Road network-level bridge group scouring systematic safety toughness mathematical modeling method, system, equipment and medium

Abstract

The invention discloses a road network level bridge group scouring systematic safety toughness mathematical modeling method, system, equipment and medium, and the method comprises the steps: obtaining the structural parameters and climate hydrological data of a regional bridge group, constructing a road network level bridge group scouring failure probability model, constructing a road network level bridge group scouring safety risk model, and constructing a road network level bridge group scouring safety toughness model. Constructing a road network level bridge group scouring safety adaptability reinforcing model, constructing a bridge group scouring systematic safety toughness multi-objective mathematical model, and integrating the road network level bridge group scouring safety adaptability reinforcing model as constraint conditions by taking road network level bridge group scouring safety risk minimization and road network level bridge group scouring safety toughness loss minimization as objective functions; and a Pareto optimal reinforcement scheme is generated based on an NSGA-II algorithm. According to the method, a multi-level, quantifiable and optimizable comprehensive modeling method for dynamic evolution from scouring to safe toughness recovery is established.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridges, and particularly relates to a road network level bridge group scour systematic safety resilience mathematical modeling method, equipment and medium. BACKGROUND

[0002] As an important part of the traffic network, the regional bridge group will be affected by various natural and human factors during its entire life cycle, and the failure of the bridge due to scour may cause serious social and economic losses. The frequency and intensity of extreme floods and other natural disasters continue to rise, and the scouring risk faced by the bridge is becoming more and more serious. Existing researches mainly focus on the scouring failure evaluation of single-bridge, and lack of mathematical modeling methods for the systematic safety resilience of road network level bridge group.

[0003] Resilience is usually defined as the ability of a social unit (such as an organization or a community) to withstand, respond to and recover from disasters, in order to reduce the disruption of traffic infrastructure operation and mitigate the scouring impact of future extreme disasters on the bridge group system. However, most current researches focus on the resilience analysis under the single-bridge target, and fail to effectively take into account the regional resource constraints and the coupling effects between multiple bridges, resulting in conflicts in the practice of improving the road network level resilience strategy. Moreover, most existing resilience quantification models rely on static parameters of bridge structure, and are difficult to dynamically reflect the evolution process of the resilience of the bridge group during the scouring process, and cannot meet the demand for the systematic risk evaluation of the road network level bridge group in actual scenarios. SUMMARY

[0004] The purpose of the present application is to provide a road network level bridge group scour systematic safety resilience mathematical modeling method, which establishes a multi-level, quantifiable and optimized comprehensive modeling method from the dynamic evolution of scouring to the recovery of safety resilience.

[0005] The second purpose of the present application is to provide a road network level bridge group scour systematic safety resilience mathematical modeling system.

[0006] The third purpose of the present application is to provide an electronic device.

[0007] The fourth purpose of the present application is to provide a computer readable storage medium.

[0008] Technical scheme: In order to achieve the above purpose, the present application discloses a road network level bridge group scour systematic safety resilience mathematical modeling method, comprising the following steps: (1) obtaining the structure parameters and the climatic and hydrological data of the regional bridge group, wherein the structure parameters include the bridge foundation embedding depth, the bridge abutment embedding depth, the bridge size information, the bridge material, the position information in the bridge group and the network topological structure information, and the climatic and hydrological data include the historical disasters, the historical upstream and downstream flow, the future climate change trend and the future flow change trend; (2) Construct a road network level bridge group erosion failure probability model, the road network level bridge group erosion failure probability model is composed of the annual failure probability of a single bridge in the bridge group, first, the probability density function of the annual maximum flow in the whole life cycle of a single bridge conforming to Pearson Type-III distribution is established, the erosion depth is dynamically calculated based on the probability density function using the improved HEC-18 model, and the failure condition of exceeding the limit of the erosion depth is defined, and finally the annual failure probability of a single bridge is calculated; (3) Construct a road network level bridge group erosion safety risk model, the road network level bridge group erosion safety risk model is composed of the road network level bridge group erosion safety risk corresponding to all erosion disaster conditions in the whole life cycle, wherein the road network level bridge group erosion safety risk corresponding to each erosion disaster condition in each year is calculated, the loss consequence of the regional bridge group under each erosion disaster condition is divided into direct economic loss and indirect economic loss, the direct economic loss is obtained by calculating the cost of clearing up the ruins after the bridge failure and the cost of rebuilding the bridge, and 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 erosion safety resilience model, the road network level bridge group erosion safety resilience model is composed of the safety resilience risk corresponding to all erosion disaster conditions in the whole life cycle, a time-space two-dimensional road network level safety resilience function is constructed by combining the graph theory method and the road network level resilience analysis technology; (5) Construct a road network level bridge group erosion safety adaptability reinforcement model, the road network level bridge group erosion safety adaptability reinforcement model is composed of the adaptability reinforcement cost of all bridges corresponding to all erosion disaster conditions in the whole life cycle, the function expression of the adaptability reinforcement cost of a single bridge in the regional bridge group system is established by comprehensively considering the budget constraint and the reliability requirement of the reinforcement target, and the bridge group erosion failure probability under different conditions after active adaptability reinforcement, the road network level bridge group erosion safety risk after active adaptability reinforcement of the regional bridge group, and the safety resilience risk of the bridge group system are calculated; (6) Construct a bridge group erosion systematic safety resilience multi-objective mathematical model, the minimum adaptability reinforcement cost of the road network level bridge group erosion safety risk after adaptability reinforcement and the minimum adaptability reinforcement cost of the road network level bridge group erosion safety resilience loss after adaptability reinforcement are taken as the objective functions, the annual budget cost limit of the road network level bridge group erosion safety adaptability reinforcement model and the reinforcement frequency limit of a single bridge in the whole life cycle are integrated as constraint conditions, and the Pareto optimal reinforcement scheme is generated based on the NSGA-II algorithm.

[0009] Optionally, the step (2) specifically comprises the following steps: (2.1) Based on the historical annual maximum flow sequence of the regional bridge group statistics , the logarithmic sequence The mean, variance and skewness of the log series are denoted as , and respectively. By the future climate change trend and the future flow change trend, it is assumed that the natural logarithm of the annual maximum flow of the regional bridge group in the whole life cycle obeys the Pearson Type-III distribution, and the probability density function of the annual maximum flow in the whole life cycle is denoted as: , , wherein denotes the shape parameter of each component bridge in the regional bridge group; denotes the scale parameter of the group bridge; denotes the location parameter of the group bridge in the year, which is used to reflect the baseline value of the log flow; denotes the gamma function operation; denotes the unit flow upstream of the bridge; wherein the calculation formulae of the related parameters of the Pearson Type-III distribution are as follows: , , , wherein denotes the reduction rate of the annual maximum flow considering the influence of climate change, denotes the location parameter of the annual maximum flow under the current climate condition, which is calculated by the position information of the bridge in the bridge group in the obtained structural parameters; denotes the time interval between the (2.2) For the bridge affected by scour caused by extreme hydrological events in the whole life cycle, the scour depth of the bridge is calculated by the improved HEC-18 model, and the specific calculation formula is as follows: , , wherein denotes the model error coefficient; denotes the geometric amplification factor of the water flow and the abutment, which is calculated by the bridge size information obtained from the structural parameters; denotes the flow upstream of the bridge in the year, denotes the unit flow at the bridge hole in the year, and and ​The probability of flow distribution over the entire life of the bridge calculate; is the upstream water depth before scour; (2.3) Define No. 1 among regional bridge groups in 2018 The scour failure conditions of the bridge are: Scour depth of bridge abutments per year Exceeding the critical scour depth of the bridge , critical scour depth The structural parameters that can be obtained include the buried depth of the bridge foundation, the buried depth of the bridge abutment and the information of the bridge material; Year Annual failure probability of a bridge Expressed as: , in Indicates the The scour depth of the bridge abutment exceeds the critical scour depth of the bridge probability; (2.4) Under the trend of climate change, the regional bridge group Scour disaster conditions occurred each year The probability of scour failure of the network-level bridge group is , the specific calculation formula is: , in Indicates the total number of bridges in the bridge group system.

[0010] Optionally, step (3) specifically includes the following steps: (3.1) The scour safety risk of bridge groups at the road network level is assessed through comprehensive network-level cost risk assessment. Safety risk of scour of road network-level bridge groups The expression is: , in, Indicates the regional bridge group Scour disaster conditions occurred each year The probability of scour failure of a network-level bridge group; Indicates that the bridges in the area are in scour disaster conditions the corresponding loss consequences; (3.2) Regional bridge groups in disaster damage conditions The corresponding loss consequences It is divided into direct economic losses and indirect economic losses, and the calculation formula is: , in It represents the perception coefficient of indirect economic losses of regional bridge groups; For the Direct economic losses caused by the bridge; For scour disaster conditions corresponding indirect economic losses; (3.3) Section Direct economic losses from bridge construction is the cost of clearing the debris after the bridge fails and the cost of rebuilding the bridge, and the calculation formula is: , in, represents the cost of clearing debris per unit area of ​​the bridge, represents the reconstruction cost per unit area of ​​the bridge, Indicates the The width of the bridge, Indicates the Length of the bridge; (3.4) Scour disaster conditions Corresponding indirect economic losses refers to the scour disaster condition The corresponding economic impact on traffic users during the bridge failure and related reconstruction work, indirect economic losses Divided into additional travel time loss due to detours or congestion and additional vehicle operating costs ; , (3.5) Scour disaster conditions Additional travel time loss due to detours or congestion in the corresponding regional bridge groups The calculation formula is: , in, represents the traveler’s unit time value, Indicates the time the traveler takes to detour. Indicates the intersection node and intersection nodes The connecting roads between Represents all bridge-connected roads between regional road networks, 、 as well as Calculated by using the acquired network topology information; Indicates connecting roads In scour disaster conditions The hourly traffic volume, Indicates connecting roads Impedance of connecting road under flood disaster working condition , Impedance of connecting road under free flow condition , Impedance of connecting road under free flow condition , Impedance of connecting road under free flow condition , Impedance of connecting road under flood disaster working condition , , Impedance of connecting road under free flow condition , Impedance of connecting road under free flow condition , Impedance of connecting road under free flow condition , Impedance of connecting road under free flow condition , Impedance of connecting road under free flow condition , , , , , Impedance of connecting road under free flow condition , Actual capacity of connecting road under free flow condition , , , , , , , , Impedance of connecting road under free flow condition , Impedance of connecting road under free flow condition , , , , Signal cycle of intersection node , Green ratio of intersection node , Saturation flow rate of intersection node , (3.7) In the case of scour disaster Additional vehicle operating costs The calculation formula is: , in, Indicates that the bridge network is in scour disaster condition Lower connecting road detour distance; represents the unit travel cost of the car; represents the unit travel cost of the truck; represents the traffic proportion of trucks; The network-level bridge group scour safety risk model constructed in (3.8) is calculated as follows: , In the formula, the road network level bridge scour disaster condition The total number is , ; Indicates the starting time point of the study; Represents the entire life of the regional bridge group.

[0011] Optionally, step (4) specifically includes the following steps: (4.1) Section Annual scour disaster conditions Corresponding safety and resilience risks of the bridge group system The expression is: , in, Indicates the Annual scour disaster conditions Corresponding road network-level safety resilience function; (4.2) Section Annual scour disaster conditions The corresponding network-level security resilience function expression is: , in, It represents the performance index of the bridge scour system at the network level under normal operation of all bridges; Represents the performance index of the bridge group scour system at the road network level under the condition that all bridges are out of service; the road network level safety resilience function The value is Within the range, a larger value indicates a stronger functionality maintained in the current state; Indicates the Annual scour disaster conditions The corresponding road network-level bridge group scour system performance index; (4.3) The year scour disaster working condition corresponding road network level bridge group scour system performance index The calculation formula is: , Among them, represents the total travel time corresponding to the year scour disaster working condition ; represents the total travel distance corresponding to the year scour disaster working condition ; is a time-dependent balancing factor, measured in time units; is a travel distance-dependent balancing factor, measured in length units; , , Among them, represents the distance between roads , represents the automobile trip volume corresponding to the year scour disaster working condition ; represents the truck trip volume corresponding to the year scour disaster working condition ; represents the impedance of the connecting road corresponding to the scour disaster working condition ; represents the truck impedance of the connecting road corresponding to the scour disaster working condition ; (4.4) The expression of the truck impedance of the connecting road corresponding to the scour disaster working condition is: , Among them, represents the sensitivity coefficient of the amplification strength of the truck flow to the impedance; represents the truck flow in the original state; represents the sensitivity threshold affecting the road congestion effect; represents the traffic capacity of the connecting road ; (4.5) The calculation formula of the road network level bridge group scour safety resilience model is: .

[0012] ​​Optionally, step (5) specifically includes the following steps: (5.1) The cost of riprap as a scour protection measure includes labor cost, transportation cost and material cost; The first regional bridge group system Adaptive reinforcement cost of bridge The function expression is: , in, represents the cost coefficient of adaptive reinforcement; represents the target reliability index of the abutment; Indicates the bridge group The bridge is in Reliability index when adaptive reinforcement measures are taken in the year; For the Annual foundation reinforcement cost; Adaptive reinforcement model for scour safety of bridge groups at the road network level The calculation formula is: , in, Indicates the time period for adaptive reinforcement of regional bridge groups; (5.2) Due to Bridge bridge to achieve reliability To strengthen the goal, Year Failure probability of a bridge after adaptive reinforcement Back to The state of annual reliability, the corresponding failure probability is , the corresponding mathematical expression is: , Under the trend of climate change, after the regional bridge group actively carried out adaptive reinforcement, the regional bridge group Scour disaster conditions occurred each year The probability of scour failure is , the specific calculation formula is: , (5.3) Under the trend of climate change, after the regional bridge groups actively carry out adaptive reinforcement, the 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 groups actively carried out adaptive reinforcement, the Annual scour disaster conditions Corresponding safety and resilience risks of the bridge group system The expression is: .

[0013] Optionally, step (6) specifically includes the following steps: (6.1) Based on the network-level bridge group scour safety adaptive reinforcement model in step (5), construct the constraints of the multi-objective mathematical model. The constraints include at least: the annual adaptive budget cost limit of the regional bridge group and the number of reinforcement times of a single bridge during its entire life cycle; The constraints are expressed as follows: , , in, Indicates the Annual budget pool for road network reinforcement; represents a step function, where hour, , otherwise 0, It represents the maximum number of reinforcements allowed for a single bridge during its entire lifespan; (6.2) Based on the constraints, combined with the network-level bridge group scour safety risk model of step (3), the network-level bridge group scour safety resilience model of step (4), and the network-level bridge group scour safety adaptive reinforcement model of step (5.1), after proactively conducting adaptive reinforcement intervention for regional bridge groups, a multi-objective mathematical model with the goals of minimizing the network-level bridge group scour safety risk of step (5.3) and the adaptive reinforcement cost of step (5.1) and minimizing the network-level bridge group scour safety resilience loss of step (5.3) is used to solve the optimal adaptive reinforcement schedule for regional bridge groups. The objective function of the multi-objective mathematical model is expressed as: Goal 1: Minimize: , Goal 2: Minimize: , (6.3) In order 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. The specific expression is as follows: , , in, and is the penalty coefficient, which is used to control the cost of constraint violation; (6.4) solving by using NSGA-II algorithm, while minimizing systematic safety risk, adaptive reinforcement cost and safety resilience risk, generating the active adaptive intervention bridge group reinforcement schedule under the regional bridge scour situation caused by climate change, which minimizes the scour safety and minimizes the safety resilience loss of the bridge group reinforcement schedule under the budget and reliability constraints, including the bridge reinforcement sequence and the time when the bridge needs to be reinforced.

[0014] Based on the same inventive concept, the application discloses a road network level bridge group scour systematic safety resilience mathematical modeling system, comprising: A data acquisition module is configured to acquire structural parameters of a regional bridge group and climatic and hydrological data, wherein the structural parameters include bridge foundation embedding depth, bridge abutment embedding depth, bridge size information, bridge material, position information in the bridge group, and network topology structure information, and the climatic and hydrological data include historical disasters, historical upstream and downstream flow, future climate change trend, and future flow change trend. A failure probability model construction module is configured to construct a road network level bridge group scour failure probability model, wherein the road network level bridge group scour failure probability model is composed of annual failure probabilities of single bridges in the bridge group, a probability density function of annual maximum flow in the whole life cycle of a single bridge conforming to Pearson Type-III distribution is first established, the scour depth is dynamically calculated based on the probability density function by using an improved HEC-18 model, and a failure condition of exceeding the scour depth is defined, and finally the annual failure probability of the single bridge is calculated. A safety risk model construction module is configured to construct a road network level bridge group scour safety risk model, wherein the road network level bridge group scour safety risk model is composed of road network level bridge group scour safety risks corresponding to all scour disaster working conditions in the whole life cycle, wherein the road network level bridge group scour safety risk corresponding to each scour disaster working condition each year is calculated, the loss consequences of the regional bridge group under each scour disaster working condition are divided into direct economic loss and indirect economic loss, the direct economic loss is obtained by calculating the cost of clearing up the ruins after the bridge failure and the cost of rebuilding the bridge, and 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. A safety resilience model construction module is configured to construct a road network level bridge group scour safety resilience model, wherein the road network level bridge group scour safety resilience model is composed of safety resilience risks corresponding to all scour disaster working conditions in the whole life cycle, and a space-time two-dimensional road network level safety resilience function is constructed by combining a graph theory method and a road network level resilience analysis technology. The reinforcement model construction module is used to construct a network-level bridge group scour safety adaptive reinforcement model. The 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 the budget constraints and the reliability requirements of the reinforcement target, 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 working conditions after active adaptive reinforcement, as well as the network-level bridge group scour safety risk and the safety resilience 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 for the systematic safety and resilience of bridge groups under scour conditions. The objective functions are to minimize the scour safety risk and adaptive reinforcement cost of the road network-level bridge group after adaptive reinforcement, and to minimize the loss of scour safety resilience of the road network-level bridge group after adaptive reinforcement. The annual budget cost limit of the road network-level bridge group scour safety adaptive reinforcement model and the limit on the number of reinforcements for a single bridge during its entire life cycle are integrated as constraints, and a Pareto optimal reinforcement plan is generated based on the NSGA-II algorithm.

[0015] Optionally, the multi-objective mathematical model construction module is specifically: 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 number of reinforcement times of a single bridge during its entire life cycle; The constraints are expressed as follows: , , in, Indicates the Annual budget pool for road network reinforcement; represents a step function, where hour, , otherwise 0, It represents the maximum number of reinforcement times allowed for a single bridge during its entire life cycle; Based on the constraints, combined with the network-level bridge group scour safety risk model, the network-level bridge group scour safety resilience model, and the network-level bridge group scour safety adaptive reinforcement model, after proactively carrying out adaptive reinforcement intervention for regional bridge groups, a multi-objective mathematical model was developed with the goals of minimizing the scour safety risk and adaptive reinforcement cost of the network-level bridge group after adaptive reinforcement, as well as minimizing the scour safety resilience loss of the network-level bridge group after adaptive reinforcement. This model was used to solve the optimal adaptive reinforcement schedule for the regional bridge group. The objective function of the multi-objective mathematical model is expressed as follows: Goal 1: Minimize: , Goal 2: Minimize: , To constrain the individual who violates the budget or the reinforcement frequency limit, a dynamic penalty function mechanism is introduced, and a penalty term is added to the objective function to punish the solution that does not meet the constraint, which is specifically expressed as follows: , , Wherein, And Penalty coefficient, used to control the cost brought by constraint violation; NSGA-II algorithm is used for solving, while minimizing systematic safety risk, adaptive reinforcement cost and safety resilience risk, under the constraints of budget and reliability, the active adaptive intervention bridge group reinforcement schedule minimizing the erosion safety and minimizing the safety resilience loss under the regional bridge erosion situation caused by climate change is generated, and the bridge group reinforcement schedule includes bridge reinforcement sequence and time when the bridge needs to be reinforced.

[0016] Based on the same inventive concept, the electronic device of the application comprises a processor and a storage medium; The storage medium is used for storing instructions; The processor is used for operating according to the instructions to perform the steps of the method as described above.

[0017] Based on the same inventive concept, the computer readable storage medium of the application has a computer program stored thereon, characterized in that the program is executed by the processor to realize the steps of the method as described above.

[0018] Advantages: compared with the prior art, the application has the following remarkable advantages: (1) The bridge structure parameters and climate hydrological data are obtained, the dynamic calculation erosion depth based on the improved HEC-18 model is constructed, the full life cycle erosion risk quantification of the bridge group under different climate change scenarios is realized, the erosion safety resilience evaluation and planning at the road network level are supported, and data-driven basis support is provided for long-term bridge management strategy; (2) The erosion failure probability model and the safety risk model are established at the regional bridge group scale, the direct economic loss (such as debris cleaning and bridge reconstruction) and the indirect economic loss (such as detour time cost and operation cost) are integrated. At the same time, combined with the design of graph theory and space function function, the system level function attenuation and recovery mechanism is introduced, the influence of erosion on the operation resilience of the whole bridge group system is quantified, and the double coupling modeling of bridge group erosion disaster risk and safety resilience risk is realized for the first time; (3) The application proposes a multi-objective mathematical modeling framework with "minimizing disaster damage risk" and "minimizing safety resilience risk" as objective functions, constructs an optimization constraint system considering budget constraints and bridge reliability requirements, uses an 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 realize the optimization of the safety resilience of the bridge group erosion system at the road network level. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 is a schematic diagram of the framework of the application; Figure 2 is a schematic diagram of the optimal time arrangement of adaptive repair of each bridge in the RCP4.5 climate change scenario in the application; Figure 3 is a comparison chart of the economic loss risk reduction effect corresponding to whether adaptive repair is implemented for the regional bridge group in the application. DETAILED DESCRIPTION

[0020] The technical solutions of the application will be further described below with reference to the drawings.

[0021] Example 1: Taking a typical highway road network in a certain region as the research object, 7 representative bridges in the highway road network are selected to form the research sample, as shown in Figure 1 The application discloses a road network level bridge group erosion system safety resilience mathematical modeling method, comprising the following steps: (1) Obtain the structure parameters and climate and hydrology data of the regional bridge group, the structure parameters include the bridge foundation embedding depth, the bridge abutment embedding depth, the bridge size information, the bridge material, the position information in the bridge group and the network topology structure information, and the climate and hydrology data include historical disasters, historical upstream and downstream flow, future climate change trend and future flow change trend; specifically, future climate prediction based on the RCP4.5 scenario can be selected to generate flood flow data for 80 years in the future.

[0022] (2) Construct a road network level bridge group erosion failure probability model, the road network level bridge group erosion failure probability model is composed of the annual failure probability of a single bridge in the bridge group, first, the probability density function of the annual maximum flow in the whole life cycle of a single bridge conforming to the Pearson Type-III distribution is established, the improved HEC-18 model is used to dynamically calculate the erosion depth based on the probability density function, and the failure condition of the erosion depth exceeding the limit is defined, and finally the annual failure probability of a single bridge is calculated.

[0023] Step (2) specifically comprises the following steps: (2.1) Based on the historical annual maximum flow sequence of the regional bridge group statistics, the Pearson Type-III distribution is fitted to the historical annual maximum flow sequence, and the Pearson Type-III distribution parameters are obtained. , calculate the logarithmic sequence The sample moments of the logarithmic series, the mean, variance and skewness are expressed as 、 as well as Based on the future climate change trend and the future flow change trend, it is assumed that the annual maximum flow of the regional bridge group during its entire lifespan The natural logarithm of follows the Pearson Type-III distribution, and the probability density function of the annual maximum flow rate over the entire life cycle is Expressed as: , , in, Represents the shape parameters of each bridge in the regional bridge group; represents the scale parameter of the bridge group; Indicates the The location parameters of the annual group bridges are used to reflect the baseline value of logarithmic flow; Represents the gamma function operation; represents the unit flow upstream of the bridge; The calculation formulas for the relevant parameters of the Pearson Type-III distribution are: , , Location parameters used to characterize changes in hydrological conditions The SWAT model, the climate and hydrological data obtained based on the low-resolution Earth system model MPI-ESM-LR and statistical downscaling were used to determine The spatial and temporal variation of the location parameter The calculation formula is: ,in, represents the annual maximum flow reduction rate considering the impact of climate change, The location parameter representing the annual maximum flow under current climate conditions is calculated using the location information of the bridge in the bridge group obtained from the structural parameters; represents the time interval between the tth year and the starting year; (2.2) For bridges affected by scour caused by extreme hydrological events during their lifespan, the scour depth of the bridge The improved HEC-18 model is used for calculation, and the specific calculation formula is: , , in represents the model error coefficient; The geometric magnification factor of the water flow and the abutment is calculated by the obtained structural parameter bridge size information; Indicates the Annual bridge upstream flow, Indicates the Unit flow at the bridge hole in the year, during the entire life and The probability of flow distribution over the entire life of the bridge calculate; is the upstream water depth before scour; (2.3) Define No. 1 among regional bridge groups in 2018 The scour failure conditions of the bridge are: Scour depth of bridge abutments per year Exceeding the critical scour depth of the bridge , critical scour depth The structural parameters that can be obtained include the buried depth of the bridge foundation, the buried depth of the bridge abutment and the information of the bridge material; Year Annual failure probability of bridges Expressed as: , in Indicates the The scour depth of the bridge abutment exceeds the critical scour depth of the bridge probability; (2.4) Under the trend of climate change, the regional bridge group Scour disaster conditions occurred each year The probability of scour failure of the network-level bridge group is , the specific calculation formula is: , in Indicates the total number of bridges in the bridge group system.

[0024] (3) Construct a network-level bridge group scour safety risk model. The network-level bridge group scour safety risk model consists of the network-level bridge group scour safety risks corresponding to all scour disaster conditions during the entire life cycle. Scour disaster conditions occurred each year The probability of scour failure of network-level bridge groups and the regional bridge groups under scour disaster conditions The corresponding loss consequence calculation is as follows The annual road network bridge group scour safety risk, regional bridge group in scour disaster conditions The corresponding loss consequences under the scour disaster working condition are divided into direct economic loss and indirect economic loss. The direct economic loss is obtained by calculating the cost of debris cleaning and the cost of bridge reconstruction after the bridge 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.

[0025] Step (3) specifically comprises the following steps: (3.1) The scour safety risk of the bridge group at the road network level is obtained by comprehensive evaluation of the network level cost risk. The expression of the scour safety risk of the bridge group at the road network level in the year of is as follows: , wherein, represents the scour failure probability of the bridge group at the road network level under the scour disaster working condition of the bridge group in the year of represents the corresponding loss consequences of the bridge group in the year of under the scour disaster working condition. (3.2) The corresponding loss consequences of the bridge group under the disaster loss working condition are divided into direct economic loss and indirect economic loss, and the calculation formula is as follows: , wherein, represents the perception coefficient of the bridge group to the indirect economic loss; represents the direct economic loss of the bridge in the th position; represents the corresponding indirect economic loss of the scour disaster working condition . (3.3) The direct economic loss of the bridge in the th position is the cost of debris cleaning and the cost of bridge reconstruction after the bridge failure, and the calculation formula is as follows: , wherein, represents the debris cleaning cost per unit area of the bridge, represents the reconstruction cost per unit area of the bridge, represents the width of the bridge in the th position, represents the length of the bridge in the th position. (3.4) The corresponding indirect economic loss of the scour disaster working condition is the economic impact on the traffic users caused by the bridge failure and the related reconstruction work during the scour disaster working condition , and the indirect economic loss is​​​​ Additional travel time loss due to detour or congestion and additional vehicle operation cost ; , (3.5) Scour disaster working condition The calculation formula of additional travel time loss due to detour or congestion of the corresponding regional bridge group is: , Wherein, represents the value per unit time of the traveler, represents the time of the traveler detour, represents the connecting road between the intersection node and the intersection node , and represents all bridge connecting roads between the regional road network, , and are obtained by calculation through the obtained network topology information; represents the hourly traffic volume of the connecting road under the scour disaster working condition , represents the impedance of the connecting road under the scour disaster working condition , represents the traffic volume of the connecting road under the undamaged state of the road network, represents the traffic impedance of the connecting road under the undamaged state of the road network; (3.6) Scour disaster working condition The additional travel time loss due to detour or congestion of the corresponding regional bridge group can be divided into link delay time and intersection delay time, so the impedance of the connecting road under the scour disaster working condition , is the link delay impedance of the connecting road under the traffic flow , is the intersection delay impedance of the front intersection node and the rear intersection node of the connecting road at the adjacent entrance; The calculation formula of the link delay impedance of the connecting road under the traffic flow is: , ​ , , denotes the connecting road impedance in free flow state; denotes the connecting road actual capacity in free flow state; parameter and parameter are calibrated by the actual survey data of the road network corresponding to the area bridge group, and the survey data , , and , the parameters and the numerical value of parameter are obtained by linear fitting.

[0026] The intersection node of the connecting road and the intersection node of the connecting road The calculation formula of the delay impedance of the adjacent entrance road is: , wherein, denotes the signal cycle of the intersection node , is the green ratio (effective green time / signal cycle) of the intersection node , is the saturation flow rate of the intersection node ; (3.7) The calculation formula of the additional vehicle operation cost under the scour disaster working condition is: , wherein, denotes the bypass distance of the connecting road under the scour disaster working condition of the bridge network ; denotes the unit travel cost of the automobile; denotes the unit travel cost of the truck; denotes the flow proportion of the truck; (3.8) The calculation of the constructed road network level bridge group scour safety risk model is as follows: , In the formula, the total number of the scour disaster working conditions of the road network level bridge is , ; denotes the starting time point of the study; denotes the whole life cycle of the area bridge group.

[0027] ​​(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 risks corresponding to all scour disaster conditions throughout the entire life cycle. Combining graph theory methods with road network-level resilience analysis technology, a road network-level safety resilience function function with dual dimensions of time and space is constructed to quantify the dynamic recovery capacity of the road network-level function under different scour disaster conditions.

[0028] Step (4) specifically includes the following steps: (4.1) Section Annual scour disaster conditions Corresponding safety and resilience risks of the bridge group system The expression is: , in, Indicates the Annual scour disaster conditions Corresponding road network-level safety resilience function; (4.2) Section Annual scour disaster conditions The corresponding road network-level security resilience function expression is: , in, It represents the performance index of the bridge scour system at the network level when all bridges are operating normally (bridge network is completely unobstructed); Represents the performance index of the bridge group scour system at the road network level when all bridges are out of service (bridge network is completely paralyzed); road network level safety resilience function The value is Within the range, a larger value indicates a stronger functionality maintained in the current state; Indicates the Annual scour disaster conditions The corresponding road network-level bridge group scour system performance index; (4.3) Section Annual scour disaster conditions Corresponding road network-level bridge group scour system performance index The calculation formula is: , in, Indicates the Annual scour disaster conditions The corresponding total travel time; Indicates the Annual scour disaster conditions The corresponding total travel distance; is a time-related equilibrium factor, measured in time units; is a balance factor related to the passing distance, measured in length units; , , wherein, denotes the distance of the connecting road , denotes the corresponding automobile traffic flow of the scour disaster working condition in the year ; denotes the corresponding truck traffic flow of the scour disaster working condition in the year ; denotes the impedance of the connecting road corresponding to the scour disaster working condition , denotes the truck impedance of the connecting road corresponding to the scour disaster working condition ; (4.4) the expression of the truck impedance of the connecting road corresponding to the scour disaster working condition is as follows: , wherein, denotes the sensitive coefficient of the amplification intensity of the truck flow to the impedance; denotes the truck flow in the original state; denotes the sensitive threshold of the influence of the road congestion effect; denotes the passing capacity of the connecting road ; (4.5) the calculation formula of the bridge group scour safety resilience model at the road network level is as follows: .

[0029] (5) a bridge group scour safety adaptability reinforcement model at the road network level is constructed, the bridge group scour safety adaptability reinforcement model at the road network level is composed of the adaptability reinforcement costs of all bridges corresponding to all scour disaster working conditions in the whole life cycle, a function expression of the adaptability reinforcement cost of a single bridge in the regional bridge group system is established by comprehensively considering the budget constraint and the reinforcement target reliability requirement, and the bridge group scour failure probability under different working conditions after active adaptability reinforcement, the road network level bridge group scour safety risk and the safety resilience risk of the bridge group system after active adaptability reinforcement of the regional bridge group are calculated.

[0030] Step (5) specifically includes the following steps: (5.1) the ripraps are used as scour protection measures for reinforcement, and the cost of the ripraps includes the labor cost, the transportation cost and the material cost; the cost of the ripraps in the first year is denoted as ​The failure probability of the bridge group system in the year The adaptive reinforcement cost of the bridge group system in the year The function expression is: , Wherein, represents the cost coefficient of adaptive reinforcement; represents the target reliability index of the abutment; represents the reliability index of the bridge in the bridge group system in the year when adaptive reinforcement measures are taken; is the basic reinforcement cost in the year ; The calculation formula of the adaptive reinforcement model of the bridge group system in the year is: , Wherein, represents the time period of adaptive reinforcement of the regional bridge group; (5.2) Since the bridge in the year achieves the reliability of as the reinforcement target, the failure probability of the bridge in the year after adaptive reinforcement is , and the failure probability corresponding to the reliability of the year is , and the corresponding mathematical expression is: , , Under the trend of climate change, the failure probability of the bridge group system in the year after active adaptive reinforcement of the regional bridge group is , and the specific calculation formula is: , (5.3) Under the trend of climate change, the failure probability of the bridge group system in the year after active adaptive reinforcement of the regional bridge group is , and the expression of the risk of the bridge group system in the year is: , Under the trend of climate change, the failure probability of the bridge group system in the year after active adaptive reinforcement of the regional bridge group is , and the expression of the risk of the bridge group system in the year is: .

[0031] ​(6) Constructing a multi-objective mathematical model of the system safety resilience of bridge groups, taking the minimum of the bridge group scour safety risk and the adaptive reinforcement cost of the road network level and the minimum of the loss of the scour safety resilience of the bridge group after adaptive reinforcement of the road network level as the objective functions, integrating the annual budget cost limit of the adaptive reinforcement model of the road network level and the reinforcement frequency limit of the single bridge in the whole life cycle as the constraint conditions, and generating the Pareto optimal reinforcement scheme based on the NSGA-II algorithm.

[0032] Step (6) specifically includes the following steps: (6.1) Based on the adaptive reinforcement model of the road network level of the bridge group in step (5), the constraint conditions of the multi-objective mathematical model are constructed, including at least the annual adaptive budget cost limit of the regional bridge group and the reinforcement frequency limit of the single bridge in the whole life cycle. The constraint conditions are expressed as follows: , , Wherein, represents the reinforcement budget pool for the road network in the year; represents a step function, where , , otherwise 0, represents the maximum reinforcement frequency constraint of the single bridge in the whole life cycle; (6.2) Based on the constraint conditions, combined with the road network level bridge group scour safety risk model in step (3), the road network level bridge group scour safety resilience model in step (4), and the road network level bridge group scour safety adaptive reinforcement model in step (5.1), after the active adaptive reinforcement intervention of the regional bridge group, the multi-objective mathematical model of the road network level bridge group scour safety risk in step (5.3) and the minimum adaptive reinforcement cost in step (5.1) and the minimum loss of the road network level bridge group scour safety resilience in step (5.3) is used to solve the optimal adaptive reinforcement schedule of the regional bridge group. The expression of the objective function of the multi-objective mathematical model is: Objective 1: Minimize: , Objective 2: Minimize: , (6.3) For individuals who violate the budget or reinforcement frequency limit, a dynamic penalty function mechanism is introduced to increase the penalty term in the objective function to punish solutions that do not meet the constraints, which is specifically expressed as follows: , , Wherein, and a penalty coefficient for controlling the cost of constraint violation; (6.4) The NSGA-II algorithm is used for solving, while minimizing the systematic safety risk, the adaptive reinforcement cost and the safety resilience risk, to generate the active adaptive intervention bridge group reinforcement schedule under the budget and reliability constraints, which minimizes the erosion safety and minimizes the safety resilience loss under the regional bridge erosion situation caused by climate change, the bridge group reinforcement schedule includes the bridge reinforcement sequence and the time when the bridge needs to be reinforced. The bridge group reinforcement schedule provides a scientific decision basis for the traffic infrastructure management department, such as Figure 2 and Figure 3 as shown, Figure 3 is the comparative diagram of the economic loss risk reduction effect corresponding to whether the regional bridge group implements adaptive repair in the present application.

[0033] Embodiment 2: The present application discloses a road network level bridge group erosion systematic safety resilience mathematical modeling system, comprising: A data acquisition module is configured to acquire structural parameters of a regional bridge group and climatic and hydrological data, wherein the structural parameters include bridge foundation embedding depth, bridge abutment embedding depth, bridge size information, bridge material, position information in the bridge group, and network topology structure information, and the climatic and hydrological data include historical disasters, historical upstream and downstream flow, future climate change trend, and future flow change trend.

[0034] A failure probability model construction module is configured to construct a road network level bridge group erosion failure probability model, wherein the road network level bridge group erosion failure probability model is composed of annual failure probabilities of single bridges in the bridge group, a probability density function of annual maximum flow in the whole life cycle of a single bridge is first established to conform to a Pearson Type-III distribution, an improved HEC-18 model is used to dynamically calculate erosion depth based on the probability density function, and a failure condition of exceeding the erosion depth is defined, and finally the annual failure probability of the single bridge is calculated.

[0035] The failure probability model construction module specifically comprises: Based on the historical disasters and the historical upstream and downstream flow, a historical annual maximum flow sequence of the regional bridge group is statistically acquired , a sample matrix of a logarithmic sequence is calculated, and the mean, variance and skewness of the logarithmic sequence are respectively represented as , and ; based on the future climate change trend and the future flow change trend, it is assumed that the natural logarithm of the annual maximum flow in the whole life cycle of the regional bridge group conforms to a Pearson Type-III distribution, and a probability density function of the annual maximum flow in the whole life cycle is represented as: , , in, Represents the shape parameters of each bridge in the regional bridge group; represents the scale parameter of the bridge group; Indicates the The location parameters of the annual group bridges are used to reflect the baseline value of logarithmic flow; Represents the gamma function operation; represents the unit flow upstream of the bridge; The calculation formulas for the relevant parameters of the Pearson Type-III distribution are: , , Location parameters used to characterize changes in hydrological conditions The SWAT model, the climate and hydrological data obtained based on the low-resolution Earth system model MPI-ESM-LR and statistical downscaling were used to determine The spatial and temporal variation of the location parameter The calculation formula is: ,in, represents the annual maximum flow reduction rate considering the impact of climate change, The location parameter representing the annual maximum flow under current climate conditions is calculated using the location information of the bridge in the bridge group obtained from the structural parameters; represents the time interval between the tth year and the starting year; For bridges affected by scour caused by extreme hydrological events during their lifespan, the scour depth of the bridge The improved HEC-18 model is used for calculation, and the specific calculation formula is: , , in represents the model error coefficient; The geometric magnification factor of the water flow and the abutment is calculated by the obtained structural parameter bridge size information; Indicates the Annual bridge upstream flow, Indicates the Unit flow at the bridge hole in the year, during the entire life and The probability of flow distribution over the entire life of the bridge calculate; is the upstream water depth before scour; Definition No. 1 among regional bridge groups in 2018 The scour failure conditions of the bridge are: Scour depth of bridge abutments per year Exceeding the critical scour depth of the bridge , critical scour depth The structural parameters that can be obtained include the buried depth of the bridge foundation, the buried depth of the bridge abutment and the information of the bridge material; Year Annual failure probability of bridges Expressed as: , in Indicates the The scour depth of the bridge abutment exceeds the critical scour depth of the bridge probability.

[0036] Under the trend of climate change, the regional bridge group Scour disaster conditions occurred each year The probability of scour failure of the network-level bridge group is , the specific calculation formula is: , in Indicates the total number of bridges in the bridge group system.

[0037] 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 is composed of the road network-level bridge group scour safety risks 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 each year. The loss consequences corresponding to the regional bridge group under each scour disaster condition are divided into direct economic losses and indirect economic losses. The direct economic loss is obtained by calculating the cost of rubble cleaning and bridge reconstruction after bridge failure, and the indirect economic loss is obtained by calculating the detour time cost and vehicle operating cost based on the road network traffic flow, impedance and linear fitting parameter calibration method.

[0038] The security risk model construction module specifically includes the following steps: The scour safety risk of bridge groups at the road network level is comprehensively assessed through network-level cost risk. Safety risk of scour of road network-level bridge groups The expression is: , in, Indicates the regional bridge group Scour disaster conditions occurred each year The probability of scour failure of a network-level bridge group; Indicates that the bridges in the area are in scour disaster conditions The corresponding loss consequences are as follows.

[0039] Regional bridge groups in disaster damage conditions The corresponding loss consequences It is divided into direct economic losses and indirect economic losses, and the calculation formula is: , in It represents the perception coefficient of indirect economic losses of regional bridge groups; For the Direct economic losses caused by the bridge; For scour disaster conditions Corresponding indirect economic losses.

[0040] No. Direct economic losses from bridge construction is the cost of clearing the debris after the bridge fails and the cost of rebuilding the bridge, and the calculation formula is: , in, represents the cost of clearing debris per unit area of ​​the bridge, represents the reconstruction cost per unit area of ​​the bridge, Indicates the The width of the bridge, Indicates the The length of the bridge.

[0041] Scour disaster conditions Corresponding indirect economic losses refers to the scour disaster condition The corresponding economic impact on traffic users during the bridge failure and related reconstruction work, indirect economic losses Divided into additional travel time loss due to detours or congestion and additional vehicle operating costs ; , Scour disaster conditions Additional travel time loss due to detours or congestion in the corresponding regional bridge group The calculation formula is: , in, represents the traveler’s unit time value, Indicates the time it takes for travelers to detour. Indicates the intersection node and intersection nodes The connecting roads between Represents all bridge-connected roads between regional road networks, 、 as well as Calculated by using the acquired network topology information; Indicates connecting roads In scour disaster conditions The hourly traffic volume, Indicates connecting roads In scour disaster conditions The impedance under Indicates connecting roads Traffic flow under the condition of intact road network, Indicates connecting roads The traffic impedance when the road network is in an undamaged state.

[0042] Scour disaster conditions The additional travel time caused by detours or congestion in the corresponding regional bridge group can be divided into road section delay time and intersection delay time, so the connecting road In scour disaster conditions Impedance under , For connecting roads In traffic flow The delay impedance of the next link, For connecting roads The intersection delay impedance of the front intersection node and the rear intersection node at the adjacent entrance road; Connecting roads In traffic flow The delay impedance of the link below The calculation formula is: , , in, Indicates connecting roads Impedance in free-flow state; Indicates connecting roads Actual capacity under free flow conditions; parameters With parameters The survey data is calibrated by the actual survey data of the road network corresponding to the regional bridge group. 、 、 and , and obtain the parameters by linear fitting With parameters The numerical value of .

[0043] Connecting roads The intersection delay impedance of the front intersection node and the rear intersection node at the adjacent entrance road The calculation formula is: , in, Indicates the intersection node The signal period, It is a fork node Green-to-signal ratio (effective green light time / signal cycle), It is a fork node saturation flow rate.

[0044] In scour disaster conditions Additional vehicle operating costs The calculation formula is: , in, Indicates that the bridge network is in scour disaster condition Lower connecting road detour distance; represents the unit travel cost of the car; represents the unit travel cost of the truck; Indicates the traffic proportion of trucks.

[0045] The constructed road network-level bridge group scour safety risk model is calculated as follows: , In the formula, the road network level bridge scour disaster condition The total number is , ; Indicates the starting time point of the study; Represents the entire life of the regional bridge group.

[0046] 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 is composed of the safety resilience risks corresponding to all scour disaster conditions throughout the entire life cycle. Combining graph theory methods with road network-level resilience analysis technology, a road network-level safety resilience function function with dual dimensions of time and space is constructed.

[0047] The security resilience model building blocks are as follows: No. Annual scour disaster conditions Corresponding safety and resilience risks of the bridge group system The expression is: , in, Indicates the Annual scour disaster conditions The corresponding road network level safety resilience function function.

[0048] The year flood disaster scenario The expression of the corresponding road network level safety resilience function function is: , Wherein, represents the road network level bridge group flood system performance index under the normal operation of all bridges (the bridge network is completely unobstructed); represents the road network level bridge group flood system performance index under the withdrawal of all bridges (the bridge network is completely paralyzed); road network level safety resilience function function The value is in the interval , the larger the value, the stronger the functionality maintained under the current state; represents the year flood disaster scenario The corresponding road network level bridge group flood system performance index.

[0049] The year flood disaster scenario The calculation formula of the corresponding road network level bridge group flood system performance index is: , Wherein, represents the year flood disaster scenario The corresponding total travel time; represents the year flood disaster scenario The corresponding total travel distance; is a time-dependent balancing factor, measured in time units; is a travel distance-dependent balancing factor, measured in length units; , , Wherein, represents the distance between roads , the represents the year flood disaster scenario The corresponding automobile trip flow; represents the year flood disaster scenario The corresponding truck trip flow; represents the impedance of the connecting road under the flood disaster scenario , Indicates scour disaster conditions Corresponding connecting roads Truck impedance.

[0050] Scour disaster conditions Corresponding connecting roads Truck impedance The expression is: , in, The sensitivity coefficient of truck traffic to the amplification strength of impedance; represents the truck flow in the original state; Indicates the sensitivity threshold affecting the road congestion effect; Indicates connecting roads traffic capacity.

[0051] The calculation formula of the scour safety resilience model of the road network bridge group is: .

[0052] 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 the budget constraints and the reliability requirements of the reinforcement target, a functional expression for the adaptive reinforcement cost of a single bridge in the regional bridge group system is established, and the probability of bridge group scour failure under different working conditions after active adaptive reinforcement is calculated, as well as the road network-level bridge group scour safety risk and the safety resilience risk of the bridge group system after active adaptive reinforcement of the regional bridge group.

[0053] The reinforcement model construction modules are as follows: The cost of riprap includes labor cost, transportation cost and material cost. The first regional bridge group system Adaptive reinforcement cost of bridge The function expression is: , in, represents the cost coefficient of adaptive reinforcement; represents the target reliability index of the abutment; Indicates the bridge group The bridge is in Reliability index when adaptive reinforcement measures are taken in the year; For the Annual foundation reinforcement cost; Adaptive reinforcement model for scour safety of bridge groups at the road network level The calculation formula is: , wherein, represents the time period of adaptive reinforcement of the group of regional bridges; Since the first group of bridges is reinforced to achieve a reliability of , the target of reinforcement, the first group of bridges is subjected to adaptive reinforcement, and the failure probability of the first group of bridges after adaptive reinforcement is , and the failure probability of the first group of bridges after adaptive reinforcement is , and the corresponding mathematical expression is: , After the group of regional bridges is actively subjected to adaptive reinforcement under the trend of climate change, the failure probability of the first group of bridges under the scour disaster working condition in the year is , and the specific calculation formula is: , After the group of regional bridges is actively subjected to adaptive reinforcement under the trend of climate change, the expression of the scour safety risk of the group of bridges at the road network level under the scour disaster working condition in the year is: , After the group of regional bridges is actively subjected to adaptive reinforcement under the trend of climate change, the expression of the safety resilience risk of the group of bridges under the scour disaster working condition in the year is: .

[0054] The multi-objective mathematical model construction module is used to construct a multi-objective mathematical model of the scour system safety resilience of the group of bridges, and the minimum adaptive reinforcement cost of the group of bridges at the road network level after adaptive reinforcement and the minimum loss of the scour safety resilience of the group of bridges at the road network level after adaptive reinforcement are taken as objective functions, the annual budget cost limit of the scour safety adaptive reinforcement model of the group of bridges at the road network level and the reinforcement frequency limit of a single bridge within the whole service life are integrated as constraint conditions, and a Pareto optimal reinforcement scheme is generated based on the NSGA-II algorithm.

[0055] The multi-objective mathematical model construction module specifically includes: Based on the scour safety adaptive reinforcement model of the group of bridges at the road network level, the constraint conditions of the multi-objective mathematical model are constructed, and the constraint conditions at least include: the annual adaptive budget cost limit of the group of regional bridges and the reinforcement frequency limit of a single bridge within the whole service life; ​​​​The constraint condition is expressed as follows:

[0056]

[0057] wherein, represents the reinforcement budget pool for the road network in the year; represents a step function, wherein when , , otherwise 0, represents the maximum number of reinforcements allowed for a single bridge in the entire life cycle; Based on the constraint condition, in combination with the road network level bridge group scour safety risk model, the road network level bridge group scour safety resilience model and the road network level bridge group scour safety adaptive reinforcement model, after active adaptive reinforcement intervention of the regional bridge group, the multi-objective mathematical model with the minimum adaptive reinforcement cost and the minimum loss of scour safety resilience of the road network level bridge group after adaptive reinforcement as the target is used to solve the optimal adaptive reinforcement schedule of the regional bridge group, and the expression of the objective function of the multi-objective mathematical model is: Objective 1: Minimize: , Objective 2: Minimize: , For individuals who violate the budget or reinforcement frequency limit, a dynamic penalty function mechanism is introduced, and a penalty term is added to the objective function to punish solutions that do not meet the constraints, which is specifically expressed as follows: , , wherein, and are penalty coefficients for controlling the cost brought by constraint violation; NSGA-II algorithm is used for solving, while minimizing the systematic safety risk, adaptive reinforcement cost and safety resilience risk, under the constraints of budget and reliability, generating an active adaptive intervention bridge group reinforcement schedule that minimizes scour safety and minimizes safety resilience loss in the regional bridge scour situation caused by climate change. The bridge group reinforcement schedule includes the bridge reinforcement sequence and the time when the bridge needs to be reinforced. The bridge group reinforcement schedule provides a scientific basis for decision-making for the traffic infrastructure management department, as shown in FIG. 1. Figure 2

[0058] Embodiment 3: An electronic device, comprising a processor and a storage medium; The storage medium is used to store instructions; The processor is used to operate according to the instructions to perform the steps of the method as described above.​​

[0059] Example 4: A computer readable storage medium described in the present application, having stored thereon a computer program which, when executed by a processor, implements the steps of the method described above.

Claims

1. A mathematical modeling method for the safety resilience of bridge scour systems at the road network level, characterized by: The steps include: (1) Obtain the structural parameters and climate and hydrological data of the regional bridge group. The structural parameters include the buried depth of the bridge foundation, the buried depth of the bridge abutment, the bridge size, the bridge material, the location information of the bridge in the bridge group, and the network topology information. The climate and hydrological data include historical disasters, historical downstream flow, future climate change trends, and future flow change trends; (2) Construct a network-level bridge group scour failure probability model. The network-level bridge group scour failure probability model is composed of the annual failure probability of each bridge in the bridge group. First, a probability density function of the annual maximum flow rate that conforms to the Pearson Type-III distribution over the life of each bridge is established. Based on the probability density function, the scour depth is dynamically calculated using the improved HEC-18 model, and the failure condition for exceeding the scour depth limit is defined. Finally, the annual failure probability of each bridge is calculated. (3) Construct a network-level bridge group scour safety risk model. The network-level bridge group scour safety risk model consists of the network-level bridge group scour safety risks corresponding to all scour disaster conditions during the entire life cycle. The network-level bridge group scour safety risk corresponding to each scour disaster condition is calculated each year. The loss consequences corresponding to each scour disaster condition of the regional bridge group are divided into direct economic losses and indirect economic losses. The direct economic losses are obtained by calculating the cost of clearing the ruins and the cost of rebuilding the bridge after the failure of the bridge. The indirect economic losses are obtained by calculating the detour time cost and vehicle operating cost based on the road network traffic flow, impedance and linear fitting parameter calibration method; (4) Construct a network-level bridge group scour safety resilience model. The 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 with network-level resilience analysis technology, a network-level safety resilience function with dual dimensions of time and space is constructed. (5) Construct a network-level adaptive reinforcement model for bridge group scour safety. The model consists of the adaptive reinforcement costs of all bridges corresponding to all scour disaster conditions during the entire life cycle. Taking into account the budget constraint and the reliability requirements of the reinforcement target, a functional expression for the adaptive reinforcement cost of a single bridge in the regional bridge group system is established. The probability of bridge group scour failure under different working conditions after active adaptive reinforcement is calculated, as well as the network-level bridge group scour safety risk and the safety resilience risk of the bridge group system after active adaptive reinforcement of the regional bridge group. (6) A multi-objective mathematical model of the systematic safety resilience of bridge groups under scour conditions is constructed. The objective functions are to minimize the scour safety risk and adaptive reinforcement cost of the road network-level bridge groups after adaptive reinforcement, and to minimize the loss of scour safety resilience of the road network-level bridge groups after adaptive reinforcement. The annual budget cost limit of the adaptive reinforcement model for scour safety of the road network-level bridge groups and the limit on the number of reinforcements of a single bridge during its entire life cycle are integrated as constraints, and a Pareto optimal reinforcement scheme is generated based on the NSGA-II algorithm.

2. The method for mathematical modeling of the safety resilience of a road network-level bridge group scour system according to claim 1 is characterized by: The step (2) specifically includes the following steps: (2.1) Based on the historical disasters and historical downstream flows, the historical annual maximum flow sequence of regional bridge groups is obtained. , calculate the logarithmic sequence The sample moments of the logarithmic series, the mean, variance and skewness are expressed as 、 as well as Based on the future climate change trend and the future flow change trend, it is assumed that the annual maximum flow of the regional bridge group during its entire lifespan The natural logarithm of follows the Pearson Type-III distribution, and the probability density function of the annual maximum flow rate over the entire life cycle is Expressed as: ， ， in, Represents the shape parameters of each bridge in the regional bridge group; represents the scale parameter of the bridge group; Indicates the The location parameters of the annual group bridges are used to reflect the baseline value of logarithmic flow; Represents the gamma function operation; represents the unit flow upstream of the bridge; The calculation formulas for the relevant parameters of the Pearson Type-III distribution are: ， ， ， in, represents the annual maximum flow reduction rate considering the impact of climate change, The location parameter representing the annual maximum flow under current climate conditions is calculated using the location information of the bridge in the bridge group obtained from the structural parameters; represents the time interval between the tth year and the starting year; (2.2) For bridges affected by scour caused by extreme hydrological events during their lifespan, the scour depth of the bridge The improved HEC-18 model is used for calculation, and the specific calculation formula is: ， ， in represents the model error coefficient; The geometric magnification factor of the water flow and the abutment is calculated by the obtained structural parameter bridge size information; Indicates the Annual bridge upstream flow, Indicates the Unit flow at the bridge hole in the year, during the entire life and The probability of flow distribution over the entire life of the bridge calculate; is the upstream water depth before scour; (2.3) Define No. 1 among regional bridge groups in 2018 The scour failure conditions of the bridge are: Scour depth of bridge abutments per year Exceeding the critical scour depth of the bridge , critical scour depth The structural parameters that can be obtained include the buried depth of the bridge foundation, the buried depth of the bridge abutment and the information of the bridge material; Year Annual failure probability of a bridge Expressed as: ， in Indicates the The scour depth of the bridge abutment exceeds the critical scour depth of the bridge probability; (2.4) Under the trend of climate change, the regional bridge group Scour disaster conditions occurred each year The probability of scour failure of the network-level bridge group is , the specific calculation formula is: ， in Indicates the total number of bridges in the bridge group system.

3. The method for mathematical modeling of the safety resilience of a network-level bridge group scour system according to claim 2 is characterized by: The step (3) specifically includes the following steps: (3.1) The scour safety risk of bridge groups at the road network level is assessed through comprehensive network-level cost risk assessment. Safety risk of scour of road network-level bridge groups The expression is: ， in, Indicates the regional bridge group Scour disaster conditions occurred each year The probability of scour failure of a network-level bridge group; Indicates that the bridges in the area are in scour disaster conditions the corresponding loss consequences; (3.2) Regional bridge groups in disaster damage conditions The corresponding loss consequences It is divided into direct economic losses and indirect economic losses, and the calculation formula is: ， in It represents the perception coefficient of indirect economic losses of regional bridge groups; For the Direct economic losses caused by the bridge; For scour disaster conditions corresponding indirect economic losses; (3.3) Section Direct economic losses from bridge construction is the cost of clearing the debris after the bridge fails and the cost of rebuilding the bridge, and the calculation formula is: ， in, represents the cost of clearing debris per unit area of ​​the bridge, represents the reconstruction cost per unit area of ​​the bridge, Indicates the The width of the bridge, Indicates the Length of the bridge; (3.4) Scour disaster conditions Corresponding indirect economic losses refers to the scour disaster condition The corresponding economic impact on traffic users during the bridge failure and related reconstruction work, indirect economic losses Divided into additional travel time loss due to detours or congestion and additional vehicle operating costs ; ， (3.5) Scour disaster conditions Additional travel time loss due to detours or congestion in the corresponding regional bridge groups The calculation formula is: ， in, represents the traveler's unit time value, Indicates the time the traveler takes to detour. Indicates the intersection node and intersection nodes The connecting roads between Represents all bridge-connected roads between regional road networks, 、 as well as Calculated by using the acquired network topology information; Indicates connecting roads In scour disaster conditions The hourly traffic volume, Indicates connecting roads In scour disaster conditions The impedance under Indicates connecting roads Traffic flow under the condition of intact road network, Indicates connecting roads The traffic impedance when the road network is intact; (3.6) Scour disaster conditions The additional travel time caused by detours or congestion in the corresponding regional bridge group can be divided into road section delay time and intersection delay time, so the connecting road In scour disaster conditions Impedance under , For connecting roads In traffic flow The delay impedance of the next link, For connecting roads The intersection delay impedance of the front intersection node and the rear intersection node at the adjacent entrance road; Connecting roads In traffic flow The delay impedance of the link below The calculation formula is: ， ， in, Indicates connecting roads Impedance in free-flow state; Indicates connecting roads Actual capacity under free flow conditions; parameters With parameters The survey data is calibrated by the actual survey data of the road network corresponding to the regional bridge group. 、 、 and , and obtain the parameters by linear fitting With parameters The value of Connecting roads The intersection delay impedance of the front intersection node and the rear intersection node at the adjacent entrance road The calculation formula is: ， in, Indicates the intersection node The signal period, It is a fork node The green letter ratio, It is a fork node saturation flow rate; (3.7) In the case of scour disaster Additional vehicle operating costs The calculation formula is: ， in, Indicates that the bridge network is in scour disaster condition Lower connecting road detour distance; represents the unit travel cost of the car; represents the unit travel cost of the truck; represents the traffic proportion of trucks; The network-level bridge group scour safety risk model constructed in (3.8) is calculated as follows: ， In the formula, the road network level bridge scour disaster condition The total number is , ; Indicates the starting time point of the study; Represents the entire life of the regional bridge group.

4. The mathematical modeling method for the safety resilience of a road network-level bridge group scour system according to claim 3 is characterized by: The step (4) specifically includes the following steps: (4.1) Section Annual scour disaster conditions Corresponding safety and resilience risks of the bridge group system The expression is: ， in, Indicates the Annual scour disaster conditions Corresponding road network-level safety resilience function; (4.2) Section Annual scour disaster conditions The corresponding network-level security resilience function expression is: ， in, It represents the performance index of the bridge scour system at the network level under normal operation of all bridges; Represents the performance index of the bridge group scour system at the road network level under the condition that all bridges are out of service; the road network level safety resilience function The value is Within the range, a larger value indicates a stronger functionality maintained in the current state; Indicates the Annual scour disaster conditions The corresponding road network-level bridge group scour system performance index; (4.3) Section Annual scour disaster conditions Corresponding road network-level bridge group scour system performance index The calculation formula is: ， in, Indicates the Annual scour disaster conditions The corresponding total travel time; Indicates the Annual scour disaster conditions The corresponding total travel distance; is a time-related equilibrium factor, measured in time units; is a balancing factor related to the travel distance, measured in units of length; ， ， in, Indicates connecting roads distance, Indicates the Annual scour disaster conditions The corresponding car travel flow; Indicates the Annual scour disaster conditions The corresponding truck travel flow; Indicates scour disaster conditions Corresponding connecting roads The impedance, Indicates scour disaster conditions Corresponding connecting roads Truck impedance; (4.4) Scour disaster conditions Corresponding connecting roads Truck impedance The expression is: ， in, The sensitivity coefficient of truck traffic to the amplification strength of impedance; represents the truck flow in the original state; Indicates the sensitivity threshold affecting the road congestion effect; Indicates connecting roads traffic capacity; (4.5) The calculation formula for the scour safety resilience model of a network-level bridge group is: 。 5. The method for mathematical modeling of the safety resilience of a network-level bridge group scour system according to claim 4 is characterized by: The step (5) specifically includes the following steps: (5.1) The cost of riprap as a scour protection measure includes labor cost, transportation cost and material cost; The first regional bridge group system Adaptive reinforcement cost of bridge The function expression is: ， in, represents the cost coefficient of adaptive reinforcement; represents the target reliability index of the abutment; Indicates the bridge group The bridge is in Reliability index when adaptive reinforcement measures are taken in the year; For the Annual foundation reinforcement cost; Adaptive reinforcement model for scour safety of bridge groups at the road network level The calculation formula is: ， in, Indicates the time period for adaptive reinforcement of regional bridge groups; (5.2) Due to Bridge bridge to achieve reliability To strengthen the goal, Year Failure probability of a bridge after adaptive reinforcement Back to The state of annual reliability, the corresponding failure probability is , the corresponding mathematical expression is: ， Under the trend of climate change, after the regional bridge group actively carried out adaptive reinforcement, the regional bridge group Scour disaster conditions occurred each year The probability of scour failure is , the specific calculation formula is: ， (5.3) Under the trend of climate change, after the regional bridge groups actively carry out adaptive reinforcement, the 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 groups actively carried out adaptive reinforcement, the Annual scour disaster conditions Corresponding safety and resilience risks of the bridge group system The expression is: 。 6. The method for mathematical modeling of the safety resilience of a road network-level bridge group scour system according to claim 5 is characterized by: The step (6) specifically includes the following steps: (6.1) Based on the network-level bridge group scour safety adaptive reinforcement model in step (5), construct the constraints of the multi-objective mathematical model. The constraints include at least: the annual adaptive budget cost limit of the regional bridge group and the number of reinforcement times of a single bridge during its entire life cycle; The constraints are expressed as follows: ， ， in, Indicates the Annual budget pool for road network reinforcement; represents a step function, where hour, , otherwise 0, It represents the maximum number of reinforcement times allowed for a single bridge during its entire life cycle; (6.2) Based on the constraints, combined with the network-level bridge group scour safety risk model of step (3), the network-level bridge group scour safety resilience model of step (4), and the network-level bridge group scour safety adaptive reinforcement model of step (5.1), after proactively conducting adaptive reinforcement intervention for regional bridge groups, a multi-objective mathematical model with the goals of minimizing the network-level bridge group scour safety risk of step (5.3) and the adaptive reinforcement cost of step (5.1) and minimizing the network-level bridge group scour safety resilience loss of step (5.3) is used to solve the optimal adaptive reinforcement schedule for regional bridge groups. The objective function of the multi-objective mathematical model is expressed as: Goal 1: Minimize: , Goal 2: Minimize: , (6.3) In order 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. The specific expression is as follows: ， ， in, and is the penalty coefficient, which is used to control the cost of constraint violation; (6.4) The NSGA-II algorithm is used to solve the problem, minimizing systemic safety risk, adaptive reinforcement cost, and safety resilience risk. Under budget and reliability constraints, a proactive adaptive intervention bridge reinforcement schedule is generated to minimize scour safety and minimize safety resilience loss in the regional bridge scour scenario caused by climate change. The bridge reinforcement schedule includes the bridge reinforcement sequence and the time when the bridges need to be reinforced.

7. A road network-level bridge group scour system safety resilience mathematical modeling system, characterized by: include: The data acquisition module is used to obtain the structural parameters and climate and hydrological data of regional bridge groups. The structural parameters include the buried depth of bridge foundations, the buried depth of bridge abutments, bridge dimensions, bridge materials, the location of the bridge in the bridge group, and network topology information. The climate and hydrological data include historical disasters, historical downstream flow, future climate change trends, and future flow change trends. The failure probability model construction module is used to construct a network-level bridge group scour failure probability model. The network-level bridge group scour failure probability model is composed of the annual failure probability of each bridge in the bridge group. First, a probability density function of the annual maximum flow rate that conforms to the Pearson Type-III distribution over the life of each bridge is established. Based on the probability density function, the improved HEC-18 model is used to dynamically calculate the scour depth, and the failure condition for exceeding the scour depth limit is defined. Finally, the annual failure probability of each bridge is calculated. The safety risk model construction module is used to construct a network-level bridge group scour safety risk model. The network-level bridge group scour safety risk model consists of the network-level bridge group scour safety risks corresponding to all scour disaster conditions throughout the entire life cycle. The network-level bridge group scour safety risk corresponding to each scour disaster condition is calculated each year. The loss consequences corresponding to each scour disaster condition of the regional bridge group are divided into direct economic losses and indirect economic losses. The direct economic loss is obtained by calculating the cost of rubble clearance and bridge reconstruction after bridge failure. The indirect economic loss is obtained by calculating the detour time cost and vehicle operating cost based on the road network traffic flow, impedance and linear fitting parameter calibration method; A safety resilience model construction module is used to construct a network-level bridge group scour safety resilience model. The network-level bridge group scour safety resilience model is composed of the safety resilience risks corresponding to all scour disaster conditions throughout the entire life cycle. By combining graph theory methods with network-level resilience analysis technology, a network-level safety resilience function function with dual dimensions of time and space is constructed. The reinforcement model construction module is used to construct a network-level bridge group scour safety adaptive reinforcement model. The 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 the budget constraints and the reliability requirements of the reinforcement target, 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 working conditions after active adaptive reinforcement, as well as the network-level bridge group scour safety risk and the safety resilience 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 for the systematic safety and resilience of bridge groups under scour conditions. The objective functions are to minimize the scour safety risk and adaptive reinforcement cost of the road network-level bridge group after adaptive reinforcement, and to minimize the loss of scour safety resilience of the road network-level bridge group after adaptive reinforcement. The annual budget cost limit of the road network-level bridge group scour safety adaptive reinforcement model and the limit on the number of reinforcements for a single bridge during its entire life cycle are integrated as constraints, and a Pareto optimal reinforcement plan is generated based on the NSGA-II algorithm.

8. The road network-level bridge group scour system safety resilience mathematical modeling system according to claim 7 is characterized by: The multi-objective mathematical model construction module is specifically: 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 number of reinforcement times of a single bridge during its entire life cycle; The constraints are expressed as follows: ， ， in, Indicates the Annual budget pool for road network reinforcement; represents a step function, where hour, , otherwise 0, It represents the maximum number of reinforcement times allowed for a single bridge during its entire life cycle; Based on the constraints, combined with the network-level bridge group scour safety risk model, the network-level bridge group scour safety resilience model, and the network-level bridge group scour safety adaptive reinforcement model, after proactively carrying out adaptive reinforcement intervention for regional bridge groups, a multi-objective mathematical model was developed with the goals of minimizing the scour safety risk and adaptive reinforcement cost of the network-level bridge group after adaptive reinforcement, as well as minimizing the scour safety resilience loss of the network-level bridge group after adaptive reinforcement. This model was used to solve the optimal adaptive reinforcement schedule for the regional bridge group. The objective function of the multi-objective mathematical model is expressed as follows: Goal 1: Minimize: , Goal 2: Minimize: , In order to constrain individuals that violate the budget or reinforcement times 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. The specific expression is as follows: ， ， in, and is the penalty coefficient, which is used to control the cost of constraint violation; The NSGA-II algorithm is used to solve the problem, minimizing systemic safety risk, adaptive reinforcement cost, and safety resilience risk. Under budget and reliability constraints, an active adaptive intervention bridge group reinforcement schedule is generated to minimize scour safety and minimize safety resilience loss in the regional bridge scour scenario 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 processors and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute 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 the program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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