual capacity of the physical transfer channels will nonlinearly decrease, macroscopically manifested as a sharp drop in spatial queuing and individual movement speed. To quantitatively measure the penalty effect caused by this dynamic agglomeration, the system introduces an improved variable-weight impedance formula. The mathematical expression for this dynamic impedance is: ; In the formula, Indicates at time Traffic flow passes through the target hub node From the origin network layer Transfer to the destination network layer The dynamic transfer impedance. The physical dimension of this parameter is expressed as the equivalent travel time to complete the inter-layer transfer. This indicates the positive static asymmetric free-flow impedance established in the preceding steps. The superscript 0 indicates the initial ideal state without passenger congestion, and the subscript arrow indicates a specific directed transfer path. Indicates the target hub node at the current moment. The actual storage capacity. This indicates the previously specified maximum physical storage capacity of the hub. This represents the impedance amplification penalty factor that is strongly correlated with a specific transfer direction. This represents the nonlinear sensitivity index.

[0056] When computer equipment executes the variable-weighted impedance formula, the system strictly defines the value range and calibration logic of each parameter. As a preferred method, the impedance amplification penalty factor... The value is set to a real number between 0.15 and 3.0, with the specific value differentiated based on the physical bottleneck characteristics of the transfer passage. For example, for restricted passages containing one-way security gates or narrow scissor escalators, the system will assign a higher penalty coefficient. Nonlinear sensitivity index The value of is set to a constant between 4 and 6, which strictly references the engineering experience value of the state change boundary in macroscopic traffic flow theory. To ensure the robustness of the algorithm in extreme data environments, the system is configured with underlying overflow prevention logic when performing division calculations within parentheses. When the base database returns... When a parameter is missing or its value abnormally approaches 0 (below the set safety minimum), the system will actively intercept the calculation thread and forcibly assign the division result to 1, thereby preventing the program from throwing an illegal memory overflow error. The technical purpose of setting this variable weight function is to use the exponential characteristics of the power function to make the transfer impedance increase non-linearly when the internal storage capacity gradually approaches the physical capacity limit, accurately mapping the scenario of physical movement restriction caused by dense crowds.

[0057] Considering that extreme transient pulse flows may cause physical flow disruptions in the hub space, the system further executes step S153, applying a hard-truncation penalty constraint based on multi-dimensional physical states. Simply relying on mathematical nonlinear formulas will still continuously output finite numerical solutions when dealing with extreme conditions where the storage capacity exceeds the safety threshold. However, in the real physical world, once passenger flow exceeds a critical point, management will inevitably implement rigid circuit breaker measures such as passenger flow control or suspending security checks. Therefore, the system monitors multi-dimensional state indicators in real time, not only extracting the relative ratio between the current storage capacity and the capacity limit, but also obtaining the instantaneous rate of change of the storage capacity within adjacent time steps through differential calculation. When the system determines the actual storage capacity... Reaching maximum physical storage capacity When the preset safety warning threshold (usually set to 0.95) is met, and the instantaneous rate of change of the storage flow is greater than zero (indicating that congestion is still worsening and shows no signs of easing), the system immediately triggers a mathematical hard-truncation mechanism based on the data characteristics of the two dimensions mentioned above. This mechanism bypasses the variable-weight impedance formula and dynamically adjusts the transfer impedance. The value is directly overwritten as the system-defined infinite constant. This strong intervention logic based on physical security boundaries instantly severs the mathematical connectivity of the hub node in the topology, forcing the upper-layer routing algorithm to redirect subsequent traffic flows to other nodes. Thus, it rigorously supports the causal derivation of the evolution from local overload to network-wide cascading failure in the underlying computing domain. For the specific code implementation of array element condition judgment and infinite extreme value assignment in computer memory, those skilled in the art can use standard matrix masking operations combined with floating-point extreme value declaration algorithms for deployment. The data structure-level overwriting processing is a well-known technology in this field and will not be elaborated here.

[0058] In this embodiment, after dynamically updating the static asymmetric transfer impedance matrix, the system needs to perform a comprehensive connectivity assessment of the global topology, encompassing both single-layer physical networks and integrated hubs. In complex systems engineering, directly calling graph traversal pathfinding algorithms to assess the cascading congestion status of the entire network is not only computationally expensive but also fails to effectively capture the implicit ripple effects during traffic flow transfer. To address this computational bottleneck, the system introduces an equivalent physical mapping framework based on Kirchhoff's laws. By establishing equivalent mathematical isomorphisms between traffic impedance and electrical resistance, and between traffic flow and current, the system transforms the nonlinear dynamic connectivity calculation of heterogeneous traffic networks into a linear matrix algebra problem suitable for efficient solution.

[0059] Based on the aforementioned equivalent physical mapping framework, the transient evolution calculation module executes step S161 to calculate the transient equivalent admittance parameters of various connections in the global topology network. The system traverses the global single-layer network graph model, extracting the dynamic traffic impedance of physical road segment connections within the single-layer network and virtual connections for cross-modal transfers within hubs in the current time slice. Traffic impedance reflects the degree of physical obstruction encountered by traffic flow in the network. The system converts this impedance parameter into an equivalent admittance characterizing the smoothness of network flow by calculating its reciprocal. The mathematical equation for this conversion process is: ; In the formula, Indicates the time of calculation From the starting node Point to the end node The transient equivalent admittance corresponding to this specific directed connection. The physical dimension of this parameter characterizes the current admittance per unit impedance. This represents the dynamic impedance parameter of the connection at the current moment. When the computer performs this division operation, there is a potential engineering problem of the divisor being zero. When the extracted physical channel is extremely unobstructed or belongs to a mapping of co-located nodes with no physical distance, the basic impedance... It may be missing or approach 0. To prevent system crashes caused by division-by-zero exceptions thrown by the underlying calculation module, the system forcibly incorporates minimum value tolerance protection into the calculation logic. When determining... Less than the preset safety lower limit threshold (this threshold is usually set to 10). -5 The system will automatically reset the denominator to the safety lower limit, thereby ensuring that the admittance value is within a controllable and legal range.

[0060] After obtaining the transient equivalent admittance parameters of various edges in the global topology network, the transient evolution calculation module executes step S162 to assemble an asymmetric global phasor admittance matrix according to the graph theory Laplace matrix construction rules. The system initializes a square matrix in memory with a dimension equal to the total number of global nodes. For each edge in the topology graph, the system fills its admittance value into the corresponding row and column coordinates of the square matrix according to specific sign rules. Since the transfer impedance of a transportation network typically does not possess bidirectional symmetry (i.e., forward impedance is not equal to reverse impedance), the specific assembly logic of the global phasor admittance matrix is ​​given by the following piecewise function: ; In the formula, Indicates time Global phasor admittance matrix The Middle Line number The matrix elements of the columns. To completely eliminate the mapping ambiguity between the two-dimensional matrix data structure and the network graph theory model, the system performed strict coordinate isomorphism binding when constructing this function. Specifically, the row index of the square matrix. It is uniquely and absolutely mapped to the global identifier of the starting node of the directed edge in the topology graph, and is the column index number of the matrix. It is uniquely and absolutely mapped to the global identifier of the endpoint node of the directed edge. This represents the set of all legal directed edges in the global topology model. Indicates the relationship with the starting node The set of all downstream neighbor nodes that have direct edge relationships, i.e., starting from the origin node. The set of target nodes that is directly pointed to ensures that the elements on the main diagonal strictly represent the sum of the out-degree admittances of the nodes. This is the index of the internal successor node for traversing the set of downstream neighbor nodes. This represents the regularized grounding parameters configured on the main diagonal elements of the matrix.

[0061] During matrix assembly, the main diagonal elements reflect the overall dispersal capacity of a single node's radiating traffic to the entire network, while the off-diagonal elements record the direct connectivity constraints between nodes. As a preferred approach, to ensure the robustness of matrix operations during subsequent congestion diffusion solutions, the system must prevent singularities (i.e., a determinant of 0 leading to irreversibility) in square matrices with dimensions equal to the total number of global nodes. Since real traffic networks contain isolated nodes or topological disconnections caused by extreme congestion, simply relying on the accumulation of edge admittances easily generates non-full-rank singular matrices. Based on the aforementioned algebraic constraints, the system forcibly injects a small regularized grounding parameter into the main diagonal. The value range of this parameter is set to 10. -6 Up to 10 -4 The real numbers between these values ​​are equivalent in the physical topology graph to configuring a virtual dissipative branch pointing to the sink for each traffic node. This operation ensures that the global phasor admittance matrix satisfies the strict diagonal dominance condition, completely eliminating the singularity risk of matrix inversion failure from a mathematical perspective.

[0062] After matrix assembly and regularization, the transient evolution calculation module executes step S163 to assess the cascading failure status of the entire network based on the algebraic characteristics of the matrix. The system avoids relying solely on extreme congestion at individual nodes for biased judgments; instead, it extracts the eigenvalues ​​and eigenvectors corresponding to the global phasor admittance matrix to construct a multi-dimensional weighted topological connectivity evaluation logic. Given that the eigenvalues ​​of the asymmetric global phasor admittance matrix may contain complex numbers, the system extracts the real parts of the eigenvalue set for calculation. The combination of the algebraic connectivity (i.e., the real part of the smallest non-zero eigenvalue) and locality centrality of the asymmetric global phasor admittance matrix accurately reflects the topological bottleneck location where physical overload at local nodes propagates to the global network. The technical significance of outputting the global phasor admittance matrix result lies in using it as the core system state transition operator, providing a rigorous numerical driving engine for subsequent calculations of large-scale traffic flow redistribution caused by cross-modal capacity mismatch. For the optimization of storage structure and matrix eigenvalue decomposition of large sparse square matrices, those skilled in the art can use compressed row storage format combined with Lanczos iterative solution algorithm for code implementation. The underlying linear algebra calculation processing is a well-known technology in the field and will not be described in detail here.

[0063] In this embodiment, after constructing the global phasor admittance matrix, the transient evolution calculation module needs to inject external excitation sources into the network graph structure to drive the evolution calculation of the system state variables. Based on the isomorphic relationship between electrical engineering networks and macroscopic traffic flow theory, distributed travel demand and local passenger flow surges caused by sudden events are essentially manifested as the injection or extraction of traffic flow into the topological nodes of the traffic network. The system uniformly maps these non-stationary boundary conditions into equivalent node current vectors, thereby providing complete source term inputs for subsequent solutions to node potentials (i.e., equivalent congestion potential energy).

[0064] Based on the isomorphic mapping relationship between non-stationary boundary conditions and equivalent node current vectors, the transient evolution calculation module executes step S171, extracting the nominal current component under normal travel conditions based on the dynamic origin-destination (OD) demand matrix. Under normal operating conditions, the displacement of traffic entities in the network has a clear origin and destination. Based on the conservation mechanism of traffic flow spatiotemporal evolution, the system extracts the transient OD matrix from the basic travel demand database according to a set time slice. For any network node in the topology graph, traffic flow originating from that node is equivalent to positive current injection, and traffic flow received from that node as its destination is equivalent to negative current extraction. The mathematical expression of this nominal current component is: ; In the formula, This represents the specific target node entity currently performing source item mapping in the global network topology model. This physical node is strictly hard-bound to a globally unique identifier index in the memory structure of the underlying computing domain to ensure absolute uniqueness of addressing. It is the set of all legally mapped nodes in the network. and These represent local node entity variables specifically used for traversing the origin and destination of requirements, respectively. Strict set scope isolation is performed here to avoid referential coupling with the topological pathfinding index. Indicates the time of calculation From the target node entity Depart for the destination node The instantaneous passenger flow demand equivalent. This indicates that at the same moment, from the point of origin of demand... Head to the target node entity The equivalent of passenger flow demand. Indicates time Target node entity The corresponding nominal equivalent injection current. The purpose of setting up this summation and difference correlation operation is to accurately quantify the net flow source and sink attributes of each node at a specific time section. When the calculation result is positive, it indicates that the node is a net source; when the result is negative, it indicates that it is a net sink.

[0065] After obtaining the nominal current component, the transient evolution calculation module executes step S172 to quantify the transient abnormal surge current component caused by the sudden disturbance. In multimodal transport networks, local passenger flow delays caused by hub capacity mismatch or line blockage constitute nonlinear pulse impacts on the system's stable state. The system accesses external heterogeneous data sources (including ticketing refund and change system logs or abnormal event video alarm streams) to perform transient increment assessments on hub nodes located at the disturbance center or affected by the disturbance. To ensure the timeliness consistency of multi-source heterogeneous data before inputting it into the mathematical model, the system presets a basic sliding time synchronization window (e.g., 1 minute), forcibly aligning asynchronous ticketing records and discrete video frame features falling within this window to the same calculation time. The timestamp alignment variance is calculated accordingly. The mapping relationship of the transient abnormal surge current component is as follows: ; In the formula, This indicates that the target node entity was affected by a sudden external disturbance event. The abnormally high surge current component generated. This represents the absolute cumulative number of passengers remaining at this node at the current moment, obtained by parsing multi-source heterogeneous data that has been time-aligned. This represents the node-specific passenger flow release coefficient, whose physical meaning is used to characterize the mobilization penetration rate of the remaining population into actual network load. As a preferred method, The value is set to a real number between 0.1 and 0.9, and its specific value is dynamically calibrated based on the buffer area of ​​the platform of the hub and the flow restriction level of the on-site control strategy. This represents an emergency intervention imposed on the node by external physical forces, such as the negative traffic extraction capability resulting from deploying emergency shuttle buses. The technical significance of introducing this perturbation mapping component lies in transforming discrete abnormal events, which are originally difficult to directly digest by classical allocation algorithms, into continuous mathematical excitation sources that are strictly aligned with the network topology, thereby achieving a unified integration of normal and abnormal boundary conditions in the mathematical computation domain.

[0066] After completing the analysis of the nominal current component and the transient abnormal surge current component for regular travel, respectively quantized, the transient evolution calculation module executes step S173 to assemble the global node equivalent current vector and perform a flow conservation check based on multi-dimensional judgment. In the graph theory linear algebra solution framework, isolated source injections can easily break the mathematical equilibrium of Kirchhoff's Current Law (KCL), resulting in a non-singular but non-valid real solution for the subsequently constructed linear equation system. The system algebraically superimposes the nominal current and the disturbance current and performs strict conservation constraint judgments on the vectors of the entire network node dimension. The conservation equation and its overflow prevention compensation logic are given by the following piecewise conditional expression: ; In the formula, This indicates the moment when the final output is used to solve the equation. Target node entity The global equivalent current input element. This is the loop control variable for traversing all network node entities. It represents the algebraic sum of the initial current scalars of the entire network under the current time slice, that is, the global physical flow residual of the system. This represents the total number of legitimate nodes on the entire network. This represents the absolute value threshold of the system's flow imbalance tolerance, used to shield against truncation errors caused by underlying floating-point calculations. A value of 10 is typically used. -4 . This represents the data alignment variance of timestamps from multiple sources. The effective data confidence threshold set for the system, as a preferred method, is set to a value between 0.5 seconds and 2.0 seconds, specifically determined based on the average latency jitter characteristics of the basic communication network.

[0067] The system makes output decisions based on the above multi-dimensional weighted logic: only when the system determines the absolute value of the global residual... Greater than the absolute value threshold of the tolerance Data alignment variance The confidence level requirement is met, and the total number of valid nodes in the entire network is [number missing]. When the residual is strictly greater than zero, the system confirms that the residual is not caused by data communication delay, but by macroscopic mass non-conservation due to the sensor's actual detection blind zone or disturbance estimation bias. At this point, the system triggers global amortized compensation logic to adjust the residual. After equal distribution, the current is injected back into the current vector of each node. The addition of a node cardinality determination mechanism aims to prevent the risk of division-by-zero crashes caused by topology graph initialization failures or local network hard blockages. The technical purpose of performing this conservation-forced intervention operation is to force a closed-loop global flow distribution of the system from the linear algebraic level under harsh operating conditions such as missing heterogeneous data or fluctuating detection accuracy. This step completely eliminates the risk of pseudo-singularities caused by data source imbalance, ensuring that the system equations jointly constructed by the current vector and the global phasor admittance matrix can output analytical results with unique true physical meaning. For timestamp alignment interpolation preprocessing involving heterogeneous data streams in a distributed cluster environment, those skilled in the art can use Kalman filtering combined with a sliding time window algorithm for calibration. The alignment and synchronization of the data time dimension is a well-known technique in the field and will not be elaborated here.

[0068] In this embodiment, after assembling the global phasor admittance matrix and injecting the equivalent current vector, the system constructs an isomorphic mapping relationship between the static topology conduction base and the dynamic source term input at the bottom layer. Based on complex network theory and the conservation laws of fluid mechanics, the system needs to solve the transient state-space equations of all network nodes within a continuous time domain or discrete time step. This solution process aims to obtain the node pressure vector characterizing the local congestion potential energy, and use this pressure vector as the core driving force to deduce the actual conduction of physical flow in the network topology, the accumulation and overflow of node buffer containers, and thus trigger the closed-loop iterative evolution of local topology blockage and system cascading failure.

[0069] Based on the computational requirement of solving the transient state-space equations of all network nodes, the transient evolution calculation module executes step S181 to construct and solve the system state-space linear equations of the traffic network. In classical electrical network theory, the node potential is determined by the injected current and the network admittance. The system transfers this physical law to the macroscopic traffic flow distribution domain, and calculates the equivalent pressure distribution of all network topology nodes under the current time slice by algebraically combining the global phasor admittance matrix and the global node equivalent current vector. The system state-space linear equations of the traffic network are: ; In the formula, Indicates time The system's total network node pressure column vector, where any element within it... Represents the corresponding target node entity The transient congestion potential energy at that moment. The dimension of this physical quantity characterizes the equivalent pressure state required for a unit node to absorb or disperse traffic flow; the higher the value, the heavier the passenger flow retention and carrying capacity of that node. The global phasor admittance matrix at time t represents the value of the global phasor admittance matrix at time The inverse matrix. This represents the global equivalent current column vector output after multidimensional flow conservation verification. When the computer performs the matrix inversion and multiplication operations, the pre-step steps have already forcibly injected regularized grounding parameters into the main diagonal of the admittance matrix (preferably, this grounding conductance value is set to 10). -6 (insignificant real numbers on the order of magnitude), matrix It satisfies the strict diagonal dominance property. This mathematical safeguard ensures the full-rank property of the matrix, completely avoiding the anomalies of pseudo-inverses or singularities caused by local disconnections in the network topology, and guaranteeing that the state equation has a unique real solution under any extreme road network truncation condition. For solving matrix equations in large sparse networks, those skilled in the art can use LU decomposition or Krylov subspace iteration algorithms to accelerate the process. The underlying linear algebraic solution of sparse matrices is a well-known technique in the field and will not be elaborated here.

[0070] After obtaining the pressure vector of all nodes in the network, the transient evolution calculation module executes step S182, calculating the actual transmission flow on the microscopic physical connection based on the potential energy gradient driving logic between adjacent nodes. In the real physical space, the macroscopic movement of traffic flow always follows the natural law of dispersing from high-pressure congestion areas to low-pressure unobstructed areas. The system extracts adjacent node pairs with direct connection relationships in the global topology model, and combines the current dynamic connectivity of the link to deduce the actual output flow on the directed connection. This physical deduction logic is given by the following piecewise function: ; In the formula, Indicates the time of calculation From the starting node entity Along the physical connection to the end node entity The actual instantaneous traffic flow injected. Indicates the time of calculation From the starting node The transient equivalent admittance corresponding to the specific directed edge pointing to the endpoint node v. and These represent the equivalent congestion potential energy of the starting and ending nodes at the current moment. In this computational logic, a directional truncation protection mechanism is forcibly implemented: positive actual physical flow is only allowed when the pressure at the upstream node is absolutely greater than that at the downstream node; when the pressure at the upstream node is less than or equal to that at the downstream node, the system forcibly sets the actual transmission volume to zero. The technical purpose of introducing this nonlinear truncation logic is to accurately simulate the unidirectional conduction saturation property of diodes in directed traffic networks (such as one-way streets and one-way transfer channels), preventing reverse backflow flow that violates physical principles from occurring in the computational domain.

[0071] After calculating the actual flow transmission at the micro-level connection edges, the transient evolution calculation module executes step S183, which, based on the flow time integral and the principle of physical conservation, performs overflow determination of the node buffer container. Physical hubs, intersections, or transfer halls in the transportation network all possess a rigid upper limit for their occupancy capacity, determined by both physical space area and safety density. The system extracts all inflow and outflow branch flows of a specific physical node within the current time slice, calculates its net inflow rate, and performs discrete integration along the time axis to update the actual accumulated occupancy flow within the node. The logic for this integral accumulation and overflow determination is as follows: ; To avoid delays in paralysis detection due to reliance on a single residence extremum, the system introduces multi-dimensional detection conditions based on capacity saturation and instantaneous shear difference: ; In the formula, Indicates time Target node entity The actual cumulative physical dwell time inside. These are the dwell state parameters left over from the previous calculation time step. This represents the discrete time step set when the computer solves the model. and These respectively represent pointers to the target node entity. The set of input and output adjacent nodes. The hard boundary threshold for the physical capacity configured inside this node entity. This represents the system's set critical capacity saturation threshold, with a value ranging from 0.85 to 0.95, specifically determined based on the topological depth of the internal buffer channels of the hub. The system comprehensively assesses whether the current accumulated volume percentage exceeds the critical threshold. Furthermore, it is determined whether the instantaneous net inflow shear difference (i.e., inflow minus outflow) is still positive. When both of these conditions are met, the system determines that the physical node has experienced buffer overflow paralysis. This multidimensional weighted logic truly maps the nonlinear collapse process of the effective throughput capacity of a traffic entity when high-density congestion is superimposed and continues to worsen.

[0072] Based on the above multi-dimensional judgment results, the transient evolution calculation module executes step S184, triggering the physical blocking and admittance cutoff logic, and reconstructs the evolution matrix for the next time step to complete the backtracking loop of cascading failure. When a hub node falls into a paralyzed state, its physical space is completely filled, objectively losing the ability to receive any new external traffic. The system prepares for the next time step. When examining the underlying data structure, iterate through all entities in the global topology that directly point to the paralyzed target node. The input edges are forcibly truncated by setting the local admittance to zero. Mathematically, this is expressed as: for any upstream adjacent node... The system forcibly sets the corresponding connection admittance. The forced zeroing of admittance parameters is physically equivalent to cutting off the corresponding conduction branches, simulating entry closure control or road deadlock caused by congestion backflow in real-world scenarios. Simultaneously, to prevent the node from becoming mathematically isolated after cutting off all input branches and inducing Jacobian matrix singularity, the system maintains and amplifies the node's main diagonal self-admittance element (i.e., retains its virtual ground-to-ground dissipation branch) while forcibly zeroing the mutual admittance parameters. After performing admittance zeroing and self-admittance compensation, the system, based on the updated set of global network edge admittance parameters, re-invokes the matrix assembly logic to reconstruct the time step. Asymmetric global phasor admittance matrix .

[0073] After triggering the asymmetric global phasor admittance moment reconstruction, the transient evolution calculation module executes step S185, driving the system into the time-domain derivation of the next time step. The system steps the current timestamp to... The reconstructed admittance matrix and the equivalent current vector of the external source term at that moment are then substituted back into step S181 to initiate a new round of closed-loop iteration. The system incorporates a composite termination criterion, including anti-dead-loop and anti-zero overflow measures, into the global loop control logic. The logic for determining the relative rate of change is as follows: ; In the formula, It represents the relative rate of change of the L2 norm of the global pressure vector between two consecutive time steps. This is a forced smoothing constant introduced into the system to prevent zero removal; it is typically set to a value of 10. -8 This is used to protect the underlying floating-point arithmetic unit from triggering an overflow exception when the reference pressure vector approaches zero. The system continues to execute this closed-loop evolution calculation until the loop terminates when either of the following conditions is met: First, Less than the preset steady-state convergence threshold (usually 10). -5The system has fully absorbed the disturbance source and established a new steady-state of flow balance. Secondly, all legitimate nodes in the network meet the overflow paralysis condition, indicating that the entire topology network is trapped in a complete cascading deadlock. Thirdly, the total number of current iterations exceeds the system's preset maximum number of safe steps. (e.g., 5000 times) to forcibly break the dead loop caused by high-frequency numerical oscillations. This closed-loop extrapolation architecture based on strict state feedback achieves a high degree of mathematical analysis in reproducing the dynamic ripple effect of local congestion spreading to the global network in real traffic networks, providing a data foundation with clear physical causal relationships for vulnerability analysis of complex networks.

[0074] In this embodiment, the system, through time-domain extrapolation at the next time step, has fully captured the dynamic evolution trajectory of pressure and flow at each node in the road network. Based on the isomorphic mapping of the work principles of fluid mechanics and electrical engineering, the process of network dissipating external input passenger flow demand is physically equivalent to the process of the system doing negative work. In traditional transportation network vulnerability assessment, purely static graph theory indicators such as topological connectivity or maximum connected subgraph size are usually used for state discrimination. These traditional methods can only reflect the binary accessibility of the network's physical structure and are difficult to characterize the nonlinear efficiency loss caused by congestion during the dynamic transmission of physical traffic flow. Therefore, the system introduces the dimension of instantaneous effective traffic power, a continuous physical quantity, to accurately quantify the actual work done by the system in transporting effective passenger flow to its destination at any time slice.

[0075] Based on the aforementioned measurement requirements, the system evaluation module executes step S191 to extract the set of all legitimate destination nodes in the network and their corresponding instantaneous successful arrival traffic. The core effective capacity of a transportation network depends not only on the connectivity of intermediate trunk links but also directly on the absolute throughput capacity of destination nodes in actually receiving and processing passenger flow. The system traverses the global dynamic traffic matrix output from the preceding closed-loop iterative deduction, filters out destination nodes with net reception attributes, and synchronously analyzes the actual physical transmission traffic of all input branches pointing to these nodes along the time axis. The transient traffic aggregation logic is as follows: ; In the formula, This represents the destination node entity in the global topology model that undertakes the function of passenger flow arrival. Indicates the time of calculation The entire network successfully reached the destination node. The actual aggregated passenger flow. This indicates that the destination is directly pointed to within the current topology. And the set of valid input adjacent nodes that are not logically isolated by the overflow admittance. This is the control index for traversing the set of input nodes. Indicates from the upstream node Actual injection into the destination along the physical connection edge The transient flow rate. The technical purpose of extracting this actual aggregated flow rate is to separate the ineffective stagnant flow rate that is intercepted in the intermediate hub buffer container due to congestion overflow from the total departure demand, and only include the traffic flow that actually completes the physical displacement demand into the effective transport efficiency accounting domain of the system.

[0076] After filtering the destination arrival traffic, the system evaluation module executes step S192, calculating the instantaneous effective traffic power of the entire network in conjunction with the destination receiving pressure. In physical transmission dynamics, the effective power output by the system is strictly equal to the product of the driving potential difference and the actual traffic flow. The system performs an algebraic summation of this work product for all effective destinations in normal operation across the entire network. The power calculation formula is: ; In the formula, Indicates the system at time 10:00 The output is the instantaneous effective traffic power. Its physical dimensions map the overall kinetic energy of the global road network in absorbing effective transport demand within this time slice. This represents the set of legitimate destination nodes that have not experienced buffer capacity overflow and still possess physical receiving capabilities. Indicates the calculation time Destination Node The equivalent congestion potential energy, i.e., the receiving pressure of the system. As a preferred approach, this pressure value is derived from the state-space equations. The solution is obtained directly through mapping. When the road network is relatively unobstructed, passenger flow arrives smoothly and destination pressure is low, resulting in a stable and continuous base power output from the system. When local congestion or cascading failures occur in the road network, upstream flow dispersion is obstructed, leading to a decrease in actual arrival volume. The load decreases, while the system passively increases the receiving pressure at the destination in order to maintain network transmission. The product of these two factors mathematically continuously represents the abnormal work state of high pressure and low flow. This continuous variable measurement mechanism overcomes the numerical passivation deficiency of traditional connectivity indicators in assessing congestion evolution.

[0077] After obtaining the instantaneous effective traffic power of the entire network, the system evaluation module executes step S193, performing zero-prevention and normalization processing on the instantaneous power vector and outputting a multi-dimensional network performance evaluation benchmark. Due to the significant heterogeneity of traffic networks of different sizes in terms of passenger flow base and topological depth, directly outputting absolute power values ​​cannot provide a unified horizontal evaluation standard for the disturbance resistance capabilities of different networks. The system introduces the nominal effective power under normal baseline conditions as the absolute alignment basis, and outputs a dimensionless instantaneous system performance index through dynamic ratio mapping. The normalization operation and zero-prevention protection logic are as follows: ; In the formula, Indicates the calculation time The dimensionless instantaneous traffic efficiency index. This represents the ideal baseline effective power generated by the system solely based on the nominal travel demand matrix at the same moment, without any sudden disturbance current source being injected. This is a singularity-preventing smoothing tolerance that is forcibly injected into the system at the computational level, typically with a value of 10. -6 The magnitude is a floating-point real number. The purpose of setting this smoothing tolerance is to protect the underlying microprocessor from throwing a floating-point division-zero overflow exception when the denominator approaches zero, during periods when the network is completely idle or basic travel demand is extremely low, such as in the early morning.

[0078] In this embodiment, through time-domain derivation of the state-space equations and dynamic quantification of network performance, the system has fully acquired the temporal evolution trajectory of instantaneous traffic power in the road network. Based on macroscopic systems engineering and reliability analysis theories, transient performance fluctuations cannot fully characterize the physical network's resilience and self-recovery capabilities throughout the entire cycle of sudden disturbances. The system needs to integrate scattered transient characteristics from a macroscopic time dimension to quantify the overall network's resilience. Based on the concept of controlled variable contingency planning, the system further locates the key physical topology entities that cause the maximum gradient decrease in the system's overall resilience through controlled traversal of the underlying computational domain, thereby providing quantitative decision support with clear causal relationships for the infrastructure investment strategy and emergency resource scheduling of the external network.

[0079] Based on the computational requirements for full-cycle performance evaluation during disturbances, the system evaluation module executes step S201, performing a definite integral operation on the instantaneous effective traffic power along the time axis to output the system's comprehensive resilience index. In temporal evolution dynamics, transient power only reflects the work state of a certain slice, while the cumulative total energy of the physical network maintaining effective transmission throughout the entire cycle is the core benchmark for measuring its disturbance resistance capability. Before performing the integral comparison, the system forces a spatiotemporal multidimensional feature alignment check on the multi-source benchmark data. The system extracts the attribute labels (including weekday features, time period features, and weather conditions) for the current disturbed period and strictly matches nominal power curves with the same multidimensional feature labels from the historical static library as the comparison basis to ensure the objective consistency of the physical measurement scale. The power integral and index mapping logic in this time dimension is given by the following code block: ; In the formula, This represents the calculated dimensionless comprehensive resilience index of the system, with its value strictly defined between 0 and 1. The closer the value is to 1, the higher the overall energy retention rate of the system in absorbing disturbances and maintaining its original transmission work. This indicates the evolution start timestamp of the detected sudden disturbance source injection. This represents the termination timestamp when the system's state-space evolution satisfies steady-state convergence or recovers to its nominal efficiency. The definite integral term in the numerator represents the total effective work actually performed by the perturbed network throughout the entire evolution cycle. The denominator represents the baseline total work that the network should output under strictly aligned conditions when it is undisturbed. The zero-smoothing constant is forcibly set by the system and is typically set to 10. -6 This is used to prevent the division-by-zero overflow anomaly of the underlying floating-point computing unit when performing definite integral division operations during absolutely empty periods such as nighttime shutdowns. The technical purpose of performing this integral operation is to transform discrete high-frequency transient performance indicators into low-frequency macroscopic physical work measurements, effectively filtering out local numerical noise generated by microscopic traffic flow fluctuations.

[0080] After obtaining the resilience quantification index, the system evaluation module executes step S202, calculating the resilience gradient descent value of each candidate physical node and its connection based on the topology traversal mechanism of control variables. In vulnerability analysis of complex topology networks, identifying core weak links cannot rely solely on static graph centrality; it is necessary to simulate and quantify the true impact depth of the failure of a specific entity on the global dynamic work capacity. The system introduces N-1 expected fault traversal calculation logic, forcibly performing iterative isolation operations in the underlying mathematical matrix for each candidate node or key connection entity in the topology set. Specifically, when traversing and isolating a specific physical connection, the system forcibly clears its equivalent admittance parameter to zero; when traversing and isolating a specific physical node, the system cuts off all mutual admittances with the outside world, while retaining its small main diagonal self-admittance, thereby preventing the Jacobian matrix singularity collapse during the reassembly of the global phasor admittance matrix, which would lead to solution interruption. For each entity isolation, the system re-calls the previous state-space equations for time-domain closed-loop deduction, calculating the residual network resilience quantification index under the condition of missing that entity. The logic for determining the resilience gradient is as follows: ; In the formula, Indicates the removal of the first The relative gradient descent rate of the system's comprehensive resilience quantification index after considering candidate physical entities (nodes or edges). This is a discrete device index for traversing the candidate entity set of the current road network topology. This is the global baseline resilience quantification index corresponding to the current complete topology before the isolation operation is performed. To strip entities from the underlying simulation domain The residual toughness quantification index was then recalculated. To prevent computational overflow caused by the baseline resilience quantization index approaching zero, the underlying smoothing tolerance is typically set to 10. -8The physical significance of this gradient value lies in its direct characterization of the irreplaceable role of this specific physical entity in the global energy dissipation network. The larger the value, the more dependent the entire pipeline network's performance is on this entity. If it fails due to overload, it will trigger a global cascading performance degradation. For the multi-threaded concurrent allocation of the underlying computation for traversing the massive number of entities, those skilled in the art can use the MapReduce architecture or Message Passing Interface (MPI) to accelerate the parallelization of the computing power cluster. The distributed parallel deduction mechanism is a well-known technology in this field and will not be elaborated here.

[0081] After obtaining the resilience gradient descent sequence of all entities in the network, the system evaluation module executes step S203, combining multi-dimensional constraint boundaries to output the decision configuration for weak nodes, and distributes it to the decision support end. To ensure the executability of the output results in a real engineering environment, the system abandons the one-sided judgment relying solely on a single gradient descent extreme value, and introduces resource constraint parameters such as entity modification investment or emergency connection deployment to construct a multi-dimensional weighted decision matrix. The system performs simultaneous algebraic operations on the absolute gradient descent value of each entity and the preset intervention cost accounting coefficient. The extraction logic of this comprehensive decision index is as follows: ; In the formula, Indicates targeting candidate physical entities The output is a comprehensive indicator for assessing the value of intervention. and The system sets multi-dimensional weighting coefficients based on different decision-making scenarios to satisfy... As a preferred approach, when the system is in emergency response mode for sudden large passenger flows, the following settings are configured: The value range is 0.7 to 0.9, prioritizing rapid recovery of network resilience; when the system is under normal infrastructure upgrade conditions, the following setting is used. The value range is 0.4 to 0.6, in order to balance the long-term resilience gain with the current renovation cost. This represents the global available resource limit parameter dynamically injected by an external decision-making system. Indicates targeting that specific entity The estimated cost of performing emergency transport capacity replenishment or physical topology expansion is quantified in the specific dimensions of the cost parameter, which are exemplified by the number of shuttle bus trips expected to be consumed or the amount of engineering modification funds required, depending on the business scenario. The system sets a valid data confidence threshold. The system bases its decisions on the calculated comprehensive value index. A dynamic descending sequence is constructed for all entities in the network, and entities above a specific dynamic identification threshold are selected as key weak network components. As a preferred approach, the selection ratio for this dynamic identification threshold is set within the floating-point range of the first 5% to 10% of the sequence, with the specific truncation depth depending on the current... The system adaptively scales based on resource availability. Ultimately, the intercepted queue is encapsulated into a standardized decision support data packet, containing the entity's precise topological coordinates, the proposed expansion equivalent, and the expected resilience recovery gain. The technical purpose of outputting this closed-loop decision is to guide the external dispatch center, under extreme conditions of hard resource constraints, to allocate limited emergency response capacity or infrastructure investment to the physical topological bottleneck that generates the maximum marginal resilience benefit, avoiding intervention waste caused by inefficient resource allocation.

[0082] Application example: To better understand the technical solution of this invention, the following describes the system's workflow in detail, taking into account a typical urban multimodal transport network (such as a rail transit and bus connection network) experiencing a sudden disturbance during the morning rush hour.

[0083] Network topology initialization and nominal flow input: Assume the target calculation area contains 5 core entity nodes: residential area station A (origin), transfer station B, transfer station C, core hub station D, and business district station E (end). During the regular morning rush hour (setting the initial time as base 0 seconds, i.e., attached...), Figure 2 The system starts at point 0 in the evolution time of the horizontal axis system. The system extracts travel demand from the OD demand matrix. According to step S171, the system equates the massive commuter flow to the nominal current injection in the power grid. Residential site A acts as a net source, with its equivalent injection current being positive; business area site E acts as a net sink, with its equivalent extraction current being negative. At this time, network traffic flows smoothly along the physical connections A→B / C→D→E, and the equivalent pressure on all network nodes is in a low-level equilibrium state, as shown in the attached diagram. Figure 3 Figure (a) shows that the system stably outputs 10W of equivalent effective traffic power in the 0 to 15 minute interval.

[0084] Sudden disturbance access and abnormal current surge: At the 15-minute mark of the simulation, a sudden signal failure occurred at the core hub station D, causing widespread train delays. The system, by accessing external heterogeneous data (such as gate card swipe data), calculated the accumulated passenger flow at hub station D according to step S172. Combined with the station's unique passenger flow release coefficient, the system instantly generated a huge positive transient abnormal surge current component at hub station D. This disrupted the original steady state, leading to an increase in the equivalent congestion potential energy at hub station D. A sharp rise.

[0085] Nonlinear truncation and mass conservation compensation: With the congestion potential of hub station D The pressure continued to rise, and at the 22nd minute, it first surpassed the potential energy of the upstream transfer station B (i.e., (See appendix) Figure 3 Figure (b) shows the comparison curve of the macroscopic quality non-conservation error rate. If the "traditional linear matrix truncation algorithm" (represented by the dotted line marked with a hollow circle in the figure) is used, forced truncation will lead to the loss of physical flow, with the error rate soaring to a maximum of 19%. At this point, if the traditional linear matrix solution is used, the flow will exhibit an illogical "backflow from D to B". However, according to the truncation logic in step S182, the system forcibly resets the actual transmission flow from B to D to zero, accurately simulating the unidirectional saturation attribute of the traffic network. At the same time, the system triggers the residual compensation mechanism, converting the theoretically truncated flow into a fully obstructed residual and accumulating it in the buffer container of transfer station B, absolutely ensuring 100% conservation of macroscopic passenger flow physical quality and avoiding the loss of passenger flow data out of thin air. This effect is shown in the attached figure. Figure 3 Figure (b) provides a clear illustration of this, showing that the curve representing the nonlinear residual full reverse compensation mechanism of the present invention (represented by a solid line marked with an asterisk in the figure) stays close to the horizontal axis from beginning to end, with the error rate perfectly maintained at 0%.

[0086] Overflow paralysis determination and cascade failure: By the 30th minute, the physical occupancy of hub station D exceeded 90% of its critical capacity hard boundary (i.e., the critical capacity saturation threshold), and there was still net inflow at that moment. Based on the dual judgment conditions in step S183, the system officially marked hub station D as an Overflow (overflow paralysis) state. Subsequently, the system triggered step S184, forcibly setting the admittance of all input connections pointing to hub station D to zero and dynamically amplifying its main diagonal self-admittance element. Mathematically, this prevented computational collapse caused by the singularity of the Jacobian matrix, and physically, it realistically simulated the entire cascading failure process caused by the closure of station D spreading upstream to stations B and C.

[0087] Evaluation of the absolute value of the system's effective power: Throughout the entire emergency, the system continuously monitors the work done by the network in transporting passenger flow to destination E. Since destination E is a negative extraction point, its original potential solution is negative. (See attached...) Figure 3 As shown in Figure (a), if the comparison file algorithm is used (represented by the dashed line marked with hollow squares in the figure), the system exhibits an absurd drop in negative work done (as low as -22W) after the disturbance occurs. According to step S192, the system extracts the absolute value of the congestion potential energy at the endpoint E. The actual arrival flow rate was multiplied by the actual flow rate. The results show that although the actual arrival flow rate decreased sharply after the disturbance, the impedance (absolute potential energy) that the system had to overcome to maintain transmission increased, successfully outputting a continuous and consistently positive system effective power curve. This completely eliminated the negative work paradox in the traditional algorithm, as shown in the attached figure. Figure 3 The curves representing the absolute potential constraint algorithm of this invention in Figure (a) are shown as solid lines with gray background and solid triangles. The effective power output of the system climbs to a maximum of 42W during the disturbance period and remains positive throughout, which perfectly conforms to the objective laws of physics.

[0088] To verify the effectiveness of the nonlinear fluid dynamics analogy algorithm proposed in this invention, its performance was compared with that of the traditional static traffic assignment algorithm (STA) and the pure linear equivalent circuit algorithm without the introduction of truncation and compensation mechanisms. The specific experimental index statistics are shown in Table 1.

[0089] Table 1. Core quantitative indicators for traffic network simulation under extreme sudden disturbances. In the table, "-" indicates that it is not applicable.

[0090] in conclusion: The multidimensional controlled constraint logic and quality residual compensation mechanism proposed in this invention not only rigorously uphold the macroscopic mass conservation law of fluid mechanics at the theoretical level (reducing the error rate to 0.00%), but also completely eliminates computational collapse and the paradox of negative work in the process of network cascading failure deduction in engineering practice. Compared with existing technologies, this invention has achieved progress in both the prediction accuracy of transient evolution of complex traffic networks and the robustness of the underlying data structure.

Claims

1. A method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling, characterized in that, Includes the following steps: Obtain road network topology, traffic demand, and disaster disturbance conditions from the basic traffic database. Based on the road network topology, establish a single-layer physical network topology model for each mode of transportation. Configure equivalent energy storage buffer components at the intersection nodes of the single-layer physical network topology model and set the flow input model. Based on the storage capacity of the equivalent energy storage buffer component, an asymmetric variable weight impedance function is constructed, which transforms the dynamic passage impedance into transient equivalent admittance parameters and assembles them to generate a global phasor admittance matrix. The traffic demand and the disaster disturbance conditions are transformed into the equivalent current vectors of the corresponding nodes. The state space equations are solved by combining the global phasor admittance matrix and the equivalent current vectors to obtain the equivalent pressure distribution and actual conduction flow. When the residence of the equivalent energy storage buffer component triggers the capacity boundary, local admittance truncation is performed and the global phasor admittance matrix is ​​reconstructed and iteratively evolved to a steady state. The instantaneous effective power is calculated based on the actual conduction flow and the equivalent pressure distribution after evolution calculation. The time integral value of the instantaneous effective power under disturbance and reference conditions is compared to generate the system resilience quantification index. Based on the node isolation mechanism, the set of physical nodes or lines that cause the system resilience quantification index to decrease the most is output.

2. The method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling as described in claim 1, characterized in that, The establishment of single-layer physical network topology models for each mode of transportation and the configuration of equivalent energy storage buffer components specifically include: Extract the spatial coordinates of physical nodes of each mode of transportation to generate a set of physical nodes, extract the trajectory data of the lines connecting adjacent physical nodes to generate a set of physical lines, and combine the upper limit of the design capacity of each line to generate the single-layer physical network topology model. Based on the spatial distance matching threshold and topological connectivity, the intersection space boundary of cross-level physical nodes is delineated, a cross-mode coupling hub node set is generated, the equivalent energy storage buffer component is configured for the elements in the cross-mode coupling hub node set, and the maximum physical current storage capacity of the equivalent energy storage buffer component is calibrated based on the weighted sum of the product of the actual effective transfer area and the safe space density threshold parameter.

3. The method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling as described in claim 1, characterized in that, The construction of the asymmetric variable-weighted impedance function and the conversion of the dynamic passage impedance into transient equivalent admittance parameters specifically include: Extract the absolute physical time required for cross-modal transfer streamlines in a congestion-free free-flow state, and generate a static asymmetric transfer impedance matrix. The buffer flow rate of the equivalent energy storage buffer component at the current moment is obtained. The ratio of the buffer flow rate to the maximum physical storage capacity is processed by the upper and lower bound truncation functions. The ratio is combined with the nonlinear sensitivity index and the impedance amplification penalty coefficient to dynamically amplify and calculate the static asymmetric transfer impedance matrix, thereby obtaining the dynamic passage impedance of the cross-level transfer channel. The reciprocal of the dynamic passage impedance of each physical line and the cross-level transfer channel is calculated and converted into a transient equivalent admittance parameter characterizing the smoothness of network flow.

4. The method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling as described in claim 1, characterized in that, The assembly to generate the global phasor admittance matrix specifically includes: The admittance matrix is ​​initialized based on the total number of nodes in the global network topology, and the starting node identifier and the ending node identifier are uniquely mapped to the row index and column index of the admittance matrix. The transient equivalent admittance parameters are filled into the off-diagonal row and column coordinates of the admittance matrix according to the inflow and outflow sign rules, and the sum of the out-degree transient equivalent admittances of the nodes is filled into the main diagonal coordinates. Regularized ground conductance parameters are forcibly injected into the main diagonal elements of the admittance matrix to make the global phasor admittance matrix satisfy the diagonal dominance condition.

5. The method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling as described in claim 1, characterized in that, The process of converting the traffic demand and the disaster disturbance conditions into equivalent current vectors for the corresponding nodes specifically includes: Based on the spatiotemporally aligned dynamic start and end point demand matrix, the flow difference between the target node as the net source and the net sink is calculated, and the nominal equivalent injected current component under normal travel conditions is extracted. The cumulative amount of stranded passenger flow at the target node is obtained by analyzing multi-source heterogeneous monitoring data of sudden disturbance events. The transient abnormal surge current component is calculated by multiplying the cumulative amount of stranded passenger flow with a preset passenger flow release coefficient. The nominal equivalent injected current component and the transient abnormal surge current component are algebraically superimposed to form an equivalent current vector. When the absolute value of the global initial current scalar algebraic residual is determined to be greater than the set flow imbalance tolerance threshold, the global amortization compensation logic is triggered, and the global initial current scalar algebraic residual is injected in reverse average into the equivalent current vector of each node to perform flow conservation verification.

6. The method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling as described in claim 5, characterized in that, The acquisition of the equivalent pressure distribution and actual conduction flow specifically includes: Calculate the inverse matrix of the global phasor admittance matrix, and multiply the inverse matrix with the equivalent current vector after flow conservation verification to obtain the equivalent pressure distribution containing the current transient equivalent congestion potential energy of all network nodes; Extract the equivalent congestion potential energy difference between the starting node and the ending node with a direct connection at the current moment. Multiply the equivalent congestion potential energy difference with the transient equivalent admittance parameter of the corresponding physical connection to calculate the actual transmission flow. When it is determined that the equivalent congestion potential energy of the starting node is less than or equal to the equivalent congestion potential energy difference of the ending node, a directional truncation protection mechanism is triggered to force the actual transmission flow of the physical connection to zero. The actual transmission flow that is forced to zero is used as the obstructed residual to fully compensate the equivalent energy storage buffer component inside the starting node in reverse to maintain global flow conservation.

7. The method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling as described in claim 1, characterized in that, The process of performing local admittance truncation and reconstructing the global phasor admittance matrix specifically includes: Extract the instantaneous total input flow rate and instantaneous total output flow rate of the equivalent energy storage buffer component within the current time step, and update the actual cumulative physical dwell time at the current moment based on the time integral of the difference between the two and combined with the extreme value truncation boundary. When the ratio of the actual cumulative physical dwell time to the configured physical capacity hard boundary threshold is greater than the preset critical capacity saturation threshold, and the instantaneous net inflow shear difference is greater than zero, the target node is determined to have overflow paralysis. The physical blocking logic is triggered, and the input edge admittance parameters of all nodes in the global network that directly point to the overflow paralysis target node are forcibly overwritten to zero. At the same time, the main diagonal self-admittance elements of the overflow paralysis target node are retained and amplified. The global phasor admittance matrix of the next time step is reconstructed based on the updated edge admittance parameters.

8. A method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling, as described in claim 5, is characterized in that... The calculation of instantaneous effective power specifically includes: Filter out the set of legal destination nodes with net reception attributes and no buffer capacity overflow, and extract the actual aggregated passenger flow that is actually injected into each node in the set of legal destination nodes along all valid input adjacent edges in the current time step; The absolute value of the equivalent congestion potential energy of each node in the set of legal destination nodes in the equivalent pressure distribution is extracted as the receiving pressure variable. The actual aggregated passenger flow of each legitimate destination node is multiplied with the corresponding receiving pressure variable, and the product result of all nodes in the set of legitimate destination nodes is algebraically summed to obtain the instantaneous effective power characterizing the transmission efficiency of the system in the current time slice.

9. A method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling, as described in claim 8, is characterized in that... The generation system resilience quantification index and output physical node or line set specifically include: The instantaneous effective power is integrally processed along the set disturbance evolution time axis to obtain the actual total work done during the disturbance period. The total work done during the disturbance period is obtained by comparing the feature matching label and dividing it by the time integral of the undisturbed reference effective power to output a normalized system resilience quantification index. A node isolation traversal mechanism is constructed to sequentially remove each candidate physical entity in the single-layer physical network topology model by clearing its equivalent admittance, and then re-execute the evolution calculation loop to obtain the residual system resilience quantification index under the condition of missing specific physical entities. Based on the difference in the index before and after isolation, the relative gradient descent rate of the comprehensive resilience corresponding to the physical entity is calculated. The comprehensive resilience relative gradient descent rate of each candidate physical entity is weighted and simultaneously algebraically calculated with the expected resource intervention cost to generate a comprehensive intervention value index. Physical entities whose comprehensive intervention value index is higher than the dynamic identification threshold are output as physical nodes or line sets.

10. A system for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling, characterized in that, The method for constructing and assessing the resilience of a transportation hypernetwork considering cross-modal coupling, as described in any one of claims 1-9, includes: The data acquisition module is used to obtain static road network topology data for highways, railways, civil aviation and waterways from the basic transportation database, as well as historical passenger and freight flow operation data for the corresponding modes of transportation. The hypernetwork mapping module is connected to the data acquisition module. The hypernetwork mapping module is used to establish a single-layer physical network topology model based on static road network topology data. The hypernetwork mapping module also establishes equivalent energy storage buffer components at the intersections of physical nodes of different transportation modes to characterize the physical storage capacity of the integrated transportation hub. The transient evolution calculation module is connected to the hypernetwork mapping module. It is used to calculate the state-dependent variable-weight impedance of the cross-layer transfer channel based on the instantaneous current storage state of the equivalent energy storage buffer components. The transient evolution calculation module converts the physical line impedance and state-dependent variable-weight impedance of each layer into admittance values ​​and assembles them to generate a global node admittance matrix. The resilience assessment and output module is connected to the transient evolution calculation module. The resilience assessment and output module is used to calculate the instantaneous effective traffic power based on the actual flow rate reaching the endpoint node and the equivalent node pressure within a set time period.

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