A regional flood under bridge network recovery analysis method, device and medium oriented to water resistance

Abstract

The application discloses a regional flood resistance-oriented network recovery analysis method and device for bridge groups under floods, and a medium, and comprises the following steps: calculating a representative flood intensity parameter, a representative flood parameter and a Froude number; calculating a scour failure demand ratio, a horizontal water dynamic instability demand ratio, a bridge deck submergence demand ratio and a flood duration demand ratio; determining a bridge damage state, calibrating a failure probability model, calculating a bridge failure probability and a bridge traffic capacity reduction coefficient; calculating an effective traffic capacity, a vehicle type flow, a road network system performance index and a road network function resilience function; calculating a repair action time consumption, a cost consumption and a state transition result; constructing a reward function, solving an optimal recovery strategy, and outputting an optimal recovery action, a repair priority and a repair plan; and calculating a recovery period function resilience curve, a recovery loss index, an average function maintenance level, a recovery time and a regional flood resistance comprehensive index. The application improves the function resilience and disaster recovery capability of the bridge group.

Description

Technical Field

[0001] This invention belongs to the technical field of regional bridge groups, and particularly relates to a method, equipment and medium for restorative analysis of bridge group networks under regional floods with regard to water resistance and resilience. Background Technology

[0002] With the increasing frequency of extreme weather events and flood disasters, regional bridge networks, as a crucial component of transportation infrastructure, face increasingly severe flood risks. In flood disasters, bridge damage not only leads to traffic disruptions but can also trigger significant economic and social losses. Traditional bridge failure assessment methods often focus on the analysis of individual bridges, neglecting the overall performance of the bridge network in terms of post-disaster functional recovery and systemic resilience. Restorative analysis of regional bridge networks is of great significance for improving the rapid post-disaster recovery capabilities of bridge networks, optimizing repair sequences, and reducing socio-economic losses.

[0003] However, existing research methods mainly focus on the vulnerability assessment of individual bridges, lacking systematic restorative analysis of regional bridge networks. This is particularly true when considering the resilience and recovery capacity of bridge networks under the impact of flood disasters, often failing to effectively integrate the coupling effects and resource constraints between bridge groups. Resilience in post-disaster recovery is generally defined as the system's ability to cope with disasters and restore normal function, but most current research focuses on the recovery of individual bridges, neglecting the complex recovery challenges faced by bridge networks after disasters. Furthermore, existing bridge network restorative analysis models are mostly based on static data, failing to dynamically reflect the changes and evolution of bridge networks during the recovery process under the impact of flood disasters. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method, equipment, and medium for analyzing the resilience of bridge network under regional floods, focusing on water resistance. This invention can effectively analyze the resilience of bridge network under different flood conditions, optimize post-disaster repair schemes, and improve the functional resilience and disaster recovery capabilities of bridge network.

[0005] Technical Solution: To achieve the above objectives, the present invention provides a method for restorative analysis of bridge network under regional floods, focusing on water resistance resilience, comprising the following steps: S1. Obtain basic bridge data, bridge flood resistance failure criteria data, road network data, traffic demand data, flood scenario data, post-disaster repair resource data, recovery optimization parameter data, and water resistance toughness evaluation parameter data for the regional bridge group; S2, For any flood scenario Calculate the representative flood intensity parameters at the bridge site, the representative flood parameters at the abutments and piers, and the corresponding Froude numbers, and construct the bridge. In flood scenarios Flood intensity parameters at the bridge site; S3, Calculate the bridges separately. In flood scenarios The bridge damage status was further determined by the following criteria: scour failure demand ratio, horizontal hydrodynamic instability demand ratio, bridge deck inundation demand ratio, and flood duration demand ratio. The failure probability model was calibrated, and the bridge failure probability and bridge capacity reduction coefficient were calculated. S4. Construct a regional bridge network and map the bridge damage status, bridge failure probability, and bridge capacity reduction factor at the bridge level to the connecting road network level; calculate flood scenarios. and time Effective traffic capacity of connecting roads, traffic flow by vehicle type, road network system performance index, and road network functional resilience function; S5. Determine the flood scenario Given a set of bridge-road units to be repaired, construct a recovery optimization state vector, a set of recovery actions, and a state transition function, and calculate the time consumption of repair actions, the cost consumption of repair actions, and the state transition results; S6. Construct a reward function centered on functional resilience improvement, system performance improvement, repair time, and repair cost; solve the flood scenario under resource and budget constraints. The optimal recovery strategy is determined, and the optimal set of recovery actions at each time point, the repair priority of each bridge-road unit, and the repair plan of the bridge network are output. S7. Calculate the recovery period functional resilience curve, recovery loss index, average functional retention level, recovery time, and comprehensive regional water resistance resilience index of the regional bridge network during the recovery period.

[0006] Optionally, the bridge foundation data in step S1 includes the first... The location coordinates of the bridge Collection of bridge abutment locations , Collection of representative locations of bridge piers Effective burial depth of bridge foundation Pier width Bridge deck clearance height and historical damage repair records The historical damage repair record Including the The bridge was built during a historical flood event. Historical engineering requirements parameters and historical failure markers Among them, historical flood events Indicates the first A sample of floods that have occurred and been recorded. , For the first The number of historical flood events used for bridge failure probability model calibration; each historical flood event Corresponding to a set of historical engineering requirement parameters and historical failure markers The historical engineering requirements parameters include the historical scour failure ratio. Historical level hydrodynamic instability demand ratio The demand for submerging historical bridge surfaces is higher than The demand ratio of the continued impact of historical floods The historical failure marker Used to indicate the first The bridge was built during a historical flood event. Has a failure occurred? The bridge flood control failure criterion data includes the first... Correction factor for the shape of the bridge pier ends Water flow angle of attack correction factor Riverbed condition correction coefficient Bridge abutment type correction factor Correction factor for the angle between the bridge abutment and the water flow Length of water obstruction of bridge abutment drag coefficient Water-facing projection area Lateral resistance of bridges Overturning moment bearing capacity Long-term riverbed scouring and deposition Flood scenario The lower shrinkage scour depth Flood scenario Down by the dominant water flow direction Determined water-facing direction correction function The lever arm from the point of application of the horizontal hydrodynamic force to the anti-overturning reference point Reference flood duration Reference flood cumulative impact intensity Duration weighting coefficient Cumulative impact intensity weighting coefficient Damage status determination threshold , , and ; The road network data includes a set of road nodes, intersection nodes, and bridge-related nodes. , by connecting nodes and nodes connecting roads The set of connecting roads , No. Bridges and connecting roads mapping relationship connecting roads Road length Free-flow travel time Design capacity under disaster-free conditions Flow relationship parameters Impedance relationship parameters Connecting roads Truck impedance amplification factor Time weighting coefficient Distance weighting coefficient Economic cost weighting coefficient Baseline system performance index under disaster-free conditions and the benchmark system performance index under extreme failure conditions ; The traffic demand data includes the OD (Original Demand) matrix. Connecting roads Vehicle baseline flow Connecting roads Truck baseline flow Unit vehicle operating cost and unit truck operating costs ; The flood scenario data includes a set of flood scenarios. Flood scenario The underwater depth field Flood scenario The flow field below Flood scenario The direction field of water flow below Flood scenario The duration of the flood Effective flood depth threshold Water density and gravitational acceleration ; The post-disaster recovery resource data includes time data. Available repair resources ,time Available repair budget , No. Repair time of bridge-road unit , No. Repair costs of a bridge-road unit Recovery and optimization time step and recovery period time range ; The recovery optimization parameter data includes repair time normalization parameters. Repair cost normalization parameters Functional resilience enhancement weight System performance improvement weight Repair time penalty weight Repair cost penalty weight Reinforcement learning discount factor Action value network parameters and target action value network parameters ; The water resistance toughness evaluation parameter data includes the target recovery threshold. Average Functional Level Preservation Preference Coefficient Recovery speed preference coefficient Recovery loss control preference coefficient And to prevent the smallest positive number of weighted denominator from being zero .

[0007] Optionally, step S2 specifically includes the following steps: S2.1, according to the first The location coordinates of the bridge , will water depth field Flow velocity field and water flow direction field Mapping to the bridge site location yields the bridge site water depth sequence, bridge site flow velocity sequence, and bridge site flow direction sequence: , , , in, For a moment No. The water depth at the bridge For a moment No. The water flow speed at the bridge For a moment No. The direction of water flow at the bridge, and , For any flood scenario The duration of the flood; For the first The location coordinates of the bridge The water depth field at the location; For the first The location coordinates of the bridge The flow velocity field at that location, For the first The location coordinates of the bridge The direction of water flow at the location; Definition of the first The bridge in the flood scene The following is the effective flooding time set : , in, The effective flood depth threshold; S2.2. Based on the bridge site water depth sequence, bridge site flow velocity sequence, and bridge site flow direction sequence, calculate the... Representative flood intensity parameters for the bridge: , , , , , in, For the maximum water depth at the bridge site, For the maximum flow velocity at the bridge site, To guide the direction of water flow For the effective duration of flooding, This represents the cumulative impact intensity of the flood. This refers to selecting the set of effective flooding times. The maximum value in the following data. This refers to the dominant water flow direction corresponding to the maximum water depth and maximum flow velocity at the bridge site. It refers to length; S2.3, based on the first Collection of bridge abutment locations and the set of locations represented by bridge piers Extract the water depth represented by the abutment, the flow velocity represented by the abutment, the water depth represented by the pier, and the flow velocity represented by the pier. For any representative location point The representative location point is either the abutment representative location point or the pier representative location point, and its water depth sequence is... and flow velocity sequence The maximum water depth and maximum flow velocity within the effective flooding time are respectively taken as the representative water depth of the representative location point. And represents flow rate ,Right now: , , Based on the Collection of bridge abutment locations and the set of locations represented by bridge piers Representative flood parameters at the abutments and piers were calculated using the finite set averaging method. , , , , in, For the first The bridge abutments represent a set of locations. For the first The piers of the bridge represent a set of locations; and These represent the number of points in the corresponding set of locations; Flood scenario The lower part represents the location point. The location represents the water depth; Flood scenario The lower part represents the location point. The representative flow velocity at that location; This represents the water depth at the bridge abutment. This represents the flow velocity at the bridge abutment. This represents the water depth at the bridge pier. This represents the flow velocity at the bridge pier. S2.4 Calculate the flood scenario based on the representative water depth and representative flow velocity at the bridge abutments and piers. Next The bridge abutments of the Froude number And the number of bridge piers by Froude : , , S2.5, Constructing the first The bridge in the flood scene Flood intensity parameters : .

[0008] Optionally, step S3 specifically includes the following steps: S3.1, Calculate the first... The bridge in the flood scene Local scour depth of the bridge piers : , in, The width of the bridge pier. This is a correction factor for the shape of the bridge pier ends. This is the correction factor for the angle of attack of the water flow. This is a correction factor for riverbed conditions; This represents the water depth at the bridge pier. Flood scenario Next Froude number at the piers of the bridge; Calculate the first The bridge in the flood scene Local scour depth of the bridge abutment : , in, The water depth at the bridge abutment is representative of the water depth. This is a correction factor for the abutment type. This is a correction factor for the angle between the bridge abutment and the water flow. This is the length of the abutment that blocks water. Flood scenario Next Froude numbered the bridge abutments; Based on the The bridge in the flood scene Local scour depth of the bridge piers Local scour depth of bridge abutments Long-term riverbed scouring and deposition and shrinkage scour depth Calculate the total scour depth : , Further calculation of the scour failure demand ratio: , in, This indicates the total scour depth relative to the effective burial depth of the bridge foundation. The proportion; S3.2, Based on maximum bridge site flow velocity and the dominant water flow direction and drag coefficient Water-facing projection area and flood scenarios Down by the dominant water flow direction Determined water-facing direction correction function Calculate the horizontal hydrodynamic forces generated by floods on bridge piers or superstructure. : , in, Density of water; Calculate the overturning moment generated by horizontal hydrodynamics : , in, The lever arm is the distance from the point of application of the horizontal hydrodynamic force to the anti-overturning reference point; Furthermore, the horizontal hydrodynamic instability demand ratio is calculated: , in, This indicates the horizontal effect of floodwater relative to the lateral resistance of the bridge. and overturning moment bearing capacity The degree of demand; S3.3, Based on the maximum water depth at the bridge site and bridge deck clearance height Calculate the bridge deck flooding demand ratio : , in, This indicates the degree to which the floodwater level exceeds the clearance height of the bridge deck; when This indicates that the bridge surface has not been flooded. This indicates a risk of bridge flooding or traffic disruption. S3.4, Based on the effective flooding duration and cumulative impact intensity of floods Calculate the demand ratio for the sustained effect of floods : , in, For duration weighting coefficients, For the first The reference flooding duration for each bridge This is the cumulative impact intensity weighting coefficient. For the first The reference cumulative impact intensity of floods corresponding to each bridge; S3.5, the first The bridge in the flood scene The engineering requirement parameters are defined as follows: , in, Characterizes the risk of foundation scour failure. Characterizing the risk of horizontal hydrodynamic instability, This indicates the risk of bridge flooding or traffic disruption. Characterizes the risk of prolonged flood action and cumulative impact; S3.6, Based on project requirements parameters Calculate the overall damage demand ratio : , And determine the threshold based on the damage status. , , and Judgment No. The bridge in the flood scene Damage status of the lower bridge : , in, , , , and The level of bridge damage; S3.7, Based on historical damage repair records , construct the first Failure probability calibration sample set of bridges : , in, For historical flood events Next The historical scour failure demand ratio of the bridge For historical flood events Next The historical level of hydrodynamic instability demand ratio of the bridge For historical flood events Next The historical bridge deck of the bridge requires more water to be submerged than... For historical flood events Next The bridge's historical flood resistance and demand ratio For historical flood events Next The bridge's historical failure markers, Indicates invalidity. This indicates that the product is not invalid. A bridge failure probability model was constructed using logistic regression to analyze historical flood events. Next Predicting the failure probability of the bridge: , in: , , in, The first prediction obtained by the bridge failure probability model The bridge was built during a historical flood event. Predicted failure probability of bridges; For constant terms, , , , These are the weighting coefficients corresponding to the historical scour failure demand ratio, the historical horizontal hydrodynamic instability demand ratio, the historical bridge deck inundation demand ratio, and the historical flood continuous effect demand ratio, respectively. Based on failure probability calibration sample set By minimizing historical failure markers Bridge prediction failure probability The cross-entropy loss between the two parameters is used to calibrate the bridge failure probability model. , in: , in, For the first The cross-entropy loss function corresponding to each bridge; For the first The number of historical flood events that can be used to calibrate bridge failure probability models; After obtaining the calibrated model parameters , , , and Then, the current flood situation will be discussed. Next Substituting the engineering requirements parameters of the bridge into the bridge failure probability model, the first failure is calculated. The bridge in the current flood situation Predicted failure probability : , in, , , and These are the current flood scenarios. Next The demand ratios for bridge failure due to scour, horizontal hydrodynamic instability, bridge deck inundation, and continuous flood effects. S3.8, Based on bridge damage status and bridge failure probability Determine the first The bridge in the flood scene Capacity reduction factor ; Specifically, first, based on the state of bridge damage... Determine the basic capacity reduction value: , Furthermore, considering the bridge failure probability Calculate the first The bridge in the flood scene Bridge capacity reduction factor : , in, The range of values ​​is ,when This indicates that the bridge's traffic capacity has not been reduced. The time indicates that the bridge-road unit corresponding to the bridge is not passable.

[0009] Optionally, step S4 specifically includes the following steps: S4.1 Constructing a regional bridge network: , in, For regional bridge network, It is a set of road nodes, intersection nodes, and bridge-related nodes. Let be the set of connecting roads, and let any connecting road be denoted as . ,in , Numbering nodes in the road network; Establish the first Bridges and connecting roads Mapping relationship between them: , Based on the The bridge in the flood scene The bridge capacity reduction factor is used to determine the first bridge. The connecting roads corresponding to the bridge At that time, the bridge capacity reduction factor is mapped to the connecting road capacity reduction factor: , in, To connect roads In flood scenarios and time The capacity reduction factor for connecting roads is as follows: For the first The bridge in the flood scene and time The bridge capacity reduction factor; Based on the capacity reduction factor of connecting roads Calculate connecting roads In flood scenarios and time Effective traffic capacity of the connecting roads below: , in, Design capacity for traffic under disaster-free conditions; S4.2, Based on connecting roads Vehicle baseline flow and truck baseline flow Determine the connecting roads benchmark truck ratio : , And determine the connecting roads benchmark car ratio : , In flood scenarios and time Below, based on the OD traffic demand matrix Effective traffic capacity of connecting roads Connecting roads benchmark car ratio and connecting roads benchmark truck ratio For regional bridge network Traffic allocation is performed to obtain connecting roads. Traffic flow and truck traffic : , in, This is a traffic assignment model used to allocate the OD traffic demand matrix to each connecting road in a regional bridge network, while satisfying the conditions of OD traffic demand conservation and connecting road capacity constraints, and outputs the connecting roads. Car and truck traffic on the road; The traffic assignment satisfies the capacity constraints of the connecting roads: , And satisfy the conservation of OD traffic demand; when At that time, connecting roads Not involved in feasible path allocation; S4.3 Calculate connecting roads Total traffic flow : , Based on free-flow travel time Total traffic flow and the effective traffic capacity of connecting roads Calculate the foundation impedance of the connecting road : , in, For flow relationship parameters, These are impedance relationship parameters; Based on truck traffic Truck base flow and the effective traffic capacity of connecting roads Calculate the corrected impedance of the truck : , in, To connect roads The truck impedance amplification factor; S4.4 Calculating Flood Scenarios and time Total travel time of the road network below : , S4.5 Calculating Flood Scenarios and time Total travel distance of the road network : , in, To connect roads The length of the road; S4.6 Calculate additional vehicle operating costs: Based on unit vehicle operating cost Unit truck operating cost and connecting roads Road length Calculate flood scenarios Lower vehicle operating costs : , Based on vehicle baseline flow and truck baseline flow Calculate the operating cost of disaster-free baseline vehicles : , Calculate additional vehicle operating costs : , S4.7, Based on total travel time of the road network Total travel distance of the road network and additional vehicle operating costs Calculate flood scenarios and time Road network system performance index : , in, For time weighting coefficients, This is the distance weighting coefficient. This is the economic cost weighting coefficient; S4.8, Benchmark System Performance Index Based on Disaster-Free Conditions and the benchmark system performance index under extreme failure conditions The performance index of the road network system is normalized to obtain the flood scenario. and time Road network functional resilience function : .

[0010] Optionally, step S5 specifically includes the following steps: S5.1. Taking the bridge-road units affected by floods in the regional bridge network as the objects of restoration and optimization, a flood scenario is formed. The following is a collection of bridge-road units to be repaired. : , in, No. The bridge in the flood scene and time The bridge capacity reduction factor; S5.2, during the recovery period Below, construct a flood scenario. Next moment Recovery optimization state vector : , in, For the first The bridge in the flood scene and time The bridge capacity reduction factor; Flood scenario and time The connecting road below Effective traffic capacity; To connect roads In flood scenarios and time Traffic flow below; To connect roads In flood scenarios and time Truck traffic below; Flood scenario and time The performance index of the road network system under the following conditions; Flood scenario and time The road network functional resilience function is as follows; For a moment Available repair resources For a moment Available repair budget; S5.3 Define the repair selection of the bridge-road unit to be repaired as a recovery action, and obtain the set of recovery actions. : , Among them, recovery action , is represented as: , The set of recovery actions satisfies resource constraints: , in, For a moment Available repair resources; If budget constraints for repair are taken into account, the set of recovery actions also satisfies: , in, For the first The cost of repairing a bridge-road unit, For a moment Available repair budget; S5.4, based on the first Repair time of bridge-road unit and repair costs Calculate the set of recovery actions Repair time consumption: , in, This indicates the time consumption of repair actions when multiple repair tasks are executed in parallel at the current moment; This refers to the set of bridge-road units to be repaired. The maximum value of the data within the parentheses; Calculate the set of recovery actions Cost of repair work: , in, This indicates the cost of the repair actions consumed by the current set of recovery actions; S5.5, When dealing with the first Repair work was carried out on each bridge-road unit. At that time, the update is based on the repair completion rate. Bridge capacity reduction factor for each bridge-road unit; Definition of the first Each bridge-road unit at time Repair completion rate for: , in, To restore the optimized time step, For the first Repair time for each bridge-road unit; Update the bridge capacity reduction factor: , in, For the first The bridge in the flood scene and time The bridge capacity reduction factor; S5.6, Based on the updated bridge capacity reduction factor Update connecting roads The capacity reduction factor for connecting roads: , And update the effective traffic capacity of connecting roads: , in, To connect roads In flood scenarios and time The effective traffic capacity of the connecting roads below; Based on the updated effective traffic capacity of connecting roads Traffic demand matrix with OD Recalculate vehicle traffic flow in the regional bridge network. and truck traffic And recalculate the road network system performance index. and road network functional resilience function ; S5.7. Assume that available repair resources and repair costs are uniform during the repair process. For a moment Available repair resources , For a moment Available repair budget, Then based on time Recovery optimization state vector under and recovery action set ,get State transition result at time t : , , in, This is the state transition function, used to represent the update process of the bridge-road unit's capacity reduction coefficient, traffic flow assignment, system performance index, and road network functional resilience function due to repair actions.

[0011] Optionally, step S6 specifically includes the following steps: S6.1, In the flood scenario and recovery time Below, based on the bridge-road unit set to be repaired Constructing a timeframe that satisfies repair resource constraints Set of possible actions : , in, To restore the action set, For a moment Available repair resources; S6.2 Road network functional resilience function before and after state transition and Calculate and execute the set of recovery actions The resulting increase in single-step functional resilience : , Performance index of road network system before and after state transition and Calculate the performance improvement of a single-step system. : , S6.3. Based on the single-step functional resilience improvement, single-step system performance improvement, repair action time consumption, and repair action cost consumption, construct a reward function: , in, In order to restore the optimized state Perform recovery actions And transfer to the state transition result The reward value obtained; Increase the weight of functional resilience. To improve system performance, To fix the time penalty weight, Weighting for cost-based penalties; To fix the time normalization parameters, To normalize parameters for repair costs; This is an increase in the resilience of single-step functionality; This represents the performance improvement of a single-step system. To fix the action time consumption, Cost of repair work; in: , and: , S6.4, within the recovery period time range Internally, a cumulative reward target for constructing a recovery strategy based on a reward function is defined. : , in, To enhance the learning discount factor, Flood scenario The following recovery strategy is used to represent the flood scenario. The sequence of repair actions throughout the entire recovery period; the recovery strategy Represented as: , in, During the recovery period The set of recovery actions selected for repair. During the recovery period The set of recovery actions selected for repair. During the recovery period The set of recovery actions selected for the repair action; The optimization goal of the recovery strategy is: , in, Flood scenario The optimal or near-optimal bridge group network recovery strategy is as follows. This represents all recovery strategies that satisfy both resource and budget constraints. Select cumulative rewards The most important recovery strategy; S6.5, to recover the optimized state vector As input to the agent, a set of actionable actions The set of recovery actions As the output action of the agent, the reward function is used as the feedback signal, and the recovery strategy is solved by deep reinforcement learning. Constructing the action value function: , in, Let the action value function be... This indicates that in restoring the optimized state vector Execute the set of recovery actions The subsequent action value function value, which represents the expected cumulative reward that can be obtained. For action value network parameters; At each recovery time From the set of actionable actions Select the optimal set of recovery actions at the current moment. : , in, Indicating flood scenario and recovery time The optimal set of recovery actions is determined by the action value function. Indicates the set of possible actions In the process, we search for the value of the action-value function. The recovery action that achieves the maximum value; Execute the optimal set of recovery actions Then, according to the state transition function, we get: , S6.6 Constructing the target action value function: , in, The value of the target action function. Parameters for the target action value network; To enhance the learning discount factor; This represents the set of possible actions in the next moment. Select the action value function value that is the largest among them; Update the action value network parameters by minimizing the action value error. : , in, For training the loss function; After multiple rounds of training or iterative search, the flood scenario was obtained. Optimal recovery strategy : , , S6.7, Based on the optimal recovery strategy Determine the repair priority for each bridge-road unit, namely: , in, For the first Bridge-road units in flood scenarios The repair begins at the following time; This indicates the recovery time in the optimal recovery strategy. For the Repairs were carried out on each bridge-road unit; Indicates satisfaction The earliest recovery time; This leads to a repair plan for the bridge group network: , in, Flood scenario The restoration plan for the under-bridge network includes bridge-road unit numbering. Repair start time Repair time and repair costs .

[0012] Optionally, step S7 specifically includes the following steps: S7.1, According to the bridge group network repair plan Within the recovery period The optimal set of recovery actions is executed sequentially at each time step. And update the bridge capacity reduction factor, the effective capacity of connecting roads, vehicle traffic flow, and truck traffic flow; At each recovery moment Recalculate and adopt the recovery strategy The subsequent road network system performance index And calculate the corresponding road network functional resilience function: , in, To adopt a recovery strategy Later in the flood situation and time The value of the road network functional resilience function; This yields the functional resilience curve during the recovery period, expressed as follows: , S7.2 Setting the baseline function level : , Calculate the recovery loss index based on the functional resilience curve during the recovery period. : , in, The positive part function is defined as follows: , in, This indicates the adoption of the optimal recovery strategy. Post-flood scenario Next recovery time The road network functional resilience function value; when hour, ;when hour, ; S7.3 Calculate flood scenarios based on the functional resilience curve during the recovery period. The average functional level of the regional bridge network will remain at the following recovery period. : , S7.4, Based on the target recovery threshold Calculate the recovery time required for functional resilience to initially recover to the target recovery threshold. : , in, Set the target recovery threshold; The lower boundary refers to Road network functional resilience function value within the range The first time the target recovery threshold is reached or exceeded The earliest moment; If within the recovery period If the target recovery threshold is not reached, then let: , S7.5. Construct three normalized evaluation indicators respectively: , , , in, This indicates that the average function remains at a level. Indicates the recovery speed level. This indicates the restoration of the loss control level; S7.6. Determine the objective weights based on the dispersion of the three normalized evaluation indicators under different flood scenarios, and introduce a decision preference coefficient for correction. For the A normalized evaluation index is used to calculate its application in a set of flood scenarios. mean : , in, , Represents a set of flood scenarios The number of flood scenarios; Calculate the first The dispersion of each normalized evaluation index : , Based on the average function retention level preference coefficient Recovery speed preference coefficient Recovery loss control preference coefficient And to prevent the smallest positive number of weighted denominator from being zero Calculate the first Comprehensive evaluation weight of each normalized evaluation indicator : , Therefore, we can conclude that: , in, , , These correspond to the comprehensive evaluation weights for average functional retention level, recovery speed, and recovery loss control level, respectively. S7.7 Calculating Flood Scenarios The following recovery strategy is adopted. The subsequent regional water resistance toughness comprehensive index : .

[0013] Based on the same inventive concept, the present invention provides an electronic device, including a processor and a storage medium; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the restorative analysis method for regional flood-resistant bridge network as described above.

[0014] Based on the same inventive concept, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the restorative analysis method for bridge group networks under regional floods oriented towards water-resistant resilience as described above.

[0015] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) By incorporating the water depth, flow velocity, flow direction, effective flooding duration, cumulative flood impact intensity, and representative flood parameters at the abutment and pier into the flood intensity characterization system, this invention can more comprehensively and meticulously reflect the actual effects of regional floods on different bridge locations. (2) By simultaneously considering four key failure modes—scour failure, horizontal hydrodynamic instability, bridge deck submersion, and continuous flooding—and combining historical flood events to calibrate the bridge failure probability model, this invention can achieve a joint assessment of bridge damage status and failure risk, making the analysis of bridge flood vulnerability more refined. (3) By mapping the damage state, failure probability and traffic capacity reduction coefficient of the bridge level to the regional road network, and combining the traffic allocation by vehicle type, the road network system performance index and the road network functional resilience function, this invention can quantitatively reveal the transmission impact of damage to a single bridge and bridge group on the traffic function of the regional road network. (4) This invention constructs a recovery optimization model that includes recovery state, recovery action, state transition, repair time and repair cost, and solves the optimal recovery strategy under repair resource constraints and budget constraints. It can output the repair priority of each bridge-road unit and the bridge group network repair plan, providing an executable basis for post-disaster recovery decision-making. (5) By constructing a functional resilience curve during the recovery period, a recovery loss index, an average functional retention level, a recovery time, and a comprehensive index of regional water resistance resilience, this invention can conduct a full-process and comprehensive evaluation of the water resistance resilience of regional bridge networks during flood action and recovery, thereby providing quantitative support for disaster prevention, mitigation, and recovery management of regional bridge networks. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of the regional bridge group network and bridge sample partitioning in this invention; Figure 3 This is a schematic diagram showing the distribution of bridge damage and detour routes under a flood scenario in this invention; Figure 4 This is the evolution diagram of the road network functional resilience function under the optimal recovery strategy in this invention; Figure 5 This is a reward-cost-time trade-off diagram for the optimal recovery action in this invention. Detailed Implementation

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0018] like Figure 1 As shown, the present invention provides a method for restoring bridge network under regional floods with water resistance resilience, comprising the following steps: S1. Obtain basic bridge data, bridge flood failure criterion data, road network data, traffic demand data, including flood scenario sets for the regional bridge group. Flood scenario data, post-disaster restoration resource data, recovery optimization parameter data, and water resistance resilience evaluation parameter data are used to form a standardized dataset. .

[0019] Among them, the bridge basic data includes the first The location coordinates of the bridge Collection of bridge abutment locations , Collection of representative locations of bridge piers Effective burial depth of bridge foundation Pier width Bridge deck clearance height and historical damage repair records Historical damage repair records Including the The bridge was built during a historical flood event. Historical engineering requirements parameters and historical failure markers Among them, historical flood events Indicates the first A sample of floods that have occurred and been recorded. , For the first The number of historical flood events used for bridge failure probability model calibration; each historical flood event Corresponding to a set of historical engineering requirement parameters and historical failure markers Historical engineering requirements parameters include the historical scour failure ratio. Historical level hydrodynamic instability demand ratio The demand for submerging historical bridge surfaces is higher than The demand ratio of the continued impact of historical floods Historical failure markers Used to indicate the first The bridge was built during a historical flood event. Does the following fail?

[0020] Bridge flood control failure criterion data includes the first Correction factor for the shape of the bridge pier ends Water flow angle of attack correction factor Riverbed condition correction coefficient Bridge abutment type correction factor Correction factor for the angle between the bridge abutment and the water flow Length of water obstruction of bridge abutment drag coefficient Water-facing projection area Lateral resistance of bridges Overturning moment bearing capacity Long-term riverbed scouring and deposition Flood scenario The lower shrinkage scour depth Flood scenario Down by the dominant water flow direction Determined water-facing direction correction function The lever arm from the point of application of the horizontal hydrodynamic force to the anti-overturning reference point Reference flood duration Reference flood cumulative impact intensity Duration weighting coefficient Cumulative impact intensity weighting coefficient Damage status determination threshold , , and .

[0021] Road network data includes a set of road nodes, intersection nodes, and bridge-related nodes. , by connecting nodes and nodes connecting roads The set of connecting roads , No. Bridges and connecting roads mapping relationship connecting roads Road length Free-flow travel time Design capacity under disaster-free conditions Flow relationship parameters Impedance relationship parameters Connecting roads Truck impedance amplification factor Time weighting coefficient Distance weighting coefficient Economic cost weighting coefficient Baseline system performance index under disaster-free conditions and the benchmark system performance index under extreme failure conditions .

[0022] Traffic demand data includes the OD (Original Direction) traffic demand matrix. Connecting roads Vehicle baseline flow Connecting roads Truck baseline flow Unit vehicle operating cost and unit truck operating costs .

[0023] Flood scenario data includes a set of flood scenarios. Flood scenario The underwater depth field Flood scenario The flow field below Flood scenario The direction field of water flow below Flood scenario The duration of the flood Effective flood depth threshold Water density and gravitational acceleration .

[0024] Post-disaster recovery resource data includes time. Available repair resources ,time Available repair budget , No. Repair time of bridge-road unit , No. Repair costs of a bridge-road unit Recovery and optimization time step and recovery period time range .

[0025] Recovery optimization parameter data includes repair time normalization parameters. Repair cost normalization parameters Functional resilience enhancement weight System performance improvement weight Repair time penalty weight Repair cost penalty weight Reinforcement learning discount factor Action value network parameters and target action value network parameters .

[0026] Water resistance toughness evaluation parameters include target recovery threshold. Average Functional Level Preservation Preference Coefficient Recovery speed preference coefficient Recovery loss control preference coefficient And to prevent the smallest positive number of weighted denominator from being zero .

[0027] S2, based on standardized datasets And flood scenario set For any flood scenario , will water depth field Flow velocity field and water flow direction field Mapped to the Based on the bridge site location, representative abutment location, and representative pier location of the bridge, calculate the representative flood intensity parameters at the bridge site, the representative flood parameters at the abutments and piers, and the corresponding Froude numbers, and construct the first... The bridge in the flood scene Flood intensity parameters at the bridge site .

[0028] Step S2 specifically includes the following steps: S2.1, according to the first The location coordinates of the bridge , will water depth field Flow velocity field and water flow direction field Mapping to the bridge site location yields the bridge site water depth sequence, bridge site flow velocity sequence, and bridge site flow direction sequence: , , , in, For a moment No. The water depth at the bridge For a moment No. The water flow speed at the bridge For a moment No. The direction of water flow at the bridge, and , For any flood scenario The duration of the flood; For the first The location coordinates of the bridge The water depth field at the location; For the first The location coordinates of the bridge The flow velocity field at that location, For the first The location coordinates of the bridge The direction of water flow at that location.

[0029] Definition of the first The bridge in the flood scene The following is the effective flooding time set: , in, For the effective set of flooding times, The effective flood depth threshold.

[0030] S2.2. Based on the bridge site water depth sequence, bridge site flow velocity sequence, and bridge site flow direction sequence, calculate the... Representative flood intensity parameters for the bridge: , , , , , in, For the maximum water depth at the bridge site, For the maximum flow velocity at the bridge site, To guide the direction of water flow For the effective duration of flooding, This represents the cumulative impact intensity of the flood. This refers to selecting the set of effective flooding times. The maximum value in the following data. This refers to the dominant water flow direction corresponding to the maximum water depth and maximum flow velocity at the bridge site. It refers to length.

[0031] S2.3, based on the first Collection of bridge abutment locations and the set of locations represented by bridge piers Extract the water depth represented by the abutment, the flow velocity represented by the abutment, the water depth represented by the pier, and the flow velocity represented by the pier.

[0032] For any representative location point The representative location point is either the abutment representative location point or the pier representative location point, and its water depth sequence is... and flow velocity sequence The maximum water depth and maximum flow velocity within the effective flooding time are respectively taken as the representative water depth of the representative location point. And represents flow rate ,Right now: , Furthermore, based on the first Collection of bridge abutment locations and the set of locations represented by bridge piers Representative flood parameters at the abutments and piers were calculated using the finite set averaging method. , , , ,

[0033] in, For the first The bridge abutments represent a set of locations. For the first The piers of the bridge represent a set of locations; and These represent the number of points in the corresponding set of locations; Flood scenario The lower part represents the location point. The location represents the water depth; Flood scenario The lower part represents the location point. The representative flow velocity at that location; This represents the water depth at the bridge abutment. This represents the flow velocity at the bridge abutment. This represents the water depth at the bridge pier. This represents the flow velocity at the bridge pier.

[0034] S2.4. Calculate the Froude number for the abutments and the Froude number for the piers based on the representative water depth and representative flow velocity at the abutments and piers: , , in, Flood scenario Next Froude counts at the abutments of the bridge. Flood scenario Next Froude numbered the number of bridge piers. This is the acceleration due to gravity.

[0035] S2.5, Constructing the first The bridge in the flood scene The following flood intensity parameters: , in, Used to characterize the impact of floods on the first The local load strength of the bridge.

[0036] S3, Based on bridge site flood intensity parameters And the bridge flood control failure criterion data, respectively calculate the first The bridge in the flood scene The ratios of scour failure demand, horizontal hydrodynamic instability demand, bridge deck inundation demand, and flood duration demand are used to form engineering demand parameters. Further determine the state of bridge damage. Based on historical damage repair records Calibrate the failure probability model and calculate the bridge failure probability. and capacity reduction factor .

[0037] Step S3 specifically includes the following steps: S3.1 Calculate the local scour depth of the bridge pier: , in, For the first The bridge in the flood scene The depth of local scour of the bridge piers below The width of the bridge pier. This is a correction factor for the shape of the bridge pier ends. This is the correction factor for the angle of attack of the water flow. This is a correction factor for riverbed conditions; This represents the water depth at the bridge pier. Flood scenario Next Froude numbered the piers of the bridge.

[0038] Calculate the local scour depth of the bridge abutment: , in, For the first The bridge in the flood scene The depth of local scour at the bridge abutment. The water depth at the bridge abutment is representative of the water depth. This is a correction factor for the abutment type. This is a correction factor for the angle between the bridge abutment and the water flow. This is the length of the abutment that blocks water. Flood scenario Next Froude counts the bridge abutments.

[0039] Based on the local scour depth of the bridge pier Local scour depth of bridge abutments Long-term riverbed scouring and deposition and flood scenarios The lower shrinkage scour depth Calculate the total scour depth: , in, This represents the total scour depth.

[0040] Further calculation of the scour failure demand ratio: , in, This indicates the total scour depth relative to the effective burial depth of the bridge foundation. The percentage.

[0041] S3.2, The maximum bridge site flow velocity obtained from step S2 and the dominant water flow direction and the drag coefficient in step S1 Water-facing projection area and flood scenarios Down by the dominant water flow direction Determined water-facing direction correction function Calculate the horizontal hydrodynamic forces exerted by floods on bridge piers or superstructure: , in, For horizontal hydrodynamics, This represents the density of the water.

[0042] Calculate the overturning moment generated by horizontal hydrodynamics : , in, It is the lever arm from the point of application of the horizontal hydrodynamic force to the anti-overturning reference point.

[0043] Furthermore, the horizontal hydrodynamic instability demand ratio is calculated: , in, This indicates the horizontal effect of floodwater relative to the lateral resistance of the bridge. and overturning moment bearing capacity The degree of demand, For the lateral resistance of the bridge, This refers to the bearing capacity against overturning bending moment.

[0044] S3.3, The maximum water depth at the bridge site obtained based on step S2 and the bridge deck clearance height in step S1 Calculate the bridge deck flooding demand ratio : , in, This indicates the degree to which the floodwater level exceeds the clearance height of the bridge deck; when This indicates that the bridge surface has not been flooded. This indicates a risk of bridge flooding or traffic disruption.

[0045] S3.4 Effective flooding duration obtained from step S2 and cumulative impact intensity of floods Calculate the demand ratio for the sustained effect of floods : , in, For duration weighting coefficients, For the first The reference flooding duration for each bridge This is the cumulative impact intensity weighting coefficient. For the first The reference cumulative impact intensity of floods corresponding to each bridge.

[0046] S3.5, the first The bridge in the flood scene The engineering requirement parameters are defined as follows: , in, Characterizes the risk of foundation scour failure. Characterizing the risk of horizontal hydrodynamic instability, This indicates the risk of bridge flooding or traffic disruption. It characterizes the risk of long-term effects and cumulative impact of floods.

[0047] S3.6, Based on project requirements parameters Calculate the overall damage demand ratio: , And determine the threshold based on the damage status. , , and Determine the bridge damage status: , in, For the first The bridge in the flood scene The damage state is as follows; in one embodiment, , , , Take respectively , , and In other embodiments, adjustments may be made based on bridge design specifications, historical damage samples, or test calibration results. , , , and This indicates the level of damage to the bridge.

[0048] S3.7 Based on the historical damage repair records in step S1 Construct a failure probability calibration sample set. For the first Failure probability calibration sample set for the bridge: , in, For historical flood events Next The historical scour failure demand ratio of the bridge For historical flood events Next The historical level of hydrodynamic instability demand ratio of the bridge For historical flood events Next The historical bridge deck of the bridge requires more water to be submerged than... For historical flood events Next The bridge's historical flood resistance and demand ratio For historical flood events Next The bridge's historical failure markers, Indicates invalidity. This indicates that the code is still valid.

[0049] A bridge failure probability model was constructed using logistic regression to analyze historical flood events. Next Predicting the failure probability of the bridge: , in: , , in, The first prediction obtained by the bridge failure probability model The bridge was built during a historical flood event. Predicted failure probability of bridges; For constant terms, , , , These are the weighting coefficients corresponding to the historical scour failure demand ratio, the historical horizontal hydrodynamic instability demand ratio, the historical bridge deck inundation demand ratio, and the historical flood continuous effect demand ratio, respectively.

[0050] Based on failure probability calibration sample set By minimizing historical failure markers Bridge prediction failure probability The cross-entropy loss between the two parameters is used to calibrate the bridge failure probability model. , in: , in, For the first The cross-entropy loss function corresponding to each bridge; For the first The number of historical flood events that can be used to calibrate bridge failure probability models.

[0051] After obtaining the calibrated model parameters , , , and Then, the current flood situation will be discussed. Next The engineering requirements parameters of the bridge are substituted into the bridge failure probability model to calculate the predicted failure probability of the bridge: , in, For the first The bridge in the current flood situation The predicted failure probability is as follows; , , and These are the current flood scenarios. Next The demand ratios for bridge failure due to scour, horizontal hydrodynamic instability, bridge deck submersion, and the sustained effects of flooding.

[0052] S3.8. Bridge damage state obtained from step S3.6 The bridge failure probability obtained in step S3.7 Determine the first The bridge in the flood scene Capacity reduction factor ; First, based on the bridge damage condition Determine the basic capacity reduction value: , in, Indicates the state of bridge damage Determined basic capacity reduction value.

[0053] Furthermore, considering the bridge failure probability Calculate the bridge capacity reduction factor: , in, For the first The bridge in the flood scene The bridge capacity reduction factor is as follows, and its value range is: ;when This indicates that the bridge's traffic capacity has not been reduced. The time indicates that the bridge-road unit corresponding to the bridge is not passable.

[0054] S4. Based on the set of road nodes, intersection nodes, and bridge-related nodes in the road network data. and connecting road sets Constructing a regional bridge network Furthermore, the bridge damage status, bridge failure probability, and bridge capacity reduction factor at the bridge level are mapped to the connecting road network level; flood scenarios are calculated. and time Underpass Effective traffic capacity, traffic flow by vehicle type, and road network system performance index and road network functional resilience function Traffic flow by vehicle type includes car traffic and truck traffic.

[0055] Step S4 specifically includes the following steps: S4.1 Constructing a regional bridge network: , in, For regional bridge network, It is a set of road nodes, intersection nodes, and bridge-related nodes. Let be the set of connecting roads, and let any connecting road be denoted as . ,in , This refers to the node number in the road network.

[0056] Establish the first Bridges and connecting roads Mapping relationship between them: , Based on the output of step S3, the first The bridge in the flood scene The bridge capacity reduction factor is used to determine the first bridge. The connecting roads corresponding to the bridge At that time, the bridge capacity reduction factor is mapped to the connecting road capacity reduction factor: , in, To connect roads In flood scenarios and time The capacity reduction factor for connecting roads is as follows: For the first The bridge in the flood scene and time The bridge capacity reduction factor.

[0057] Based on the capacity reduction factor of connecting roads Calculate connecting roads Effective traffic capacity: , in, Flood scenario and time The connecting road below Effective traffic capacity, Designed for traffic capacity under disaster-free conditions.

[0058] S4.2, Based on connecting roads Vehicle baseline flow and truck baseline flow Determine the connecting roads benchmark truck ratio : , And determine the connecting roads benchmark car ratio : , In flood scenarios and time Below, based on the OD traffic demand matrix Connecting roads Effective traffic capacity Connecting roads benchmark car ratio and connecting roads benchmark truck ratio For regional bridge network Traffic allocation is performed to obtain connecting roads. Traffic flow and truck traffic : , in, To connect roads In flood scenarios and time Traffic flow below To connect roads In flood scenarios and time The truck traffic below, This is a traffic assignment model used to allocate the OD traffic demand matrix to each connecting road in a regional bridge network, while satisfying the conditions of OD traffic demand conservation and connecting road capacity constraints, and outputs the connecting roads. The traffic flow includes both car and truck traffic; the traffic assignment model is a capacity-constrained multi-vehicle user equilibrium traffic assignment model, which is a mature existing traffic assignment model.

[0059] Traffic assignment satisfies the capacity constraints of connecting roads: , And satisfy the conservation of OD traffic demand; when At that time, connecting roads It does not participate in the allocation of feasible paths.

[0060] S4.3 Calculate connecting roads Total traffic flow: , Based on the free-flow travel time obtained in step S1 Total traffic flow and the effective traffic capacity of connecting roads Calculate the foundation impedance of the connecting road: , in, To connect the road foundation impedance, For flow relationship parameters, These are impedance relationship parameters.

[0061] Based on truck traffic Truck base flow and the effective traffic capacity of connecting roads Calculate the corrected impedance of the truck: , in, Correcting the impedance for the truck, To connect roads The truck impedance amplification factor.

[0062] S4.4 Calculate the total travel time of the road network: , in, Flood scenario and time Total travel time for the road network.

[0063] S4.5 Calculate the total travel distance of the road network: , in, Flood scenario and time Total travel distance of the road network below; To connect roads The length of the road.

[0064] S4.6 Calculate additional vehicle operating costs: Based on the unit vehicle operating cost obtained in step S1 Unit truck operating cost and connecting roads Road length Calculate flood scenarios Vehicle operating costs: , Based on vehicle baseline flow and truck baseline flow Calculate the operating cost of a disaster-free baseline vehicle: , Calculate additional vehicle operating costs: , in, Additional vehicle operating costs are used to characterize the increased vehicle operating costs relative to a disaster-free baseline following damage to bridge-road units and traffic redistribution caused by flooding.

[0065] S4.7, Based on total travel time of the road network Total travel distance of the road network and additional vehicle operating costs Calculate flood scenarios and time The following road network system performance index: , in, This is a performance index for the road network system. For time weighting coefficients, This is the distance weighting coefficient. This is the economic cost weighting coefficient.

[0066] S4.8, Benchmark System Performance Index Based on Disaster-Free Conditions and the benchmark system performance index under extreme failure conditions The performance index of the road network system is normalized to obtain the flood scenario. and time The following road network resilience function: , in, This is the road network resilience function; a larger value indicates that the bridge group road network is more resilient to flood scenarios. and time The stronger the traffic service function maintained, the better.

[0067] S5. Determine the flood scenario The following is a collection of bridge-road units to be repaired. Combining post-disaster recovery resource data and flood scenarios and time The effective traffic capacity of the connecting roads, traffic flow by vehicle type, road network system performance index, and road network functional resilience function are used to construct a recovery optimization state vector. Recovery Action Set and state transition function It also calculates the time consumption of the repair action, the cost consumption of the repair action, and the state transition result.

[0068] Step S5 specifically includes the following steps: S5.1. Take the bridge-road units affected by floods in the regional bridge network as the objects of restoration and optimization, and form a set of bridge-road units to be repaired. : , in, Flood scenario The following is a collection of bridge-road units awaiting repair. No. The bridge in the flood scene and time The bridge capacity reduction factor.

[0069] For the bridge-road unit set to be repaired Any bridge-road unit in The repair aims to reduce the probability of bridge failure and the reduction factor of bridge capacity, and to connect it to relevant roads. Effective traffic capacity is gradually being restored.

[0070] S5.2, during the recovery period Next, construct the recovery optimization state vector: , in, Flood scenario Next moment The recovered optimized state vector; For the first The bridge in the flood scene and time The bridge capacity reduction factor; Flood scenario and time The connecting road below Effective traffic capacity; To connect roads In flood scenarios and time Traffic flow below; To connect roads In flood scenarios and time Truck traffic below; Flood scenario and time The performance index of the road network system under the following conditions; Flood scenario and time The road network functional resilience function is as follows; For a moment Available repair resources For a moment Repair budget available.

[0071] S5.3 Define the repair selection of the bridge-road unit to be repaired as a recovery action, and obtain the set of recovery actions. : , Among them, recovery action , is represented as: , The set of recovery actions satisfies resource constraints: , in, For a moment Resources are available for repair.

[0072] If budget constraints for repair are taken into account, the set of recovery actions also satisfies: , in, For the first The cost of repairing a bridge-road unit, For a moment Repair budget available.

[0073] S5.4, Based on the first step obtained in step S1 Repair time of bridge-road unit and repair costs Calculate the set of recovery actions Repair time consumption: , in, This indicates the time consumption of repair actions when multiple repair tasks are executed in parallel at the current moment; This refers to the set of bridge-road units to be repaired. The maximum value of the data within the parentheses.

[0074] Calculate the set of recovery actions Cost of repair work: , in, This indicates the cost of repair actions consumed by the current set of recovery actions.

[0075] S5.5, When dealing with the first Repair work was carried out on each bridge-road unit. At that time, the update is based on the repair completion rate. Bridge capacity reduction factor for each bridge-road unit.

[0076] Definition of the first Each bridge-road unit at time The repair completion rate is: , in, For the current time step The percentage of repairs completed within the facility. To restore the optimized time step, For the first Repair time for each bridge-road unit.

[0077] Update the bridge capacity reduction factor: , in, For the first The bridge in the flood scene and time The bridge capacity reduction factor.

[0078] S5.6, Based on the updated bridge capacity reduction factor Update the connecting roads according to the mapping method in step S4. The capacity reduction factor for connecting roads: , And update the effective traffic capacity of connecting roads: , in, To connect roads In flood scenarios and time The effective traffic capacity of the connecting roads.

[0079] Based on the updated effective traffic capacity of connecting roads Traffic demand matrix with OD Recalculate the vehicle flow in the regional bridge network according to the traffic assignment method in step S4. and truck traffic ; And recalculate the road network system performance index according to step S4. and road network functional resilience function .

[0080] S5.7. Assume that available repair resources and repair costs are uniform during the repair process. For a moment Available repair resources , For a moment Available repair budget, Then based on time Recovery optimization state vector under and recovery action set ,get State transition result at time t : , , in, This is the state transition function, used to represent the update process of the bridge-road unit's capacity reduction coefficient, traffic flow assignment, system performance index, and road network functional resilience function due to repair actions.

[0081] S6, Based on recovery optimization state vector Recovery Action Set State transition results Repair action time consumption and repair costs A reward function is constructed with functional resilience enhancement, system performance improvement, repair time, and repair cost as its core components. Under resource and budget constraints, a deep reinforcement learning method is used to solve the flood scenario. Optimal recovery strategy It outputs the optimal set of recovery actions at each time point, the repair priority of each bridge-road unit, and the repair plan for the bridge network. .

[0082] Step S6 specifically includes the following steps: S6.1, In the flood scenario and recovery time Next, based on the set of bridge-road units to be repaired obtained in step S5... Construct a set of feasible actions that satisfy the repair resource constraints: , in, For a moment The set of possible actions To restore the action set, For a moment Resources are available for repair.

[0083] S6.2, Based on the road network functional resilience function before and after the state transition in step S5 and Calculate and execute the set of recovery actions The resulting increase in single-step functional resilience: , in, To restore the set of actions The effect on improving the resilience of the road network.

[0084] Based on the road network system performance index before and after the state transition in step S5 and Calculate the performance improvement of the system in a single step: , in, To restore the set of actions The effect on improving the performance index of the road network system.

[0085] S6.3. Based on the single-step functional resilience improvement, single-step system performance improvement, repair action time consumption, and repair action cost consumption, construct a reward function: , in, In order to restore the optimized state Perform recovery actions And transfer to the state transition result The reward value obtained; Increase the weight of functional resilience. To improve system performance, To fix the time penalty weight, Weighting for cost-based penalties; To fix the time normalization parameters, To normalize parameters for repair costs; This is an increase in the resilience of single-step functionality; This represents the performance improvement of a single-step system. To fix the action time consumption, Costs incurred for repair work.

[0086] in: , and: , Therefore, the reward function is used to encourage priority to bridge-road unit repair actions that can improve functional resilience and system performance, while having shorter repair time and lower repair costs.

[0087] S6.4, within the recovery period time range Internally, the cumulative reward objective for the recovery strategy is constructed based on the reward function: , in, For recovery strategy The cumulative reward target, To enhance the learning discount factor, Flood scenario The following recovery strategy is used to represent the flood scenario. The sequence of repair actions throughout the entire recovery period; the recovery strategy Represented as: , in, During the recovery period The set of recovery actions selected for repair. During the recovery period The set of recovery actions selected for repair. During the recovery period The set of recovery actions selected for the repair action.

[0088] The optimization goal of the recovery strategy is: , in, Flood scenario The optimal or near-optimal bridge group network recovery strategy is as follows. This represents all recovery strategies that satisfy both resource and budget constraints. Select cumulative rewards The most important recovery strategy.

[0089] S6.5, The recovery optimization state vector constructed in step S5 As input to the agent, a set of actionable actions The set of recovery actions As the agent's output action, the reward function constructed in step S6.3 is used as the feedback signal, and a deep reinforcement learning method is used to solve the recovery strategy.

[0090] Constructing the action value function: , in, Let the action value function be... This indicates that in restoring the optimized state vector Execute the set of recovery actions The subsequent action value function value, which represents the expected cumulative reward that can be obtained. These are the parameters of the action value network.

[0091] At each recovery time From the set of actionable actions Select the optimal set of recovery actions at the current moment. : , in, Indicating flood scenario and recovery time The optimal set of recovery actions is determined by the action value function. Indicates the set of possible actions In the process, we search for the value of the action-value function. The recovery action that achieves the maximum value.

[0092] Execute the optimal set of recovery actions Then, according to the state transition function in step S5, we obtain: .

[0093] S6.6 Constructing the target action value function: , in, The value of the target action function. Parameters for the target action value network; To enhance the learning discount factor; This represents the set of possible actions in the next moment. The action value function with the largest value is selected to evaluate the optimal subsequent benefit in the next state.

[0094] Update the action value network parameters by minimizing the action value error. : , in, This is the training loss function.

[0095] After multiple rounds of training or iterative search, the flood scenario was obtained. Optimal recovery strategy : , .

[0096] S6.7, Based on the optimal recovery strategy Determine the repair priority for each bridge-road unit: that is: , in, For the first Bridge-road units in flood scenarios The repair begins at the following time; This indicates the recovery time in the optimal recovery strategy. For the Repairs were carried out on each bridge-road unit; Indicates satisfaction The earliest recovery time.

[0097] This leads to a repair plan for the bridge group network: , in, Flood scenario The restoration plan for the under-bridge network includes bridge-road unit numbering. Repair start time Repair time and repair costs .

[0098] S7. Flood scenario based on the output of step S6 Optimal recovery strategy The optimal set of recovery actions at each time point Repair priorities for each bridge-road unit Repair plan for bridge network The recovery period functional resilience curve, recovery loss index, average functional retention level, recovery time, and regional water resistance resilience comprehensive index of the regional bridge network were calculated during the recovery period.

[0099] Step S7 specifically includes the following steps: S7.1 Repair plan for the bridge group network output in step S6 Within the recovery period The optimal set of recovery actions is executed sequentially at each time step. The bridge capacity reduction factor, the effective capacity of connecting roads, vehicle traffic flow, and truck traffic flow are updated according to the state transition method in step S5.

[0100] At each recovery moment Recalculate and adopt the recovery strategy according to step S4. The subsequent road network system performance index And calculate the corresponding road network functional resilience function: , in, To adopt a recovery strategy Later in the flood situation and time The value of the road network functional resilience function.

[0101] This yields the functional resilience curve during the recovery period, expressed as follows: .

[0102] S7.2 Setting the baseline function level: , in, This indicates the baseline function when there is no flood damage or the target recovery level has been reached.

[0103] Based on the functional resilience curve during the recovery period, the recovery loss index is calculated: , in, The recovery loss index is used to characterize the cumulative functional loss caused by flood damage and the road network function falling below the baseline functional level during the post-disaster recovery process; The positive part function is defined as follows: , in, This indicates the adoption of the optimal recovery strategy. Post-flood scenario Next recovery time The road network functional resilience function value; when hour, ;when hour, Therefore, only when the baseline function level Higher than the actual road network functional resilience function value The difference between the two is only included in the recovery loss when the actual road network functional resilience function value reaches or exceeds the benchmark functional level; the recovery loss at that moment is taken as... .

[0104] S7.3. Calculate the average functional retention level based on the functional resilience curve during the recovery period: , in, Flood scenario The average functionality of the regional bridge network remained at a certain level during the next recovery period.

[0105] S7.4 Based on the target recovery threshold in step S1 Calculate the recovery time required for functional resilience to initially recover to the target recovery threshold. : , in, Set the target recovery threshold; The lower boundary refers to Road network functional resilience function value within the range The first time the target recovery threshold is reached or exceeded The earliest moment.

[0106] If within the recovery period If the target recovery threshold is not reached, then let: , This is used to characterize whether the recovery strategy failed to achieve the target recovery during the evaluation period.

[0107] S7.5 To eliminate the differences in the dimensions of different indicators, three normalized evaluation indicators are constructed respectively: , , , in, This indicates that the average function remains at a level. Indicates the recovery speed level. This indicates the restoration of the loss control level; , and The larger the value, the better the water resistance performance of the corresponding dimension.

[0108] S7.6 To avoid setting weight coefficients arbitrarily, objective weights are determined based on the dispersion of the three normalized evaluation indicators under different flood scenarios, and a decision preference coefficient is introduced for correction.

[0109] For the A normalized evaluation index is used to calculate its application in a set of flood scenarios. Mean of: , in, , Represents a set of flood scenarios The number of flood scenarios.

[0110] Calculate the first The dispersion of each normalized evaluation index: , Among them, dispersion The larger the value, the higher the value. The stronger the ability of a normalized evaluation index to distinguish the water resistance resilience performance under different flood scenarios, the better.

[0111] Based on the average function preservation level preference coefficient in step S1 Recovery speed preference coefficient Recovery loss control preference coefficient And to prevent the smallest positive number of weighted denominator from being zero Calculate the overall evaluation weight: , in, For the first The comprehensive evaluation weight of each normalized evaluation indicator. To prevent extremely small positive numbers with a weighted denominator of zero; Therefore, we can conclude that: , in, , , These correspond to the comprehensive evaluation weights for average functional retention level, recovery speed, and recovery loss control level, respectively.

[0112] S7.7 Calculating Flood Scenarios The following is a comprehensive index of regional water resistance toughness: , in, Flood scenario The following recovery strategy is adopted. The comprehensive index of regional water resistance toughness.

[0113] Taking a typical urban road network in a certain region as the research object, 44 representative bridges were selected to form the research sample, such as... Figure 2 As shown, Figure 2 This is a schematic diagram of the regional bridge network and bridge group zoning. Figure 2In the diagram, large yellow circles represent bridge nodes, small orange circles represent road nodes, solid black lines represent road connections, and dark blue dashed lines delineate bridge group zones. Based on the spatial location of bridge nodes and their connectivity within the regional road network, the study area is divided into western, north-central, core, and southern bridge groups. "Inflow" indicates the inflow boundary and direction of floodwater entering the study area, while "Outflow" indicates the outflow boundary and direction of floodwater leaving the study area, characterizing the hydrological boundary conditions during the regional flood evolution process. The scale bar and north arrow indicate the spatial scale and orientation of the illustrated area, respectively.

[0114] Figure 3 This diagram illustrates the damage to bridges and detour routes for vehicles under the influence of regional flooding. Figure 3 Different colored circular nodes are used to represent the bridge's minor, moderate, severe, and near-failure states, with the bridge's traffic capacity reduction factor also indicated. Used to characterize the degree of damage to the corresponding bridge. The higher the value, the more severe the bridge damage. The blue dashed arrows indicate the alternative routes available to vehicles after the bridge is damaged. Figure 3 This is used to illustrate the spatial distribution of different bridge damage conditions in the regional road network, as well as the impact of bridge damage on existing travel routes and road network connectivity.

[0115] Figure 4 This is a schematic diagram illustrating the change of the road network functional resilience function with recovery time under the optimal recovery strategy. The horizontal axis represents the recovery time, and the vertical axis represents the road network functional resilience function. Each marked point on the curve represents the value of the road network functional resilience function at the corresponding recovery time. to This represents the optimal recovery action selected at each recovery time. As the optimal recovery actions are implemented sequentially, the damaged bridge is gradually repaired, and the road network's functional resilience function gradually improves.

[0116] Figure 5 This diagram illustrates the changes in reward, repair cost, and repair time for the optimal recovery action at different recovery times. The horizontal axis represents the recovery time, the left vertical axis represents the reward function value, and the right vertical axis represents the normalized cost and time value. The bar chart shows the reward function value corresponding to the optimal recovery action at each recovery time; the purple solid line represents the normalized repair cost value, and the blue dashed line represents the normalized repair time value. This diagram illustrates the comprehensive trade-off between reward function value, repair cost, and repair time made by the reinforcement learning model when selecting the optimal recovery action.

[0117] Example 2: An electronic device of the present invention includes a processor and a storage medium; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the restorative analysis method for regional flood-resistant bridge network as described above.

[0118] Example 3: A computer-readable storage medium of the present invention stores a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for restorative analysis of bridge group networks under regional floods with water-resistant resilience.

Claims

1. A method for restorative analysis of bridge network under regional floods with water resistance resilience, characterized in that, Includes the following steps: S1. Obtain basic bridge data, bridge flood resistance failure criteria data, road network data, traffic demand data, flood scenario data, post-disaster repair resource data, recovery optimization parameter data, and water resistance toughness evaluation parameter data for the regional bridge group; S2, For any flood scenario Calculate the representative flood intensity parameters at the bridge site, the representative flood parameters at the abutments and piers, and the corresponding Froude numbers, and construct the bridge. In flood scenarios Flood intensity parameters at the bridge site; S3, Calculate the bridges separately. In flood scenarios The bridge damage status was further determined by the following criteria: scour failure demand ratio, horizontal hydrodynamic instability demand ratio, bridge deck inundation demand ratio, and flood duration demand ratio. The failure probability model was calibrated, and the bridge failure probability and bridge traffic capacity reduction coefficient were calculated. S4. Construct a regional bridge network and map the bridge damage status, bridge failure probability, and bridge capacity reduction factor at the bridge level to the connecting road network level; calculate flood scenarios. and time Effective traffic capacity of connecting roads, traffic flow by vehicle type, road network system performance index, and road network functional resilience function; S5. Determine the flood scenario Given a set of bridge-road units to be repaired, construct a recovery optimization state vector, a set of recovery actions, and a state transition function, and calculate the time consumption of repair actions, the cost consumption of repair actions, and the state transition results; S6. Construct a reward function centered on functional resilience improvement, system performance improvement, repair time, and repair cost; solve the flood scenario under resource and budget constraints. The optimal recovery strategy is determined, and the optimal set of recovery actions at each time point, the repair priority of each bridge-road unit, and the repair plan of the bridge network are output. S7. Calculate the recovery period functional resilience curve, recovery loss index, average functional retention level, recovery time, and comprehensive regional water resistance resilience index of the regional bridge network during the recovery period.

2. The method for restorative analysis of bridge network under regional floods with water resistance resilience as described in claim 1, characterized in that, The bridge foundation data mentioned in step S1 includes the first The location coordinates of the bridge Collection of bridge abutment locations Collection of bridge pier locations Effective burial depth of bridge foundation Pier width Bridge deck clearance height and historical damage repair records The historical damage repair record Including the The bridge was built during a historical flood event. Historical engineering requirements parameters and historical failure markers Among them, historical flood events Indicates the first A sample of floods that have occurred and been recorded. , For the first The number of historical flood events used for bridge failure probability model calibration; each historical flood event Corresponding to a set of historical engineering requirement parameters and historical failure markers The historical engineering requirement parameters include the historical scour failure requirement ratio. Historical level hydrodynamic instability demand ratio The demand for submerging historical bridge surfaces is higher than The demand ratio of the continued impact of historical floods The historical failure marker Used to indicate the first The bridge was built during a historical flood event. Has a failure occurred? The bridge flood control failure criterion data includes the first... Correction factor for the shape of the bridge pier ends Water flow angle of attack correction factor Riverbed condition correction coefficient Bridge abutment type correction factor Correction factor for the angle between the bridge abutment and the water flow Length of water obstruction of bridge abutment drag coefficient Water-facing projection area Lateral resistance of bridges Overturning moment bearing capacity Long-term riverbed scouring and deposition Flood scenario The lower shrinkage scour depth Flood scenario The direction of the dominant water flow Determined water-facing direction correction function The lever arm from the point of application of the horizontal hydrodynamic force to the anti-overturning reference point Reference flood duration Reference flood cumulative impact intensity Duration weighting coefficient Cumulative impact intensity weighting coefficient Damage status determination threshold , , and ; The road network data includes a set of road nodes, intersection nodes, and bridge-related nodes. , by connecting nodes and nodes connecting roads The set of connecting roads , No. Bridges and connecting roads mapping relationship connecting roads Road length Free-flow travel time Design capacity under disaster-free conditions Flow relationship parameters Impedance relationship parameters Connecting roads Truck impedance amplification factor Time weighting coefficient Distance weighting coefficient Economic cost weighting coefficient Baseline system performance index under disaster-free conditions and the benchmark system performance index under extreme failure conditions ; The traffic demand data includes the OD (Original Demand) matrix. Connecting roads Vehicle baseline flow Connecting roads Truck baseline flow Unit vehicle operating cost and unit truck operating costs ; The flood scenario data includes a set of flood scenarios. Flood scenario The underwater depth field Flood scenario The flow field below Flood scenario The direction field of water flow below Flood scenario The duration of the flood Effective flood depth threshold Water density and gravitational acceleration ; The post-disaster recovery resource data includes time data. Available repair resources ,time Available repair budget , No. Repair time of bridge-road unit , No. Repair costs of a bridge-road unit Recovery and optimization time step and recovery period time range ; The recovery optimization parameter data includes repair time normalization parameters. Repair cost normalization parameters Functional resilience enhancement weight System performance improvement weight Repair time penalty weight Repair cost penalty weight Reinforcement learning discount factor Action value network parameters and target action value network parameters ; The water resistance toughness evaluation parameter data includes the target recovery threshold. Average Functional Level Preservation Preference Coefficient Recovery speed preference coefficient Recovery loss control preference coefficient And to prevent the smallest positive number of weighted denominator from being zero .

3. The method for restorative analysis of bridge network under regional floods with water resistance resilience as described in claim 1, characterized in that, Step S2 specifically includes the following steps: S2.1, according to the first The location coordinates of the bridge , will water depth field Flow velocity field and water flow direction field Mapping to the bridge site location yields the bridge site water depth sequence, bridge site flow velocity sequence, and bridge site flow direction sequence: ， ， ， in, For a moment No. The water depth at the bridge For a moment No. The water flow speed at the bridge For a moment No. The direction of water flow at the bridge, and , For any flood scenario The duration of the flood; For the first The location coordinates of the bridge The water depth field at the location; For the first The location coordinates of the bridge The flow velocity field at that location, For the first The location coordinates of the bridge The direction of water flow at the location; Definition of the first The bridge in the flood scene The following is the effective flooding time set : ， in, The effective flood depth threshold; S2.

2. Based on the bridge site water depth sequence, bridge site flow velocity sequence, and bridge site flow direction sequence, calculate the... Representative flood intensity parameters for the bridge: ， ， ， ， ， in, For the maximum water depth at the bridge site, For the maximum flow velocity at the bridge site, To guide the direction of water flow For the effective duration of flooding, This represents the cumulative impact intensity of the flood. This refers to selecting the set of effective flooding times. The maximum value in the following data. This refers to the dominant water flow direction corresponding to the maximum water depth and maximum flow velocity at the bridge site. It refers to length; S2.3, based on the first Collection of bridge abutment locations and the set of locations represented by bridge piers Extract the water depth represented by the abutment, the flow velocity represented by the abutment, the water depth represented by the pier, and the flow velocity represented by the pier. For any representative location point The representative location point is either the abutment representative location point or the pier representative location point, and its water depth sequence is... and flow velocity sequence The maximum water depth and maximum flow velocity within the effective flooding time are respectively taken as the representative water depth of the representative location point. And represents flow rate ,Right now: ， ， Based on the Collection of bridge abutment locations and the set of locations represented by bridge piers Representative flood parameters at the abutments and piers were calculated using the finite set averaging method. ， ， ， ， in, For the first The bridge abutments represent a set of locations. For the first The piers of the bridge represent a set of locations; and These represent the number of points in the corresponding set of locations; Flood scenario The lower part represents the location point. The location represents the water depth; Flood scenario The lower part represents the location point. The representative flow velocity at that location; This represents the water depth at the bridge abutment. This represents the flow velocity at the bridge abutment. This represents the water depth at the bridge pier. This represents the flow velocity at the bridge pier. S2.4 Calculate the flood scenario based on the representative water depth and representative flow velocity at the bridge abutments and piers. Next The bridge abutments of the Froude number And the number of bridge piers by Froude : ， ， S2.5, Constructing the first The bridge in the flood scene Flood intensity parameters : 。 4. The method for restorative analysis of bridge network under regional floods with water resistance resilience as described in claim 1, characterized in that, Step S3 specifically includes the following steps: S3.1, Calculate the first... The bridge in the flood scene Local scour depth of the bridge piers : ， in, The width of the bridge pier. This is a correction factor for the shape of the bridge pier ends. This is the correction factor for the angle of attack of the water flow. This is a correction factor for riverbed conditions; This represents the water depth at the bridge pier. Flood scenario Next Froude number at the piers of the bridge; Calculate the first The bridge in the flood scene Local scour depth of the bridge abutment : ， in, The water depth at the bridge abutment is representative of the water depth. This is a correction factor for the abutment type. This is a correction factor for the angle between the bridge abutment and the water flow. This is the length of the abutment that blocks water. Flood scenario Next Froude numbered the bridge abutments; Based on the The bridge in the flood scene Local scour depth of the bridge piers Local scour depth of bridge abutments Long-term riverbed scouring and deposition and shrinkage scour depth Calculate the total scour depth : ， Further calculation of the scour failure demand ratio: ， in, This indicates the total scour depth relative to the effective burial depth of the bridge foundation. The proportion; S3.2, Based on maximum bridge site flow velocity and the dominant water flow direction and drag coefficient Water-facing projection area and flood scenarios The direction of the dominant water flow Determined water-facing direction correction function Calculate the horizontal hydrodynamic forces generated by floods on bridge piers or superstructure. : ， in, Density of water; Calculate the overturning moment generated by horizontal hydrodynamics : ， in, The lever arm is the distance from the point of application of the horizontal hydrodynamic force to the anti-overturning reference point; Furthermore, the horizontal hydrodynamic instability demand ratio is calculated: ， in, This indicates the horizontal effect of floodwater relative to the lateral resistance of the bridge. and overturning moment bearing capacity The degree of demand; S3.3, Based on the maximum water depth at the bridge site and bridge deck clearance height Calculate the bridge deck inundation demand ratio : ， in, This indicates the degree to which the floodwater level exceeds the clearance height of the bridge deck; when This indicates that the bridge surface has not been flooded. This indicates a risk of bridge flooding or traffic disruption. S3.4, Based on the effective flooding duration and cumulative impact intensity of floods Calculate the demand ratio for the sustained effect of floods : ， in, For duration weighting coefficients, For the first The reference flooding duration for each bridge This is the cumulative impact intensity weighting coefficient. For the first The reference cumulative impact intensity of floods corresponding to each bridge; S3.5, the first The bridge in the flood scene The engineering requirement parameters are defined as follows: ， in, Characterizes the risk of foundation scour failure. Characterizing the risk of horizontal hydrodynamic instability, This indicates the risk of bridge flooding or traffic disruption. Characterizes the risk of prolonged flood action and cumulative impact; S3.6, Based on project requirements parameters Calculate the overall damage demand ratio : ， And determine the threshold based on the damage status. , , and Judgment No. The bridge in the flood scene Damage status of the lower bridge : ， in, , , , and The level of bridge damage; S3.7, Based on historical damage repair records , construct the first Failure probability calibration sample set of bridges : ， in, For historical flood events Next The historical scour failure demand ratio of the bridge For historical flood events Next The historical level of hydrodynamic instability demand ratio of the bridge For historical flood events Next The historical bridge deck of the bridge requires more water to be submerged than... For historical flood events Next The bridge's historical flood resistance and demand ratio For historical flood events Next The bridge's historical failure markers, Indicates invalidity. This indicates that the product is not invalid. A bridge failure probability model was constructed using logistic regression to analyze historical flood events. Next Predicting the failure probability of the bridge: ， in: ， ， in, The first prediction obtained by the bridge failure probability model The bridge during a historical flood event Predicted failure probability of bridges; For constant terms, , , , These are the weighting coefficients corresponding to the historical scour failure demand ratio, the historical horizontal hydrodynamic instability demand ratio, the historical bridge deck inundation demand ratio, and the historical flood continuous effect demand ratio, respectively. Based on failure probability calibration sample set By minimizing historical failure markers Bridge prediction failure probability The cross-entropy loss between the two parameters is used to calibrate the bridge failure probability model. ， in: ， in, For the first The cross-entropy loss function corresponding to each bridge; For the first The number of historical flood events that can be used to calibrate bridge failure probability models; After obtaining the calibrated model parameters , , , and Then, the current flood situation will be discussed. Next Substituting the engineering requirements parameters of the bridge into the bridge failure probability model, the first failure is calculated. The bridge in the current flood situation Predicted failure probability : ， in, , , and These are the current flood scenarios. Next The demand ratios for bridge failure due to scour, horizontal hydrodynamic instability, bridge deck inundation, and continuous flood effects. S3.8, Based on bridge damage status and bridge failure probability Determine the first The bridge in the flood scene Capacity reduction factor ; Specifically, first, based on the state of bridge damage... Determine the basic capacity reduction value: ， Furthermore, considering the bridge failure probability Calculate the first The bridge in the flood scene Bridge capacity reduction factor : ， in, The range of values ​​is ,when This indicates that the bridge's traffic capacity has not been reduced. The time indicates that the bridge-road unit corresponding to the bridge is not passable.

5. The method for restorative analysis of bridge network under regional floods with water resistance resilience according to claim 1, characterized in that, Step S4 specifically includes the following steps: S4.1 Constructing a regional bridge network: ， in, For the regional bridge network, It is a set of road nodes, intersection nodes, and bridge-related nodes. Let be the set of connecting roads, and let any connecting road be denoted as . ,in , Numbering nodes in the road network; Establish the first Bridges and connecting roads Mapping relationship between them: ， Based on the The bridge in the flood scene The bridge capacity reduction factor is used to determine the first bridge. The connecting roads corresponding to the bridge At that time, the bridge capacity reduction factor is mapped to the connecting road capacity reduction factor: ， in, To connect roads In flood scenarios and time The capacity reduction factor for connecting roads is as follows: For the first The bridge in the flood scene and time The bridge capacity reduction factor; Based on the capacity reduction factor of connecting roads Calculate connecting roads In flood scenarios and time Effective traffic capacity of the connecting roads below: ， in, Design capacity for traffic under disaster-free conditions; S4.2, Based on connecting roads Vehicle baseline flow and truck baseline flow Determine the connecting roads benchmark truck ratio : ， And determine the connecting roads benchmark car ratio : ， In flood scenarios and time Below, based on the OD traffic demand matrix Effective traffic capacity of connecting roads Connecting roads benchmark car ratio and connecting roads benchmark truck ratio For regional bridge network Traffic allocation is performed to obtain connecting roads. Traffic flow on the road and truck traffic : ， in, This is a traffic assignment model used to allocate the OD traffic demand matrix to each connecting road in a regional bridge network, while satisfying the conditions of OD traffic demand conservation and connecting road capacity constraints, and outputs the connecting roads. Car and truck traffic on the road; The traffic assignment satisfies the capacity constraints of the connecting roads: ， And satisfy the conservation of OD traffic demand; when At that time, connecting roads Not involved in feasible path allocation; S4.3 Calculate connecting roads Total traffic flow : ， Based on free-flow travel time Total traffic flow and the effective traffic capacity of connecting roads Calculate the foundation impedance of the connecting road : ， in, For flow relationship parameters, These are impedance relationship parameters; Based on truck traffic Truck base flow and the effective traffic capacity of connecting roads Calculate the corrected impedance of the truck : ， in, To connect roads The truck impedance amplification factor; S4.4 Calculating Flood Scenarios and time Total travel time of the road network below : ， S4.5 Calculating Flood Scenarios and time Total travel distance of the road network : ， in, To connect roads The length of the road; S4.6 Calculate additional vehicle operating costs: Based on unit vehicle operating cost Unit truck operating cost and connecting roads Road length Calculate flood scenarios Lower vehicle operating costs : ， Based on vehicle baseline flow and truck baseline flow Calculate the disaster-free baseline vehicle operating cost : ， Calculate additional vehicle operating costs : ， S4.7, Based on total travel time of the road network Total travel distance of the road network and additional vehicle operating costs Calculate flood scenarios and time Road network system performance index : ， in, For time weighting coefficients, This is the distance weighting coefficient. This is the economic cost weighting coefficient; S4.8, Benchmark System Performance Index Based on Disaster-Free Conditions and the benchmark system performance index under extreme failure conditions The performance index of the road network system is normalized to obtain the flood scenario. and time Road network functional resilience function : 。 6. The method for restorative analysis of bridge network under regional floods with water-resistant resilience as described in claim 1, characterized in that, Step S5 specifically includes the following steps: S5.

1. Taking the bridge-road units affected by floods in the regional bridge network as the objects of restoration and optimization, a flood scenario is formed. The following is a collection of bridge-road units to be repaired. : ， in, No. The bridge in the flood scene and time The bridge capacity reduction factor; S5.2, during the recovery period Below, construct a flood scenario. Next moment Recovery optimization state vector : ， in, For the first The bridge in the flood scene and time The bridge capacity reduction factor; Flood scenario and time The connecting road below Effective traffic capacity; To connect roads In flood scenarios and time Traffic flow below; To connect roads In flood scenarios and time Truck traffic below; Flood scenario and time The performance index of the road network system under the following conditions; Flood scenario and time The road network functional resilience function is as follows; For a moment Available repair resources For a moment Available repair budget; S5.3 Define the repair selection of the bridge-road unit to be repaired as a recovery action, and obtain the set of recovery actions. : ， Among them, recovery action , is represented as: ， The set of recovery actions satisfies resource constraints: ， in, For a moment Available repair resources; If budget constraints for repair are taken into account, the set of recovery actions also satisfies: ， in, For the first The cost of repairing a bridge-road unit, For a moment Available repair budget; S5.4, based on the first Repair time of bridge-road unit and repair costs Calculate the set of recovery actions Repair time consumption: ， in, This indicates the time consumption of repair actions when multiple repair tasks are executed in parallel at the current moment; This refers to the set of bridge-road units to be repaired. The maximum value of the data within the parentheses; Calculate the set of recovery actions Cost of repair work: ， in, This indicates the cost of the repair actions consumed by the current set of recovery actions; S5.5, When dealing with the first Repair work was carried out on each bridge-road unit. At that time, the number of repairs completed is updated based on the repair completion rate. Bridge capacity reduction factor for each bridge-road unit; Definition of the first Each bridge-road unit at time Repair completion rate for: ， in, To restore the optimized time step, For the first Repair time for each bridge-road unit; Update the bridge capacity reduction factor: ， in, For the first The bridge in the flood scene and time The bridge capacity reduction factor; S5.6, Based on the updated bridge capacity reduction factor Update connecting roads The capacity reduction factor for connecting roads: ， And update the effective traffic capacity of connecting roads: ， in, To connect roads In flood scenarios and time The effective traffic capacity of the connecting roads below; Based on the updated effective traffic capacity of connecting roads Traffic demand matrix with OD Recalculate vehicle traffic flow in the regional bridge network. and truck traffic And recalculate the road network system performance index. and road network functional resilience function ; S5.

7. Assume that available repair resources and repair costs are uniform during the repair process. For a moment Available repair resources , For a moment Available repair budget, Then based on time Recovery optimization state vector under and recovery action set ,get State transition result at time t : ， ， in, This is the state transition function, used to represent the update process of the bridge-road unit's capacity reduction coefficient, traffic flow assignment, system performance index, and road network functional resilience function due to repair actions.

7. The method for restorative analysis of bridge network under regional floods with water resistance resilience according to claim 1, characterized in that, Step S6 specifically includes the following steps: S6.1, In the flood scenario and recovery time Below, based on the bridge-road unit set to be repaired Constructing a timeframe that satisfies repair resource constraints Set of possible actions : ， in, To restore the action set, For a moment Available repair resources; S6.2 Road network functional resilience function before and after state transition and Calculate and execute the set of recovery actions The resulting increase in single-step functional resilience : ， Performance index of road network system before and after state transition and Calculate the performance improvement of a single-step system. : ， S6.

3. Based on the single-step functional resilience improvement, single-step system performance improvement, repair action time consumption, and repair action cost consumption, construct a reward function: ， in, In order to restore the optimized state Perform recovery actions And transfer to the state transition result The reward value obtained; Increase the weight of functional resilience. To improve system performance, To fix the time penalty weight, Weighting for cost-based penalties; To fix the time normalization parameters, To normalize parameters for repair costs; This is an increase in the resilience of single-step functionality; This represents the performance improvement of a single-step system. To fix the action time consumption, Cost of repair work; in: ， and: ， S6.4, within the recovery period time range Internally, a cumulative reward target for constructing a recovery strategy based on a reward function is defined. : ， in, To enhance the learning discount factor, Flood scenario The following recovery strategy is used to represent the flood scenario. The sequence of repair actions throughout the entire recovery period; the recovery strategy Represented as: ， in, During the recovery period The set of recovery actions selected for repair. During the recovery period The set of recovery actions selected for repair. During the recovery period The set of recovery actions selected for the repair action; The optimization goal of the recovery strategy is: ， in, Flood scenario The optimal or near-optimal bridge group network recovery strategy is as follows. This represents all recovery strategies that satisfy both resource and budget constraints. Select cumulative rewards The most important recovery strategy; S6.5, to recover the optimized state vector As input to the agent, a set of actionable actions The set of recovery actions As the output action of the agent, the reward function is used as the feedback signal, and the recovery strategy is solved by deep reinforcement learning. Constructing the action value function: ， in, Let the action value function be... This indicates that in restoring the optimized state vector Execute the set of recovery actions The subsequent action value function value, which represents the expected cumulative reward that can be obtained. For action value network parameters; At each recovery time From the set of actionable actions Select the optimal set of recovery actions at the current moment. : ， in, Indicating flood scenario and recovery time The optimal set of recovery actions is determined by the action value function. Indicates the set of possible actions In the process, we search for the value of the action-value function. The recovery action that achieves the maximum value; Execute the optimal set of recovery actions Then, according to the state transition function, we get: ， S6.6 Constructing the target action value function: ， in, The value of the target action function. Parameters for the target action value network; To enhance the learning discount factor; This represents the set of possible actions in the next moment. Select the action value function value that is the largest among them; Update the action value network parameters by minimizing the action value error. : ， in, For training the loss function; After multiple rounds of training or iterative search, the flood scenario was obtained. Optimal recovery strategy : ， ， S6.7, Based on the optimal recovery strategy Determine the repair priority for each bridge-road unit, namely: ， in, For the first Bridge-road units in flood scenarios The repair begins at the following time; This indicates the recovery time in the optimal recovery strategy. For the first Repairs were carried out on each bridge-road unit; Indicates satisfaction The earliest recovery time; This leads to a repair plan for the bridge group network: ， in, Flood scenario The restoration plan for the under-bridge network includes bridge-road unit numbering. Repair start time Repair time and repair costs .

8. The method for restorative analysis of bridge network under regional floods with water resistance resilience according to claim 1, characterized in that, Step S7 specifically includes the following steps: S7.1, According to the bridge group network repair plan Within the recovery period The optimal set of recovery actions is executed sequentially at each time step. And update the bridge capacity reduction factor, the effective capacity of connecting roads, vehicle traffic flow, and truck traffic flow; At each recovery moment Recalculate and adopt the recovery strategy The subsequent road network system performance index And calculate the corresponding road network functional resilience function: ， in, To adopt a recovery strategy Later in the flood situation and time The value of the road network functional resilience function; This yields the functional resilience curve during the recovery period, expressed as follows: ， S7.2 Setting the baseline function level : ， Calculate the recovery loss index based on the functional resilience curve during the recovery period. : ， in, The positive part function is defined as follows: ， in, This indicates the adoption of the optimal recovery strategy. Post-flood scenario Next recovery time The road network functional resilience function value; when hour, ;when hour, ; S7.3 Calculate flood scenarios based on the functional resilience curve during the recovery period. The average functional level of the regional bridge network will remain at the following recovery period. : ， S7.4, Based on the target recovery threshold Calculate the recovery time required for functional resilience to initially recover to the target recovery threshold. : ， in, Set the target recovery threshold; The lower boundary refers to Road network functional resilience function value within the range The first time the target recovery threshold is reached or exceeded The earliest moment; If within the recovery period If the target recovery threshold is not reached, then: ， S7.

5. Construct three normalized evaluation indicators respectively: ， ， ， in, This indicates that the average function remains at a level. Indicates the recovery speed level. This indicates the restoration of the loss control level; S7.

6. Determine the objective weights based on the dispersion of the three normalized evaluation indicators under different flood scenarios, and introduce a decision preference coefficient for correction. For the A normalized evaluation index is used to calculate its application in a set of flood scenarios. mean : ， in, , Represents a set of flood scenarios The number of flood scenarios; Calculate the first The dispersion of each normalized evaluation index : ， Based on the average function retention level preference coefficient Recovery speed preference coefficient Recovery loss control preference coefficient And to prevent the smallest positive number of weighted denominator from being zero Calculate the first Comprehensive evaluation weight of each normalized evaluation indicator : ， Therefore, we can conclude that: ， in, , , These correspond to the comprehensive evaluation weights for average functional retention level, recovery speed, and recovery loss control level, respectively. S7.7 Calculating Flood Scenarios The following recovery strategy is adopted. The subsequent regional water resistance toughness comprehensive index : 。 9. An electronic device, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the restorative analysis method for regional flood-resistant bridge network under water-resistance as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the restorative analysis method for regional flood-resistant bridge network under water-resistance as described in any one of claims 1-8.

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