A method, system, device and medium for mathematical modeling of system safety resilience of bridge group scour in a road network

Abstract

The application discloses a kind of road network level bridge group scour system safety resilience mathematical modeling method, system, equipment and medium, the structure parameters of acquisition regional bridge group and climatic hydrology data, construct road network level bridge group scour failure probability model, construct road network level bridge group scour safety risk model, construct road network level bridge group scour safety resilience model, construct road network level bridge group scour safety adaptability reinforcement model, construct bridge group scour system safety resilience multi-objective mathematical model, with road network level bridge group scour safety risk minimization and road network level bridge group scour safety resilience loss minimization as objective function, integrate road network level bridge group scour safety adaptability reinforcement model as constraint condition, and based on NSGA-II algorithm generates Pareto optimal reinforcement scheme.The application establishes the comprehensive modeling method of multilevel, quantifiable, optimizable from scour dynamic evolution to safety resilience recovery.

Description

Technical Field

[0001] This invention belongs to the field of bridge technology, and in particular relates to a mathematical modeling method, equipment and medium for the safety and toughness of road network-level bridge group scour systems. Background Technology

[0002] As a crucial component of transportation networks, regional bridge groups are subject to various natural and anthropogenic factors throughout their lifespan. Bridge failure due to scour can lead to severe socioeconomic losses. With the increasing frequency and intensity of natural disasters such as extreme floods, the scour risk faced by bridges is becoming increasingly serious. Existing research primarily focuses on the scour failure assessment of individual bridges, lacking mathematical modeling methods for the systemic safety and resilience of road network-level bridge groups.

[0003] Resilience is generally defined as the capacity of social units (such as organizations and communities) to withstand, respond to, and recover from disasters, aiming to reduce disruptions to transportation infrastructure and mitigate the scouring impact of future extreme disasters on bridge systems. However, most current research focuses on resilience analysis under single-bridge objectives, failing to effectively consider regional resource constraints and the coupling effects between multiple bridges, leading to conflicts in the practical application of strategies to improve road network-level resilience. Furthermore, existing resilience quantification models mostly rely on static parameters of bridge structures, making it difficult to dynamically reflect the evolution of bridge group resilience during scouring, and thus failing to meet the needs of systemic risk assessment of road network-level bridge groups in real-world scenarios. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a mathematical modeling method for the systematic safety and resilience of road network-level bridge group scour, and to establish a multi-level, quantifiable, and optimizable comprehensive modeling method from the dynamic evolution of scour to the recovery of safety and resilience.

[0005] The second objective of this invention is to provide a mathematical modeling system for the systematic safety and resilience of road network-level bridge group scour.

[0006] A third objective of this invention is to provide an electronic device.

[0007] A fourth objective of this invention is to provide a computer-readable storage medium.

[0008] Technical Solution: To achieve the above objectives, this invention discloses a mathematical modeling method for the systematic safety resilience of road network-level bridge group scour, comprising the following steps:

[0009] (1) Obtain the structural parameters and climate and hydrological data of the regional bridge group. The structural parameters include the bridge foundation burial depth, bridge abutment burial depth, bridge size information, bridge material, location information and network topology information of the bridge in the bridge group. The climate and hydrological data include historical disasters, historical upstream and downstream flow, future climate change trends and future flow change trends.

[0010] (2) Construct a road network-level bridge group scour failure probability model. The road network-level bridge group scour failure probability model is composed of the annual failure probability of individual bridges in the bridge group. First, establish the probability density function of the annual maximum flow rate that conforms to the Pearson Type-III distribution during the entire life of a single bridge. Based on the probability density function, use the improved HEC-18 model to dynamically calculate the scour depth and define the failure condition of exceeding the scour depth limit. Finally, calculate the annual failure probability of a single bridge.

[0011] (3) Construct a road network-level bridge group scour safety risk model. The road network-level bridge group scour safety risk model consists of the road network-level bridge group scour safety risk corresponding to all scour disaster conditions throughout the entire life cycle. The road network-level bridge group scour safety risk corresponding to each scour disaster condition is calculated every year. The loss consequences of the regional bridge group under each scour disaster condition are divided into direct economic loss and indirect economic loss. The direct economic loss is obtained by calculating the cost of clearing debris and the cost of rebuilding the bridge after failure. The indirect economic loss is obtained by calculating the detour time cost and vehicle operation cost based on the road network traffic flow, impedance and linear fitting parameter calibration method.

[0012] (4) Construct a road network-level bridge group scour safety resilience model. The road network-level bridge group scour safety resilience model consists of the safety resilience risk corresponding to all scour disaster conditions throughout the entire life cycle. Combining graph theory methods and road network-level resilience analysis technology, construct a road network-level safety resilience function with a two-dimensional spatiotemporal dimension.

[0013] (5) Construct a road network-level bridge group scour safety adaptive reinforcement model. The road network-level bridge group scour safety adaptive reinforcement model consists of the adaptive reinforcement costs of all bridges corresponding to all scour disaster conditions throughout the entire life cycle. Taking into account budget constraints and the reliability requirements of reinforcement targets, establish a functional expression for the adaptive reinforcement cost of a single bridge in the regional bridge group system, and calculate the scour failure probability of the bridge group under different conditions after active adaptive reinforcement, as well as the road network-level bridge group scour safety risk and the safety toughness risk of the bridge group system after active adaptive reinforcement of the regional bridge group.

[0014] (6) Construct a multi-objective mathematical model of the systematic safety and toughness of bridge group scour. The objective functions are minimizing the safety risk and cost of adaptive reinforcement of the road network-level bridge group after adaptive reinforcement and minimizing the loss of safety and toughness of the road network-level bridge group after adaptive reinforcement. The annual budget cost limit of the adaptive reinforcement model of road network-level bridge group scour safety and the limit of the number of times a single bridge is reinforced during its entire lifespan are integrated as constraints. The Pareto optimal reinforcement scheme is generated based on the NSGA-II algorithm.

[0015] Optionally, step (2) specifically includes the following steps:

[0016] (2.1) Based on the historical disaster data and historical upstream and downstream flows obtained, the historical annual maximum flow sequence of regional bridge groups is statistically analyzed. Calculate the logarithmic sequence The sample moments, mean, variance, and skewness of the logarithmic sequence are expressed as follows: , as well as Based on future climate change trends and future traffic flow trends, we assume the maximum annual traffic flow over the entire lifespan of the regional bridge group. The natural logarithm follows a Pearson Type-III distribution, and the probability density function of the annual maximum flow over the entire lifespan is... Represented as:

[0017] ,

[0018] ,

[0019] in, This indicates the shape parameters of each component bridge in the regional bridge group; The dimensional parameters of the bridge group; Indicates the first The location parameters of the annual bridge cluster are used to reflect the baseline value of the logarithmic flow. Indicates gamma function operation; This indicates the unit flow rate upstream of the bridge;

[0020] The formulas for calculating the relevant parameters of the Pearson Type-III distribution are as follows:

[0021] ,

[0022] ,

[0023] ,

[0024] in, This represents the annual maximum flow reduction rate that takes into account the impact of climate change. The location parameter representing the annual maximum flow under current climatic conditions is calculated using the location information of the bridge group where the bridge is located from the obtained structural parameters. This represents the time interval between year t and the starting year;

[0025] (2.2) For bridges affected by scouring due to extreme hydrological events throughout their entire lifespan, the scouring depth of the bridge. The calculation is performed using the improved HEC-18 model, and the specific calculation formula is as follows:

[0026] ,

[0027] ,

[0028] in Indicates the model error coefficients; The geometric magnification factor represents the water flow and the bridge abutment. The geometric magnification factor is calculated using the obtained structural parameters and bridge size information. Indicates the first Annual upstream flow of the bridge Indicates the first Annual flow rate at the bridge opening, over the entire lifespan and The distribution of traffic flow is determined by the probability of traffic flow distribution throughout the bridge's lifespan. calculate; The depth of the upstream water before scouring;

[0029] (2.3) Define the first The first in the regional bridge group in 2018 The scour failure condition of the bridge is: The scouring depth of the bridge abutment Exceeding the critical scour depth of the bridge Critical scour depth The calculations can be performed using structural parameters including the bridge foundation embedment depth, bridge abutment embedment depth, and bridge material information; therefore, the first... Year Annual failure probability of the bridge Represented as:

[0030] ,

[0031] in Indicates the first The scour depth of the bridge abutment exceeded the critical scour depth of the bridge. The probability of;

[0032] (2.4) Under the trend of climate change, the regional bridge group The year saw scour disaster conditions. The probability of scour failure of road network-level bridge groups is The specific calculation formula is as follows:

[0033] ,

[0034] in This indicates the total number of bridges in the bridge group system.

[0035] Optionally, step (3) specifically includes the following steps:

[0036] (3.1) The safety risk of bridge group scour at the road network level is assessed through a comprehensive cost and risk assessment at the network level. Annual road network-level bridge group scour safety risks The expression is:

[0037] ,

[0038] in, Indicates the number of regional bridge groups The year saw scour disaster conditions. The probability of road network-level bridge group scour failure; This indicates that the bridge group in the area is under scour disaster conditions. The corresponding losses and consequences;

[0039] (3.2) Regional bridge groups under disaster-damaged conditions The corresponding loss consequences Economic losses are divided into direct economic losses and indirect economic losses, and the calculation formula is as follows:

[0040] ,

[0041] in This represents the perception coefficient of indirect economic losses for the regional bridge group. For the first The direct economic losses of the bridge; To flush disaster conditions The corresponding indirect economic losses;

[0042] (3.3) Section The direct economic losses of the bridge The formulas for calculating the costs of clearing debris and rebuilding a bridge after its failure are as follows:

[0043] ,

[0044] in, This represents the cost of clearing debris per unit area of ​​the bridge. This represents the reconstruction cost per unit area of ​​the bridge. Indicates the first The width of the bridge, Indicates the first The length of the bridge;

[0045] (3.4) Scour disaster conditions Corresponding indirect economic losses This refers to the working conditions of scour disasters. Correspondingly, the indirect economic losses incurred by traffic users due to bridge failure and related reconstruction work. Additional travel time loss due to detours or congestion is categorized into two groups. and additional vehicle operating costs ;

[0046] ,

[0047] (3.5) Scour disaster conditions Additional travel time loss due to detours or congestion in the corresponding area of ​​bridges The calculation formula is:

[0048] ,

[0049] in, This represents the value of a traveler's time per unit of time. Indicates the time travelers spend taking detours. Indicates the intersection node Intersection node Connecting roads between them This indicates all bridges connecting roads within the regional road network. , as well as It is calculated using the obtained network topology information; Indicates connecting roads Under scouring disaster conditions The hourly traffic flow. Indicates connecting roads Under scouring disaster conditions The impedance below, Indicates connecting roads Traffic flow under conditions of no damage to the road network Indicates connecting roads Traffic impedance under undamaged road network conditions;

[0050] (3.6) Scour disaster conditions The additional travel time caused by detours or congestion in the corresponding regional bridge complex can be divided into road segment delay time and intersection delay time. Therefore, the connecting roads Under scouring disaster conditions impedance , To connect roads In traffic flow The following section of the road has a delay impedance. To connect roads The delay impedance at the intersection of the front and rear intersection nodes at adjacent entrances;

[0051] Connecting roads In traffic flow The following section delay impedance The calculation formula is:

[0052] ,

[0053] ,

[0054] in, Indicates connecting roads Impedance in free-flow state; Indicates connecting roads Actual throughput capacity in free-flowing conditions; parameters With parameters The survey data was calibrated using actual road network survey data corresponding to the regional bridge group. , , and Parameters are obtained through linear fitting. With parameters The value;

[0055] Connecting roads The delay impedance at the intersection of the preceding and following junction nodes at adjacent approach lanes. The calculation formula is:

[0056] ,

[0057] in, Indicates the intersection node The signal period, It is a junction node The green credit ratio, It is a junction node saturation flow rate;

[0058] (3.7) Under scour disaster conditions Additional vehicle operating costs The calculation formula is:

[0059] ,

[0060] in, This indicates the bridge network under scour disaster conditions. Underpass The detour distance; This indicates the unit cost of a car trip. This indicates the unit trip cost for trucks; This indicates the percentage of traffic flow from trucks;

[0061] (3.8) The calculated safety risk model for the scour of the road network-level bridge group is as follows:

[0062] ,

[0063] In the formula, the scour disaster conditions of road network-level bridges are... The total number is , ; Indicates the starting point of the study; This indicates the full lifespan of the regional bridge group.

[0064] Optionally, step (4) specifically includes the following steps:

[0065] (4.1) Section Annual scour disaster conditions The corresponding safety resilience risks of the bridge group system The expression is:

[0066] ,

[0067] in, Indicates the first Annual scour disaster conditions The corresponding road network-level safety resilience function;

[0068] (4.2) Section Annual scour disaster conditions The expression for the corresponding road network-level safety resilience function is:

[0069] ,

[0070] in, This represents the performance index of the road network-level bridge scour system under normal operating conditions for all bridges; This represents the performance index of the road network-level bridge scour system when all bridges are no longer in operation; road network-level safety and resilience function. The value is in Within the range, the larger the value, the stronger the functionality maintained in the current state; Indicates the first Annual scour disaster conditions The corresponding performance index of the road network-level bridge group scour system;

[0071] (4.3) Section Annual scour disaster conditions Corresponding performance index of road network-level bridge group scour system The calculation formula is:

[0072] ,

[0073] in, Indicates the first Annual scour disaster conditions Corresponding total travel time; Indicates the first Annual scour disaster conditions The corresponding total travel distance; It is a time-related balance factor, measured in units of time; It is a balance factor related to travel distance, measured in units of length;

[0074] ,

[0075] ,

[0076] in, Indicates connecting roads distance, Indicates the first Annual scour disaster conditions Corresponding car traffic volume; Indicates the first Annual scour disaster conditions The corresponding truck traffic volume; Indicates scour disaster conditions Corresponding connecting roads impedance, Indicates scour disaster conditions Corresponding connecting roads Truck impedance;

[0077] (4.4) Scour disaster conditions Corresponding connecting roads Truck resistance The expression is:

[0078] ,

[0079] in, The sensitivity coefficient representing the amplification of the truck's flow rate by impedance; This represents the truck flow rate in its original state. This indicates the sensitivity threshold affecting the road congestion effect; Indicates connecting roads Traffic capacity;

[0080] (4.5) The calculation formula for the scour safety toughness model of road network-level bridge groups is as follows:

[0081] .

[0082] Optionally, step (5) specifically includes the following steps:

[0083] (5.1) Reinforcement using riprap as a scour protection measure; the cost of riprap includes labor costs, transportation costs, and material costs; The first in the regional bridge group system in 2018 Adaptive reinforcement cost of the bridge The function expression is:

[0084] ,

[0085] in, This represents the cost coefficient for adaptive reinforcement; Indicates the target reliability index of the bridge abutment; Indicates the first in the bridge group The bridge is in Reliability indicators when adaptive reinforcement measures are taken annually; For the first Annual basic reinforcement costs;

[0086] A model for scour-resistant adaptive reinforcement of road network-level bridge groups. The calculation formula is:

[0087] ,

[0088] in, Indicates the time period for adaptive reinforcement of regional bridge groups;

[0089] (5.2) Due to the first Bridges to achieve reliability To reinforce the target, therefore the first Year Failure probability of the bridge after adaptive reinforcement Back to the The annual reliability status corresponds to the failure probability as follows: The corresponding mathematical expression is:

[0090] ,

[0091] Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the regional bridge group's first The year saw scour disaster conditions. The probability of scouring failure is The specific calculation formula is as follows:

[0092] ,

[0093] (5.3) Under the trend of climate change, after the regional bridge group actively carries out adaptive reinforcement, the first Annual scour disaster conditions Corresponding road network-level bridge group scour safety risks The expression is:

[0094] ,

[0095] Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the first Annual scour disaster conditions The corresponding safety resilience risks of the bridge group system The expression is:

[0096] .

[0097] Optionally, step (6) specifically includes the following steps:

[0098] (6.1) Based on the road network-level bridge group scour safety adaptive reinforcement model in step (5), construct the constraints of the multi-objective mathematical model. The constraints shall include at least the following: the annual budget cost limit for regional bridge group adaptability and the limit on the number of times a single bridge can be reinforced throughout its lifespan.

[0099] The constraints are expressed as follows:

[0100] ,

[0101] ,

[0102] in, Indicates the first Annual budget pool for road network reinforcement; Denotes the step function, where when hour, Otherwise, it is 0. This indicates the maximum number of reinforcements allowed for a single bridge throughout its entire lifespan;

[0103] (6.2) Based on the constraints, combined with the road network-level bridge group scour safety risk model in step (3), the road network-level bridge group scour safety toughness model in step (4), and the road network-level bridge group scour safety adaptive reinforcement model in step (5.1), after actively carrying out regional bridge group adaptive reinforcement intervention, a multi-objective mathematical model is used to solve for the optimal adaptive reinforcement schedule of the regional bridge group, with the objectives of minimizing the road network-level bridge group scour safety risk in step (5.3), minimizing the adaptive reinforcement cost in step (5.1), and minimizing the road network-level bridge group scour safety toughness loss in step (5.3). The expression of the objective function of the multi-objective mathematical model is:

[0104] Objective 1: Minimize: ,

[0105] Objective 2: Minimize: ,

[0106] (6.3) To constrain individuals that violate the budget or reinforcement limit, a dynamic penalty function mechanism is introduced. A penalty term is added to the objective function to penalize solutions that do not meet the constraints, as shown below:

[0107] ,

[0108] ,

[0109] in, and This is the penalty coefficient, used to control the cost of constraint violation;

[0110] (6.4) The NSGA-II algorithm is used to solve the problem. At the same time, the systemic safety risk, adaptive reinforcement cost and safety toughness risk are minimized. Under budget and reliability constraints, an active adaptive intervention bridge group reinforcement schedule is generated to minimize scour safety and minimize safety toughness loss in the context of regional bridge scour caused by climate change. The bridge group reinforcement schedule includes the bridge reinforcement sequence and the time when the bridges need to be reinforced.

[0111] Based on the same inventive concept, this invention discloses a mathematical modeling system for the systematic safety resilience of road network-level bridge group scour, comprising:

[0112] The data acquisition module is used to acquire the structural parameters and climate and hydrological data of the regional bridge group. The structural parameters include the bridge foundation burial depth, bridge abutment burial depth, bridge size information, bridge materials, the location information of the bridge in the bridge group and network topology information. The climate and hydrological data include historical disasters, historical upstream and downstream flow, future climate change trends and future flow change trends.

[0113] The failure probability model construction module is used to construct a road network-level bridge group scour failure probability model. The road network-level bridge group scour failure probability model is composed of the annual failure probability of individual bridges in the bridge group. First, the probability density function of the annual maximum flow rate conforming to the Pearson Type-III distribution during the entire life of a single bridge is established. Based on the probability density function, the improved HEC-18 model is used to dynamically calculate the scour depth and define the failure condition of exceeding the scour depth limit. Finally, the annual failure probability of a single bridge is calculated.

[0114] The safety risk model construction module is used to construct a road network-level bridge group scour safety risk model. The road network-level bridge group scour safety risk model consists of the road network-level bridge group scour safety risks corresponding to all scour disaster conditions throughout the entire life cycle. It calculates the road network-level bridge group scour safety risk corresponding to each scour disaster condition every year. The loss consequences of the regional bridge group under each scour disaster condition are divided into direct economic losses and indirect economic losses. The direct economic losses are obtained by calculating the cost of clearing debris and rebuilding the bridge after failure. The indirect economic losses are obtained by calculating the detour time cost and vehicle operation cost based on the road network traffic flow, impedance and linear fitting parameter calibration method.

[0115] The safety resilience model construction module is used to construct a road network-level bridge group scour safety resilience model. The road network-level bridge group scour safety resilience model consists of the safety resilience risks corresponding to all scour disaster conditions throughout the entire life cycle. Combining graph theory methods and road network-level resilience analysis technology, a spatiotemporal dual-dimensional road network-level safety resilience function is constructed.

[0116] The reinforcement model construction module is used to construct a road network-level bridge group scour safety adaptive reinforcement model. The road network-level bridge group scour safety adaptive reinforcement model consists of the adaptive reinforcement costs of all bridges corresponding to all scour disaster conditions throughout the entire life cycle. Taking into account budget constraints and the reliability requirements of reinforcement targets, a functional expression for the adaptive reinforcement cost of a single bridge in the regional bridge group system is established. The module also calculates the scour failure probability of the bridge group under different conditions after active adaptive reinforcement, as well as the road network-level bridge group scour safety risk and the safety toughness risk of the bridge group system after active adaptive reinforcement of the regional bridge group.

[0117] The multi-objective mathematical model construction module is used to construct a multi-objective mathematical model of the systemic safety and toughness of bridge group scour. The objective functions are minimizing the scour safety risk and cost of adaptive reinforcement of the road network-level bridge group after adaptive reinforcement, and minimizing the loss of safety and toughness of the road network-level bridge group after adaptive reinforcement. The module integrates the annual budget cost limit of the adaptive reinforcement model for road network-level bridge group scour safety and the limit on the number of reinforcements of a single bridge throughout its life as constraints, and generates the Pareto optimal reinforcement scheme based on the NSGA-II algorithm.

[0118] Optionally, the multi-objective mathematical model construction module specifically comprises:

[0119] Based on the road network-level bridge group scour safety adaptive reinforcement model, the constraints of the multi-objective mathematical model are constructed. The constraints include at least: the annual adaptive budget cost limit of the regional bridge group and the limit on the number of times a single bridge can be reinforced throughout its lifespan.

[0120] The constraints are expressed as follows:

[0121] ,

[0122] ,

[0123] in, Indicates the first Annual budget pool for road network reinforcement; Denotes the step function, where when hour, Otherwise, it is 0. This indicates the maximum number of reinforcements allowed for a single bridge throughout its entire lifespan.

[0124] Based on constraints, and combining a road network-level bridge group scour safety risk model, a road network-level bridge group scour safety toughness model, and a road network-level bridge group scour safety adaptive reinforcement model, a multi-objective mathematical model is used to solve for the optimal adaptive reinforcement schedule for the regional bridge group after proactive regional bridge group adaptive reinforcement intervention. The model aims to minimize the scour safety risk and cost of the road network-level bridge group after adaptive reinforcement, and to minimize the loss of scour safety toughness of the road network-level bridge group after adaptive reinforcement. The expression of the objective function of the multi-objective mathematical model is as follows:

[0125] Objective 1: Minimize: ,

[0126] Objective 2: Minimize: ,

[0127] To constrain individuals that violate budget or reinforcement limits, a dynamic penalty function mechanism is introduced. A penalty term is added to the objective function to penalize solutions that do not meet the constraints, as shown below:

[0128] ,

[0129] ,

[0130] in, and This is the penalty coefficient, used to control the cost of constraint violation;

[0131] The NSGA-II algorithm is used to solve the problem, while minimizing systemic safety risk, adaptive reinforcement cost, and safety resilience risk. Under budget and reliability constraints, a proactive adaptive intervention bridge group reinforcement schedule is generated to minimize scour safety and safety resilience loss in the context of regional bridge scour caused by climate change. The bridge group reinforcement schedule includes the bridge reinforcement sequence and the time when the bridges need to be reinforced.

[0132] Based on the same inventive concept, the present invention provides an electronic device including a processor and a storage medium;

[0133] The storage medium is used to store instructions;

[0134] The processor is configured to operate according to the instructions to perform the steps of the method described above.

[0135] Based on the same inventive concept, the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that the program, when executed by a processor, implements the steps of the method described above.

[0136] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0137] (1) This invention obtains bridge structural parameters and climate and hydrological data, and by constructing a dynamic calculation of scour depth based on the improved HEC-18 model, it realizes the quantification of the full life cycle scour risk of bridge groups under different climate change scenarios, supports the assessment and planning of road network-level scour safety resilience, and provides data-driven basic support for long-term bridge management strategies.

[0138] (2) This invention establishes a scour failure probability model and a safety risk model at the regional bridge group scale, integrating direct economic losses (such as debris clearing and bridge reconstruction) and indirect economic losses (such as detour time costs and operating costs). At the same time, by combining graph theory and spatiotemporal function design, a system-level function decay and recovery mechanism is introduced to quantify the impact of scour on the operational resilience of the entire bridge group system, and for the first time realizes the dual coupling modeling of bridge group scour disaster risk and safety resilience risk;

[0139] (3) This invention proposes a multi-objective mathematical modeling framework with “minimizing disaster risk” and “minimizing safety resilience risk” as objective functions, constructs an optimization constraint system that considers budget constraints and bridge reliability requirements, and uses the improved NSGA-II multi-objective evolutionary algorithm to solve the optimal repair resource allocation strategy; and can output the optimal bridge reinforcement schedule and scheme combination to achieve the optimal improvement of safety resilience of the road network-level bridge group scour system. Attached Figure Description

[0140] Figure 1 This is a schematic diagram of the framework of the present invention;

[0141] Figure 2 This is a schematic diagram illustrating the optimal timing for adaptive repairs of various bridges under the RCP4.5 climate change scenario in this invention.

[0142] Figure 3 This is a comparison chart showing the reduction effect of economic loss risk under whether or not adaptive repairs are implemented for the regional bridge group in this invention. Detailed Implementation

[0143] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0144] Example 1: Taking a typical highway network in a certain region as the research object, seven representative bridges were selected to form a research sample, such as... Figure 1 As shown, this invention discloses a mathematical modeling method for the systematic safety resilience of road network-level bridge group scour, comprising the following steps:

[0145] (1) Obtain the structural parameters and climate and hydrological data of the regional bridge group. The structural parameters include the bridge foundation burial depth, bridge abutment burial depth, bridge size information, bridge material, location information and network topology information of the bridge in the bridge group. The climate and hydrological data include historical disasters, historical upstream and downstream flow, future climate change trends and future flow change trends. Specifically, you can choose to generate flood flow data for the next 80 years based on future climate prediction under the RCP4.5 scenario.

[0146] (2) Construct a road network-level bridge group scour failure probability model. The road network-level bridge group scour failure probability model is composed of the annual failure probability of individual bridges in the bridge group. First, establish the probability density function of the annual maximum flow rate of an individual bridge that conforms to the Pearson Type-III distribution throughout its entire lifespan. Based on the probability density function, use the improved HEC-18 model to dynamically calculate the scour depth and define the failure condition of exceeding the scour depth limit. Finally, calculate the annual failure probability of an individual bridge.

[0147] Step (2) specifically includes the following steps:

[0148] (2.1) Based on the historical disaster data and historical upstream and downstream flows obtained, the historical annual maximum flow sequence of regional bridge groups is statistically analyzed. Calculate the logarithmic sequence The sample moments, mean, variance, and skewness of the logarithmic sequence are expressed as follows: , as well as Based on future climate change trends and future traffic flow trends, we assume the maximum annual traffic flow over the entire lifespan of the regional bridge group. The natural logarithm follows a Pearson Type-III distribution, and the probability density function of the annual maximum flow over the entire lifespan is... Represented as:

[0149] ,

[0150] ,

[0151] in, This indicates the shape parameters of each component bridge in the regional bridge group; The dimensional parameters of the bridge group; Indicates the first The location parameters of the annual bridge cluster are used to reflect the baseline value of the logarithmic flow. Indicates gamma function operation; This indicates the unit flow rate upstream of the bridge;

[0152] The formulas for calculating the relevant parameters of the Pearson Type-III distribution are as follows:

[0153] ,

[0154] ,

[0155] Location parameters used to characterize changes in hydrological conditions Climate and hydrological data obtained through SWAT model, MPI-ESM-LR based low-resolution Earth system model, and statistical downscaling were used to determine The spatiotemporal variation of the position parameters; therefore, the position parameters The calculation formula is: ,in, This represents the annual maximum flow reduction rate that takes into account the impact of climate change. The location parameter representing the annual maximum flow under current climatic conditions is calculated using the location information of the bridge group where the bridge is located from the obtained structural parameters. This represents the time interval between year t and the starting year;

[0156] (2.2) For bridges affected by scouring due to extreme hydrological events throughout their entire lifespan, the scouring depth of the bridge. The calculation is performed using the improved HEC-18 model, and the specific calculation formula is as follows:

[0157] ,

[0158] ,

[0159] in Indicates the model error coefficients; The geometric magnification factor represents the water flow and the bridge abutment. The geometric magnification factor is calculated using the obtained structural parameters and bridge size information. Indicates the first Annual upstream flow of the bridge Indicates the first Annual flow rate at the bridge opening, over the entire lifespan and The distribution of traffic flow is determined by the probability of traffic flow distribution throughout the bridge's lifespan. calculate; The depth of the upstream water before scouring;

[0160] (2.3) Define the first The first in the regional bridge group in 2018 The scour failure condition of the bridge is: The scouring depth of the bridge abutment Exceeding the critical scour depth of the bridge Critical scour depth The calculations can be performed using structural parameters including the bridge foundation embedment depth, bridge abutment embedment depth, and bridge material information; therefore, the first... Year Annual failure probability of the bridge Represented as:

[0161] ,

[0162] in Indicates the first The scour depth of the bridge abutment exceeded the critical scour depth of the bridge. The probability of;

[0163] (2.4) Under the trend of climate change, the regional bridge group The year saw scour disaster conditions. The probability of scour failure of road network-level bridge groups is The specific calculation formula is as follows:

[0164] ,

[0165] in This indicates the total number of bridges in the bridge group system.

[0166] (3) Construct a road network-level bridge group scour safety risk model. The road network-level bridge group scour safety risk model consists of the road network-level bridge group scour safety risks corresponding to all scour disaster conditions throughout the entire lifespan. Among them, the model is based on the regional bridge group's first... The year saw scour disaster conditions. The probability of scour failure of road network-level bridge groups and regional bridge groups under scour disaster conditions The following is the calculation of the corresponding loss consequences. Annual road network-level bridge group scour safety risks, regional bridge groups under scour disaster conditions The corresponding consequences of the loss are divided into direct economic loss and indirect economic loss. Direct economic loss is obtained by calculating the cost of clearing debris and rebuilding the bridge after its failure. Indirect economic loss is obtained by calculating detour time cost and vehicle operating cost based on road network traffic flow, impedance and linear fitting parameter calibration method.

[0167] Step (3) specifically includes the following steps:

[0168] (3.1) The safety risk of bridge group scour at the road network level is assessed through a comprehensive cost and risk assessment at the network level. Annual road network-level bridge group scour safety risks The expression is:

[0169] ,

[0170] in, Indicates the number of regional bridge groups The year saw scour disaster conditions. The probability of road network-level bridge group scour failure; This indicates that the bridge group in the area is under scour disaster conditions. The corresponding losses and consequences;

[0171] (3.2) Regional bridge groups under disaster-damaged conditions The corresponding loss consequences Economic losses are divided into direct economic losses and indirect economic losses, and the calculation formula is as follows:

[0172] ,

[0173] in This represents the perception coefficient of indirect economic losses for the regional bridge group. For the first The direct economic losses of the bridge; To flush disaster conditions The corresponding indirect economic losses;

[0174] (3.3) Section The direct economic losses of the bridge The formulas for calculating the costs of clearing debris and rebuilding a bridge after its failure are as follows:

[0175] ,

[0176] in, This represents the cost of clearing debris per unit area of ​​the bridge. This represents the reconstruction cost per unit area of ​​the bridge. Indicates the first The width of the bridge, Indicates the first The length of the bridge;

[0177] (3.4) Scour disaster conditions Corresponding indirect economic losses This refers to the working conditions of scour disasters. Correspondingly, the indirect economic losses incurred by traffic users due to bridge failure and related reconstruction work. Additional travel time loss due to detours or congestion is categorized into two groups. and additional vehicle operating costs ;

[0178] ,

[0179] (3.5) Scour disaster conditions Additional travel time loss due to detours or congestion in the corresponding area of ​​bridges The calculation formula is:

[0180] ,

[0181] in, This represents the value of a traveler's time per unit of time. Indicates the time travelers spend taking detours. Indicates the intersection node Intersection node Connecting roads between them This indicates all bridges connecting roads within the regional road network. , as well as It is calculated using the obtained network topology information; Indicates connecting roads Under scouring disaster conditions The hourly traffic flow. Indicates connecting roads Under scouring disaster conditions The impedance below, Indicates connecting roads Traffic flow under conditions of no damage to the road network Indicates connecting roads Traffic impedance under undamaged road network conditions;

[0182] (3.6) Scour disaster conditions The additional travel time caused by detours or congestion in the corresponding regional bridge complex can be divided into road segment delay time and intersection delay time. Therefore, the connecting roads Under scouring disaster conditions impedance , To connect roads In traffic flow The following section of the road has a delay impedance. To connect roads The delay impedance at the intersection of the front and rear intersection nodes at adjacent entrances;

[0183] Connecting roads In traffic flow The following section delay impedance The calculation formula is:

[0184] ,

[0185] ,

[0186] in, Indicates connecting roads Impedance in free-flow state; Indicates connecting roads Actual throughput capacity in free-flowing conditions; parameters With parameters The survey data was calibrated using actual road network survey data corresponding to the regional bridge group. , , and Parameters are obtained through linear fitting. With parameters The value.

[0187] Connecting roads The delay impedance at the intersection of the preceding and following junction nodes at adjacent approach lanes. The calculation formula is:

[0188] ,

[0189] in, Indicates the intersection node The signal period, It is a junction node The green light ratio (effective green light time / signal cycle). It is a junction node saturation flow rate;

[0190] (3.7) Under scour disaster conditions Additional vehicle operating costs The calculation formula is:

[0191] ,

[0192] in, This indicates the bridge network under scour disaster conditions. Underpass The detour distance; This indicates the unit cost of a car trip. This indicates the unit trip cost for trucks; This indicates the percentage of traffic flow from trucks;

[0193] (3.8) The calculated safety risk model for the scour of the road network-level bridge group is as follows:

[0194] ,

[0195] In the formula, the scour disaster conditions of road network-level bridges are... The total number is , ; Indicates the starting point of the study; This indicates the full lifespan of the regional bridge group.

[0196] (4) Construct a road network-level bridge group scour safety resilience model. The road network-level bridge group scour safety resilience model consists of the safety resilience risk corresponding to all scour disaster conditions throughout the entire life cycle. Combining graph theory methods and road network-level resilience analysis technology, construct a spatiotemporal dual-dimensional road network-level safety resilience function to quantify the dynamic recovery capability of road network-level functions under different scour disaster conditions.

[0197] Step (4) specifically includes the following steps:

[0198] (4.1) Section Annual scour disaster conditions The corresponding safety resilience risks of the bridge group system The expression is:

[0199] ,

[0200] in, Indicates the first Annual scour disaster conditions The corresponding road network-level safety resilience function;

[0201] (4.2) Section Annual scour disaster conditions The expression for the corresponding road network-level safety resilience function is:

[0202] ,

[0203] in, This represents the performance index of the road network-level bridge scour system under the condition that all bridges are operating normally (the bridge network is fully unobstructed). This represents the performance index of the road network-level bridge scour system when all bridges are out of service (the bridge network is completely paralyzed); road network-level safety resilience function. The value is in Within the range, the larger the value, the stronger the functionality maintained in the current state; Indicates the first Annual scour disaster conditions The corresponding performance index of the road network-level bridge group scour system;

[0204] (4.3) Section Annual scour disaster conditions Corresponding performance index of road network-level bridge group scour system The calculation formula is:

[0205] ,

[0206] in, Indicates the first Annual scour disaster conditions Corresponding total travel time; Indicates the first Annual scour disaster conditions The corresponding total travel distance; It is a time-related balance factor, measured in units of time; It is a balance factor related to travel distance, measured in units of length;

[0207] ,

[0208] ,

[0209] in, Indicates connecting roads distance, Indicates the first Annual scour disaster conditions Corresponding car traffic volume; Indicates the first Annual scour disaster conditions The corresponding truck traffic volume; Indicates scour disaster conditions Corresponding connecting roads impedance, Indicates scour disaster conditions Corresponding connecting roads Truck impedance;

[0210] (4.4) Scour disaster conditions Corresponding connecting roads Truck resistance The expression is:

[0211] ,

[0212] in, The sensitivity coefficient representing the amplification of the truck's flow rate by impedance; This represents the truck flow rate in its original state. This indicates the sensitivity threshold affecting the road congestion effect; Indicates connecting roads Traffic capacity;

[0213] (4.5) The calculation formula for the scour safety toughness model of road network-level bridge groups is as follows:

[0214] .

[0215] (5) Construct a road network-level bridge group scour safety adaptive reinforcement model. The road network-level bridge group scour safety adaptive reinforcement model consists of the adaptive reinforcement costs of all bridges corresponding to all scour disaster conditions throughout the entire life cycle. Taking into account budget constraints and the reliability requirements of reinforcement targets, establish a functional expression for the adaptive reinforcement cost of a single bridge in the regional bridge group system, and calculate the scour failure probability of the bridge group under different conditions after active adaptive reinforcement, as well as the road network-level bridge group scour safety risk and the safety toughness risk of the bridge group system after active adaptive reinforcement of the regional bridge group.

[0216] Step (5) specifically includes the following steps:

[0217] (5.1) Reinforcement using riprap as a scour protection measure; the cost of riprap includes labor costs, transportation costs, and material costs; The first in the regional bridge group system in 2018 Adaptive reinforcement cost of the bridge The function expression is:

[0218] ,

[0219] in, This represents the cost coefficient for adaptive reinforcement; Indicates the target reliability index of the bridge abutment; Indicates the first in the bridge group Reliability indicators when adaptive reinforcement measures are taken for a bridge; For the first Annual basic reinforcement costs;

[0220] A model for scour-resistant adaptive reinforcement of road network-level bridge groups. The calculation formula is:

[0221] ,

[0222] in, Indicates the time period for adaptive reinforcement of regional bridge groups;

[0223] (5.2) Due to the first Bridges to achieve reliability To reinforce the target, therefore the first Year Failure probability of the bridge after adaptive reinforcement Back to the The annual reliability status corresponds to the failure probability as follows: The corresponding mathematical expression is:

[0224] ,

[0225] Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the regional bridge group's first The year saw scour disaster conditions. The probability of scouring failure is The specific calculation formula is as follows:

[0226] ,

[0227] (5.3) Under the trend of climate change, after the regional bridge group actively carries out adaptive reinforcement, the first Annual scour disaster conditions Corresponding road network-level bridge group scour safety risks The expression is:

[0228] ,

[0229] Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the first Annual scour disaster conditions The corresponding safety resilience risks of the bridge group system The expression is:

[0230] .

[0231] (6) Construct a multi-objective mathematical model of the systematic safety and toughness of bridge group scour. The objective functions are minimizing the safety risk and cost of adaptive reinforcement of the road network-level bridge group after adaptive reinforcement and minimizing the loss of safety and toughness of the road network-level bridge group after adaptive reinforcement. The annual budget cost limit of the adaptive reinforcement model of road network-level bridge group scour safety and the limit of the number of times a single bridge is reinforced during its entire lifespan are integrated as constraints. The Pareto optimal reinforcement scheme is generated based on the NSGA-II algorithm.

[0232] Step (6) specifically includes the following steps:

[0233] (6.1) Based on the road network-level bridge group scour safety adaptive reinforcement model in step (5), construct the constraints of the multi-objective mathematical model. The constraints shall include at least the following: the annual budget cost limit for regional bridge group adaptability and the limit on the number of times a single bridge can be reinforced throughout its lifespan.

[0234] The constraints are expressed as follows:

[0235] ,

[0236] ,

[0237] in, Indicates the first Annual budget pool for road network reinforcement; Denotes the step function, where when hour, Otherwise, it is 0. This indicates the maximum number of reinforcements allowed for a single bridge throughout its entire lifespan.

[0238] (6.2) Based on the constraints, combined with the road network-level bridge group scour safety risk model in step (3), the road network-level bridge group scour safety toughness model in step (4), and the road network-level bridge group scour safety adaptive reinforcement model in step (5.1), after actively carrying out regional bridge group adaptive reinforcement intervention, a multi-objective mathematical model is used to solve for the optimal adaptive reinforcement schedule of the regional bridge group, with the objectives of minimizing the road network-level bridge group scour safety risk in step (5.3), minimizing the adaptive reinforcement cost in step (5.1), and minimizing the road network-level bridge group scour safety toughness loss in step (5.3). The expression of the objective function of the multi-objective mathematical model is:

[0239] Objective 1: Minimize: ,

[0240] Objective 2: Minimize: ,

[0241] (6.3) To constrain individuals that violate the budget or reinforcement limit, a dynamic penalty function mechanism is introduced. A penalty term is added to the objective function to penalize solutions that do not meet the constraints, as shown below:

[0242] ,

[0243] ,

[0244] in, and This is the penalty coefficient, used to control the cost of constraint violation;

[0245] (6.4) The NSGA-II algorithm is used for solution, simultaneously minimizing systemic safety risk, adaptive reinforcement cost, and safety resilience risk. Under budget and reliability constraints, a proactive adaptive intervention bridge group reinforcement schedule is generated to minimize scour safety and safety resilience loss under the regional bridge scour scenario caused by climate change. The bridge group reinforcement schedule includes the bridge reinforcement sequence and the time required for reinforcement. The bridge group reinforcement schedule provides a scientific basis for decision-making by transportation infrastructure management departments, such as... Figure 2 and Figure 3 As shown, Figure 3 This is a comparison chart showing the reduction effect of economic loss risk under whether or not adaptive repairs are implemented for the regional bridge group in this invention.

[0246] Example 2: This invention discloses a mathematical modeling system for the systematic safety resilience of road network-level bridge group scour, comprising:

[0247] The data acquisition module is used to acquire structural parameters and climate and hydrological data of the regional bridge group. The structural parameters include the bridge foundation burial depth, bridge abutment burial depth, bridge size information, bridge materials, the location information of the bridge in the bridge group and network topology information. The climate and hydrological data include historical disasters, historical upstream and downstream flow, future climate change trends and future flow change trends.

[0248] The failure probability model construction module is used to construct a road network-level bridge group scour failure probability model. The road network-level bridge group scour failure probability model is composed of the annual failure probability of individual bridges in the bridge group. First, the probability density function of the annual maximum flow rate conforming to the Pearson Type-III distribution during the entire life of a single bridge is established. Based on the probability density function, the improved HEC-18 model is used to dynamically calculate the scour depth and define the failure condition of exceeding the scour depth limit. Finally, the annual failure probability of a single bridge is calculated.

[0249] The failure probability model construction module is specifically as follows:

[0250] Based on historical disaster data and historical upstream and downstream flow patterns, and using historical annual maximum flow sequences from regional bridge cluster statistics, Calculate the logarithmic sequence The sample moments, mean, variance, and skewness of the logarithmic sequence are expressed as follows: , as well as Based on future climate change trends and future traffic flow trends, we assume the maximum annual traffic flow over the entire lifespan of the regional bridge group. The natural logarithm follows a Pearson Type-III distribution, and the probability density function of the annual maximum flow over the entire lifespan is... Represented as:

[0251] ,

[0252] ,

[0253] in, This indicates the shape parameters of each component bridge in the regional bridge group; The dimensional parameters of the bridge group; Indicates the first The location parameters of the annual bridge cluster are used to reflect the baseline value of the logarithmic flow. Indicates gamma function operation; This indicates the unit flow rate upstream of the bridge;

[0254] The formulas for calculating the relevant parameters of the Pearson Type-III distribution are as follows:

[0255] ,

[0256] ,

[0257] Location parameters used to characterize changes in hydrological conditions Climate and hydrological data obtained through SWAT model, MPI-ESM-LR based low-resolution Earth system model, and statistical downscaling were used to determine The spatiotemporal variation of the position parameters; therefore, the position parameters The calculation formula is: ,in, This represents the annual maximum flow reduction rate that takes into account the impact of climate change. The location parameter representing the annual maximum flow under current climatic conditions is calculated using the location information of the bridge group where the bridge is located from the obtained structural parameters. This represents the time interval between year t and the starting year;

[0258] For bridges affected by scouring due to extreme hydrological events throughout their entire lifespan, the scouring depth of the bridge... The calculation is performed using the improved HEC-18 model, and the specific calculation formula is as follows:

[0259] ,

[0260] ,

[0261] in Indicates the model error coefficients; The geometric magnification factor represents the water flow and the bridge abutment. The geometric magnification factor is calculated using the obtained structural parameters and bridge size information. Indicates the first Annual upstream flow of the bridge Indicates the first Annual flow rate at the bridge opening, over the entire lifespan and The distribution of traffic flow is determined by the probability of traffic flow distribution throughout the bridge's lifespan. calculate; The depth of the upstream water before scouring;

[0262] Definition of the first The first in the regional bridge group in 2018 The scour failure condition of the bridge is: The scouring depth of the bridge abutment Exceeding the critical scour depth of the bridge Critical scour depth The calculations can be performed using structural parameters including the bridge foundation embedment depth, bridge abutment embedment depth, and bridge material information; therefore, the first... Year Annual failure probability of the bridge Represented as:

[0263] ,

[0264] in Indicates the first The scour depth of the bridge abutment exceeded the critical scour depth of the bridge. The probability of.

[0265] Under the trend of climate change, the regional bridge group The year saw scour disaster conditions. The probability of scour failure of road network-level bridge groups is The specific calculation formula is as follows:

[0266] ,

[0267] in This indicates the total number of bridges in the bridge group system.

[0268] The safety risk model construction module is used to construct a road network-level bridge group scour safety risk model. The road network-level bridge group scour safety risk model consists of the road network-level bridge group scour safety risks corresponding to all scour disaster conditions throughout the entire life cycle. It calculates the road network-level bridge group scour safety risk corresponding to each scour disaster condition every year. The loss consequences of the regional bridge group under each scour disaster condition are divided into direct economic losses and indirect economic losses. The direct economic losses are obtained by calculating the cost of clearing debris and rebuilding the bridge after failure. The indirect economic losses are obtained by calculating the detour time cost and vehicle operation cost based on the road network traffic flow, impedance, and linear fitting parameter calibration method.

[0269] The security risk model construction module includes the following steps:

[0270] The safety risks of bridge scour at the road network level are assessed through a comprehensive network-level cost and risk assessment. Annual road network-level bridge group scour safety risks The expression is:

[0271] ,

[0272] in, Indicates the number of regional bridge groups The year saw scour disaster conditions. The probability of road network-level bridge group scour failure; This indicates that the bridge group in the area is under scour disaster conditions. The corresponding losses and consequences.

[0273] Regional bridge clusters under disaster-damaged conditions The corresponding loss consequences Economic losses are divided into direct economic losses and indirect economic losses, and the calculation formula is as follows:

[0274] ,

[0275] in This represents the perception coefficient of indirect economic losses for the regional bridge group. For the first The direct economic losses of the bridge; To flush disaster conditions The corresponding indirect economic losses.

[0276] No. The direct economic losses of the bridge The formulas for calculating the costs of clearing debris and rebuilding a bridge after its failure are as follows:

[0277] ,

[0278] in, This represents the cost of clearing debris per unit area of ​​the bridge. This represents the reconstruction cost per unit area of ​​the bridge. Indicates the first The width of the bridge, Indicates the first The length of the bridge.

[0279] Scouring disaster conditions Corresponding indirect economic losses This refers to the working conditions of scour disasters. Correspondingly, the indirect economic losses incurred by traffic users due to bridge failure and related reconstruction work. Additional travel time loss due to detours or congestion is categorized into two groups. and additional vehicle operating costs ;

[0280] ,

[0281] Scouring disaster conditions Additional travel time loss due to detours or congestion in the corresponding area of ​​bridges The calculation formula is:

[0282] ,

[0283] in, This represents the value of a traveler's time per unit of time. Indicates the time travelers spend taking detours. Indicates the intersection node Intersection node Connecting roads between them This indicates all bridges connecting roads within the regional road network. , as well as It is calculated using the obtained network topology information; Indicates connecting roads Under scouring disaster conditions The hourly traffic flow. Indicates connecting roads Under scouring disaster conditions The impedance below, Indicates connecting roads Traffic flow under conditions of no damage to the road network Indicates connecting roads Traffic impedance under undamaged road network conditions.

[0284] Scouring disaster conditions The additional travel time caused by detours or congestion in the corresponding regional bridge complex can be divided into road segment delay time and intersection delay time. Therefore, the connecting roads Under scouring disaster conditions impedance , To connect roads In traffic flow The following section of the road has a delay impedance. To connect roads The delay impedance at the intersection of the front and rear intersection nodes at adjacent entrances;

[0285] Connecting roads In traffic flow The following section delay impedance The calculation formula is:

[0286] ,

[0287] ,

[0288] in, Indicates connecting roads Impedance in free-flow state; Indicates connecting roads Actual throughput capacity in free-flowing conditions; parameters With parameters The survey data was calibrated using actual road network survey data corresponding to the regional bridge group. , , and Parameters are obtained through linear fitting. With parameters The value.

[0289] Connecting roads The delay impedance at the intersection of the preceding and following junction nodes at adjacent approach lanes. The calculation formula is:

[0290] ,

[0291] in, Indicates the intersection node The signal period, It is a junction node The green light ratio (effective green light time / signal cycle). It is a junction node saturation flow rate.

[0292] Under scouring disaster conditions Additional vehicle operating costs The calculation formula is:

[0293] ,

[0294] in, This indicates the bridge network under scour disaster conditions. Underpass The detour distance; This indicates the unit cost of a car trip. This indicates the unit trip cost for trucks; This indicates the percentage of traffic flow from trucks.

[0295] The calculated safety risk model for the scour of the road network-level bridge group is as follows:

[0296] ,

[0297] In the formula, the scour disaster conditions of road network-level bridges are... The total number is , ; Indicates the starting point of the study; This indicates the full lifespan of the regional bridge group.

[0298] The safety resilience model construction module is used to construct a road network-level bridge group scour safety resilience model. The road network-level bridge group scour safety resilience model consists of the safety resilience risks corresponding to all scour disaster conditions throughout the entire life cycle. Combining graph theory methods and road network-level resilience analysis technology, a spatiotemporal dual-dimensional road network-level safety resilience function is constructed.

[0299] The specific modules for building the safety resilience model are as follows:

[0300] No. Annual scour disaster conditions The corresponding safety resilience risks of the bridge group system The expression is:

[0301] ,

[0302] in, Indicates the first Annual scour disaster conditions The corresponding road network-level safety resilience function.

[0303] No. Annual scour disaster conditions The expression for the corresponding road network-level safety resilience function is:

[0304] ,

[0305] in, This represents the performance index of the road network-level bridge scour system under the condition that all bridges are operating normally (the bridge network is fully unobstructed). This represents the performance index of the road network-level bridge scour system when all bridges are out of service (the bridge network is completely paralyzed); road network-level safety resilience function. The value is in Within the range, the larger the value, the stronger the functionality maintained in the current state; Indicates the first Annual scour disaster conditions The corresponding performance index of the road network-level bridge group scour system.

[0306] No. Annual scour disaster conditions Corresponding performance index of road network-level bridge group scour system The calculation formula is:

[0307] ,

[0308] in, Indicates the first Annual scour disaster conditions Corresponding total travel time; Indicates the first Annual scour disaster conditions The corresponding total travel distance; It is a time-related balance factor, measured in units of time; It is a balance factor related to travel distance, measured in units of length;

[0309] ,

[0310] ,

[0311] in, Indicates connecting roads distance, Indicates the first Annual scour disaster conditions Corresponding car traffic volume; Indicates the first Annual scour disaster conditions The corresponding truck traffic volume; Indicates scour disaster conditions Corresponding connecting roads impedance, Indicates scour disaster conditions Corresponding connecting roads Truck resistance.

[0312] Scouring disaster conditions Corresponding connecting roads Truck resistance The expression is:

[0313] ,

[0314] in, The sensitivity coefficient representing the amplification of the truck's flow rate by impedance; This represents the truck flow rate in its original state. This indicates the sensitivity threshold affecting the road congestion effect; Indicates connecting roads Traffic capacity.

[0315] The calculation formula for the scour safety toughness model of road network-level bridge groups is as follows:

[0316] .

[0317] The reinforcement model construction module is used to construct a road network-level bridge group scour safety adaptive reinforcement model. The road network-level bridge group scour safety adaptive reinforcement model consists of the adaptive reinforcement costs of all bridges corresponding to all scour disaster conditions throughout the entire life cycle. Taking into account budget constraints and the reliability requirements of reinforcement targets, a functional expression for the adaptive reinforcement cost of a single bridge in the regional bridge group system is established. The module also calculates the scour failure probability of the bridge group under different conditions after active adaptive reinforcement, as well as the road network-level bridge group scour safety risk and the safety toughness risk of the bridge group system after active adaptive reinforcement of the regional bridge group.

[0318] The reinforcement model construction module is specifically as follows:

[0319] Using riprap as a scour protection measure for reinforcement, the cost of riprap includes labor costs, transportation costs, and material costs; The first in the regional bridge group system in 2018 Adaptive reinforcement cost of the bridge The function expression is:

[0320] ,

[0321] in, This represents the cost coefficient for adaptive reinforcement; Indicates the target reliability index of the bridge abutment; Indicates the first in the bridge group The bridge is in Reliability indicators when adaptive reinforcement measures are taken annually; For the first Annual basic reinforcement costs;

[0322] A model for scour-resistant adaptive reinforcement of road network-level bridge groups. The calculation formula is:

[0323] ,

[0324] in, Indicates the time period for adaptive reinforcement of regional bridge groups;

[0325] Due to the Bridges to achieve reliability To reinforce the target, therefore the first Year Failure probability of the bridge after adaptive reinforcement Back to the The annual reliability status corresponds to the failure probability as follows: The corresponding mathematical expression is:

[0326] ,

[0327] Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the regional bridge group's first The year saw scour disaster conditions. The probability of scouring failure is The specific calculation formula is as follows:

[0328] ,

[0329] Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the first Annual scour disaster conditions Corresponding road network-level bridge group scour safety risks The expression is:

[0330] ,

[0331] Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the first Annual scour disaster conditions The corresponding safety resilience risks of the bridge group system The expression is:

[0332] .

[0333] The multi-objective mathematical model construction module is used to construct a multi-objective mathematical model of the systemic safety and toughness of bridge group scour. The objective functions are minimizing the scour safety risk and cost of adaptive reinforcement of the road network-level bridge group after adaptive reinforcement, and minimizing the loss of safety and toughness of the road network-level bridge group after adaptive reinforcement. The module integrates the annual budget cost limit of the adaptive reinforcement model for road network-level bridge group scour safety and the limit on the number of reinforcements of a single bridge throughout its life as constraints, and generates the Pareto optimal reinforcement scheme based on the NSGA-II algorithm.

[0334] The multi-objective mathematical model construction module is specifically as follows:

[0335] Based on the road network-level bridge group scour safety adaptive reinforcement model, the constraints of the multi-objective mathematical model are constructed. The constraints include at least: the annual adaptive budget cost limit of the regional bridge group and the limit on the number of times a single bridge can be reinforced throughout its lifespan.

[0336] The constraints are expressed as follows:

[0337]

[0338]

[0339] in, Indicates the first Annual budget pool for road network reinforcement; Denotes the step function, where when hour, Otherwise, it is 0. This indicates the maximum number of reinforcements allowed for a single bridge throughout its entire lifespan.

[0340] Based on constraints, and combining a road network-level bridge group scour safety risk model, a road network-level bridge group scour safety toughness model, and a road network-level bridge group scour safety adaptive reinforcement model, a multi-objective mathematical model is used to solve for the optimal adaptive reinforcement schedule for the regional bridge group after proactive regional bridge group adaptive reinforcement intervention. The model aims to minimize the scour safety risk and cost of the road network-level bridge group after adaptive reinforcement, and to minimize the loss of scour safety toughness of the road network-level bridge group after adaptive reinforcement. The expression of the objective function of the multi-objective mathematical model is as follows:

[0341] Objective 1: Minimize: ,

[0342] Objective 2: Minimize: ,

[0343] To constrain individuals that violate budget or reinforcement limits, a dynamic penalty function mechanism is introduced. A penalty term is added to the objective function to penalize solutions that do not meet the constraints, as shown below:

[0344] ,

[0345] ,

[0346] in, and This is the penalty coefficient, used to control the cost of constraint violation;

[0347] The NSGA-II algorithm is used for solution, simultaneously minimizing systemic safety risk, adaptive reinforcement cost, and safety resilience risk. Under budget and reliability constraints, a proactive adaptive intervention bridge group reinforcement schedule is generated to minimize scour safety and safety resilience loss under a regional bridge scour scenario caused by climate change. The bridge group reinforcement schedule includes the bridge reinforcement sequence and the time required for reinforcement. This bridge group reinforcement schedule provides a scientific basis for decision-making by transportation infrastructure management departments, such as... Figure 2 As shown.

[0348] Example 3: An electronic device according to the present invention includes a processor and a storage medium;

[0349] Storage media are used to store instructions;

[0350] The processor is configured to operate according to the instructions to perform the steps of the method described above.

[0351] Example 4: A computer-readable storage medium according to the present invention stores a computer program thereon, which, when executed by a processor, implements the steps of the method described above.

Claims

1. A mathematical modeling method for the systematic safety resilience of bridge group scour at the road network level, characterized in that, Includes the following steps: (1) Obtain the structural parameters and climate and hydrological data of the regional bridge group. The structural parameters include the bridge foundation burial depth, bridge abutment burial depth, bridge size information, bridge material, location information and network topology information of the bridge in the bridge group. The climate and hydrological data include historical disasters, historical upstream and downstream flow, future climate change trends and future flow change trends. (2) Construct a road network-level bridge group scour failure probability model. The road network-level bridge group scour failure probability model is composed of the annual failure probability of individual bridges in the bridge group. First, establish the probability density function of the annual maximum flow rate that conforms to the Pearson Type-III distribution during the entire life of a single bridge. Based on the probability density function, use the improved HEC-18 model to dynamically calculate the scour depth and define the failure condition of exceeding the scour depth limit. Finally, calculate the annual failure probability of a single bridge. (3) Construct a road network-level bridge group scour safety risk model. The road network-level bridge group scour safety risk model consists of the road network-level bridge group scour safety risk corresponding to all scour disaster conditions throughout the entire life cycle. The road network-level bridge group scour safety risk corresponding to each scour disaster condition is calculated every year. The loss consequences of the regional bridge group under each scour disaster condition are divided into direct economic loss and indirect economic loss. The direct economic loss is obtained by calculating the cost of clearing debris and the cost of rebuilding the bridge after failure. The indirect economic loss is obtained by calculating the detour time cost and vehicle operation cost based on the road network traffic flow, impedance and linear fitting parameter calibration method. (4) Construct a road network-level bridge group scour safety resilience model. The road network-level bridge group scour safety resilience model consists of the safety resilience risk corresponding to all scour disaster conditions throughout the entire life cycle. Combining graph theory methods and road network-level resilience analysis technology, construct a road network-level safety resilience function with a two-dimensional spatiotemporal dimension. (5) Construct a road network-level bridge group scour safety adaptive reinforcement model. The road network-level bridge group scour safety adaptive reinforcement model consists of the adaptive reinforcement costs of all bridges corresponding to all scour disaster conditions throughout the entire life cycle. Taking into account budget constraints and the reliability requirements of reinforcement targets, establish a functional expression for the adaptive reinforcement cost of a single bridge in the regional bridge group system, and calculate the scour failure probability of the bridge group under different conditions after active adaptive reinforcement, as well as the road network-level bridge group scour safety risk and the safety toughness risk of the bridge group system after active adaptive reinforcement of the regional bridge group. (6) Construct a multi-objective mathematical model of the systematic safety and toughness of bridge group scour. The objective functions are minimizing the safety risk and cost of adaptive reinforcement of the road network-level bridge group after adaptive reinforcement and minimizing the loss of safety and toughness of the road network-level bridge group after adaptive reinforcement. The annual budget cost limit of the adaptive reinforcement model of road network-level bridge group scour safety and the limit of the number of times a single bridge is reinforced during its entire lifespan are integrated as constraints. The Pareto optimal reinforcement scheme is generated based on the NSGA-II algorithm.

2. The method for mathematical modeling the systematic safety resilience of road network-level bridge group scour according to claim 1, characterized in that: Step (2) specifically includes the following steps: (2.1) Based on the historical disaster data and historical upstream and downstream flows obtained, the historical annual maximum flow sequence of regional bridge groups is statistically analyzed. Calculate the logarithmic sequence The sample moments, mean, variance, and skewness of the logarithmic sequence are expressed as follows: , as well as Based on future climate change trends and future traffic flow trends, we assume the maximum annual traffic flow over the entire lifespan of the regional bridge group. The natural logarithm follows a Pearson Type-III distribution, and the probability density function of the annual maximum flow over the entire lifespan is... Represented as: ， ， in, This indicates the shape parameters of each component bridge in the regional bridge group; The dimensional parameters of the bridge group; Indicates the first The location parameters of the annual bridge cluster are used to reflect the baseline value of the logarithmic flow. Indicates gamma function operation; This indicates the unit flow rate upstream of the bridge; The formulas for calculating the relevant parameters of the Pearson Type-III distribution are as follows: ， ， ， in, This represents the annual maximum flow reduction rate that takes into account the impact of climate change. The location parameter representing the annual maximum flow under current climatic conditions is calculated using the location information of the bridge group where the bridge is located from the obtained structural parameters. This represents the time interval between year t and the starting year; (2.2) For bridges affected by scouring due to extreme hydrological events throughout their entire lifespan, the scouring depth of the bridge. The calculation is performed using the improved HEC-18 model, and the specific calculation formula is as follows: ， ， in Indicates the model error coefficients; The geometric magnification factor represents the water flow and the bridge abutment. The geometric magnification factor is calculated using the obtained structural parameters and bridge size information. Indicates the first Annual upstream flow of the bridge Indicates the first Annual flow rate at the bridge opening, over the entire lifespan and The distribution of traffic flow is determined by the probability of traffic flow distribution throughout the bridge's lifespan. calculate; The depth of the upstream water before scouring; (2.3) Define the first The first in the regional bridge group in 2018 The scour failure condition of the bridge is: The scouring depth of the bridge abutment Exceeding the critical scour depth of the bridge Critical scour depth The calculations can be performed using structural parameters including the bridge foundation embedment depth, bridge abutment embedment depth, and bridge material information; therefore, the first... Year Annual failure probability of the bridge Represented as: ， in Indicates the first The scour depth of the bridge abutment exceeded the critical scour depth of the bridge. The probability of; (2.4) Under the trend of climate change, the regional bridge group The year saw scour disaster conditions. The probability of scour failure of road network-level bridge groups is The specific calculation formula is as follows: ， in This indicates the total number of bridges in the bridge group system.

3. The method for mathematical modeling the systematic safety resilience of a road network-level bridge group scour according to claim 2, characterized in that: Step (3) specifically includes the following steps: (3.1) The safety risk of bridge group scour at the road network level is assessed through a comprehensive cost and risk assessment at the network level. Annual road network-level bridge group scour safety risks The expression is: ， in, Indicates the number of regional bridge groups The year saw scour disaster conditions. The probability of road network-level bridge group scour failure; This indicates that the bridge group in the area is under scour disaster conditions. The corresponding losses and consequences; (3.2) Regional bridge groups under disaster-damaged conditions The corresponding loss consequences Economic losses are divided into direct economic losses and indirect economic losses, and the calculation formula is as follows: ， in This represents the perception coefficient of indirect economic losses for the regional bridge group. For the first The direct economic losses of the bridge; To flush disaster conditions The corresponding indirect economic losses; (3.3) Section The direct economic losses of the bridge The formulas for calculating the costs of clearing debris and rebuilding a bridge after its failure are as follows: ， in, This represents the cost of clearing debris per unit area of ​​the bridge. This represents the reconstruction cost per unit area of ​​the bridge. Indicates the first The width of the bridge, Indicates the first The length of the bridge; (3.4) Scour disaster conditions Corresponding indirect economic losses This refers to the working conditions of scour disasters. Correspondingly, the indirect economic losses incurred by traffic users due to bridge failure and related reconstruction work. Additional travel time loss due to detours or congestion is categorized into two groups. and additional vehicle operating costs ; ， (3.5) Scour disaster conditions Additional travel time loss due to detours or congestion in the corresponding area of ​​bridges The calculation formula is: ， in, This represents the value of a traveler's time per unit of time. Indicates the time travelers spend taking detours. Indicates the intersection node Intersection node Connecting roads between them This indicates all bridges connecting roads within the regional road network. , as well as It is calculated using the obtained network topology information; Indicates connecting roads Under scouring disaster conditions The hourly traffic flow. Indicates connecting roads Under scouring disaster conditions The impedance below, Indicates connecting roads Traffic flow under conditions of no damage to the road network Indicates connecting roads Traffic impedance under undamaged road network conditions; (3.6) Scour disaster conditions The additional travel time caused by detours or congestion in the corresponding regional bridge complex can be divided into road segment delay time and intersection delay time. Therefore, the connecting roads Under scouring disaster conditions impedance , To connect roads In traffic flow The following section of the road has a delay impedance. To connect roads The delay impedance at the intersection of the front and rear intersection nodes at adjacent entrances; Connecting roads In traffic flow The following section delay impedance The calculation formula is: ， ， in, Indicates connecting roads Impedance in free-flow state; Indicates connecting roads Actual throughput capacity in free-flowing conditions; parameters With parameters The survey data was calibrated using actual road network survey data corresponding to the regional bridge group. , , and Parameters are obtained through linear fitting. With parameters The value; Connecting roads The delay impedance at the intersection of the preceding and following junction nodes at adjacent approach lanes. The calculation formula is: ， in, Indicates the intersection node The signal period, It is a junction node The green credit ratio, It is a junction node saturation flow rate; (3.7) Under scour disaster conditions Additional vehicle operating costs The calculation formula is: ， in, This indicates the bridge network under scour disaster conditions. Underpass The detour distance; This indicates the unit cost of a car trip. This indicates the unit trip cost for trucks; This indicates the percentage of traffic flow from trucks; (3.8) The calculated safety risk model for the scour of the road network-level bridge group is as follows: ， In the formula, the scour disaster conditions of road network-level bridges are... The total number is , ; Indicates the starting point of the study; This indicates the full lifespan of the regional bridge group.

4. The method for mathematical modeling the systematic safety resilience of a road network-level bridge group scour according to claim 3, characterized in that: Step (4) specifically includes the following steps: (4.1) Section Annual scour disaster conditions The corresponding safety resilience risks of the bridge group system The expression is: ， in, Indicates the first Annual scour disaster conditions The corresponding road network-level safety resilience function; (4.2) Section Annual scour disaster conditions The expression for the corresponding road network-level safety resilience function is: ， in, This represents the performance index of the road network-level bridge scour system under normal operating conditions for all bridges; This represents the performance index of the road network-level bridge scour system when all bridges are no longer in operation; road network-level safety and resilience function. The value is in Within the range, the larger the value, the stronger the functionality maintained in the current state; Indicates the first Annual scour disaster conditions The corresponding performance index of the road network-level bridge group scour system; (4.3) Section Annual scour disaster conditions Corresponding performance index of road network-level bridge group scour system The calculation formula is: ， in, Indicates the first Annual scour disaster conditions Corresponding total travel time; Indicates the first Annual scour disaster conditions The corresponding total travel distance; It is a time-related balance factor, measured in units of time; It is a balance factor related to travel distance, measured in units of length; ， ， in, Indicates connecting roads distance, Indicates the first Annual scour disaster conditions Corresponding car traffic volume; Indicates the first Annual scour disaster conditions The corresponding truck traffic volume; Indicates scour disaster conditions Corresponding connecting roads impedance, Indicates scour disaster conditions Corresponding connecting roads Truck impedance; (4.4) Scour disaster conditions Corresponding connecting roads Truck resistance The expression is: ， in, The sensitivity coefficient representing the amplification of the truck's flow rate by impedance; This represents the truck flow rate in its original state. This indicates the sensitivity threshold affecting the road congestion effect; Indicates connecting roads Traffic capacity; (4.5) The calculation formula for the scour safety toughness model of road network-level bridge groups is as follows: 。 5. The method for mathematical modeling the systematic safety resilience of a road network-level bridge group scour according to claim 4, characterized in that: Step (5) specifically includes the following steps: (5.1) Reinforcement using riprap as a scour protection measure; the cost of riprap includes labor costs, transportation costs, and material costs; The first in the regional bridge group system in 2018 Adaptive reinforcement cost of the bridge The function expression is: ， in, This represents the cost coefficient for adaptive reinforcement; Indicates the target reliability index of the bridge abutment; Indicates the first in the bridge group The bridge is in Reliability indicators when adaptive reinforcement measures are taken annually; For the first Annual basic reinforcement costs; A model for scour-resistant adaptive reinforcement of road network-level bridge groups. The calculation formula is: ， in, Indicates the time period for adaptive reinforcement of regional bridge groups; (5.2) Due to the first Bridges to achieve reliability To reinforce the target, therefore the first Year Failure probability of the bridge after adaptive reinforcement Back to the The annual reliability status corresponds to the failure probability as follows: The corresponding mathematical expression is: ， Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the regional bridge group's first The year saw scour disaster conditions. The probability of scouring failure is The specific calculation formula is as follows: ， (5.3) Under the trend of climate change, after the regional bridge group actively carries out adaptive reinforcement, the first Annual scour disaster conditions Corresponding road network-level bridge group scour safety risks The expression is: ， Under the trend of climate change, after the regional bridge group proactively carried out adaptive reinforcement, the first Annual scour disaster conditions The corresponding safety resilience risks of the bridge group system The expression is: 。 6. The method for mathematical modeling the systematic safety resilience of a road network-level bridge group scour according to claim 5, characterized in that: Step (6) specifically includes the following steps: (6.1) Based on the road network-level bridge group scour safety adaptive reinforcement model in step (5), construct the constraints of the multi-objective mathematical model. The constraints shall include at least the following: the annual budget cost limit for regional bridge group adaptability and the limit on the number of times a single bridge can be reinforced throughout its lifespan. The constraints are expressed as follows: ， ， in, Indicates the first Annual budget pool for road network reinforcement; Denotes the step function, where when hour, Otherwise, it is 0. This indicates the maximum number of reinforcements allowed for a single bridge throughout its entire lifespan. (6.2) Based on the constraints, combined with the road network-level bridge group scour safety risk model in step (3), the road network-level bridge group scour safety toughness model in step (4), and the road network-level bridge group scour safety adaptive reinforcement model in step (5.1), after actively carrying out regional bridge group adaptive reinforcement intervention, a multi-objective mathematical model is used to solve for the optimal adaptive reinforcement schedule of the regional bridge group, with the objectives of minimizing the road network-level bridge group scour safety risk in step (5.3), minimizing the adaptive reinforcement cost in step (5.1), and minimizing the road network-level bridge group scour safety toughness loss in step (5.3). The expression of the objective function of the multi-objective mathematical model is: Objective 1: Minimize: , Objective 2: Minimize: , (6.3) To constrain individuals that violate the budget or reinforcement limit, a dynamic penalty function mechanism is introduced. A penalty term is added to the objective function to penalize solutions that do not meet the constraints, as shown below: ， ， in, and This is the penalty coefficient, used to control the cost of constraint violation; (6.4) The NSGA-II algorithm is used to solve the problem. At the same time, the systemic safety risk, adaptive reinforcement cost and safety toughness risk are minimized. Under budget and reliability constraints, an active adaptive intervention bridge group reinforcement schedule is generated to minimize scour safety and minimize safety toughness loss in the context of regional bridge scour caused by climate change. The bridge group reinforcement schedule includes the bridge reinforcement sequence and the time when the bridges need to be reinforced.

7. A mathematical modeling system for the systematic safety resilience of a road network-level bridge group scour, characterized in that, include: The data acquisition module is used to acquire the structural parameters and climate and hydrological data of the regional bridge group. The structural parameters include the bridge foundation burial depth, bridge abutment burial depth, bridge size information, bridge materials, the location information of the bridge in the bridge group and network topology information. The climate and hydrological data include historical disasters, historical upstream and downstream flow, future climate change trends and future flow change trends. The failure probability model construction module is used to construct a road network-level bridge group scour failure probability model. The road network-level bridge group scour failure probability model is composed of the annual failure probability of individual bridges in the bridge group. First, the probability density function of the annual maximum flow rate conforming to the Pearson Type-III distribution during the entire life of a single bridge is established. Based on the probability density function, the improved HEC-18 model is used to dynamically calculate the scour depth and define the failure condition of exceeding the scour depth limit. Finally, the annual failure probability of a single bridge is calculated. The safety risk model construction module is used to construct a road network-level bridge group scour safety risk model. The road network-level bridge group scour safety risk model consists of the road network-level bridge group scour safety risks corresponding to all scour disaster conditions throughout the entire life cycle. It calculates the road network-level bridge group scour safety risk corresponding to each scour disaster condition every year. The loss consequences of the regional bridge group under each scour disaster condition are divided into direct economic losses and indirect economic losses. The direct economic losses are obtained by calculating the cost of clearing debris and rebuilding the bridge after failure. The indirect economic losses are obtained by calculating the detour time cost and vehicle operation cost based on the road network traffic flow, impedance and linear fitting parameter calibration method. The safety resilience model construction module is used to construct a road network-level bridge group scour safety resilience model. The road network-level bridge group scour safety resilience model consists of the safety resilience risks corresponding to all scour disaster conditions throughout the entire life cycle. Combining graph theory methods and road network-level resilience analysis technology, a spatiotemporal dual-dimensional road network-level safety resilience function is constructed. The reinforcement model construction module is used to construct a road network-level bridge group scour safety adaptive reinforcement model. The road network-level bridge group scour safety adaptive reinforcement model consists of the adaptive reinforcement costs of all bridges corresponding to all scour disaster conditions throughout the entire life cycle. Taking into account budget constraints and the reliability requirements of reinforcement targets, a functional expression for the adaptive reinforcement cost of a single bridge in the regional bridge group system is established. The module also calculates the scour failure probability of the bridge group under different conditions after active adaptive reinforcement, as well as the road network-level bridge group scour safety risk and the safety toughness risk of the bridge group system after active adaptive reinforcement of the regional bridge group. The multi-objective mathematical model construction module is used to construct a multi-objective mathematical model of the systemic safety and toughness of bridge group scour. The objective functions are minimizing the scour safety risk and cost of adaptive reinforcement of the road network-level bridge group after adaptive reinforcement, and minimizing the loss of safety and toughness of the road network-level bridge group after adaptive reinforcement. The module integrates the annual budget cost limit of the adaptive reinforcement model for road network-level bridge group scour safety and the limit on the number of reinforcements of a single bridge throughout its life as constraints, and generates the Pareto optimal reinforcement scheme based on the NSGA-II algorithm.

8. The mathematical modeling system for the systematic safety and resilience of a road network-level bridge group scour according to claim 7, characterized in that: The multi-objective mathematical model construction module is specifically as follows: Based on the road network-level bridge group scour safety adaptive reinforcement model, the constraints of the multi-objective mathematical model are constructed. The constraints include at least: the annual adaptive budget cost limit of the regional bridge group and the limit on the number of times a single bridge can be reinforced throughout its lifespan. The constraints are expressed as follows: ， ， in, Indicates the first Annual budget pool for road network reinforcement; Denotes the step function, where when hour, Otherwise, it is 0. This indicates the maximum number of reinforcements allowed for a single bridge throughout its entire lifespan. Based on constraints, and combining a road network-level bridge group scour safety risk model, a road network-level bridge group scour safety toughness model, and a road network-level bridge group scour safety adaptive reinforcement model, a multi-objective mathematical model is used to solve for the optimal adaptive reinforcement schedule for the regional bridge group after proactive regional bridge group adaptive reinforcement intervention. The model aims to minimize the scour safety risk and cost of the road network-level bridge group after adaptive reinforcement, and to minimize the loss of scour safety toughness of the road network-level bridge group after adaptive reinforcement. The expression of the objective function of the multi-objective mathematical model is as follows: Objective 1: Minimize: , Objective 2: Minimize: , To constrain individuals that violate budget or reinforcement limits, a dynamic penalty function mechanism is introduced. A penalty term is added to the objective function to penalize solutions that do not meet the constraints, as shown below: ， ， in, and This is the penalty coefficient, used to control the cost of constraint violation; The NSGA-II algorithm is used to solve the problem, while minimizing systemic safety risk, adaptive reinforcement cost, and safety resilience risk. Under budget and reliability constraints, a proactive adaptive intervention bridge group reinforcement schedule is generated to minimize scour safety and safety resilience loss in the context of regional bridge scour caused by climate change. The bridge group reinforcement schedule includes the bridge reinforcement sequence and the time when the bridges need to be reinforced.

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 method according to any one of claims 1 to 6.

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 method according to any one of claims 1 to 6.

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