Coupling degree evaluation and resilience improvement method for comprehensive transportation network operation situation

Abstract

The application discloses a comprehensive traffic network operation situation coupling degree evaluation and resilience improvement method, comprising: obtaining multi-source operation data and physical layout data to construct a multi-layer network topology; determining facility coupling degree and behavior coupling degree between disturbed mode pairs in the recovery transition period; obtaining passenger flow evolution situation by using a dynamics model driven by the willingness to return and coordinated with congestion feedback according to the separation state of the two; identifying the recovery stagnation time based on the situation, and quantifying the implicit resilience loss by using the closed loop in the phase space; and outputting a hierarchical information release scheme and an operation capacity coordination strategy as targets of minimizing the implicit loss and avoiding stagnation.

Description

Technical Field

[0001] This invention relates to the field of integrated transportation hub operation and management technology, and in particular to a method for evaluating the coupling degree and improving the resilience of integrated transportation network operation status. Background Technology

[0002] In the daily operation of large-scale integrated transportation hubs, the state of the transportation network often deviates from its design steady state due to various sporadic disturbances, such as equipment failures, severe weather, or large passenger flows. Studying the state recovery mechanism of the hub after disturbances is of significant technical importance for optimizing emergency dispatch resource allocation, shortening the time of system performance degradation, and improving the overall operational resilience of the hub. Through accurate situation assessment, management departments can grasp the coordinated status between different transportation modes in real time, thereby taking scientific intervention measures during complex transition phases.

[0003] Currently, assessments of transportation hub operations primarily rely on static topology analysis or monitoring of single performance indicators, such as the number of transfers, average queuing time, or channel utilization within a predetermined time window. During the recovery phase after a system disruption, existing technologies largely focus on evaluating the progress of physical infrastructure connectivity restoration and directly inferring the regression of system service levels based on the recovery of infrastructure capacity. However, in actual operation, there is a complex nonlinear interaction between the availability of physical infrastructure and individual passenger travel decisions. Existing methods often struggle to characterize the temporal inconsistencies between supply-side capacity and demand-side behavior when dealing with such dynamic evolution processes, leading to resource misallocation or secondary congestion during the recovery transition period.

[0004] Therefore, it is urgent to address how to accurately identify and assess the dynamic evolution characteristics of integrated transportation networks during disturbance recovery, and how to quantify the implicit performance losses caused by the mismatch between supply and demand feedback. It is necessary to investigate a method that can improve the accuracy of situational awareness and the effectiveness of strategy coordination at transportation hubs under complex recovery conditions. Summary of the Invention

[0005] Therefore, this application provides a method for evaluating the coupling degree and improving the resilience of integrated transportation network operation status, in order to solve at least one of the above-mentioned problems in the prior art.

[0006] A method for assessing the coupling degree and improving the resilience of a comprehensive transportation network operation status includes:

[0007] Acquire multi-source operational and physical layout data of the integrated transportation network and construct a multi-layered network topology;

[0008] During the recovery transition period, the facility coupling degree and behavioral coupling degree between the disturbed mode pairs are determined based on multi-source operational data, physical layout data, and topology.

[0009] Based on the separation state of facility coupling degree and behavioral coupling degree, the passenger flow evolution trend of the disturbed mode pair is obtained by using a pre-constructed dynamic model of the coordination between the return intention drive and the congestion feedback.

[0010] Based on the analysis of the changes in network system performance according to the evolution of passenger flow, the moment of recovery stagnation is identified, and the implicit resilience loss is quantified according to the closed loop formed by behavioral coupling degree and system performance in phase space.

[0011] With the goal of minimizing implicit resilience loss and the constraint of avoiding recovery stagnation, we output a graded information dissemination scheme and capacity coordination strategy for the disturbed mode pairs.

[0012] Based on the above technical solutions, this invention can characterize the rebound oscillation phenomenon during the recovery period of a hub, effectively identify hidden resilience losses, and provide decision support for improving the operational resilience of a hub. Attached Figure Description

[0013] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0014] Figure 1 This is a schematic diagram of a method for assessing the coupling degree and improving the resilience of a comprehensive transportation network operation status, as provided in this application.

[0015] Figure 2 This application provides a schematic diagram of the passenger flow evolution process obtained through a set of nonlinear ordinary differential equations.

[0016] Figure 3 This is a schematic diagram of the process provided in this application for analyzing the performance change characteristics of a network system based on passenger flow evolution and identifying and recovering from stagnation.

[0017] Figure 4 This is a schematic diagram of the process for quantifying implicit toughness loss based on the closed loop formed by behavioral coupling degree and system performance in phase space, as provided in this application.

[0018] Figure 5 This is a schematic diagram of the output of the graded information release scheme and capacity coordination strategy for the disturbed mode pairs provided in this application. Detailed Implementation

[0019] Example 1

[0020] This embodiment provides a detailed description of the global process implementation of a method for assessing the coupling degree and enhancing the resilience of a comprehensive transportation network. In one possible implementation, such as... Figure 1 As shown, the method may include the following steps:

[0021] Step 101: Obtain multi-source operation data and physical layout data of the integrated transportation network, and construct a multi-layer network topology;

[0022] Multi-source operational data can refer to raw operational records extracted from different transportation mode subsystems of an integrated transportation hub. For example, card-swiping data containing entry and exit times and station codes can be obtained from the rail transit subsystem; data containing route numbers and vehicle arrival and departure timestamps can be obtained from the regular bus subsystem; and order data containing passenger pick-up and drop-off times and latitude and longitude coordinates can be obtained from ride-hailing platforms. After acquiring the above-mentioned multi-source heterogeneous data, it is necessary to perform unified processing on its spatial and temporal references. The spatial unification process maps the aforementioned latitude and longitude coordinates to a unified hub station coding system according to the nearest hub matching rule. The temporal unification process normalizes all timestamps to the same clock reference, thereby generating a unified-coded multi-mode operational record table.

[0023] Furthermore, before constructing the network topology, multi-source operational data needs to be preprocessed to eliminate abnormal disturbances. The preprocessing mainly includes time window segmentation and outlier filtering. Specifically, continuous time windows are divided according to a preset time span, such as 5 minutes, and the passenger flow for each mode within each time window is statistically analyzed. In the data cleaning stage, heuristic rules are used to handle missing records caused by equipment failures and duplicate count anomalies. For missing records within a time window, linear interpolation between adjacent time windows is used to complete the numerical values. For duplicate count anomalies caused by card-swiping devices, deduplication rules based on time thresholds are used. For example, multiple adjacent records of the same entity identifier within 2 minutes at the same station are considered as a single valid passage, and redundant entries are removed.

[0024] After the above preprocessing steps, the passenger flow statistics matrix of each traffic mode under a unified time window is obtained, avoiding the interference of basic data pollution on subsequent evolution prediction.

[0025] By collecting multi-source operational data, the dynamic passenger flow distribution of each entity within the integrated transportation hub is obtained. Simultaneously, static constraints such as channel design capacity and line rated capacity are extracted based on physical layout data. These dynamic operational states and static physical constraints are mapped onto a unified mathematical graph structure, forming a multi-layered network topology. This multi-layered network topology serves as the underlying computational container, establishing the geometric and algebraic foundation for subsequent evaluations of node load, channel flow, and inter-modal transfer relationships.

[0026] A specific modeling approach can be to model each transportation mode as an independent network layer, where nodes in the network layer correspond to physical stations, and intra-layer edges correspond to operational route connections. The weight of each intra-layer edge is directly set to the rated capacity of the corresponding route section. The independent network layers are connected through physical transfer facilities within hubs, thus constructing inter-layer edges. The weight of each inter-layer edge is set to the design capacity of the corresponding transfer corridor. By integrating the intra-layer edge sets and inter-layer edge sets of all modes, a multi-layer network topology diagram containing the rated capacity parameters of each edge is output, establishing the basic structure for subsequent evaluation of the physical carrying capacity relationship between nodes and corridors.

[0027] In some alternative implementations, the physical layout data can be a statically pre-stored structured file, or it can be periodically synchronized and updated through the application programming interface of the digital twin platform to adapt to the environment of the integrated transportation hub that is undergoing expansion or renovation.

[0028] Based on the multi-layer network topology and multi-source operational data, the affected pattern pairs are identified during disturbance events. Specifically, based on the multi-layer network topology, the set of network layer nodes directly affected by the disturbance event is extracted, and based on the detection results of abnormal passenger flow decline in the multi-source operational data, adjacent network layer node pairs that have inter-layer connections with the damaged nodes are identified as affected pattern pairs.

[0029] Step 102: During the recovery transition period, based on multi-source operational data, physical layout data, and topology, determine the facility coupling degree and behavioral coupling degree between the disturbed mode pairs respectively.

[0030] Specifically, the recovery transition period can be defined as the predetermined time window between the gradual repair and reopening of damaged facilities and the complete return of the system to normal operation after the integrated transportation network has been downgraded due to an external disturbance event. A disturbed mode pair can refer to a combination of two transportation modes with close transfer connections within a hub and affected by the aforementioned disturbance. The facility coupling degree is determined by quantifying the ratio of actual available facility capacity to design capacity, objectively reflecting the recovery level of physical hardware connectivity. Simultaneously, the behavioral coupling degree is determined by quantifying the ratio of actual transfer passenger flow to historical baseline transfer flow, reflecting the actual return-to-normal travel behavior of the affected passenger group.

[0031] This two-tiered quantification mechanism decouples traditional single assessment indicators to reveal the dynamic separation phenomenon where facility capacity has been restored but passenger behavior has not yet returned synchronously.

[0032] Furthermore, the calculation cycle of behavioral coupling degree can be dynamically set according to the sampling frequency of multi-source operational data. For example, when the push delay of rail transit entry and exit card swiping data is 1 minute, the rolling calculation step of coupling degree can be set to 1 minute to improve the real-time performance of situational awareness.

[0033] Step 103: Based on the separation state of facility coupling degree and behavior coupling degree, the passenger flow evolution trend of the disturbed mode pair is obtained by using the pre-constructed dynamic model of back-cut intention drive and congestion feedback coordination.

[0034] Specifically, the separation state can refer to the space of difference between the facility coupling degree and the behavioral coupling degree. This separation state represents the scale of disrupted passenger flow stranded on alternative travel modes, constituting the potential energy driving passengers to switch back. A pre-constructed dynamic model introduces the release of recovery announcements as an external information stimulus to simulate the temporal distribution of disrupted passengers' willingness to switch back after receiving the information. Simultaneously, the model internally sets a congestion nonlinear penalty term to simulate the delay experience of early-stage back-switching passenger flow encountering insufficient capacity during the recovery period, and the secondary avoidance behavior triggered by this delay experience. By jointly solving the aforementioned information attraction factors and congestion inhibition factors, the output reflects the passenger flow evolution trend reflecting the alternating cycle of passenger switching back and further avoidance.

[0035] As an alternative, the dynamic model can be solved using a numerical integration algorithm with a fixed time step, or an event-driven discrete simulation framework can be used to obtain the passenger flow prediction sequence over a continuous time axis.

[0036] Step 104: Based on the passenger flow evolution trend analysis, analyze the change characteristics of network system performance, identify the recovery stagnation moment, and quantify the implicit resilience loss according to the closed loop (resilient hysteresis loop) formed by behavioral coupling degree and system performance in phase space.

[0037] It can be further implemented as follows: Based on the evolution of passenger flow and the capacity recovery progress of the disrupted mode pairs, determine the network system performance; analyze the changing characteristics of system performance, identify the recovery stagnation moment, and quantify the implicit resilience loss based on the resilience hysteresis loop formed by behavioral coupling degree and system performance in phase space.

[0038] In this step, network system performance can be defined as the ratio of the system's actual effective service throughput to its rated capacity. Based on the comparison between the aforementioned passenger flow evolution trend and capacity recovery progress, the change of the derivative of system performance over time is tracked. The critical state where the passenger flow inflow rate exceeds the system capacity recovery rate, causing the performance improvement trend to be forcibly interrupted, is defined as the recovery stagnation moment.

[0039] Furthermore, a two-dimensional phase space is established with behavioral coupling degree as the horizontal coordinate and system performance as the vertical coordinate. The state evolution coordinate sequences of the system during the degradation and recovery phases are extracted, and the geometric area integral enclosed by these two phases in the phase space is defined as the implicit resilience loss. This loss value objectively reflects the additional alternative path load and hub operation dissipation caused by passenger behavioral lag.

[0040] Furthermore, when performing geometric area integration in phase space, the discrete trapezoidal approximation rule based on the coordinate point sequence can be used for numerical calculation to reduce the system's computational dependence on high-frequency state sampling.

[0041] Step 105: With the goal of minimizing implicit resilience loss and the constraint of avoiding recovery stagnation, output a tiered information dissemination plan and capacity coordination strategy for the disturbed mode pairs. Then, send the plan to the hub operation and scheduling system for execution.

[0042] In this step, the quantified results from the aforementioned assessment phase are transformed into a set of decision parameters to guide hub operations. The identified moments of recovery stagnation are converted into a lower bound for the minimum rate of capacity gradient release, forming a hard boundary constraint. Within this constraint, with the optimization objective of minimizing the implicit resilience loss, an optimization search is performed within a multi-dimensional decision space comprised of information release time points, information release channel strength, and capacity increase frequency. The final output solution guides the hub operations department to push recovery progress updates to stranded passengers at predetermined time points and with predetermined intensity, while simultaneously matching appropriate train or bus departure intervals, thereby smoothing out peak and valley fluctuations and mitigating rebound oscillations.

[0043] In some alternative implementations, for emergency response scenarios with high computational timeliness requirements, the above-mentioned optimization search process can preload a locally feasible solution set manually tuned based on historical experience, and perform gradient descent or simplex search within the neighborhood of the locally feasible solution set to shorten the generation time of the decision scheme.

[0044] Example 2

[0045] Based on the above embodiment one, the process of dynamic quantization of the dual-layer coupling degree and transfer recognition adaptation during the recovery transition period is further described in detail.

[0046] In one possible implementation, determining the facility coupling degree and behavioral coupling degree between the disturbed mode pairs respectively includes the following steps:

[0047] Step 201: Determine the actual available facility capacity between the disturbed mode pairs based on the operating status of each transfer facility in the multi-source operation data and the design capacity in the physical layout data.

[0048] Step 202: Define the ratio of the actual available facility capacity to the design capacity between the disturbed mode pairs as the facility coupling degree.

[0049] Step 203: Define the ratio of the actual transfer passenger flow between disturbed mode pairs to the pre-stored historical baseline transfer flow as the behavioral coupling degree.

[0050] Among them, the low characteristic of behavioral coupling degree lagging behind the recovery of facility coupling degree during the recovery transition period reflects the lag in passengers' failure to switch back to the recovery mode in a timely manner.

[0051] Specifically, facility coupling degree is used to characterize the real-time physical connectivity recovery status of transfer facilities within a hub. In this embodiment, facility coupling degree is calculated by reading the real-time operational status indicators of each transfer channel and connecting facility within each time window. The operational status indicators can specifically include normal, flow-limited, and closed. The availability coefficient of each facility is determined based on the indicators. The availability coefficient is set to 1 during normal operation, 0 when closed, and a value between 0 and 1 during flow-limited operation, according to the actual flow-limiting ratio. The facility coupling degree calculation formula is as follows:

[0052] C inf (t)=∑(u k (t)*κ k ) / ∑(κ k );

[0053] Among them, C inf (t) represents the facility coupling degree of the pattern pair within time window t, ∑ is the summation operator, and u k (t) is the availability coefficient of the k-th facility in time window t, κ k Let k be the design capacity of the k-th facility.

[0054] Accordingly, behavioral coupling is used to dynamically reflect the passenger rollback progress in the demand dimension. In this embodiment, the actual transfer passenger flow between disturbed pattern pairs is extracted from the passenger flow matrix. To eliminate the interference of periodic fluctuations in passenger flow, this method calls pre-stored historical benchmark transfer flow as a reference. The historical benchmark transfer flow is specifically obtained by calculating the transfer passenger flow statistics for the corresponding time period within a preset historical time window before the disturbance occurs. The behavioral coupling calculation formula is as follows:

[0055] C beh (t)=F ij (t) / F0;

[0056] Among them, C beh (t) represents the coupling degree of the behavior of the pattern pair in time window t, F ij (t) represents the actual transfer passenger flow of the mode pair in time window t, and F0 represents the pre-stored historical baseline transfer flow, which is the baseline flow of the total transfer demand of the disturbed mode pair under normal operation.

[0057] During the recovery transition period, once the operating schedules and access routes of the disrupted mode pairs reopen, the facility coupling degree quickly recovers to 1 or close to 1. However, due to factors such as passenger route inertia, information lag, and lack of trust, the recovery of transfer passenger traffic usually lags behind facility recovery, resulting in a significantly lower behavioral coupling degree compared to the facility coupling degree. Through the above two-layer definition, this spatiotemporal separation phenomenon can be accurately captured and quantified.

[0058] In one possible implementation, for the actual passenger transfer flow, the matching degree (identifier matching relationship) between the pairs of disturbed modes is determined according to the passenger identification system of their respective traffic subsystems based on the disturbed mode, and a differentiated identification method is used to determine this, specifically including the following processing:

[0059] If the identifiers of the disturbed mode pairs can be matched directly or indirectly, then the entry and exit time windows and spatial constraints are used to perform individual-level transfer association to obtain the actual transfer passenger flow. If the identifiers of the disturbed mode pairs cannot be matched, then the correlation coefficients of the entry and exit flow of the disturbed mode pairs are used in conjunction with the pre-configured empirical transfer ratio to perform aggregate-level transfer estimation to obtain the actual transfer passenger flow.

[0060] This can be further implemented as follows: if the identifiers between the disturbed mode pairs can be matched directly or indirectly, then the entry and exit time windows in the multi-source operation data and the spatial constraints in the physical layout data are used to perform individual-level transfer association to obtain the actual transfer passenger flow; if the identifiers between the disturbed mode pairs cannot be matched, then the entry and exit flow correlation coefficient of the disturbed mode pairs is calculated based on the multi-source operation data, and the aggregated transfer estimation is performed in conjunction with the pre-configured experience transfer ratio to obtain the actual transfer passenger flow.

[0061] In this embodiment, the matching degree between the identifiers of the disturbed mode pairs is determined by the payment or identification system used by different transportation subsystems. For scenarios where identifiers can be directly matched, such as when both rail transit and regular buses use the same city transportation card system, the system directly searches for the entry and exit records of the same entity identifier within the hub. A transfer time threshold is set during identification, and this threshold is calibrated based on the physical scale of the hub and walking speed. If the time difference between the exit time of the entity identifier in the first mode and the entry time in the second mode is less than the transfer time threshold, it is determined to be a valid transfer.

[0062] For scenarios where identifiers can be indirectly matched, such as different payment methods linked to real-name accounts, spatial constraints are added while performing time window verification. It is determined that the straight-line distance between the exit and entry station coordinates does not exceed the physical radius of the hub, and transfer connections are determined in conjunction with account association relationships.

[0063] For scenarios where identifiers cannot be matched, such as cash-paid buses and anonymous ride-hailing services, the system cannot establish an individual-level identity correspondence. In this case, an aggregate statistical method is used for estimation. By calculating the correlation coefficient between the outbound passenger flow sequence of the first mode and the inbound passenger flow sequence of the second mode within a preset time delay window, the dynamic correlation characteristics of the traffic flow are obtained. This correlation characteristic is multiplied by a pre-configured empirical transfer ratio to obtain an estimated value of the actual transfer passenger flow. The empirical transfer ratio can be obtained by statistically averaging the ratio of inter-mode transfer passenger flow to the total outbound passenger flow of the relevant modes in the historical data of the hub for the same period. Those skilled in the art can determine an appropriate empirical transfer ratio value based on historical data accumulated from the actual operation of the hub.

[0064] The aforementioned differentiated identification mechanism improves the coverage and accuracy of passenger flow identification in heterogeneous data environments.

[0065] One possible implementation, which involves determining the facility coupling degree and behavioral coupling degree between the disturbed mode pairs respectively, further includes:

[0066] Define the proportion of disturbed passengers who remain on alternative modes of transportation; establish an inverse mapping relationship between behavioral coupling degree and the proportion of passengers remaining on alternative modes of transportation; determine the proportion of disturbed passengers who remain on alternative modes of transportation based on behavioral coupling degree through the inverse mapping relationship; define the difference between facility coupling degree and behavioral coupling degree as coupling separation degree, and use the proportion of passengers remaining on alternative modes of transportation to explicitly express the coupling separation degree in order to eliminate the circular dependency between system state variables.

[0067] Specifically, the proportion of disrupted passengers who choose alternative modes of transportation rather than switching back to the recovery mode within a time window t is defined as the retention rate, denoted by p. a (t) represents the principle of commutation conservation. Disturbed passengers who are not stuck on alternative modes are those who have switched back and changed modes. Therefore, there is a linear inverse mapping relationship between behavioral coupling degree and the commutation rate:

[0068] C beh (t)=1-p a (t);

[0069] Among them, C beh (t) represents the behavioral coupling degree, p a (t) represents the retention rate.

[0070] Accordingly, the difference between facility coupling degree and behavioral coupling degree is defined as coupling separation degree. By substituting the above inverse mapping relationship, coupling separation degree is explicitly expressed using the retention ratio:

[0071] ΔC ij (t)=C inf (t)-1+p a (t);

[0072] Where, ΔC ij (t) represents the coupling separation degree of the mode pair within the time window t, C inf (t) represents the facility coupling degree, p a (t) represents the retention rate.

[0073] Through the explicit expression above, the coupling separation degree is directly transformed into a function of the state variable p. a The linear function of (t) eliminates the circular dependency caused by the nesting of state variables in subsequent dynamic modeling, which is beneficial to the self-consistent solution of the differential equation system.

[0074] As an example, suppose that after normalization, the facility coupling degree C of the current time window is... inf The retention rate is 1.0, and the retention ratio p a The value is 0.8. Substituting into the above mapping relationship, the coupling degree C of the current behavior is calculated. beh The coefficient of coupling separation is 1.0 - 0.8 = 0.2. Further calculation yields a coupling separation degree of 1.0 - 1.0 + 0.8 = 0.8. The calculation results indicate that although the current facility capacity has been fully restored, 80% of the passenger flow is still stuck on alternative routes, and the system faces a significant risk of coupling separation.

[0075] Example 3

[0076] Based on the above embodiment 2, this embodiment further describes the specific process of obtaining the passenger flow evolution of the disturbed mode pair by using a pre-constructed dynamic model of back-cut intention driven by congestion feedback.

[0077] In one possible implementation, the following steps are included:

[0078] Step 301: Based on the release time of the recovery announcement, the pre-configured initial response strength, and the attention decay rate in the multi-source operation data, construct a pulse function representing the change of the willingness of disturbed passengers to switch back after receiving the recovery announcement over time;

[0079] In this step, the willingness to switch back can refer to the subjective tendency of affected passengers to abandon their current alternative mode of transportation and decide to return to their original mode of transport after learning that the transportation hub service has been partially or fully restored. Because there is a propagation delay in information being pushed to the passenger group via station broadcasts or mobile applications, and because individual passenger response times are discretely distributed, this dynamically changing group response state over time is abstracted into a continuous impulse function. By constructing this function, the non-physical information dissemination event is transformed into a continuous driving signal that can be read by the dynamic model.

[0080] Step 302: The back-cut intention impulse function has a time-dependent characteristic of first rising and then falling, and the peak time and decay trend of the back-cut intention impulse function are jointly controlled by the pre-configured initial response intensity and attention decay rate.

[0081] Specifically, the dissemination of information exhibits physical timeliness characteristics. In the initial stages of the resumption announcement, as the information coverage expands, the willingness to return to the original location increases rapidly. Due to the reduction in the number of stranded passengers and the dilution effect of information, this willingness gradually diminishes over time. The initial response strength characterizes the overall reach efficiency of the information dissemination channels; the higher this value, the steeper the initial increase in the willingness to return. The attention decay rate characterizes the degree to which passengers forget or ignore the information; the higher this value, the faster the impulse decay.

[0082] In one possible implementation, the back-cut intention impulse function is a gamma impulse function; the peak moment of the back-cut intention impulse function corresponds to the instant when the information dissemination coverage is the largest after the information is released.

[0083] In this embodiment, the above physical process is quantified using the following mathematical form:

[0084] Φ(t)=Φ0*(t-t0)*exp(-λ d *(t-t0));

[0085] Where Φ(t) is the pulse intensity of the intention to cut back at the current time t, Φ0 is the pre-configured initial response intensity, and its dimension is the reciprocal of the square of a unit time, t is the current calculation time, t0 is the time when the recovery announcement is released, exp is an exponential function with the natural constant e as the base, and λ d This represents the rate of attention decay.

[0086] Based on the above formula, the time difference between the current moment and the announcement release moment is calculated. This time difference is multiplied by the negative decay rate and used as the independent variable of the natural exponential function. This result is then multiplied by the initial response intensity and the time difference. Solving for the condition that the first derivative of this function equals zero, the peak time is obtained as t0+1 / λ. d This time point physically represents the instant when information dissemination within the hub reaches maximum coverage. For example, if the calibrated attention decay rate is 0.1 per minute, then the moment with the maximum information dissemination coverage occurs 10 minutes after the announcement is released.

[0087] Step 303: Use the back-cut intention impulse function as the external driving input of the dynamic model.

[0088] After obtaining the tangent intention impulse function, it is input as a time-dependent excitation signal into the dynamic ordinary differential equations. This input acts as an excitation source that disrupts the static equilibrium of the system during disturbances, triggering the physical migration of passenger flow between different travel modes.

[0089] In one possible implementation, the dynamic model is a set of nonlinear ordinary differential equations based on the delay ratio and normalized perceived delay; the normalized perceived delay represents the ratio of the actual waiting time experienced by passengers to the maximum tolerable waiting time, and its initial value is set to zero; the evolution of passenger flow is obtained through the set of nonlinear ordinary differential equations.

[0090] This process clarifies the core state-space dimension of the dynamic model. The dynamic model comprises two coupled state variables: the loitering proportion, representing the spatial distribution state, and the normalized perceived delay, representing the service level state. The loitering proportion represents the percentage of passengers still using alternative modes of transportation, ranging from 0 to 1. The normalized perceived delay represents the ratio of the actual waiting time experienced by passengers to the maximum tolerable waiting time; under the typical recovery conditions of this invention, its steady-state value is typically between 0 and 1. By establishing time derivative equations for these two variables, the dynamic evolution of the passenger flow system is simulated.

[0091] Specifically, refer to Figure 2 The specific process of obtaining the passenger flow evolution trend through a set of nonlinear ordinary differential equations includes:

[0092] Step 1: Set the rate of decrease of the retention ratio to be positively correlated with the impulse function of the willingness to cut back and the coupling separation degree, and the rate of decrease is subject to nonlinear suppression of the normalized perception delay;

[0093] Specifically, a decrease in the retention rate indicates that stranded passengers are shifting back towards recovery. The intensity of this shift depends on the combined effect of three factors: the calculated impulse intensity of the shift intention, the retention rate itself representing the potential shift size, and the coupling separation degree from the previous time window. Multiplying these three factors yields the ideal shift rate. To accurately reflect the negative feedback of on-site congestion on passenger decisions, a nonlinear inhibition factor is introduced. The specific formula for calculating the decrease rate is as follows:

[0094] R down (t)=Φ(t)*ΔC ij (t)*p a (t)*(1 / (1+θ*d(t)));

[0095] Among them, R down Φ(t) represents the rate of decrease of the retention ratio, Φ(t) represents the intensity of the back-cut intention pulse, and ΔC ij (t) represents the coupling separation degree, p a (t) represents the current retention rate, θ represents the congestion perception sensitivity coefficient (i.e., delay perception sensitivity), and d(t) represents the normalized perception delay.

[0096] As shown by the formula, when the normalized perceived delay approaches 0, the inhibition factor approaches 1, and passenger flow switches back at the ideal rate. When the normalized perceived delay increases, the inhibition factor decreases rapidly, strongly blocking the switching behavior of subsequent passengers.

[0097] Step 2: Dynamically update the normalized perceived delay based on the actual influx of passengers and the degree of supply-demand imbalance between the real-time restored transportation capacity;

[0098] Specifically, the actual influx of passengers is calculated based on the pre-stored historical benchmark transfer flow and congestion ratio; the normalized perceived delay is dynamically updated based on the actual influx of passengers and the pre-determined supply-demand imbalance between the actual influx of passengers and the pre-determined real-time recovery capacity.

[0099] In this step, the difference between system supply and demand is used to drive the update of delay status. The product of the total disrupted passenger demand and the proportion of passengers not yet switched back is calculated to obtain the current actual influx recovery passenger flow. This influx passenger flow is subtracted from the system's real-time restored capacity, and the difference is divided by this real-time restored capacity to quantify the severity of overload. The delay update formula is as follows:

[0100] dd / dt=(1 / τ d )*(max(0,((1-p a (t))*F0-Q cap (t)) / Q cap (t))-d(t));

[0101] Where dd / dt is the normalized rate of change of perceived delay over time, and τ d The delay perception time constant is p, where max is a comparison function that selects the maximum value. a (t) represents the current retention rate, F0 represents the historical baseline transfer flow for the disrupted mode pair, and Q cap (t) represents the real-time recovery capacity, and d(t) represents the current normalized perceived delay.

[0102] This equation shows that additional delays only accumulate when the surge in demand exceeds real-time capacity. Furthermore, the delay perception time constant characterizes the time lag in passengers' perception of congestion.

[0103] Step 3: Based on the normalized perception delay, trigger the secondary transfer of the already switched passenger flow, causing the proportion of stranded passengers to rise again. This results in the formation of a rebound oscillation cycle of passenger switching and re-avoidance during the recovery transition period, and the rebound oscillation cycle is output as the passenger flow evolution trend.

[0104] Specifically, some passengers who have switched back to alternative modes of transportation may leave again and switch to other alternative modes after experiencing high delays, causing the backlog rate to rise in the opposite direction. This secondary transfer rate is proportional to the normalized perceived delay and the size of the backlog of passengers. The calculation formula is as follows:

[0105] R up (t)=β*d(t)*(1-p a (t));

[0106] Among them, R up (t) represents the recovery rate component of the retention ratio, β is the secondary transfer redistribution coefficient with dimensions in reciprocal of unit time, d(t) is the normalized perceived delay, and p a (t) represents the retention rate.

[0107] Combining step 1 and this step, the total rate of change in the retention rate is the sum of the recovery rate component and the decline rate component. At this point, the dynamic model forms a complete negative feedback physical closed loop. Information stimulation causes a sharp drop in the retention rate, triggering a supply-demand imbalance. This imbalance increases perceived delays; high delays suppress new back-cutting behavior through inhibitory factors and simultaneously stimulate secondary transfers, causing the retention rate to rebound. After the retention rate rebounds, the supply-demand imbalance eases, delays decrease, and low delays again relieve the back-cutting inhibition. The alternating fluctuations of the above physical parameters constitute a rebound oscillation cycle in the passenger flow recovery process. The passenger flow trajectory, extreme values, and decay envelope sequence contained within this oscillation cycle are used as the output of the passenger flow evolution trend, providing a computational basis for subsequent determination of bottleneck stagnation.

[0108] Furthermore, in some optional implementations, for complex hub environments with multiple concurrent connection methods, the secondary transfer redistribution coefficient can be obtained through a weighted aggregation algorithm. Specifically, passenger flow data shared by each concurrent connection method during the same historical period is extracted, and the redistribution sensitivity parameters of each independent connection method are weighted and summed according to the traffic share to calculate the overall secondary transfer redistribution coefficient of the system, thereby accommodating more complex passenger flow transfer scenarios.

[0109] Example 4

[0110] The process of extracting oscillatory features and analyzing the Jacobian matrix of nonlinear ordinary differential equation systems is further explained in detail.

[0111] In one possible implementation, after outputting the passenger flow evolution trend, the following steps are also included:

[0112] Step 401: Perform Jacobian matrix analysis on the equilibrium point of the nonlinear ordinary differential equation system to extract the oscillation angular frequency and damping ratio characteristics of the rebound oscillation cycle.

[0113] In this step, to obtain quantitative characteristics of passenger flow rebound oscillation behavior without relying entirely on successive numerical integration, the established nonlinear ordinary differential equation system is linearized analytically within the equilibrium state neighborhood. Specifically, the time derivatives of the stagnation ratio and the normalized perceived delay in the nonlinear ordinary differential equation system are simultaneously set to 0, and the steady-state equilibrium point of the system under the current capacity constraints is obtained through numerical iteration. At the steady-state equilibrium point, the original equation system is expanded using a first-order Taylor series to obtain the Jacobian matrix reflecting the evolution of the system's state deviation.

[0114] Furthermore, key elements of the Jacobian matrix are extracted to assess the dissipation and stability of the system.

[0115] Specifically, the elements in the first row and first column of the Jacobian matrix represent the convergence characteristics of the deviation of the retention ratio itself, and its calculation formula is as follows:

[0116] J 11 =-Φ star *(ΔC star +p a_star ) / (1+θ*d star )-β*d star ;

[0117] Among them, J 11 Φ is the element in the first row and first column of the Jacobian matrix. star ΔC represents the pulse intensity of the return cut intention at the equilibrium point. star p represents the coupling separation degree at the equilibrium point. a_star Let θ be the retention rate at the equilibrium point, d be the crowding perception sensitivity coefficient, and d be the retention rate at the equilibrium point. star β represents the normalized perception delay at the equilibrium point, and β is the secondary transfer redistribution coefficient.

[0118] Under typical operating conditions during the recovery transition period, i.e., C inf Approaching 1 and p a When the value is greater than 0, the calculated result of this element is negative, which makes the system state have physical dissipative properties that converge toward the equilibrium point.

[0119] The elements in the second row and first column of the Jacobian matrix represent the feedback adjustment of changes in the retention ratio on perceived delay, and the calculation formula is as follows:

[0120] J 21 =-F0 / (τ d *Q cap_star );

[0121] Among them, J 21 The element in the second row and first column of the Jacobian matrix is ​​τ, where F0 is the historical baseline transfer flow and τ is the number of transfers. d To delay the perception time constant, Q cap_star To restore transport capacity in real time at the equilibrium point.

[0122] This formula reflects the objective logic of physical conservation. When the delay rate increases, it indicates that more disrupted passengers remain on alternative modes of transportation, leading to a decrease in the actual influx of passengers using recovery modes, and consequently reducing system delays. Therefore, the partial derivative elements are negative.

[0123] The elements in the first row and second column of the Jacobian matrix represent the feedback adjustment of the retention ratio to the normalized perceived delay change, and the calculation formula is as follows:

[0124] J 12 =β·(1-p a_star )+Φ star ·ΔC star ·p a_star ·θ / (1+θ·d star ) 2 ;

[0125] Among them, J 12 This is the element in the first row and second column of the Jacobian matrix. A positive value for this element indicates that increased delay simultaneously triggers a secondary transition rebound and strengthens the crowding suppression effect.

[0126] The element in the second row and second column of the Jacobian matrix represents the decay characteristic of the normalized perceived delay itself, and the calculation formula is as follows:

[0127] J 22 =-1 / τ d ;

[0128] Among them, J 22 This is the element in the second row and second column of the Jacobian matrix. This element is always negative, reflecting the natural decay of passengers' memories of crowding.

[0129] After obtaining the complete Jacobian matrix, its trace and determinant are calculated. Based on the numerical values ​​of the matrix trace and determinant, the natural oscillation angular frequency and damping ratio are extracted by solving the characteristic equation. The specific characteristic parameters are calculated as follows:

[0130] ω n =sqrt(D) (when D>0);

[0131] Where, ω n Let be the oscillation angular frequency, be the undamped natural frequency, sqrt be the square root function, and D be the determinant of the Jacobian matrix.

[0132] ζ=-T / (2*ω n );

[0133] Where ζ is the damping ratio, T is the trace of the Jacobian matrix, and ω n ω is the oscillation angular frequency.

[0134] Step 402, wherein the oscillation angular frequency is controlled by the cross-coupling effect of congestion delay and the effect of passenger flow load reduction, and the damping ratio characteristic is adjusted by the natural decay rate of normalized perceived delay; the oscillation angular frequency and damping ratio characteristics are output as characteristic parameters of passenger flow evolution.

[0135] In this step, a direct mapping relationship is established between analytical features and actual traffic physical mechanisms. The determinant of the Jacobian matrix is ​​mainly determined by the product of the non-main diagonal elements. This product reflects the positive boosting effect of passenger flow reversal leading to increased delays, and the negative regulating effect of increased stranded people leading to reduced load. The stronger the cross-coupling effect of these two effects, the larger the calculated determinant value, the higher the corresponding oscillation angular frequency, and the more frequent the transfer and switching of passenger flow between different modes.

[0136] Meanwhile, the trace of the Jacobian matrix contains the reciprocal of the delay perception time constant. This reciprocal represents the natural decay rate of passengers' memories of past congestion. When passengers update their perception of congestion faster, the corresponding delay perception time constant decreases, the absolute value of the matrix trace increases, and consequently, the damping ratio characteristic value increases. A higher damping ratio indicates that the amplitude envelope of rebound oscillations will decay and subside more quickly, allowing the system to transition to a smooth operating state more rapidly.

[0137] In some optional implementations, the aforementioned Jacobi matrix-based local linearization analysis method is applicable to scenarios where the equilibrium point is located within the capacity bottleneck range and the amplitude of state disturbances satisfies small-signal constraints. When faced with extreme disturbance events that cause excessively large passenger flow oscillations and frequent crossings of the supply-demand balance physical boundary, the continuity of the Jacobi matrix at the switching boundary may fail. For such large-signal oscillation scenarios, the analytical derivation path can be bypassed, and the fourth-order Runge-Kutta numerical integration algorithm can be directly called to perform a full-time-domain step-by-step solution to the nonlinear ordinary differential equation system. The actual oscillation frequency and attenuation envelope characteristics can then be calculated using discrete waveform extraction techniques.

[0138] Example 5

[0139] Based on the above embodiments, the process of analyzing network system performance changes and identifying recovery stagnation moments based on passenger flow evolution is further described in detail. In one possible implementation, refer to... Figure 3 It includes the following steps:

[0140] Step 501: Define the rate of change of system performance that is constrained by both the system capacity recovery rate and the passenger flow return rate;

[0141] The passenger flow return rate is extracted based on the passenger flow evolution trend, and the system capacity recovery rate is determined based on the capacity recovery progress of the disturbed mode pair; the system performance change rate is calculated based on the passenger flow return rate and the system capacity recovery rate.

[0142] In this step, it is necessary to establish a benchmark evaluation index for quantifying the system recovery efficiency. The ratio between the current actual effective service throughput of the network system and the rated capacity after full recovery is defined as the system performance. Since the actual effective service throughput is limited by the smaller of the current passenger demand and the current capacity supply, this system performance index is physically determined by both the passenger flow return state and the capacity recovery state. Taking the time derivative of the system performance with respect to the time variable yields the rate of change of system performance, which objectively reflects the speed of the recovery of the overall service level of the hub.

[0143] Specifically, the system performance P(t) is defined as the actual effective service throughput and rated capacity Q of the network system within the time window t. cap_max The ratio. Wherein, the actual effective service throughput is taken as the current influx of passengers (1-p). a (t))·F0 and the current real-time restored capacity Q cap The smaller value in (t). The specific formula is as follows:

[0144] P(t) = min((1-p) a (t))·F0,Q cap (t)) / Q cap_max ;

[0145] Where P(t) represents the system performance, min is the function for finding the minimum value, and p a (t) represents the retention rate, F0 represents the historical baseline transfer flow, and Q cap (t) represents the real-time restoration of transport capacity, Q cap_max This is the rated transport capacity.

[0146] Step 502: Divide the dynamic supply and demand status of the network system into two conditions: a sufficient supply condition in which the actual influx of passenger flow does not exceed the system's capacity, and a capacity bottleneck condition in which the actual influx of passenger flow exceeds the system's capacity.

[0147] Specifically, based on the relative magnitude of passenger flow in actual recovery mode and the real-time recovery capacity of the system, the calculation logic of the system performance change rate exhibits segmented characteristics.

[0148] Under conditions of sufficient supply, the rate of change in system performance equals the change in passenger inflow rate divided by the rated capacity. Under conditions of capacity bottleneck, the rate of change in system performance equals the growth rate of real-time restored capacity divided by the rated capacity.

[0149] Under conditions of sufficient supply, current passenger demand is less than or equal to current real-time capacity, and actual service throughput is entirely determined by passenger volume. In this case, the system performance change rate equals the passenger flow return rate divided by the rated capacity. Under this condition, performance changes are primarily driven by passengers' willingness to return. Conversely, under conditions of capacity bottleneck, current passenger demand exceeds current real-time capacity, and actual service throughput is limited by the capacity ceiling. In this case, excess passenger flow will translate into congestion and delays, and the system performance change rate equals the system capacity recovery rate divided by the rated capacity. Under this condition, performance changes are entirely constrained by the physical limitations of capacity release and are unaffected by passenger volume increases.

[0150] Step 503: Determine the critical switching moment when the system performance change rate decreases discontinuously due to the system switching from a sufficient supply condition to a capacity bottleneck condition, or the moment when the system performance change rate is lower than the preset minimum recovery rate during the entire period of the capacity bottleneck condition, and take it as the recovery stagnation moment.

[0151] Furthermore, a recovery stagnation moment signifies a substantial obstacle encountered in the system recovery process. This embodiment establishes dual criteria to capture different types of stagnation phenomena. The first type of stagnation occurs during the transition between supply and demand states. When the system reaches supply and demand equilibrium at a certain moment, and the net inflow rate of passenger flow exceeds the capacity recovery rate after that moment, the system will be forced to switch from a supply-sufficient state to a capacity-bottled state. This switch will cause a discontinuous drop in the system performance change rate, indicating that the continuously influx of passenger flow has exceeded the capacity growth's absorption capacity, thus creating a critical switching moment where efficiency growth is hindered. The second type of stagnation occurs in scenarios with extremely high passenger flow, where the system remains in a capacity-bottled state throughout the entire recovery cycle. Due to the continuous overflow of passenger flow, performance growth depends entirely on capacity ramp-up. If the system performance change rate is extracted at this time and determined to be lower than a preset minimum recovery rate, the system is identified as being in an inefficient recovery state, and the recording moment corresponding to this state is also marked as a recovery stagnation moment.

[0152] The minimum recovery rate can be set by the hub operations management department based on the actual operational requirements for the system's full recovery time, combined with the system's rated capacity. For example, if the system is required to recover to 90% of its rated capacity within 60 minutes after a disturbance, the minimum recovery rate can be calculated accordingly. Those skilled in the art can make adaptive adjustments based on the timeliness requirements of actual operational scenarios.

[0153] In one possible implementation, the system's real-time capacity recovery is modeled as an exponentially growing function of recovery time; the growth rate of the exponentially growing function is controlled by the shift recovery rhythm in a pre-determined operation and maintenance scheduling plan.

[0154] In this process, the core supply-side variables that determine the upper limit of system performance are explicitly fitted. Considering the lag in the startup of the physical equipment system and the characteristics of subsequent gradual acceleration, the capacity ramp-up curve is calculated in exponential form. The calculation formula is as follows:

[0155] Q cap (t)=Q cap_min +(Q cap_max -Q cap_min )*(1-exp(-γ*(tt d )));

[0156] Among them, Q cap Q(t) represents the system's real-time restored capacity at time t. cap_min Q represents the residual capacity retained during the disturbance. cap_max For the fully restored rated capacity, exp is an exponential function with the natural constant e as the base, γ is the capacity recovery rate constant, and t d The time when the disturbance occurs.

[0157] According to the above formula, the transport capacity gradually approaches the rated level from the residual level. The capacity recovery rate constant determines the slope of the exponential curve. In actual calculations, the value of this constant is directly extracted from the operation and maintenance scheduling plan of the transportation operating entity. For example, when the scheduling system issues an instruction to add one subway train every 10 minutes, the theoretical capacity of the train is converted into a capacity increment on a continuous time axis, and the value of the capacity recovery rate constant is determined accordingly.

[0158] In some alternative implementations, if the real-time capacity recovery of rail transit or conventional public transportation systems exhibits discrete step characteristics rather than continuous smooth characteristics in physical performance, a piecewise step function can be used instead of the aforementioned exponential growth function. In this configuration, a backward difference algorithm is used instead of continuous-time differentiation when calculating the system performance change rate. By calculating the discrete throughput difference within adjacent time windows and comparing it with a preset difference threshold, discrete-domain identification of the recovery stagnation moment is achieved. This alternative solution can adapt to more stringent scheduled operation scenarios.

[0159] Example 6

[0160] Building upon the above embodiments, the specific process for quantifying implicit toughness loss based on the closed loop (tough hysteresis loop) formed in phase space by behavioral coupling and system performance is further described. In one possible implementation, refer to... Figure 4 It includes the following steps:

[0161] Step 601: Construct a two-dimensional phase space with behavioral coupling degree as the horizontal axis and system performance as the vertical axis;

[0162] Existing technologies only use time as a single independent variable for evaluation. This step establishes a two-dimensional geometric coordinate system that reflects the interaction between two internal state variables of the system. The behavioral coupling degree sequence calculated in the previous embodiment is mapped to the horizontal axis of the coordinate system, and the system performance sequence is mapped to the vertical axis. Under normal operating conditions, both the behavioral coupling degree and system performance of the integrated transportation network tend to approach their maximum values, and the system state corresponds to the initial equilibrium coordinate point in the upper right of the two-dimensional phase space.

[0163] Step 602: Extract the clockwise closed loop (resilient hysteresis loop) formed in the two-dimensional phase space between the disturbance degradation path and the recovery path of the network system due to the behavioral coupling degree lagging behind the system performance recovery.

[0164] Specifically, the disturbance degradation path is determined based on the time series of behavioral coupling degree and system performance from the occurrence of the disturbance to the lowest performance point; the recovery path is determined based on the time series of behavioral coupling degree and system performance from the lowest performance point to the return to normal.

[0165] Specifically, when the network system encounters a disturbance, facility service capacity and passenger traffic decrease simultaneously. The system state is depicted in two-dimensional phase space as a degraded path moving from the initial equilibrium coordinate point to the lowest performance coordinate point in the lower left. During the recovery transition period, the capacity of physical facilities gradually increases, and system performance recovers. However, due to delays in passenger route switching decisions and spatiotemporal obstructions in receiving recovery information, the recovery speed of passenger backtracking behavior is slower than the recovery speed of system performance.

[0166] The aforementioned behavioral hysteresis phenomenon manifests in two-dimensional phase space, meaning that when achieving the same system performance level, the behavioral coupling degree corresponding to the recovery path is lower than that corresponding to the perturbation degradation path. Therefore, the recovery path is located to the left of the perturbation degradation path in two-dimensional phase space. The recovery path is formed by connecting the continuous sequence of state points from the lowest performance coordinate point back to the initial equilibrium coordinate point. Connecting the perturbation degradation path and the recovery path end-to-end creates a resilient hysteresis loop opening to the right and trending clockwise in two-dimensional phase space.

[0167] Step 603: Perform area integration on the clockwise closed loop and normalize the obtained area integration value to obtain the implicit resilience loss that reflects the degree of misalignment between facility status and passenger behavior.

[0168] In this step, the area of ​​the region enclosed by the aforementioned resilient hysteresis loop is numerically quantified. The line integral rule is introduced to calculate the directed area of ​​the clockwise closed loop (resilient hysteresis loop). The calculation formula is as follows:

[0169] ;

[0170] Where H is the area integral of the closed loop, and P deg (s) represents the system performance on the disturbance degradation path, C beh,deg P represents the behavioral coupling degree on the perturbation degradation path. rec (s) is to restore system performance on the recovery path, C beh,rec To restore the behavioral coupling on the path.

[0171] Specifically, the trajectory variable s takes the value of a closed interval from 0 to 1. For the disturbance degradation path, s=0 corresponds to the normal equilibrium coordinate point before the disturbance occurs, and s=1 corresponds to the lowest performance coordinate point where the system performance is reduced to its minimum. The integral is performed along the direction of s from 0 to 1. For the recovery path, s=0 corresponds to the lowest performance coordinate point, and s=1 corresponds to the equilibrium coordinate point where the system returns to normal. The integral is also performed along the direction of s from 0 to 1. When the two paths are connected end to end, they form a clockwise closed loop in a two-dimensional phase space with behavioral coupling degree as the horizontal axis and system performance as the vertical axis, consistent with the direction of the aforementioned resilient hysteresis loop.

[0172] The area integral value H obtained through the above calculation is positive. Physically, it represents that during the recovery process, due to the misalignment between the facility status and passenger behavior, the passenger flow that could have returned to the original mode is still stuck on alternative transportation, resulting in additional load on alternative routes and additional travel delays for passengers.

[0173] Furthermore, in order to eliminate the interference of differences in absolute passenger flow and absolute transport capacity between transportation hubs of different sizes on the evaluation results, the area integral value was normalized.

[0174] H norm =H / (C beh_0 *P0);

[0175] Among them, H norm For implicit toughness loss, H is the area integral of the closed loop, and C is the area integral of the closed loop. beh_0 P0 represents the initial behavioral coupling degree under normal operation before the disturbance occurs, and P0 represents the initial system performance under normal operation before the disturbance occurs.

[0176] Implicit resilience loss is a dimensionless, purely numerical indicator. The larger the value of this indicator, the more severe the internal friction of the network system during the recovery transition period.

[0177] In some alternative implementations, if the collected system state data exhibits low-frequency discrete distribution characteristics, making it difficult to construct continuously differentiable path parameterization equations, a discrete polygon area calculation algorithm can be used as an alternative to the aforementioned line integral. Specifically, the discrete state sampling coordinate points on the disturbance degradation path and the recovery path are arranged in clockwise time order to construct a sequence of closed polygon vertices. Then, the shoelace formula is used to calculate the geometric area of ​​the discrete closed polygon and output it as the area integral value.

[0178] Example 7

[0179] The process of outputting a tiered information dissemination scheme and capacity coordination strategy for the disrupted mode pairs is further described in detail. In one possible implementation, refer to... Figure 5 It includes the following steps:

[0180] Step 701: Extract the corresponding capacity gradient release constraint set based on the recovery stagnation time;

[0181] In this step, the physical characteristics of the recovery stagnation identified in the aforementioned embodiments are transformed into boundary conditions guiding system scheduling. The peak net passenger flow cut-off rate corresponding to the recovery stagnation moment is extracted. To prevent a reversal and drop in system performance during the recovery period, the capacity recovery rate must be greater than or equal to this net passenger flow cut-off rate before the supply-demand imbalance occurs. By establishing this inequality, the minimum required lower bound of the capacity recovery rate constant is solved, and this lower bound is combined with the corresponding key time nodes to form a capacity gradient release constraint set. This constraint set physically defines the minimum legal slope of the capacity recovery curve, ensuring that the operation and maintenance scheduling plan meets the throughput requirements for absorbing passenger flow peaks.

[0182] Step 702: With minimizing the implicit resilience loss as the optimization objective and satisfying the capacity gradient release constraint set as a prerequisite, optimization calculations are performed within the preset decision space of hierarchical release timing, pulse intensity, and capacity release rate.

[0183] Specifically, the decision space consists of multiple discrete or continuous scheduling parameters. Parameters on the information dissemination side include the number of dissemination levels, the dissemination time at each level, and the pulse intensity of each information channel; parameters on the capacity coordination side include the gradient for reducing train or bus departure intervals. During the optimization calculation, each generated candidate parameter combination must first be substituted into the capacity recovery function for verification, eliminating illegal solutions that violate the capacity gradient release constraint set. For legal solutions that satisfy the constraints, the parameters are substituted into a system of dynamic ordinary differential equations for integration, and the corresponding implicit resilience loss value is calculated. In this process, the objective function is set to make the implicit resilience loss approach zero.

[0184] The mathematical formulation of the optimization problem is as follows: Let T be the set of times for hierarchical information release.pub The corresponding pulse intensity set Φ pub and capacity release rate parameter γ opt As the decision variable; with implicit resilience loss H norm The objective function is to take the minimum value; the inequality constraint is that the capacity recovery rate should not be lower than the peak value of the predicted net passenger flow cut-off rate, which is a constraint on the capacity gradient release.

[0185] One possible implementation involves a two-stage optimization process when performing optimization calculations within the decision space:

[0186] In the first stage, an offline traversal search was conducted on the number of tiered releases, the combination of release nodes, and the capacity release rate to select multiple candidate optimal combinations.

[0187] Specifically, this can also be achieved by performing an offline traversal search on the combination of release frequency and release time, pulse intensity and capacity release rate in the hierarchical release time sequence, and filtering out multiple candidate optimal combinations;

[0188] In this step, to reduce the computational dimensionality of complex nonlinear optimization problems and avoid getting trapped in local minima, a global gridded search is first performed. For example, the search range for information pulse intensity is limited to 50%–150% of historical empirical values ​​and uniformly discretely sampled; the number of tiered releases is set to a limited number of options such as single release, two-stage release, and three-stage release; for the time nodes of multi-level releases, the selection is limited to fixed key nodes where system capacity recovers to 25%, 50%, and 75%, respectively. By performing offline numerical integration of the entire combination, the implicit resilience loss of each discrete parameter combination is evaluated, and the top-ranked parameter sets are selected as candidate optimal combinations to complete coarse-grained global localization.

[0189] In the second stage, starting with the candidate optimal combination, a local search algorithm is used to refine the search within the neighborhood of each parameter to determine the final hierarchical information dissemination scheme and capacity coordination strategy.

[0190] After obtaining the candidate optimal combinations, the gradient-free simplex method is invoked to perform local refinement optimization in the continuous real domain. The coarse-grained parameter combination is used as the initial position of the simplex vertex. Based on the value of the objective function, geometric transformation operations such as reflection, expansion, contraction, and shortening are performed alternately. The objective function value is set to change by less than 10 between adjacent iterations. -3 This serves as the termination criterion for algorithm convergence. By initiating local searches concurrently at multiple points, comparing the final objective function values ​​at each convergence point, and selecting the parameter combination that minimizes the global implicit resilience loss, the optimal convergence of the strategy is achieved.

[0191] Step 703: The optimized parameter combination is output as a hierarchical information release scheme and capacity coordination strategy.

[0192] In this step, the mathematical optimization results are parsed into standardized industrial scheduling instructions. For example, the output strategy might be: maintain low-frequency departures during the initial recovery phase without issuing a full recovery announcement; once capacity recovers to 60% of its rated capacity, shorten departure intervals to normal levels and simultaneously broadcast the message at maximum intensity through all channels. This output is directly imported into the hub operation management platform.

[0193] In some alternative implementations, if the computing environment of the system is limited in terms of computational power, the simplex method can be replaced by a heuristic genetic algorithm or a particle swarm optimization algorithm for the above two-stage optimization process. By defining chromosome encoding methods or particle position and velocity update rules, the convergence time under complex constraints can be shortened while taking into account both global exploration and local development capabilities.

[0194] Example 8

[0195] Based on the above embodiments, this embodiment provides a parameter calibration and multi-alternative node aggregation method for offline construction of dynamic models. In the above embodiments, solving the dynamic ordinary differential equation system depends on several parameters characterizing the behavioral features of passenger groups. This embodiment details how to obtain the specific values ​​of these parameters based on historical data to ensure the physical objectivity of the model prediction results and the feasibility of system engineering implementation.

[0196] An offline method for acquiring dynamic model parameters was established during the parameter calibration process. The parameter calibration process ran independently of the real-time online computing environment, extracting records of similar disturbance events from the historical database of integrated transportation hubs as the training dataset. Through statistical algorithms and backfitting techniques, the abstract passenger behavior parameters were visualized as combinations of constraint values.

[0197] In one possible implementation, the initial response intensity, attention decay rate, delay perception sensitivity, and secondary transfer redistribution coefficient in the dynamic model are pre-calibrated as follows:

[0198] Step 801: Using the historical transfer passenger flow back-cut time series of the disturbed mode pair, the initial response intensity and attention decay rate are calibrated;

[0199] Specifically, records of multiple historical disturbance recovery events of the same type are extracted from the same hub database. For each disturbance event, continuous passenger transfer flow data after the release of the recovery announcement is extracted and normalized into a shear rate sequence. This shear rate sequence exhibits a distribution characteristic of first rising and then falling on the time axis. The least squares fitting algorithm is applied, with minimizing the sum of squared residuals as the objective function, to curve fit the shear rate sequence to a set gamma pulse function.

[0200] When performing curve fitting, the initial response intensity and attention decay rate are set as undetermined fitting parameters. To accelerate algorithm convergence, an initial search boundary for the decay rate is set, and the optimal value is determined by least-squares fitting. When the relative change in parameters between two adjacent iterations is less than 0.0001, the fitting algorithm is considered to have converged, and the corresponding parameter estimates are extracted and output as calibration results.

[0201] Step 802: Based on the correlation between historical congestion delay data and passenger secondary transfer rate, calibrate the delay perception sensitivity and secondary transfer redistribution coefficient.

[0202] In this step, the normalized perceived delay sequence for recovery methods and the secondary transfer rate sequence for passengers who have switched back to alternative methods are extracted from historical disturbance events. Linear regression analysis is performed with the normalized perceived delay sequence as the independent variable and the secondary transfer rate sequence as the dependent variable. The slope of the calculated regression line is the final calibration value of the secondary transfer redistribution coefficient.

[0203] Furthermore, after obtaining the aforementioned pulse parameters and secondary transfer redistribution coefficients, the delay perception sensitivity is calibrated using a backfit technique. Historical parameters are input into the dynamic ordinary differential equation system, and a grid search calculation is performed within a preset search interval, with the delay perception sensitivity as the sole unknown variable. The residuals of the model's calculated retention ratio sequence are compared point-by-point with the historical actual passenger flow distribution ratio curve, and the node coordinates that minimize the mean square error are selected as the final calibration value for the delay perception sensitivity. Simultaneously, for the hidden delay perception time constant in the model, the time lag between historical actual delay mutation records and passenger flow secondary transfer behavior records is extracted, and the median of the time lags from multiple historical events is calculated as the calibration value.

[0204] In some alternative implementations, when the target transportation hub has a short construction period resulting in an insufficient number of historical disturbance event samples, a similar hub parameter migration method can be used for downgrade calibration as a substitute. Specifically, this involves extracting parameters from other hubs of similar scale and with the same traffic pattern composition, scaling the initial response intensity proportionally to the ratio of the target hub's average daily transfer volume to that of the reference hub, and scaling the attenuation rate proportionally to the ratio of the average walking time of the two transfer lanes. This achieves the initial cold-start configuration of the parameters.

[0205] In some embodiments, when multiple alternative modes of transportation exist, the method further includes a step of parameter aggregation of the dynamics model:

[0206] Step S1: Aggregate multiple alternative travel modes into a single alternative node with equivalent capacity;

[0207] In real-world transportation network hubs, disrupted passengers are often dispersed across multiple independent alternative travel routes, such as regular buses, ride-hailing services, and shared bicycles. To avoid exponential expansion of the state matrix dimension in the dynamics model, this step performs dimensionality reduction and space aggregation processing. All parallel alternative travel modes are abstracted into a single geometric sink, i.e., a single alternative node, in terms of physical topology. The arithmetic sum of the currently available capacity of each independent alternative travel mode is calculated, and this sum is set as the equivalent capacity of the single alternative node. The proportion of the total disrupted passenger volume across all alternative modes to the total disrupted passenger flow is calculated and used as the global retention ratio required for the dynamics model calculation.

[0208] Step S2: Use the weighted average of historical passenger flow for each alternative travel mode to determine the comprehensive secondary transfer redistribution coefficient of the dynamic model.

[0209] Specifically, different alternative travel modes exhibit significant differences in their attractiveness to passengers' secondary transfers in terms of time consumption and economic costs. Historical passenger flow data actually transferred to each independent alternative travel mode during the disturbance period is extracted and used as a weighting factor. A weighted summation operation is then used to calculate the comprehensive secondary transfer redistribution coefficient.

[0210] β agg =∑(F m_ref *β m ) / ∑(F m_ref );

[0211] Where, β agg To synthesize the secondary transfer redistribution coefficients, ∑ is the summation operator, F m_ref β represents the historical passenger flow that shifted to alternative mode m during the disturbance period. m These are the secondary transfer redistribution coefficients calibrated offline for alternative method m.

[0212] The aforementioned weighted aggregation operation reduces the multidimensional complex traffic state system to a two-dimensional physical system model containing only a single recovery method and a single alternative node. This alternative scheme, while ensuring the computational efficiency of solving the ordinary differential equation system, effectively preserves the statistical macroscopic impact of heterogeneous alternative combinations on the physical process of global passenger flow secondary redistribution.

[0213] Example 9

[0214] Based on the above embodiments, a system application example of a method for evaluating the coupling degree and improving the resilience of integrated transportation network operation status is provided. This embodiment focuses on illustrating the technical deployment of the method in a real transportation hub management system, the human-computer interaction interface rendering method, and provides a normalized calculation example to verify the operation mechanism of the aforementioned dynamic model.

[0215] In one possible implementation, while outputting a graded information dissemination scheme and capacity coordination strategy for the disturbed mode pair, it also includes: real-time rendering and display of the dynamic trajectory of a clockwise closed loop (resilient hysteresis loop) in two-dimensional phase space, as well as a countdown prediction of the recovery stagnation time, to assist hub operators in performing real-time early warning.

[0216] Specifically, based on the time difference between the current moment and the recovery stagnation moment, the recovery stagnation prediction countdown is calculated; the dynamic trajectory of the resilient hysteresis loop in phase space and the recovery stagnation prediction countdown are rendered and displayed in real time to assist hub operators in implementing real-time early warnings.

[0217] In this process, the visualization output mechanism of this method on the graphical user interface side is described. Specifically, the dynamically updated behavioral coupling sequence and system performance sequence are obtained, and the corresponding two-dimensional coordinate points are mapped to the screen pixel coordinate system of the graphical interface. Using computer graphics rendering algorithms, adjacent discrete coordinate points are connected in real time to draw a clockwise rotating resilient hysteresis loop dynamic trajectory on the display terminal.

[0218] Furthermore, the predicted data of the system performance change rate is extracted. When it is determined that the system performance change rate will change from positive to negative, the time difference between the current moment and the predicted critical switching moment is calculated. This time difference is formatted as a value containing minutes and seconds and displayed with high-frequency refresh in a prominent area of ​​the graphical interface.

[0219] The combined output of the above-mentioned graphical coordinates and numerical time changes the way the original array matrix data is presented, providing intuitive data support for on-site operation and management personnel to implement the plan.

[0220] In some embodiments, the method is applied to an integrated transportation hub management system, and after the output of the hierarchical information release scheme is completed, it automatically triggers the updating of path guidance information in the hub's broadcasting system, mobile terminal application push interface, and navigation service platform.

[0221] This process describes the interaction between the evaluation method and the network interfaces of external hardware and third-party software platforms. After the optimization algorithm outputs the hierarchical information dissemination scheme, the data parsing module of the integrated transportation hub management system extracts the scheme parameters. The pulse intensity parameters of different information channels are converted into hardware control commands, which are sent to the station's broadcast control host in the physical space via fieldbus protocol to execute the audio playback task.

[0222] Simultaneously, a markup language file containing recovery progress and alternative route suggestions is generated, and a targeted message is sent by calling the background service interface of the mobile terminal application via the application layer network protocol. Furthermore, the network topology capacity change data corresponding to the capacity coordination strategy is encapsulated into a Hypertext Transfer Protocol (HTTP) request packet and pushed to a remote server providing navigation services. Upon receiving the data packet, the remote server updates its underlying road network impedance matrix memory, thereby altering the real-time route guidance calculation results sent to public terminals.

[0223] The automated invocation of the aforementioned multi-channel network interfaces enables scheduling decision instructions to be transformed into actual information-driven signals that act on the affected passenger groups with low network latency.

[0224] To facilitate understanding, here is an example scenario: Suppose that in a certain integrated transportation hub, Metro Line A is suspended during the morning rush hour due to a signal equipment malfunction. Affected passengers transfer to regular bus line B within the hub to continue their journey during the disturbance, forming a disturbance mode pair (Metro Line A, Bus Line B).

[0225] After the equipment was repaired, the system entered a recovery transition period. The facility coupling degree quickly rebounded to nearly 1.0 as passageways and train services resumed. However, the behavioral coupling degree remained at a low level because stranded passengers had not yet received information about the recovery or were taking a wait-and-see attitude towards the stability of subway operations. At this time, the coupling separation degree was relatively large, indicating that there was significant potential for passenger flow to return.

[0226] When the hub management system broadcasts the first recovery announcement, the back-switch intention impulse function is triggered. Within a short period, a large number of passengers stranded on bus line B rush back to subway line A, causing the actual influx of passengers to exceed the subway's not-yet-fully-recovered capacity. After a brief boost, system performance declines due to capacity bottlenecks, while congestion delays rapidly increase. High delays, through a nonlinear inhibition factor, block the back-switch intentions of subsequent passengers and trigger a secondary transfer of already back-switched passengers back to bus line B, causing a rebound in the congestion rate. As the influx decreases and delays ease, back-switch behavior resumes, forming a second round of oscillations. After several rounds of decreasing amplitude rebound oscillations, the system tends towards a steady state.

[0227] In the above process, the phase-space resilient hysteresis loop is represented by a clockwise curve that moves from the initial equilibrium point to the lower left along the degradation path, then rises back to the left along the recovery path and finally closes. The area enclosed by this hysteresis loop is the implicit resilience loss, reflecting the additional load on bus route B and the additional waiting time for passengers caused by the lag in passenger behavior.

[0228] Based on the quantification of the loss, the optimization module determined that a full recovery announcement should be issued only after the capacity has recovered to a certain percentage of the rated capacity, and the subway departure intervals should be increased simultaneously to control the peak of the influx of passengers within the capacity carrying capacity, effectively suppressing the oscillation amplitude and shortening the recovery time.

[0229] This invention effectively solves the problem of dynamic disconnect between supply-side capacity and demand-side behavior in traditional situation assessment by constructing a two-layer coupled quantitative system of facilities and behavior. It elevates the perception granularity of the hub recovery process from macro-statistics to dynamic mapping between mode pairs. Addressing the unique passenger flow fluctuations during the recovery period, it utilizes the nonlinear dynamic mechanism of information pulse driving and congestion feedback suppression to achieve self-consistent simulation of passenger flow switching and avoidance processes between disrupted and alternative modes. This allows the system to accurately predict the peak intensity and duration of rebound oscillations.

[0230] Furthermore, by introducing a rate competition criterion and a phase space hysteresis loop evaluation method, this invention can not only quickly pinpoint the stagnation threshold when the system switches from sufficient supply to capacity bottleneck, but also quantify the implicit resilience loss caused by behavioral lag, providing an accurate decision-making benchmark for eliminating internal friction during the recovery period. Through the synergistic optimization of multi-dimensional scheduling strategies, performance fluctuations during the recovery process are suppressed, and the overall recovery efficiency of the hub is improved.

[0231] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0232] The above are merely preferred embodiments of this application. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for evaluating the coupling degree and improving the resilience of a comprehensive transportation network operation status, characterized in that, include: Acquire multi-source operational and physical layout data of the integrated transportation network and construct a multi-layered network topology; During the recovery transition period, the facility coupling degree and behavioral coupling degree between the disturbed mode pairs are determined based on multi-source operational data, physical layout data, and topology. Based on the separation state of facility coupling degree and behavioral coupling degree, the passenger flow evolution trend of the disturbed mode pair is obtained by using a pre-constructed dynamic model of the coordination between the return intention drive and the congestion feedback. Based on the analysis of the changes in network system performance according to the evolution of passenger flow, the moment of recovery stagnation is identified, and the implicit resilience loss is quantified according to the closed loop formed by behavioral coupling degree and system performance in phase space. With the goal of minimizing implicit resilience loss and the constraint of avoiding recovery stagnation, we output a graded information dissemination scheme and capacity coordination strategy for the disturbed mode pairs.

2. The method according to claim 1, characterized in that, When determining the facility coupling degree and behavioral coupling degree between the disturbed mode pairs respectively, the following are included: The ratio of the actual available facility capacity to the design capacity between disturbed mode pairs is defined as the facility coupling degree. The ratio of the actual transfer passenger flow between disturbed mode pairs to the pre-stored historical baseline transfer flow is defined as the behavioral coupling degree.

3. The method according to claim 2, characterized in that, For actual passenger transfer traffic, the matching degree between disturbance mode pairs is determined according to the passenger identification system of their respective traffic subsystems based on the disturbance mode, and a differentiated identification method is used to determine this, including: If the identifiers of the disturbed pattern pairs can be matched directly or indirectly, then the entry and exit time windows and spatial constraints are used to establish individual-level transfer associations to obtain the actual transfer passenger flow. If the identifiers between the disturbed mode pairs cannot be matched, the correlation coefficients of the inbound and outbound traffic of the disturbed mode pairs are combined with the pre-configured empirical transfer ratios to perform aggregated-level transfer estimation, thereby obtaining the actual transfer passenger traffic.

4. The method according to claim 1, characterized in that, Using a pre-constructed dynamic model that combines shearing intention with congestion feedback, the passenger flow evolution of the disturbed mode pairs is obtained, including: Construct a cutback intention impulse function to characterize the change in cutback intention over time after the disturbed passenger receives the recovery announcement; The impulse function of the intention to cut back has a time-dependent characteristic of rising first and then falling, and its peak time and decay trend are jointly controlled by the pre-configured initial response intensity and attention decay rate. The shear intention impulse function is used as the external driving input of the dynamic model.

5. The method according to claim 1, characterized in that, When analyzing the changing characteristics of network system performance based on passenger flow evolution and identifying moments of recovery from stagnation, the following should be included: Define the rate of change of system performance that is constrained by both the system capacity recovery rate and the passenger flow return rate; The dynamic supply and demand status of the network system is divided into two conditions: a sufficient supply condition where passenger demand does not exceed the system's capacity, and a capacity bottleneck condition where passenger demand exceeds the system's capacity. The critical switching moment when the system performance change rate begins to decline discontinuously due to the system switching from a state of sufficient supply to a state of capacity bottleneck, or the moment when the system performance change rate is lower than the preset minimum recovery rate during the entire period of the capacity bottleneck, is determined as the recovery stagnation moment.

6. The method according to claim 1, characterized in that, The implicit toughness loss is quantified based on the closed loop formed by the behavioral coupling degree and system performance in phase space, including: Construct a two-dimensional phase space with behavioral coupling degree as the horizontal axis and system performance as the vertical axis; Extract the clockwise closed loop formed in the two-dimensional phase space between the disturbance degradation path and the recovery path of the network system, due to the behavioral coupling degree lagging behind the system performance recovery; Perform area integration on a clockwise closed loop and normalize the resulting area integration value to obtain the implicit resilience loss that reflects the degree of misalignment between facility status and passenger behavior.

7. The method according to claim 1, characterized in that, The initial response intensity, attention decay rate, delay perception sensitivity, and secondary transfer redistribution coefficients in the dynamic model are pre-calibrated using the following method: Using the historical transfer flow back-cut time series of the disturbed pattern pairs, the initial response strength and attention decay rate are calibrated; Based on the correlation between historical congestion delay data and passenger secondary transfer rate, the delay perception sensitivity and secondary transfer redistribution coefficient are calibrated.

8. The method according to claim 1, characterized in that, When multiple alternative modes of transportation exist, parameter aggregation of the dynamics model is also included: Aggregate multiple alternative modes of transportation into a single alternative node with equivalent capacity; The weighted average of historical passenger flow data for each alternative mode of transportation is used to determine the comprehensive secondary transfer redistribution coefficient of the dynamic model.

9. The method according to claim 6, characterized in that, In addition to providing tiered information dissemination schemes and capacity coordination strategies for disrupted mode pairs, it also includes: It renders and displays the dynamic trajectory of a clockwise closed loop in two-dimensional phase space in real time, as well as the predicted countdown of the recovery stagnation time, to assist hub operators in implementing real-time early warnings.

10. The method according to claim 1, characterized in that, The method is applied to the integrated transportation hub management system, and after the output of the hierarchical information release scheme is completed, it automatically triggers the updating of route guidance information in the hub's broadcasting system, mobile terminal application push interface, and navigation service platform.

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