CN115114715B

CN115114715B - City infrastructure group network elasticity analysis method, electronic device and storage medium

Info

Publication number: CN115114715B
Application number: CN202211028737.5A
Authority: CN
Inventors: 林涛; 周子益; 贾磊; 童青峰; 刘星
Original assignee: Shenzhen Traffic Science Research Institute Co ltd; Shenzhen Urban Transport Planning Center Co Ltd
Current assignee: Shenzhen Traffic Science Research Institute Co ltd; Shenzhen Urban Transport Planning Center Co Ltd
Priority date: 2022-08-26
Filing date: 2022-08-26
Publication date: 2023-01-31
Anticipated expiration: 2042-08-26
Also published as: CN115114715A

Abstract

A city infrastructure group network elasticity analysis method, electronic equipment and a storage medium belong to the field of city infrastructure group analysis. The method aims to solve the problem of analysis of urban cascade failure influence. The method comprises the steps of constructing a cascading failure model of an urban infrastructure group network; adopting the theory and the model of the classical elastic triangle from the two aspects of time and space to carry out elastic analysis on the infrastructures in the urban infrastructure group; elasticity analysis for city infrastructure groups: and (3) introducing a fault mode in which multipoint failures occur simultaneously to calculate network elastic parameters of the urban infrastructure group, introducing spatial position information at the same time, analyzing the elastic parameter conditions of the infrastructure group in a central area and an edge area, and finally performing tree analysis on the cascading failure model process. The invention establishes an elasticity analysis system of the urban infrastructure group network, and provides effective support for researching and improving the elasticity of the urban infrastructure.

Description

City infrastructure group network elasticity analysis method, electronic device and storage medium

Technical Field

The invention belongs to the field of urban infrastructure group analysis, and particularly relates to an urban infrastructure group network elasticity analysis method, electronic equipment and a storage medium.

Background

In recent years, with global warming and a series of natural disasters caused by global warming, urban infrastructures face huge challenges, and how to design and build urban infrastructures capable of resisting the impacts is significant for guaranteeing the stable development of normal operation and economy of cities. Similarly, due to the rapid development of urban economy and the increasing progress and level of urbanization, various countries have established urban groups of various sizes. Among the urban systems, some important infrastructures and complex systems, such as urban traffic networks, urban power supply line networks, urban large airports and the like, which are responsible for urban operation and economic development play a crucial role in normal urban operation. Also, these systems are also referred to as city critical infrastructure because they tend to have a large scale, significant support functions, and complex system interactions. More and more research shows that deliberate "attacks" on these critical urban infrastructures will cause significant urban losses, including economic losses and even casualties. Because of the large impact of these critical infrastructures on other system facilities, their failure and malfunction often mean the occurrence of large-scale system outages. The various challenges faced by cities are unknown, uncontrollable and unpredictable, and therefore city managers need to start from the key infrastructures of the cities, utilize effective theoretical knowledge and construct 'protective covers' for guaranteeing the normal operation of the cities through rich practical methods. Among all the problems, how to make the city recover from the inevitable attacks quickly is an important and necessary research topic.

In addition, with global warming, extreme weather and various man-made reasons, the environmental pollution is a disturbing factor influencing the normal operation of the infrastructure. The external disturbances affecting the actual operation directly affect the normal operation of the infrastructure and a series of possible "domino effect", which is generally called "cascade failure", and generally means that in a system and a network, failure of one or a few nodes or wires causes other nodes to also fail through the coupling relationship between the nodes, so as to generate the cascade effect, and finally cause the breakdown of a part of nodes and even the whole network. Cascading failures have in fact been the largest cause of impact on the proper functioning of urban infrastructure. Therefore, how to analyze the correlation between infrastructures based on the operating conditions of infrastructures in extreme weather and specific scenes, analyze the operating conditions of infrastructures in a non-isolated manner, and implement effective reliable operation measures is one of the problems to be solved.

The importance of the actual city infrastructure is known by city managers, and a lot of operation monitoring devices and facilities are correspondingly distributed, but because the operation rule of the city-level system cannot be mastered, effective comprehensive utilization among all data acquisition sources cannot be achieved, and meanwhile, how to extract effective data from the data and analyze the actual state of the system operation lacks corresponding knowledge and theory. Meanwhile, the disturbance of the actual outside to the infrastructure occurs locally, the influence of the disturbance on the local part is analyzed, and then the disturbance gradually expands to a part along with the relevance of the system structure and function, and finally the disturbance spreads to the whole system. How to grasp the whole fault propagation process and establish a whole set of effective analysis means aiming at the fault propagation process are the problems to be solved at present.

Disclosure of Invention

In order to improve the effectiveness of analysis of urban cascade failure influence, the invention provides an urban infrastructure group network elasticity analysis method, electronic equipment and a storage medium, wherein an urban infrastructure group network elasticity analysis system is constructed from the aspects of establishment of an urban infrastructure group cascade failure model and facility group elasticity analysis.

In order to realize the purpose, the invention is realized by the following technical scheme:

a method for analyzing network elasticity of a city infrastructure group comprises the following steps:

s1, constructing a cascading failure model of an urban infrastructure group network;

s1, the specific implementation method for constructing the cascade failure model of the urban infrastructure group network comprises the following steps:

s1.1, counting the operation data of the urban infrastructure, and converting the operation data of the urban infrastructure into an operation function value of the urban infrastructure;

s1.2, establishing an urban infrastructure group as an analysis basic unit based on the running function value of the urban infrastructure, and performing primary division on the urban infrastructure group;

s1.3, establishing a cascading failure model of the urban infrastructure group;

s1.4, correcting the cascading failure model of the urban infrastructure group to obtain a cascading failure model of an urban infrastructure group network;

s2, elasticity analysis of infrastructures in the urban infrastructure group: based on the cascade failure model of the city infrastructure group obtained in the step S1.3 and the step S1.4, performing elastic analysis by adopting the theory and the model of the classical elastic triangle from two aspects of time and space;

the specific implementation method of the step S2 comprises the following steps:

s2.1, setting the fault propagation time as follows based on the cascade failure model of the urban infrastructure group:

is composed ofjIs propagated tokThe time of (2) is greater than the time of (c),

is composed ofjTokThe time taken for the euclidean distance;

s2.2, setting the state parameter of the urban infrastructure group as the total overload load SCP of the urban infrastructure group, and obtaining the elastic parameter according to the elastic triangle theoryRComprises the following steps:

wherein R is an elasticity parameter without considering the load distribution strategy among the infrastructure groups,t ₀ which represents the starting moment of the elastic triangle,t ₁ which represents the end time of the elastic triangle,Yfor the total number of stages in which overload occurs,

is shown ashThe average time of load shifting objects of the cascade failure related failure infrastructure of a stage,Q _h is as followshA first order neighbor set of infrastructure overloaded in cascading failures of stages,N _h is shown ashThe number of infrastructure overloaded in a cascade failure of a stage;

s2.3, calculating the system elasticity under the improved cascade failure model, wherein a network elasticity index RSL is as follows:

wherein

To take into account the load between infrastructure groupsAllocating elastic parameters under the condition of strategy, and then sorting the infrastructure group according to the parameter of the infrastructure groupFIG1(l)There are three types:

wherein,

a 30% quantile of a sequence of resource supply level values for an infrastructure group,

70% quantiles of the sequence of resource supply level values for the infrastructure group,lfor multiples of initial load increaselAnalyzing the condition of more than 1;

s2.4, analyzing the load distribution condition in and among the urban infrastructure groups under the condition of different load increase multiples, and setting a threshold, wherein for FIG1, the following conditions are adopted:

l _c0 under the condition of the threshold value, the method,

represents a threshold valuel _c0 The portion of elasticity values within the infrastructure group under the conditions,

represents a threshold valuel _c0 An elasticity value part outside the urban infrastructure group under the condition;

is a threshold valuel _c0 Elastic parameters under the condition of a load distribution strategy among urban infrastructure groups are not considered;

l _c1 under the condition of the threshold value, the method,

represents a threshold valuel _c1 The portion of elasticity values within the city infrastructure group under the conditions,

represents a threshold valuel _c1 An elasticity value part outside the urban infrastructure group under the condition;

is a threshold valuel _c1 Elastic parameters under the condition of a load distribution strategy among urban infrastructure groups are not considered;

l _c2 under the condition of the threshold value, the method,

represents a threshold valuel _c2 The portion of elasticity values within the city infrastructure group under the conditions,

represents a threshold valuel _c2 An elasticity value part outside the urban infrastructure group under the condition;

is a threshold valuel _c2 Under the condition, elastic parameters under the condition of a load distribution strategy among the urban infrastructure groups are not considered, and the whole system is completely crashed;

s2.5, analyzing the spatial distribution condition of the elasticity values of the urban infrastructure group based on the obtained elasticity values of the urban infrastructure group, and introducing a calculation formula of spatial correlationC(r)The following were used:

wherein,R _s is the elasticity value of the city infrastructure group s,R _g is the elasticity value of the city infrastructure group g, FIG is the set of city infrastructure groups,

is the mean value of the elasticity values of the urban infrastructure group,

the variance is expressed in terms of the number of peaks,

representing the euclidean distance between s and g,

the function is used to screen distances ofrBy spatial correlation at different rC (r)To find the target spatial correlationThe region takes targeted elasticity management measures.

S3, elasticity analysis of the city infrastructure group: and (3) introducing a fault mode in which multipoint failures occur simultaneously to calculate network elastic parameters of the urban infrastructure group, introducing spatial position information at the same time, analyzing the elastic parameter conditions of the infrastructure group in a central area and an edge area, and finally performing tree analysis on the cascading failure model process.

Further, the step S1.2 is realized by the following steps:

s1.2.1, considering city scale, setting core infrastructure group to influence maximum radiusD _max Infrastructure-wide inclusion into infrastructure groups, arrangementsiIn order to be a core infrastructure of the system,jin order to be an infrastructure, the system is provided with a plurality of network devices,FV _i is a core infrastructureiThe value of the operating function of (c),FV _j as an infrastructurejAn operating function value of;

s1.2.2, calculating the value of the operational function of the infrastructure in the range of the infrastructure groupFVPearson correlation coefficient between sequence and i:

PPMCC _i，j is composed ofjSequence of infrastructure operational function values andipearson's correlation coefficient therebetween, cov (i，j) Is composed ofiAndjthe covariance of the running function value sequence of (a),

is composed ofiThe standard deviation of (a) is determined,

is composed ofjStandard deviation of (d);

s1.2.3 obtained from Pearson's correlation coefficient

To proceed withPrimarily dividing the urban infrastructure group;

representation to core infrastructureiIn the case of a non-woven fabric,jwhether within its central infrastructure group, a value of 1 indicates that it is inside, and 0 is outside.

Further, the step S1.3 includes the following steps:

s1.3.1, defining initial disturbance as increasing load value of infrastructure based on definition of cascade failure model, for urban infrastructurejComprises the following steps:

as an infrastructurejThe maximum capacity of the battery pack is set,TP _j as an infrastructurejThe tolerance parameter(s) of (a),

as an infrastructurejInitial load of (2):

s1.3.2, removing overloaded infrastructure after cascade failure has occurredjInfrastructure, infrastructurejWill be assigned to first-order neighbors according to connection strengthskThe distribution ratio is as follows:

is composed ofjAndkthe normalized strength of the connection therebetween is such that,

is composed ofjAndkthe strength of the connection between the two parts,

is composed ofjAndmthe strength of the connection between the two parts,mis composed ofQAny one of the above-mentioned (a) and (b),Qto and from the infrastructurejA connected first-order neighbor set;

S1.3.3、kdistributed load andkthe intensity after normalization is proportional, as follows:

is composed ofkThe value of the operational function of the assigned load,FV _j as an infrastructurejAn operating function value of;

thenkLoad of update on

Comprises the following steps:

s1.3.4, comparisonkUpdate load of (2) andkdetermines whether further removal is requiredk：

Is composed ofkIs set to a value of (a) in (b),MC _k is composed ofk0 for removal and 1 for retention;

s1.3.5, repeating S1.3.1-S1.3.4, removing the connections and connection strengths of the affected infrastructure, and normalizing again until the city infrastructure group returns to equilibrium.

Further, the step S1.4 is implemented by the following steps:

s1.4.1 defining core infrastructure loading disturbances based on considering global disturbance patterns, and not removed after overload of the core infrastructure and not participating in subsequent load distribution process; defining load distribution to keep constant for load distribution in an individual infrastructure group, distributing among the infrastructure groups, and after the distribution in the infrastructure groups is finished, distributing the rest load to the infrastructures of the adjacent infrastructure groups according to an average distribution principle under the condition of meeting correlation connection strength, then:

s1.4.2, for j, the first order neighbor of the neighboring infrastructure group assigns y the load to j as follows:

is composed ofyThe value of the operational function of the assigned load,

is composed ofdThe value of the operational function of the assigned load,Nei(j)as an infrastructurejA set of first-order neighbors within a group,dis composed ofNei(j)Any one of (1)，

Representing infrastructurejA set of first-order neighbors outside the group,y∈Nei'(j）and then:

the update load for y is the load of y,

is the value of the operating function of y,MC _j\ is composed ofjThe maximum capacity of (c);

s1.4.3, if an attribute determination of infrastructure necessity is triggered after 50% or more of infrastructure failures occur in the infrastructure group, then for the infrastructure group having H infrastructures, the connection matrix before updating is:

the updated connection matrix is a cascading failure model of the city infrastructure group network:

。

further, the specific implementation method of step S3 includes the following steps:

s3.1, presetting that 10% of urban infrastructure groups simultaneously suffer overload failure, and then calculating the network elasticity index according to the relation of permutation and combinationRNIThe method comprises the following steps:

is a network elasticity indicator of 10% infrastructure group overload failure,

the network resiliency indicator of overload failure is combined for the kth 10% infrastructure group,

the resiliency index for overload failure is combined for the kth 10% infrastructure group,

a permutation and combination formula for selecting 10% of the number of combinations of Z number from the Z infrastructure groups;

s3.2, counting two city infrastructure groups with the highest occurrence frequency in the first 10% of sets with the highest contribution degree to the network elasticity indexes as system elasticity key city infrastructure groups;

s3.3, analyzing the elasticity difference of the urban infrastructure groups in the central area and the edge according to the geographic attributes of the infrastructures;

and S3.4, performing tree analysis on the infrastructure in the cascade failure process.

Further, the specific implementation method of step S3.3 includes the following steps:

s3.3.1, calculating effective propagation distance of infrastructure cascade failure processRPD：

Wherein,W _h is composed ofhAn overloaded infrastructure set of cascaded failures of order,Q _k overloading an infrastructure for cascading failureskThe first-order neighbors of (a) a,

to representW _h Basic device in setThe number of the fertilizer is equal to the total amount of the fertilizer,

representQ _k The number of infrastructures in the set is,

is the euclidean distance between infrastructure k and m;

s3.3.2 calculating node betweenness of city infrastructure group networkBThe definition is as follows:

wherein,n _jk representing nodesjAndkthe number of shortest paths between the first and second sets,n _jk (i)representing nodesjAndkthrough nodes in the shortest path betweeniThe number of the (c) is,

to representiNode betweenness of (2);

s3.3.3, calculating elastic space parameters of urban infrastructure groupRSP：

Wherein,B _m representmNode betweenness of the infrastructure.

Further, the specific implementation method of step S3.4 includes the following steps:

s3.4.1, and analyzing the hierarchical relation in the cascade failure process. First, the ability parameter of the single infrastructure to resist disturbance, the process vulnerability parameter, is calculatedPVP：

Wherein,OL _j andOL _k are respectivelyjAndkthe number of times of overload at the time of overload failure,ias a root node, the node is a node,SP _ij to representiAndjthe shortest distance between the two elements of the first and second,La _j in a representation tree structurejThe number of layers of (a) to (b),

to representjA process vulnerability parameter of (a);

s3.4.2, calculating elastic tree structure parameters of urban infrastructure groupRTSP：

S3.4.3, calculating elastic function related parameters of city infrastructure groupRFRP：

S3.4.4, and method for improving elastic recovery efficiencyRREP：

Wherein,FS _j representing infrastructurejOverloading the set of infrastructure on the failure path on the cascading failure tree structure,

is composed ofjThe elastic recovery efficiency parameter of (a) is,RREPthe larger the value, the more efficient the resiliency boost for the infrastructure and vice versa.

The electronic equipment comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the urban infrastructure group network elasticity analysis method when executing the computer program.

Computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements a city infrastructure group network elasticity analysis method as described.

The invention has the beneficial effects that:

the urban infrastructure group network elasticity analysis method is based on established infrastructures, cascading failure models and elasticity analysis theories of cities, and an urban infrastructure group network elasticity analysis system is constructed from the aspects of establishment of urban infrastructure group cascading failure models and facility group elasticity analysis. The main contents are as follows:

a. from the point of view of the establishment of a cascading failure model for a city infrastructure group. Firstly, the city infrastructure group is established as an analysis basic unit, on one hand, because the main problem for the operation of the city system is frequent and small-scale disturbance, the actual influence range of the disturbance is not too large, and the actual influence is caused on the periphery of the occurrence point. Therefore, such disturbances and the actual system performance degradation need to be analyzed within a certain range to grasp the actual degree and range of influence. Secondly, for some disasters which have low actual occurrence probability but have huge influence on the system and even cause destructive attack, the association between each part of the whole system needs to be analyzed in detail for the black swan event, and the influence on the whole system caused by initial disturbance at the beginning of analysis and the overall evaluation in the subsequent system recovery process are necessary, so that the influence mode between each unit needs to be analyzed from a small analysis unit. Therefore, the invention establishes an analysis system which takes the urban infrastructure group as a basic unit, and restores the fault propagation process among all basic analysis units by means of a cascade failure model. Firstly, considering the most critical batches of all infrastructures in an actual city, such as an airport, a railway station, a subway junction and the like, taking the most critical batches as centers, calculating by means of the concept of spatial correlation and operation data in a certain time period, screening out the actual influence range of a central point according to a threshold value, and taking all infrastructures in the range as an infrastructure group. And then, establishing a cascading failure model of the urban infrastructure group based on the cascading failure model. The actual operation data of each infrastructure is unified into the same index through daily supply quantity of resources for daily life of urban residents, the index is used as the load of the infrastructure, the load distribution strategy after overload is calculated according to the calculated space correlation normalized connection strength, and finally the cascade failure process in the whole fault propagation path is simulated. In the process, the actual system operation condition after the system is subjected to great disturbance is considered, and the daily supply quantity of the resources of the daily life of urban residents is considered to be divided into two types: both necessary and unnecessary. After more than half of the facilities within the infrastructure group fail due to the cascade failure, unnecessary portions are removed and only necessary portions are considered. Secondly, for cascading failure propagation between different infrastructure groups, the influence on the periphery due to disturbance of local areas is really larger and more direct, and meanwhile, in the actual recovery process, more resources available in the periphery are obtained. Therefore, from the point of view of the urban infrastructure group network, the disturbance occurring in the infrastructure group and the load distribution after the cascade failure will be preferentially distributed to the infrastructures in the same infrastructure group. Meanwhile, an overloaded infrastructure occurring in an edge area of an infrastructure group cannot be further distributed to infrastructures within the same infrastructure group, and then load is distributed to infrastructures of other infrastructure groups. The actual distribution ratio is distributed according to the principle of average distribution. Meanwhile, considering the disturbance influence degree actually affecting the global infrastructure and the necessity of actually analyzing the fitting reality (it is not practical to increase the load of the edge node infrastructure in one way), the elasticity analysis of the part only involves the initial disturbance of the infrastructure group core infrastructure. Meanwhile, due to the consideration of the perfect protection measures of the real core infrastructure and the low probability of complete failure, the initial overload (the initial overload is the load of the core infrastructure is raised to be a multiple of the initial load) of the core infrastructure is not directly removed and still remains in the system, and meanwhile, the core infrastructure does not participate in the load distribution in the subsequent cascade failure process.

b. From the perspective of elasticity analysis of infrastructure within a facility group. According to the definition of the actual elasticity, the method mainly analyzes the number of the disturbance values which can be actually born by the system, namely the tolerance limit of the system elasticity; analyzing the propagation process of the actual disturbance in the whole system, including the range size in time and space, and leading out the parameter definition of elasticity; analyzing the change situation of the system elasticity capability of the system to the change of the disturbance, namely the sensitivity of the system to the disturbance; and analyzing the efficiency of the practical system elastic maintenance in the resource allocation based on the fault propagation control process, and finding the optimal recovery strategy of the system by means of the efficiency. Firstly, the invention introduces a method of elastic triangles, simulates the whole process of initial disturbance occurrence, fault accelerated propagation stage, system recovery stage and system recovery balance state, and defines the system state parameter values of the infrastructure. Meanwhile, according to the existing load redundancy upper limit value and the distribution quantity of the infrastructure in the actual load distribution process, the elastic parameter of the infrastructure is calculated by combining the fault propagation time. Then, the load distribution among the infrastructure groups and the elasticity parameters under the condition of not considering are calculated, and the ratio of the two parameters is calculated to obtain the network elasticity fluffing efficiency. And classifying the infrastructure group into three types according to the size of the network elasticity fluffing efficiency. The boundaries of the discovered load distribution within and outside the cluster are calculated based on the pattern of overload propagation for the central core infrastructure cluster. Further, the analysis system analyzes the relationship with the load overload. And finally, calculating the spatial distribution characteristics of the infrastructure elasticity values according to a spatial correlation formula.

c. From the point of view of the infrastructure group network of the overall system. The operation of all infrastructures in a city is integrated, which means that external disturbance occurring in a partial area may affect the operation of other infrastructures in the global network. Firstly, considering the initial condition of introducing a plurality of infrastructure groups to fail simultaneously, and calculating the elastic parameter condition of the whole network according to a plurality of failure core infrastructures actually selected. Failure analysis is carried out according to the scale of the urban infrastructure group network and the quantity of 10%, the overall elasticity index of the evaluation network is obtained by averaging, and then the key infrastructure with the highest frequency of occurrence in the top 10% with the largest sequence according to the elasticity parameters is analyzed. And then, considering the geographic attributes of different infrastructure groups, calculating the geographic position of each infrastructure group, calculating the effective Euclidean distance of fault propagation of the infrastructure groups, and combining the betweenness attributes of the infrastructure group structures to be used as an index for evaluating elasticity. And finally, introducing tree analysis of cascade failure of the infrastructure group. And calculating the integral elasticity capability index of the infrastructure group based on the actual path of fault propagation from the fault protection point of view.

By combining the three aspects, the invention provides an urban infrastructure group network elasticity analysis system based on a cascading failure model, which has the following advantages:

1. according to the cascade failure model of the urban infrastructure group, firstly, the model meets the actual analysis requirement, and meanwhile, the established minimum analysis unit, namely the urban infrastructure group, focuses on that the urban infrastructure group actually plays a supporting role in urban operation when the urban infrastructure deals with natural disasters, extreme weather and artificial damage and attack, and is based on the reality of a resource allocation strategy after the disasters occur. The actual analysis of the urban infrastructure is closer to the reality, and the means of dividing the urban infrastructure group enables the analysis to be more effective; secondly, introducing a spatial correlation analysis method in the dividing process, and simultaneously considering a fault introduction means of the core infrastructure; and finally, on the basis of a classical cascade failure model, considering the actual condition that the urban infrastructure group system is subjected to external disturbance, introducing attribute division of different facilities and describing the space propagation characteristics of fault propagation. By further optimizing and improving the cascade failure model, the method is more suitable for the actual situation and more effective in analysis;

2. the method firstly analyzes the elasticity analysis of the infrastructure in the infrastructure group, and introduces system elasticity parameters, analysis process and indexes reasonably based on the classical elastic trigonometric theory. Meanwhile, the infrastructure group is subjected to function classification based on the elasticity analysis of the infrastructure group: supply, dependency and equalization; 3. the method integrates two levels of local single infrastructure group and integral infrastructure group networks, and analyzes the elastic parameter condition of the urban infrastructure. The attribute characteristics of different infrastructure groups are considered more at the level of a single infrastructure group, and the overall system elasticity capability assessment and the discovery of a fragile infrastructure group are mainly considered at the level of an infrastructure group network. The method combines the micro-scale and the macro-scale, and provides effective support for the actual implementation of the elastic lifting strategy; 4. the method carries out elasticity analysis at the level of the urban infrastructure group network, analyzes and effectively delineates and explores the elasticity modes of the urban infrastructure group under different disturbance modes aiming at external disturbances such as natural disasters with huge urban influence, and evaluates the elasticity condition of the urban infrastructure group. Meanwhile, creatively providing an analysis method of the cascade failure tree structure, and formulating a corresponding elastic parameter system; 5. by combining the elasticity analysis, the invention starts from the cascade failure model, considers the real condition that the infrastructure group suffers external disturbance, and optimizes and improves the model. Then, the elasticity parameter of the system is introduced based on the elasticity triangle theory. And constructing a theoretical analysis framework of the infrastructure group through the model and the parameters. An elasticity analysis system of the urban infrastructure group network is established from the process analysis of the urban infrastructure borne disturbance energy, the sensitivity of disturbance change, the propagation process and the breadth range calculation of the disturbance in the system and the system elasticity recovery, and an effective support is provided for researching and improving the elasticity of the urban infrastructure.

Drawings

FIG. 1 is a flow chart of a model building of a city infrastructure group according to the present invention;

FIG. 2 is a schematic diagram of a model of a city infrastructure group according to the present invention;

FIG. 3 is a process diagram of an elastic triangle model of the urban infrastructure group network elasticity analysis method according to the present invention;

fig. 4 is an infrastructure tree structure diagram of a cascade failure process of the urban infrastructure group network elasticity analysis method according to the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and the detailed description. It is to be understood that the embodiments described herein are illustrative only and are not limiting, i.e., that the embodiments described are only a few embodiments, rather than all, of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations, and the present invention may have other embodiments.

Thus, the following detailed description of specific embodiments of the present invention, presented in the accompanying drawings, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the detailed description of the invention without inventive step, are within the scope of protection of the invention.

For further understanding of the contents, features and effects of the present invention, the following embodiments are exemplified in conjunction with the accompanying drawings and the following detailed description:

the first embodiment is as follows:

a method for analyzing network elasticity of urban infrastructure group comprises the following steps:

based on the support effect of the urban infrastructure on the daily activities of urban residents, the basic operation data are uniformly converted into actual operation function values, the spatial correlation is calculated by combining the longitude and latitude of the coordinates of the central point of the infrastructure, and after the threshold value is set and screened, the primary division of the infrastructure group is set by taking the core infrastructure as the center. Then, based on the theory of cascade failure, a cascade failure model of the urban infrastructure group is established, attribute division of the infrastructure and the spatial characteristics of the fault propagation process are introduced, the model is further optimized and improved, and the cascade failure model of the urban infrastructure group network is obtained.

first, the infrastructure is defined as a material engineering facility for providing public services for social production and resident life, is a public service system for ensuring normal progress of social and economic activities, is a general material condition on which society depends to survive, and occupies an important position in the construction and development of the whole city. Therefore, the operation data of the urban infrastructure is uniformly converted into the operation function value according to the support effect of each infrastructure on urban development and daily activities of urban residents. The actual controls were transformed in eight ways (see table 1 below), and the comparisons were transformed in terms of daily consumption by each person.

TABLE 1 Attribute Table for Key infrastructure

Note: the electricity, water supply and power supply are converted according to the average consumption of people, and other services are converted according to the annual service customer number of a market, for example.

further, the step S1.2 is implemented by the following steps:

is composed ofiThe standard deviation of (a) is determined,

is composed ofjStandard deviation of (d);

s1.2.3, obtained from Pearson's correlation coefficient

Carrying out primary division on the urban infrastructure group;

representation to core infrastructureiIn the case of a non-woven fabric,jwhether within its central infrastructure group, a value of 1 indicates inside, and 0 is outside;

s1.3, establishing a cascading failure model of the urban infrastructure group;

further, the step S1.3 includes the following steps:

s1.3.1 based onDefining a cascading failure model, defining an initial disturbance as an increased load value of the infrastructure, for urban infrastructuresjComprises the following steps:

as an infrastructurejInitial load of (2):

is composed ofjAndkthe strength of the connection between the two parts,

thenkLoad of update on

Comprises the following steps:

s1.3.4, comparisonkUpdate load of andkdetermines whether further removal is requiredk：

s1.3.5, repeating S1.3.1-S1.3.4, removing the connections and connection strengths of the affected infrastructures, and normalizing again until the urban infrastructure group returns to the balance state;

further, the cascade failure model is corrected: disturbance: since global perturbation patterns are considered, perturbation is only considered on the core infrastructure. While the core infrastructure is not removed after being overloaded, but does not participate in the subsequent load distribution process. Load distribution: load distribution in a single infrastructure group is kept unchanged, distribution among the infrastructure groups is distributed to infrastructures in adjacent infrastructure groups if redundant loads need to be distributed after internal distribution is finished, and meanwhile, the requirements of correlation connection strength need to be met, and the distribution is according to an average distribution principle;

further, the step S1.4 is implemented by the following steps:

s1.4.1, defining core infrastructure loading disturbance based on disturbance mode considering global state, and the core infrastructure is not removed after overload and does not participate in subsequent load distribution process; defining load distribution to keep constant for load distribution in an individual infrastructure group, distributing among the infrastructure groups, and after the distribution in the infrastructure groups is finished, distributing the rest load to the infrastructures of the adjacent infrastructure groups according to an average distribution principle under the condition of meeting correlation connection strength, then:

is composed ofyThe value of the operational function of the assigned load,

is the update load of y and is,

is the value of the operating function of y,MC _j is composed ofjThe maximum capacity of (c);

s1.4.3, when an infrastructure group fails by 50% or more, it triggers determination of the attribute of infrastructure necessity, that is, when the connection strength matrix is updated by removing unnecessary attributes of each infrastructure from the operation state values and removing the influence of the connection strength, the connection matrix before updating is:

。

because the actual fault propagation time is difficult to find a definite corresponding quantitative index in reality, the embodiment is based on a cascade failure model, and the fault propagation time is considered;

further, the specific implementation method of step S2 includes the following steps:

is composed ofjTokThe time taken for the euclidean distance;

s2.2, setting the state parameter of the urban infrastructure group as the overload load total SCP of the urban infrastructure group, setting the initial SCP of the system to be 0, then gradually increasing the SCP, and finally restoring the SCP to be 0, and obtaining the elastic parameter according to the elastic triangle theoryRComprises the following steps:

wherein R is an elasticity parameter without considering the load distribution strategy among the infrastructure groups,t ₀ which represents the starting moment of the elastic triangle,t ₁ the end time of the elastic triangle is shown, the elastic magnitude is inversely proportional to the area of the elastic triangle, therefore, the result takes a negative value, the continuous integral becomes a discrete addition,Yfor the total number of stages in which overload occurs,

is shown ashLoad shifting object of cascaded failure-related failure infrastructure of stagesThe average time is the sum of the time,Q _h is as followshA first-order neighbor set of overloaded infrastructure in a cascade failure of stages,N _h denotes the firsthThe number of infrastructure overloaded in a cascade failure of a stage;

and S2.3, calculating the system elasticity under the improved cascade failure model, and comparing with the model condition without considering load distribution among infrastructure groups. Considering the real situation, such load distribution mainly relates to the self-supply capability of the infrastructure group, and the network elasticity index RSL is:

wherein

In order to consider the elasticity parameters under the condition of the load distribution strategy among the infrastructure groups, and then sort the infrastructure groups according to the parameters of the infrastructure groupsFIG1(l)There are three types:

wherein,

l _c0 under the condition of the threshold value, the method,

is a threshold valuel _c0 Under the condition, elastic parameters under the condition of a load distribution strategy among the urban infrastructure groups are not considered;

l _c1 under the condition of the threshold value, the method,

represents a threshold valuel _c1 Urban base under the conditionA portion of elasticity values outside of the infrastructure group;

l _c2 under the condition of the threshold value, the method,

further, there is a threshold valuel _c0 So that fault propagation at this point involves load sharing among infrastructure groups, which is of guiding significance for real-world event handling; l _c1 At threshold value, R ₁ And R ₂ The parts are equal, on one hand, the method has guiding significance for the attribute classification of the infrastructure group, and on the other hand, the method can provide reference for the resource allocation of elastic recovery;

s2.5 elasticity based on the urban infrastructure group that has been acquiredAnalyzing the spatial distribution of elasticity values of city infrastructure group, and introducing the calculation formula of spatial correlationC(r)The following were used:

is the mean value of the elasticity values of the urban infrastructure group,

the variance is represented as a function of time,r _sg representing the euclidean distance between s and g,

the function is used to screen distances ofrWhen the Euclidean distance between s and g isrWhen the temperature of the water is higher than the set temperature,

the value is 1, otherwise 0, by the spatial correlation at different rC(r)The target space correlation area is found out to carry out targeted elastic management measures.

S3, elasticity analysis of the urban infrastructure group: introducing a fault mode in which multipoint failures occur simultaneously to calculate network elastic parameters of the urban infrastructure group, introducing spatial position information at the same time, analyzing the elastic parameter conditions of the infrastructure group in a central area and an edge area, and finally performing tree analysis on the cascading failure model process;

s3.1, presetting 10 percent of city infrastructure groups to simultaneously generate overload failure, and then calculating the network elasticity index according to the relation of permutation and combinationSignRNIThe method comprises the following steps:

is a network elasticity indicator of 10% infrastructure group overload failure,

selecting a permutation and combination formula of 10% of Z number of combinations from Z infrastructure groups; s3.2, counting two city infrastructure groups with the highest occurrence frequency in the first 10% of sets with the highest contribution degree to the network elasticity indexes as system elasticity key city infrastructure groups;

Wherein,W _h is composed ofhAn overloaded set of infrastructure for cascading failures of a stage,Q _k overloading an infrastructure for cascading failureskThe first-order neighbors of (a) a,

to representW _h The number of infrastructures in the set is,

representQ _k The number of infrastructures in the set is,

is the euclidean distance between infrastructure k and m;

s3.3.2, calculating node betweenness of urban infrastructure group networkBThe definition is as follows:

to representiNode betweenness of (2);

furthermore, node betweenness reflects the action and influence of the nodes in the whole network and is an important global geometric quantity;

Wherein,B _m representmNode betweenness of the infrastructure;

s3.4, performing tree analysis on the infrastructure in the cascade failure process;

and performing tree analysis on the infrastructure in the cascade failure process to obtain corresponding elastic parameters. As shown in fig. 4, the overload connection of the cascade failure process is shown, wherein the node generation is composed of the overload failure and the infrastructure of the continuous overload after the load distribution, each node in the graph is an infrastructure, and the hierarchical relationship in the cascade failure process is analyzed;

s3.4.1, and analyzing the hierarchical relationship in the cascade failure process. First, the ability parameter of the single infrastructure to resist disturbance, the process vulnerability parameter, is calculatedPVP：

Wherein,OL _j andOL _k are respectivelyjAndkthe number of overload times at the time of overload failure,iis a root node of the root node,SP _ij to representiAndjthe shortest distance between the two elements of the first and second,La _j in a representation tree structurejThe number of layers of (a) to (b),

to representjA process vulnerability parameter of (a);

further, by definition, the process vulnerability parameter PVP is determined in two parts: the first is the ratio of the overload load between the node and the father node, and the second is the shortest distance of the static structure and the hierarchy ratio in the actual cascade failure tree. This effectively measures structural and functional vulnerability changes;

S3.4.4, and method for improving elastic recovery efficiencyRREP：

Further, the elastic recovery efficiency parameter thus characterizes overload failures of other infrastructures due to failures of infrastructure j. Therefore, the larger the RREP value, the higher the efficiency of elastic improvement for the infrastructure, and the lower the reverse.

The second embodiment is as follows:

the electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the urban infrastructure group network elasticity analysis method according to the embodiment when executing the computer program.

Further, the computer device of the present invention may be a device including a processor, a memory, and the like, for example, a single chip microcomputer including a central processing unit, and the like. And the processor is used for implementing the steps of the recommendation method capable of modifying the relationship-driven recommendation data based on the CREO software when executing the computer program stored in the memory.

The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.

The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a sound playing function, an image playing function, etc.), and the like; the storage data area may store data (such as audio data, a phonebook, etc.) created according to the use of the cellular phone, and the like. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), at least one magnetic disk storage device, a Flash memory device, or other volatile solid state storage device.

The third concrete implementation mode:

a computer-readable storage medium, on which a computer program is stored, wherein the computer program, when executed by a processor, implements a method for resilient analysis of a city infrastructure group network according to one embodiment of the present invention.

Further, the computer readable storage medium of the present invention may be any form of storage medium read by a processor of a computer device, including but not limited to a non-volatile memory, a ferroelectric memory, etc., on which a computer program is stored, and when the computer program stored in the memory is read and executed by the processor of the computer device, the above-mentioned steps of the method for modeling modifiable relationship-driven modeling data based on CREO software may be implemented.

The computer program comprises computer program code which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, read-Only Memory (ROM), random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, and the like. It should be noted that the computer readable medium may contain content that is subject to appropriate increase or decrease in accordance with the requirements of legislation and inventive practice in jurisdictions, for example, in some jurisdictions, computer readable media does not include electrical carrier signals and telecommunications signals in accordance with legislation and inventive practice.

The invention provides a city infrastructure group network elasticity analysis system based on a cascade failure model, which has the following advantages:

1. according to the cascade failure model of the urban infrastructure group, firstly, the model meets the actual analysis requirement, and meanwhile, the established minimum analysis unit, namely the urban infrastructure group, focuses on that the urban infrastructure group actually plays a supporting role in urban operation when the urban infrastructure deals with natural disasters, extreme weather and artificial damage and attack, and is based on the reality of a resource allocation strategy after the disasters occur. The actual analysis of the urban infrastructure is closer to the reality, and the means of dividing the urban infrastructure group enables the analysis to be more effective; secondly, introducing a spatial correlation analysis method in the dividing process, and simultaneously considering a fault introduction means of the core infrastructure; and finally, on the basis of a classical cascade failure model, considering the actual condition that the urban infrastructure group system is subjected to external disturbance, introducing attribute division of different facilities and describing the space propagation characteristics of fault propagation. By further optimizing and improving the cascade failure model, the method is more suitable for the actual situation and more effective in analysis; 2. the method firstly analyzes the elasticity analysis of the infrastructure in the infrastructure group, and introduces system elasticity parameters, analysis process and indexes reasonably based on the classical elastic trigonometric theory. Meanwhile, the infrastructure group is divided into function categories based on the elasticity analysis of the infrastructure group: supply, dependency and equalization; 3. the method integrates two levels of local single infrastructure group and integral infrastructure group networks, and analyzes the elastic parameter condition of the urban infrastructure. The attribute characteristics of different infrastructure groups are considered more at the level of a single infrastructure group, and the overall system elasticity capability assessment and the discovery of a fragile infrastructure group are mainly considered at the level of an infrastructure group network. The method combines the micro-scale and the macro-scale, and provides effective support for the actual implementation of the elastic lifting strategy; 4. the method carries out elasticity analysis at the level of the urban infrastructure group network, analyzes and effectively delineates and explores the elasticity modes of the urban infrastructure group under different disturbance modes aiming at external disturbances such as natural disasters with huge urban influence, and evaluates the elasticity condition of the urban infrastructure group. Meanwhile, creatively providing an analysis method of the cascade failure tree structure, and formulating a corresponding elastic parameter system; 5. by combining the elasticity analysis, the invention starts from the cascade failure model, considers the real condition that the infrastructure group suffers external disturbance, and optimizes and improves the model. Then introducing the elasticity parameters of the system based on the elasticity triangle theory. And constructing a theoretical analysis framework of the infrastructure group through the model and the parameters. An elasticity analysis system of the urban infrastructure group network is established from the process analysis of the urban infrastructure borne disturbance energy, the sensitivity of disturbance change, the propagation process and the breadth range calculation of the disturbance in the system and the system elasticity recovery, and an effective support is provided for researching and improving the elasticity of the urban infrastructure.

The key points and points to be protected of the technology of the invention are as follows:

1. the method comprises the following steps of (1) introducing attribute division of infrastructure and description of fault propagation spatial characteristics into a cascading failure model and a correction version of the urban infrastructure group network;

2. attribute classification of infrastructure group: dividing the infrastructure group into a supply type, a dependence type and a balance type according to the analysis result of the cascading failure model of the infrastructure group;

3. a cascading failure tree analysis method of a cascading failure path based on an infrastructure group network and constructing a corresponding elasticity evaluation parameter system;

4. and (4) elastic analysis of the infrastructure group network, and establishment of an overall elasticity index and a recovery function evaluation index of the infrastructure group network.

Abbreviations and key term definitions of the invention:

abbreviations:

resilience Maintain Efficiency: RME, elastic retention efficiency; resilience Zero-Value Parameter: RZP, elastic zero parameter; fundamental Infrastructure Group: FIG, infrastructure group; maximum Resilience recovery Parameter: MRRP, maximum elastic recovery parameter; pearson Product-motion Correlation Coefficient: PPMCC, pearson correlation coefficient; network resource Dispersal Efficiency: RNDE, network resiliency grooming efficiency; initial Load: IL, initial load; maximum Capacity: MC, maximum capacity; tolerance Parameter: TP, tolerance parameter; resilience Triangle: RT, elastic triangle; parameter: PRM, parameter; system Condition Parameter: SCP, system state parameter; fuction Values: FV, functional value; network resource Index: RNI, network elasticity index; resource Supply Level: RSL, resource supply level; a resource Propagation Distance, an elastic Propagation effective Distance; node Betweenness: b, node betweenness; resilence Spatial Parameter: RSP, elastic space parameter; procedural Vulnerability Parameter: PVP, process vulnerability parameter; resilence Tree Structural Parameter: RTSP, elastic tree parameters; resilence Function relationship Parameter: RFRP, elastic function related parameters; resilence recovery Efficiency Parameter: RREP, elastic recovery efficiency parameter.

It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.

While the application has been described above with reference to specific embodiments, various modifications may be made and equivalents may be substituted for elements thereof without departing from the scope of the application. In particular, the various features of the embodiments disclosed herein may be used in any combination that is not inconsistent with the structure, and the failure to exhaustively describe such combinations in this specification is merely for brevity and resource conservation. Therefore, it is intended that the application not be limited to the particular embodiments disclosed, but that the application will include all embodiments falling within the scope of the appended claims.

Claims

1. A method for analyzing network elasticity of urban infrastructure group is characterized by comprising the following steps: the method comprises the following steps:

s1.3, establishing a cascading failure model of the urban infrastructure group;

the specific implementation method of the step S1.3 comprises the following steps:

s1.3.1, the definition of a cascade-based failure model, defining an initial disturbance as an increased load value of the infrastructure, for city infrastructure j:

MC _j ＝(1+TP _j )·IL _j

MC _j is the maximum capacity of infrastructure j, TP _j For the tolerance parameter of infrastructure j, IL _j For the initial load of infrastructure j:

s1.3.2, after cascade failure occurs, deleting the overloaded infrastructure j, and distributing the load of the infrastructure j to the first-order neighbor k according to the connection strength, where the distribution ratio is:

L′ _j,k is the normalized connection strength between j and k, L _j,k Is the strength of the connection between j and k, L _j,m Is the connection strength between j and m, m is any one of Q, Q is a first-order neighbor set connected with the infrastructure j;

s1.3.3, k the assigned load is proportional to the intensity after k normalization, as follows:

FV _j2k ＝FV _j ·L′ _j,k

FV _j2k the value of the running function, FV, of the load assigned to k _j Is the operating function value of infrastructure j;

then the updated load FV 'on k' _k Comprises the following steps:

FV′ _k ＝FV _k +FV _j2k ＝FV _k +FV _j ·L′ _j,k

s1.3.4, comparing the relationship of the update load of k to the maximum capacity of k, and determining if further removal of k:

e (k) is the state value of k, MC _k Maximum capacity of k, 0 for removal, 1 for retention;

s1.4, correcting the cascading failure model of the urban infrastructure group to obtain an improved cascading failure model of the urban infrastructure group network;

s2.1, setting the fault propagation time as follows based on an improved cascade failure model of the urban infrastructure group network:

T _j2k time for the load of j to propagate on k, t _j2k The time taken for the distance j to k in ohms;

s2.2, setting the state parameter of the urban infrastructure group as the overload total SCP of the urban infrastructure group, and obtaining an elastic parameter R according to an elastic triangle theory as follows:

wherein R is an elastic parameter without considering a load distribution strategy among infrastructure groups, t ₀ Denotes the starting time, t, of the elastic triangle ₁ The ending time of the elastic triangle is shown, Y is the total number of overload stages,

representing the mean time of load transfer objects of the cascaded failure-related failure infrastructure of the h-th stage, Q _h For the first-order neighbour set of overloaded infrastructure in cascade failure of h-th stage, N _h Representing the number of infrastructure overloaded in the cascade failure of the h-th stage;

wherein R' is an elastic parameter under consideration of a load distribution policy between infrastructure groups, and then the infrastructure group FIG1 (l) is divided into three types according to a parameter ranking condition of the infrastructure groups:

wherein, RSL _30％ 30% quantiles, RSL, of a sequence of resource supply level values for an infrastructure group _70％ Analyzing 70% quantiles of a resource supply level value sequence of an infrastructure group, wherein l is a multiple of the initial load increase, and aiming at the condition that l is larger than 1;

R ₂ (l _c0 )≠0

l _c0 at threshold value, R ₁ (l _c0 ) Represents a threshold value l _c0 Part of the elastic value, R, in the infrastructure group under the conditions ₂ (l _c0 ) Represents a threshold value l _c0 An elasticity value part outside the urban infrastructure group under the condition; r (l) _c0 ) Is a threshold value l _c0 Policy for load distribution among urban infrastructure groups under conditions without considerationElasticity parameter in the case of omission;

R ₁ (l _c1 )＝R ₂ (l _c1 )

l _c1 at threshold value, R ₁ (l _c1 ) Represents a threshold value l _c1 Part of the elastic value, R, within a city infrastructure group under conditions ₂ (l _c1 ) Represents a threshold value l _c1 An elasticity value part outside the urban infrastructure group under the condition; r (l) _c1 ) Is a threshold value l _c1 Elastic parameters under the condition of a load distribution strategy among urban infrastructure groups are not considered;

R(l _c2 )→-∞

l _c2 at threshold value, R ₁ (l _c2 ) Represents a threshold value l _c2 Part of the elastic value, R, within a city infrastructure group under conditions ₂ (l _c2 ) Represents a threshold value l _c2 An elasticity value part outside the urban infrastructure group under the condition; r (l) _c2 ) Is a threshold value l _c2 Under the condition, elastic parameters under the condition of a load distribution strategy among the urban infrastructure groups are not considered, and the whole system is completely crashed;

s2.5, analyzing the spatial distribution situation of the elasticity values of the urban infrastructure group based on the obtained elasticity values of the urban infrastructure group, and introducing a calculation formula C (r) of spatial correlation as follows:

wherein R is _s Is the elasticity value, R, of the urban infrastructure group s _g Is the elasticity value of the city infrastructure group g, FIG is the city infrastructureShi Qun, is,

is the mean value of elasticity values, σ, of the urban infrastructure group ² Represents the variance, r _sg Denotes the Euclidean distance, δ (r), between s and g _sg -r) the function is used for screening node pairs with the distance r, and a target spatial correlation area is found through distribution change curves of spatial correlation C (r) under different r to perform targeted elastic management measures;

s3, elasticity analysis of the urban infrastructure group: and (3) introducing a fault mode in which multipoint failures occur simultaneously to calculate network elastic parameters of the urban infrastructure group, introducing spatial position information at the same time, analyzing the elastic parameter conditions of the infrastructure group in a central area and an edge area, and finally performing tree analysis on the cascading failure model process.

2. The city infrastructure group network elasticity analysis method of claim 1, wherein: the specific implementation method of the step S1.2 comprises the following steps:

s1.2.1, considering city scale, setting core infrastructure group to influence maximum radius D _max Bringing infrastructure in range into infrastructure group, setting i as core infrastructure, j as infrastructure, FV _i Is the operating function value, FV, of the core infrastructure i _j Is the operating function value of infrastructure j;

s1.2.2, calculating the Pearson correlation coefficient between the FV sequence and i as the functional value of the infrastructure operation in the range of the infrastructure group:

PPMCC _i，j for Pearson's correlation coefficient between the j infrastructure running function value sequence and i, cov (i, j) is the covariance of the running function value sequences of i and j, σ _i Is the standard deviation of i, σ _j Is the standard deviation of j;

s1.2.3, transdermalThe coefficient of the Erson correlation is given as F _i (j) Carrying out primary division on the urban infrastructure group;

F _i (j) Indicating whether j is within the infrastructure group that is the center for core infrastructure i, a value of 1 indicates within, and a value of 0 is outside.

3. The city infrastructure group network elasticity analysis method of claim 2, wherein: the specific implementation method of the step S1.4 comprises the following steps:

FV _j2y operating function value, FV, of the load assigned to y _j2d The running function value of the load assigned to d, nei (j) is the first order neighbor set of infrastructure j within the group, d is any one of Nei (j), nei' (j) represents the first order neighbor set of infrastructure j outside the groupY ∈ Nei' (j), then:

FV′ _y update load of y, FV _y Is the running function value of y, MC _j Is the maximum capacity of j;

the updated connection matrix is a cascading failure model of the urban infrastructure group network:

4. the city infrastructure group network elasticity analysis method of claim 3, wherein: the specific implementation method of the step S3 comprises the following steps:

s3.1, presetting that 10% of urban infrastructure groups simultaneously suffer overload failure, and then calculating a network elasticity index (RNI) according to a permutation and combination relationship, wherein the method comprises the following steps:

RNI (10%) is a network elasticity indicator for 10% infrastructure group overload failures, RNI _k (10%) network resiliency index for the kth 10% infrastructure group combination overload failure, R _k (10%) is the resilience index of the k 10% infrastructure group combined overload failure，

Selecting a permutation and combination formula of 10% of Z number of combinations from Z infrastructure groups;

s3.2, counting two city infrastructure groups with highest occurrence frequency in the first 10% of sets with highest contribution degree to the network elasticity index as system elasticity key city infrastructure groups;

5. The city infrastructure group network elasticity analysis method of claim 4, wherein: the specific implementation method of the step S3.3 comprises the following steps:

s3.3.1, calculating the effective propagation distance RPD of the infrastructure cascade failure process:

wherein, W _h Overload infrastructure set, Q, for cascade failures of order h _k To cascade a first order neighbor set of failure overload infrastructure k,

represents W _h The number of infrastructures in the set may be,

represents Q _k Number of infrastructures in the set, r _km Is the euclidean distance between infrastructure k and m;

s3.3.2, calculating node betweenness B of the urban infrastructure group network, and defining as follows:

wherein n is _jk Number, n, representing the shortest path between nodes j and k _jk (i) Represents the number of nodes i passing through in the shortest path between nodes j and k, B _i Representing the node betweenness of i;

s3.3.3, calculating elastic space parameter RSP of city infrastructure group:

wherein, B _m Representing the node betweenness of the m infrastructures.

6. The city infrastructure group network elasticity analysis method of claim 5, wherein: the specific implementation method of the step S3.4 comprises the following steps:

s3.4.1, analyzing the hierarchical relationship in the cascade failure process: first, the disturbance resistance parameter of the single infrastructure is calculated, the process vulnerability parameter PVP:

wherein, OL _j And OL _k The overload multiples of j and k in overload failure, i is the root node, SP _ij Represents the shortest distance between i and j, la _j Representing the number of layers of j in the tree structure, and PVP (j) represents the process vulnerability parameter of j;

s3.4.2, calculating elastic tree structure parameter RTSP of city infrastructure group:

s3.4.3, calculating elastic function related parameter RFRP (FIG 1) of city infrastructure group:

s3.4.4, and from the perspective of the efficiency of the elastic recovery strategy, providing an elastic recovery efficiency parameter RREP:

wherein, FS _j And representing that the infrastructure j overloads the infrastructure set on the failure path on the cascade failure tree structure, wherein the RREP (j) is an elastic recovery efficiency parameter of the j, and the larger the RREP value is, the higher the efficiency of elastic improvement on the infrastructure is, and the lower the efficiency is otherwise.

7. Electronic device, comprising a memory and a processor, the memory storing a computer program, the processor implementing the steps of the city infrastructure group network elasticity analysis method according to any one of claims 1 to 6 when executing the computer program.

8. Computer readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements a city infrastructure group network elasticity analysis method according to any one of claims 1 to 6.