CN115114715A - City infrastructure group network elasticity analysis method, electronic device and storage medium - Google Patents

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

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CN115114715A
CN115114715A CN202211028737.5A CN202211028737A CN115114715A CN 115114715 A CN115114715 A CN 115114715A CN 202211028737 A CN202211028737 A CN 202211028737A CN 115114715 A CN115114715 A CN 115114715A
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林涛
周子益
贾磊
童青峰
刘星
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Shenzhen Traffic Science Research Institute Co ltd
Shenzhen Urban Transport Planning Center Co Ltd
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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 urban infrastructures.

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 the global warming, urban infrastructure faces huge challenges, and how to design and build urban infrastructure capable of resisting the impacts is significant for guaranteeing normal operation and stable economic development 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" against these city critical infrastructures will cause significant losses to the city, 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, global warming, extreme weather, and various human causes are all disturbing factors that affect 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 achieve the purpose, the invention is realized by the following technical scheme:
a method for analyzing network elasticity of urban infrastructure group comprises the following steps:
s1, constructing a cascading failure model of the urban infrastructure group network;
s1 the concrete implementation method of the cascade failure model for constructing 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 within the city 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 includes the following steps:
s2.1, setting the fault propagation time as follows based on the cascade failure model of the urban infrastructure group:
Figure 775393DEST_PATH_IMAGE001
Figure 751439DEST_PATH_IMAGE002
is composed ofjIs propagated tokThe time of (2) is greater than the time of (c),
Figure 229825DEST_PATH_IMAGE003
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:
Figure 873296DEST_PATH_IMAGE005
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,
Figure 146145DEST_PATH_IMAGE007
is shown ashThe average time of load shifting objects of the cascade failure related failure infrastructure of a stage,Q h is a firsthA first-order neighbor set of overloaded infrastructure in a cascade failure 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:
Figure 830328DEST_PATH_IMAGE008
wherein
Figure 909143DEST_PATH_IMAGE009
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:
Figure 344803DEST_PATH_IMAGE010
wherein, the first and the second end of the pipe are connected with each other,
Figure 850871DEST_PATH_IMAGE011
a 30% quantile of a sequence of resource supply level values for an infrastructure group,
Figure 4772DEST_PATH_IMAGE012
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 conditions in the urban infrastructure group and among the urban infrastructure groups under different load increase times, setting a threshold, and regarding the FIG1, the threshold comprises the following steps:
Figure 887277DEST_PATH_IMAGE013
Figure 177444DEST_PATH_IMAGE014
l c0 under the condition of the threshold value, the method,
Figure 57675DEST_PATH_IMAGE015
represents a threshold valuel c0 The portion of elasticity values within the infrastructure group under the conditions,
Figure 495610DEST_PATH_IMAGE016
represents a threshold valuel c0 An elasticity value part outside the urban infrastructure group under the condition;
Figure 916227DEST_PATH_IMAGE017
is a threshold valuel c0 Elastic parameters under the condition of a load distribution strategy among urban infrastructure groups are not considered;
Figure 326480DEST_PATH_IMAGE018
Figure 174350DEST_PATH_IMAGE019
l c1 under the condition of the threshold value, the method,
Figure 37264DEST_PATH_IMAGE020
represents a threshold valuel c1 The portion of elasticity values within the city infrastructure group under the conditions,
Figure 199255DEST_PATH_IMAGE021
represents a threshold valuel c1 An elasticity value part outside the urban infrastructure group under the condition;
Figure 526331DEST_PATH_IMAGE022
is a threshold valuel c1 Elastic parameters under the condition of a load distribution strategy among urban infrastructure groups are not considered;
Figure 748365DEST_PATH_IMAGE023
Figure 160892DEST_PATH_IMAGE024
l c2 under the condition of the threshold value, the method,
Figure 860995DEST_PATH_IMAGE025
represents a threshold valuel c2 The portion of elasticity values within the city infrastructure group under the conditions,
Figure 42577DEST_PATH_IMAGE026
represents a threshold valuel c2 An elasticity value part outside the urban infrastructure group under the condition;
Figure 435512DEST_PATH_IMAGE027
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:
Figure 335335DEST_PATH_IMAGE028
wherein the content of the first and second substances,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,
Figure 839129DEST_PATH_IMAGE029
is the mean value of the elasticity values of the urban infrastructure group,
Figure 875218DEST_PATH_IMAGE030
the variance is represented as a function of time,
Figure 439055DEST_PATH_IMAGE031
representing the euclidean distance between s and g,
Figure 826174DEST_PATH_IMAGE032
the function is used to screen distances ofrNode pair of (c), by 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 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.
Further, the step S1.2 is implemented 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 (a);
s1.2.2, calculating the operation function value of the infrastructure in the range of the infrastructure groupFVPearson correlation coefficient between sequence and i:
Figure 24254DEST_PATH_IMAGE034
PPMCC i，j is composed ofjSequence of infrastructure operational function values andipearson's correlation coefficient between, cov: (i，j) Is composed ofiAndjthe covariance of the running function value sequence of (a),
Figure 758992DEST_PATH_IMAGE035
is composed ofiThe standard deviation of (a) is determined,
Figure 367827DEST_PATH_IMAGE036
is composed ofjStandard deviation of (d);
s1.2.3, obtaining the correlation coefficient of Pearson
Figure 479003DEST_PATH_IMAGE037
Carrying out primary division on the urban infrastructure group;
Figure 489684DEST_PATH_IMAGE038
Figure 389464DEST_PATH_IMAGE039
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 perturbation as increasing load value of infrastructure based on definition of cascade failure model, for urban infrastructurejComprises the following steps:
Figure 485596DEST_PATH_IMAGE040
Figure 869304DEST_PATH_IMAGE041
as an infrastructurejThe maximum capacity of the battery pack is set,TP j as an infrastructurejThe tolerance parameter(s) of (a),
Figure 71DEST_PATH_IMAGE042
as an infrastructurejInitial load of (2):
s1.3.2, removing overloaded infrastructure when cascade failure occursjInfrastructure, infrastructurejWill be assigned to first-order neighbors according to connection strengthskThe distribution ratio is as follows:
Figure 76611DEST_PATH_IMAGE043
Figure 660039DEST_PATH_IMAGE044
is composed ofjAndkthe normalized strength of the connection therebetween and,
Figure 847438DEST_PATH_IMAGE045
is composed ofjAndkthe strength of the connection between the two parts,
Figure 770395DEST_PATH_IMAGE046
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:
Figure 80154DEST_PATH_IMAGE047
Figure 88561DEST_PATH_IMAGE048
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
Figure 141968DEST_PATH_IMAGE049
Comprises the following steps:
Figure 919431DEST_PATH_IMAGE050
s1.3.4, comparisonkUpdate load of andkdetermines whether further removal is requiredk：
Figure 400091DEST_PATH_IMAGE051
Figure 630215DEST_PATH_IMAGE052
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, repeat steps S1.3.1-S1.3.4, remove the connections and connection strengths of the affected infrastructure and re-normalize the connections and connection strengths 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 disturbance based on disturbance mode considering global, 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:
Figure 487312DEST_PATH_IMAGE053
s1.4.2, for j, the first order neighbors of the neighboring infrastructure group assign y the load to j as follows:
Figure 119282DEST_PATH_IMAGE054
Figure 770843DEST_PATH_IMAGE055
is composed ofyThe value of the operational function of the assigned load,
Figure 753843DEST_PATH_IMAGE056
is composed ofdIs distributed toThe value of the operating function of the load,Nei (j)as an infrastructurejA set of first-order neighbors within a group,dis composed ofNei(j)Any one of (2)，
Figure 149052DEST_PATH_IMAGE057
Representing infrastructurejA set of first-order neighbors outside the group,y∈Nei'(j）and then:
Figure 635528DEST_PATH_IMAGE058
Figure 661253DEST_PATH_IMAGE059
the update load for y is the load of y,
Figure 928286DEST_PATH_IMAGE060
is the value of the operating function of y,MC j\ is composed ofjThe maximum capacity of (c);
s1.4.3, triggering attribute judgment of infrastructure necessity after 50% or more of infrastructure failures occur based on the infrastructure group, and the connection matrix before updating is as follows for the infrastructure group with H infrastructures:
Figure 799290DEST_PATH_IMAGE061
the updated connection matrix is a cascading failure model of the urban infrastructure group network:
Figure 468169DEST_PATH_IMAGE062
。
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:
Figure 664795DEST_PATH_IMAGE063
Figure 153545DEST_PATH_IMAGE064
is a network elasticity indicator of 10% infrastructure group overload failure,
Figure 93819DEST_PATH_IMAGE065
the network resiliency indicator of overload failure is combined for the kth 10% infrastructure group,
Figure 617205DEST_PATH_IMAGE066
the resiliency index for overload failure is combined for the kth 10% infrastructure group,
Figure 719153DEST_PATH_IMAGE067
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 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;
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 the cascade failure process of the infrastructureRPD：
Figure 960778DEST_PATH_IMAGE069
Wherein the content of the first and second substances,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,
Figure 433305DEST_PATH_IMAGE070
to representW h The number of infrastructures in the set is,
Figure 748880DEST_PATH_IMAGE072
to representQ k The number of infrastructures in the set is,
Figure 349625DEST_PATH_IMAGE073
is the euclidean distance between infrastructure k and m;
s3.3.2 calculating node betweenness of city infrastructure group networkBThe definition is as follows:
Figure 750651DEST_PATH_IMAGE074
wherein, the first and the second end of the pipe are connected with each other,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,
Figure 95044DEST_PATH_IMAGE075
to representiNode betweenness of (2);
s3.3.3 calculating elastic space parameters of city infrastructure groupRSP：
Figure 530705DEST_PATH_IMAGE077
Wherein the content of the first and second substances,B m to representmNode betweenness of the infrastructure.
Further, the specific implementation method of step S3.4 includes the following steps:
s3.4.1, 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：
Figure 974456DEST_PATH_IMAGE078
Wherein the content of the first and second substances,OL j andOL k are respectivelyjAndkthe number of overload times at the time of overload failure,ias a root node, the node is a node,SP ij to representiAndjthe shortest distance between the two or more of the two,La j in a representation tree structurejThe number of layers of (a) to (b),
Figure 190673DEST_PATH_IMAGE079
to representjA process vulnerability parameter of (a);
s3.4.2 calculating elastic tree structure parameters of city infrastructure groupRTSP：
Figure 10862DEST_PATH_IMAGE080
S3.4.3 calculating elastic function related parameters of city infrastructure groupRFRP：
Figure 363346DEST_PATH_IMAGE081
S3.4.4, providing an elastic recovery efficiency parameter from the perspective of the efficiency of the elastic recovery strategyRREP：
Figure 977998DEST_PATH_IMAGE082
Wherein the content of the first and second substances,FS j representing infrastructurejOverloading the set of infrastructure on the failure path on the cascading failure tree structure,
Figure 415932DEST_PATH_IMAGE083
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 resources of 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 is really greater and more direct due to disturbance of local areas, 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, the elastic parameters of the infrastructure are calculated according to the existing load redundancy upper limit value and the distribution quantity of the infrastructure in the actual load distribution process and by combining the fault propagation time. Then, calculating the elastic parameters under the conditions of considering the load distribution among the infrastructure groups and not considering the load distribution, and calculating the ratio of the load distribution to the elastic parameters to obtain the network elastic untwining 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 elasticity values of the infrastructure 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 overall elasticity capability index of the infrastructure group based on the actual path of fault propagation from the fault protection perspective.
In combination with 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 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 analysis of the disturbance energy bearing capacity of the urban infrastructure, the disturbance change sensitivity, the propagation process and the breadth range calculation of the disturbance in the system and the system elasticity recovery process, and 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 of the present invention and are not to be construed as limiting thereof, i.e., the described embodiments are merely a subset of the embodiments of the invention and are not all embodiments. 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 a further understanding of the contents, features and effects of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
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 daily life activities of urban residents, 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 center point of the infrastructure, and after threshold value setting and screening, preliminary division of infrastructure groups 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.
S1, constructing a cascading failure model of the urban infrastructure group network;
s1 the concrete implementation method of the cascade failure model for constructing 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;
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
Figure 39812DEST_PATH_IMAGE084
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.
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;
further, the step S1.2 is implemented 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 baseInfrastructureiThe value of the operating function of (c),FV j as an infrastructurejAn operating function value of;
s1.2.2, calculating the operation function value of the infrastructure in the range of the infrastructure groupFVPearson correlation coefficient between sequence and i:
Figure 297935DEST_PATH_IMAGE085
PPMCC i，j is composed ofjSequence of infrastructure operational function values andipearson's correlation coefficient between, cov: (i，j) Is composed ofiAndjthe covariance of the running function value sequence of (a),
Figure 160849DEST_PATH_IMAGE086
is composed ofiThe standard deviation of (a) is determined,
Figure 385157DEST_PATH_IMAGE087
is composed ofjStandard deviation of (d);
s1.2.3, obtaining the correlation coefficient of Pearson
Figure 649916DEST_PATH_IMAGE088
Carrying out primary division on the urban infrastructure group;
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Figure 18897DEST_PATH_IMAGE090
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 on cascade failure modelFor urban infrastructure, defining the initial perturbation as an increase in the load value of the infrastructurejComprises the following steps:
Figure 46896DEST_PATH_IMAGE091
Figure 166162DEST_PATH_IMAGE092
as an infrastructurejThe maximum capacity of the battery pack is set,TP j as an infrastructurejThe tolerance parameter(s) of (a),
Figure 559097DEST_PATH_IMAGE093
as an infrastructurejInitial load of (2):
s1.3.2, removing overloaded infrastructure when cascade failure occursjInfrastructure, infrastructurejWill be assigned to first-order neighbors according to connection strengthskThe distribution ratio is as follows:
Figure 458920DEST_PATH_IMAGE094
Figure 962714DEST_PATH_IMAGE095
is composed ofjAndkthe normalized strength of the connection therebetween and,
Figure 998803DEST_PATH_IMAGE096
is composed ofjAndkthe strength of the connection between the two parts,
Figure 562639DEST_PATH_IMAGE097
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:
Figure 684179DEST_PATH_IMAGE098
Figure 985804DEST_PATH_IMAGE099
is composed ofkThe value of the operational function of the assigned load,FV j as an infrastructurejAn operating function value of;
then thekLoad of update on
Figure 141979DEST_PATH_IMAGE100
Comprises the following steps:
Figure 876717DEST_PATH_IMAGE101
s1.3.4, comparisonkUpdate load of andkdetermines whether further removal is requiredk：
Figure 485553DEST_PATH_IMAGE102
Figure 331149DEST_PATH_IMAGE103
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 steps S1.3.1-S1.3.4, removing the connections and connection strengths of the affected infrastructures and normalizing again until the city 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;
s1.4, correcting the cascading failure model of the urban infrastructure group to obtain a cascading failure model of an urban infrastructure group network;
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 the core infrastructure is not removed after overload and does not participate in the 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:
Figure 341830DEST_PATH_IMAGE104
s1.4.2, for j, the first order neighbors of the neighboring infrastructure group assign y the load to j as follows:
Figure 247470DEST_PATH_IMAGE105
Figure 343602DEST_PATH_IMAGE106
is composed ofyThe value of the operational function of the assigned load,
Figure 992889DEST_PATH_IMAGE107
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)，
Figure 123656DEST_PATH_IMAGE108
Representing infrastructurejA set of first-order neighbors outside the group,y∈Nei'(j）and then:
Figure 200196DEST_PATH_IMAGE109
Figure 518045DEST_PATH_IMAGE110
the update load for y is the load of y,
Figure 971023DEST_PATH_IMAGE111
is the value of the operating function of y,MC j is composed ofjThe maximum capacity of (c);
s1.4.3, when an infrastructure failure of 50% or more occurs based on the infrastructure group, triggering attribute judgment of infrastructure necessity, that is, removing unnecessary attributes of each infrastructure from the operation state values and removing the influence in connection strength, and updating the connection strength matrix, the connection matrix before updating is as follows for the infrastructure group having H infrastructures:
Figure 956297DEST_PATH_IMAGE112
the updated connection matrix is a cascading failure model of the city infrastructure group network:
Figure 476DEST_PATH_IMAGE113
。
s2, elasticity analysis of infrastructures within the city 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;
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:
s2.1, setting the fault propagation time as follows based on the cascade failure model of the urban infrastructure group:
Figure 805621DEST_PATH_IMAGE114
Figure 796711DEST_PATH_IMAGE115
is composed ofjIs propagated tokThe time of (2) is greater than the time of (c),
Figure 636491DEST_PATH_IMAGE116
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:
Figure 54834DEST_PATH_IMAGE118
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,
Figure 612854DEST_PATH_IMAGE120
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 overloaded infrastructure in a cascade failure of stages,N h is shown ashThe 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:
Figure 142056DEST_PATH_IMAGE121
wherein
Figure 39604DEST_PATH_IMAGE122
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:
Figure 691166DEST_PATH_IMAGE123
wherein the content of the first and second substances,
Figure 408586DEST_PATH_IMAGE124
a 30% quantile of a sequence of resource supply level values for an infrastructure group,
Figure 803795DEST_PATH_IMAGE125
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 conditions in the urban infrastructure group and among the urban infrastructure groups under different load increase times, setting a threshold, and regarding the FIG1, the threshold comprises the following steps:
Figure 555850DEST_PATH_IMAGE126
Figure 378313DEST_PATH_IMAGE127
l c0 under the condition of the threshold value, the method,
Figure 583029DEST_PATH_IMAGE128
represents a threshold valuel c0 The portion of elasticity values within the infrastructure group under the conditions,
Figure 719613DEST_PATH_IMAGE129
represents a threshold valuel c0 An elasticity value part outside the urban infrastructure group under the condition;
Figure 388491DEST_PATH_IMAGE130
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;
Figure 337116DEST_PATH_IMAGE131
Figure 91446DEST_PATH_IMAGE132
l c1 under the condition of the threshold value, the method,
Figure 31720DEST_PATH_IMAGE133
represents a threshold valuel c1 The portion of elasticity values within the city infrastructure group under the conditions,
Figure 555105DEST_PATH_IMAGE134
represents a threshold valuel c1 An elasticity value part outside the urban infrastructure group under the condition;
Figure 657053DEST_PATH_IMAGE135
is a threshold valuel c1 Elastic parameters under the condition of a load distribution strategy among urban infrastructure groups are not considered;
Figure 898679DEST_PATH_IMAGE136
Figure 377065DEST_PATH_IMAGE137
l c2 under the condition of the threshold value, the method,
Figure 754956DEST_PATH_IMAGE138
represents a threshold valuel c2 The portion of elasticity values within the city infrastructure group under the conditions,
Figure 293385DEST_PATH_IMAGE139
represents a threshold valuel c2 An elasticity value part outside the urban infrastructure group under the condition;
Figure 694411DEST_PATH_IMAGE140
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;
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. the 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, 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:
Figure 38804DEST_PATH_IMAGE141
wherein the content of the first and second substances,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,
Figure 208886DEST_PATH_IMAGE142
is the mean value of the elasticity values of the urban infrastructure group,
Figure 980533DEST_PATH_IMAGE143
the variance is represented as a function of time,r sg representing the euclidean distance between s and g,
Figure 868854DEST_PATH_IMAGE144
the function is used to screen distances ofrWhen the Euclidean distance between s and g isrWhen the utility model is used, the water is discharged,
Figure 751359DEST_PATH_IMAGE145
the value is 1, otherwise 0, by spatial correlation at different rC(r)The target spatial correlation area is found out to carry out targeted elastic management measures.
S3, elastic analysis of 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;
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:
Figure 41526DEST_PATH_IMAGE146
Figure 984075DEST_PATH_IMAGE147
is a network elasticity indicator of 10% infrastructure group overload failure,
Figure 359692DEST_PATH_IMAGE148
the network resiliency indicator of overload failure is combined for the kth 10% infrastructure group,
Figure 45889DEST_PATH_IMAGE149
the resiliency index for overload failure is combined for the kth 10% infrastructure group,
Figure 190562DEST_PATH_IMAGE150
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 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;
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;
further, the specific implementation method of step S3.3 includes the following steps:
s3.3.1, calculating effective propagation distance of the cascade failure process of the infrastructureRPD：
Figure 304012DEST_PATH_IMAGE152
Wherein the content of the first and second substances,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,
Figure 166925DEST_PATH_IMAGE153
to representW h The number of infrastructures in the set is,
Figure 328917DEST_PATH_IMAGE155
to representQ k The number of infrastructures in the set is,
Figure 655993DEST_PATH_IMAGE156
is the euclidean distance between infrastructure k and m;
s3.3.2 calculating node betweenness of city infrastructure group networkBThe definition is as follows:
Figure 612447DEST_PATH_IMAGE157
wherein the content of the first and second substances,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,
Figure 24974DEST_PATH_IMAGE158
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;
s3.3.3 calculating elastic space parameters of city infrastructure groupRSP：
Figure 990656DEST_PATH_IMAGE160
Wherein the content of the first and second substances,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;
further, the specific implementation method of step S3.4 includes the following steps:
s3.4.1, 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：
Figure 172239DEST_PATH_IMAGE161
Wherein the content of the first and second substances,OL j andOL k are respectivelyjAndkthe number of overload times 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),
Figure 565174DEST_PATH_IMAGE162
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;
s3.4.2 calculating elastic tree structure parameters of city infrastructure groupRTSP：
Figure 600083DEST_PATH_IMAGE163
S3.4.3 calculating elastic function related parameters of city infrastructure groupRFRP：
Figure 103877DEST_PATH_IMAGE164
S3.4.4, providing an elastic recovery efficiency parameter from the perspective of the efficiency of the elastic recovery strategyRREP：
Figure 405545DEST_PATH_IMAGE165
Wherein the content of the first and second substances,FS j representing infrastructurejOverloading the set of infrastructure on the failure path on the cascading failure tree structure,
Figure 969381DEST_PATH_IMAGE166
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.
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 for 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, etc. 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 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. according to the method, the elasticity analysis is carried out at the level of the urban infrastructure group network, and the elasticity modes of the urban infrastructure group under different disturbance modes are analyzed and effectively depicted and explored aiming at external disturbances such as natural disasters with huge urban influences, so that the elasticity condition of the urban infrastructure group is evaluated. 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 analysis of the disturbance energy bearing capacity of the urban infrastructure, the disturbance change sensitivity, the propagation process and the breadth range calculation of the disturbance in the system and the system elasticity recovery process, and 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 a corresponding elasticity evaluation parameter system are constructed;
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 present 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 an … …" does not exclude the presence of other identical elements in the 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 (9)

1. A method for analyzing network elasticity of urban infrastructure group is characterized in that: the method comprises the following steps:
s1, constructing a cascading failure model of the urban infrastructure group network;
s1 the concrete implementation method of the cascade failure model for constructing 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 an improved cascading failure model of the urban infrastructure group network;
s2, elasticity analysis of infrastructures within the city 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 includes the following steps:
s2.1, setting the fault propagation time as follows based on an improved cascade failure model of the urban infrastructure group network:
Figure 68310DEST_PATH_IMAGE001
Figure 454292DEST_PATH_IMAGE002
is composed ofjIs propagated tokThe time of (2) is greater than the time of (c),
Figure 79702DEST_PATH_IMAGE003
is composed ofjTokThe time taken for the euclidean distance;
s2.2, setting the state parameters of the urban infrastructure group as the total overload load SCP of the urban infrastructure group, and obtaining the elastic parameters according to the elastic trigonometric theoryRComprises the following steps:
Figure 943753DEST_PATH_IMAGE004
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,
Figure 617179DEST_PATH_IMAGE006
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 overloaded infrastructure in a cascade failure 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:
Figure 642904DEST_PATH_IMAGE007
wherein
Figure 254145DEST_PATH_IMAGE008
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:
Figure 921887DEST_PATH_IMAGE009
wherein the content of the first and second substances,
Figure 184241DEST_PATH_IMAGE010
a 30% quantile of a sequence of resource supply level values for an infrastructure group,
Figure 646446DEST_PATH_IMAGE011
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 conditions in and among the urban infrastructure groups under different load increase times, and setting a threshold, wherein for FIG1, the threshold comprises the following steps:
Figure 243519DEST_PATH_IMAGE012
Figure 449372DEST_PATH_IMAGE013
l c0 under the condition of the threshold value, the method,
Figure 566233DEST_PATH_IMAGE014
represents a threshold valuel c0 The portion of elasticity values within the infrastructure group under the conditions,
Figure 464918DEST_PATH_IMAGE015
represents a threshold valuel c0 An elasticity value part outside the urban infrastructure group under the condition;
Figure 785173DEST_PATH_IMAGE016
is a threshold valuel c0 Elastic parameters under the condition of a load distribution strategy among urban infrastructure groups are not considered;
Figure 794717DEST_PATH_IMAGE017
Figure 766084DEST_PATH_IMAGE018
l c1 under the condition of the threshold value, the method,
Figure 771142DEST_PATH_IMAGE019
represents a threshold valuel c1 The portion of elasticity values within the city infrastructure group under the conditions,
Figure 703326DEST_PATH_IMAGE020
represents a threshold valuel c1 An elasticity value part outside the urban infrastructure group under the condition;
Figure 375615DEST_PATH_IMAGE021
is a threshold valuel c1 Elastic parameters under the condition of a load distribution strategy among urban infrastructure groups are not considered;
Figure 608014DEST_PATH_IMAGE022
Figure 723868DEST_PATH_IMAGE023
l c2 under the condition of the threshold value, the method,
Figure 143348DEST_PATH_IMAGE024
represents a threshold valuel c2 The portion of elasticity values within the city infrastructure group under the conditions,
Figure 619329DEST_PATH_IMAGE025
represents a threshold valuel c2 An elasticity value part outside the urban infrastructure group under the condition;
Figure 440654DEST_PATH_IMAGE026
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:
Figure 117623DEST_PATH_IMAGE027
wherein the content of the first and second substances,R s is the elasticity value for 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,
Figure 398301DEST_PATH_IMAGE028
is the mean value of the elasticity values of the urban infrastructure group,
Figure 287760DEST_PATH_IMAGE029
the variance is represented as a function of time,r sg representing the euclidean distance between s and g,
Figure 353805DEST_PATH_IMAGE030
the function is used to screen distances ofrBy spatial correlation at different rC(r)Finding a target space correlation area to perform targeted elastic management measures;
s3, elastic analysis of 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 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 operation function value of the infrastructure in the range of the infrastructure groupFVPearson correlation coefficient between sequence and i:
Figure 205534DEST_PATH_IMAGE032
PPMCC i，j is composed ofjSequence of infrastructure operational function values andipearson's correlation coefficient between, cov: (i，j) Is composed ofiAndjthe covariance of the running function value sequence of (a),
Figure 164263DEST_PATH_IMAGE033
is composed ofiThe standard deviation of (a) is determined,
Figure 819235DEST_PATH_IMAGE034
is composed ofjStandard deviation of (d);
s1.2.3, obtaining the correlation coefficient of Pearson
Figure 572427DEST_PATH_IMAGE035
Carrying out primary division on the urban infrastructure group;
Figure 830627DEST_PATH_IMAGE036
Figure 327467DEST_PATH_IMAGE037
representation to core infrastructureiIn the case of a non-woven fabric,jwhether within its central infrastructure group, a value of 1 indicates inside it and 0 outside it.
3. The city infrastructure group network elasticity analysis method of claim 2, wherein: the specific implementation method of the step S1.3 comprises the following steps:
s1.3.1, defining initial perturbation as increasing load value of infrastructure based on definition of cascade failure model, for urban infrastructurejComprises the following steps:
Figure 102525DEST_PATH_IMAGE038
Figure 761040DEST_PATH_IMAGE039
as an infrastructurejThe maximum capacity of the battery pack is set,TP j as an infrastructurejThe tolerance parameter(s) of (a),
Figure 5070DEST_PATH_IMAGE040
as an infrastructurejInitial load of (2):
s1.3.2, removing overloaded infrastructure when cascade failure occursjInfrastructure, infrastructurejWill be assigned to first-order neighbors according to connection strengthskThe distribution ratio is as follows:
Figure 305602DEST_PATH_IMAGE041
Figure 76111DEST_PATH_IMAGE042
is composed ofjAndkthe normalized strength of the connection therebetween and,
Figure 30161DEST_PATH_IMAGE043
is composed ofjAndkthe strength of the connection between the two parts,
Figure 886122DEST_PATH_IMAGE044
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:
Figure 98666DEST_PATH_IMAGE045
Figure 458103DEST_PATH_IMAGE046
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
Figure 114212DEST_PATH_IMAGE047
Comprises the following steps:
Figure 191890DEST_PATH_IMAGE048
s1.3.4, comparisonkUpdate load of andkdetermines whether further removal is requiredk：
Figure 709590DEST_PATH_IMAGE049
Figure 189113DEST_PATH_IMAGE050
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, repeat steps S1.3.1-S1.3.4, remove the connections and connection strengths of the affected infrastructure and re-normalize the connections and connection strengths until the city infrastructure group returns to equilibrium.
4. The city infrastructure group network elasticity analysis method of claim 3, wherein: the specific implementation method of the step S1.4 comprises the following steps:
s1.4.1, defining core infrastructure loading disturbance based on disturbance mode considering global, 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:
Figure 750544DEST_PATH_IMAGE051
s1.4.2, for j, the first order neighbors of the neighboring infrastructure group assign y the load to j as follows:
Figure 315518DEST_PATH_IMAGE052
Figure 872794DEST_PATH_IMAGE053
is composed ofyThe value of the operational function of the assigned load,
Figure 206824DEST_PATH_IMAGE054
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)，
Figure 939156DEST_PATH_IMAGE055
Representing infrastructurejA set of first-order neighbors outside the group,y∈Nei'(j）and then:
Figure 991426DEST_PATH_IMAGE056
Figure 585350DEST_PATH_IMAGE057
the update load for y is the load of y,
Figure 305044DEST_PATH_IMAGE058
is the value of the operating function of y,MC j is composed ofjThe maximum capacity of (c);
s1.4.3, triggering attribute judgment of infrastructure necessity after 50% or more of infrastructure failures occur based on the infrastructure group, and the connection matrix before updating is as follows for the infrastructure group with H infrastructures:
Figure 942699DEST_PATH_IMAGE059
the updated connection matrix is a cascading failure model of the urban infrastructure group network:
Figure 747844DEST_PATH_IMAGE060
。
5. the city infrastructure group network elasticity analysis method of claim 4, wherein: the specific implementation method of the 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:
Figure 378414DEST_PATH_IMAGE061
Figure 687036DEST_PATH_IMAGE062
is a network elasticity indicator of 10% infrastructure group overload failure,
Figure 761171DEST_PATH_IMAGE063
the network resiliency indicator of overload failure is combined for the kth 10% infrastructure group,
Figure 522453DEST_PATH_IMAGE064
the resiliency index for overload failure is combined for the kth 10% infrastructure group,
Figure 723759DEST_PATH_IMAGE065
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 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;
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.
6. The city infrastructure group network elasticity analysis method of claim 5, wherein: the specific implementation method of the step S3.3 comprises the following steps:
s3.3.1, calculating effective propagation distance of the cascade failure process of the infrastructureRPD：
Figure 621308DEST_PATH_IMAGE066
Wherein the content of the first and second substances,W h is composed ofhAn overloaded infrastructure set of cascaded failures of order,Q k overloading an infrastructure for cascading failureskThe first-order set of neighbors of (a),
Figure 866344DEST_PATH_IMAGE067
to representW h The number of infrastructures in the set is,
Figure 380502DEST_PATH_IMAGE068
to representQ k The number of infrastructures in the set is,
Figure 621384DEST_PATH_IMAGE069
is the euclidean distance between infrastructure k and m;
s3.3.2 calculating node betweenness of city infrastructure group networkBThe definition is as follows:
Figure 639018DEST_PATH_IMAGE070
wherein the content of the first and second substances,n jk representing nodesjAndkthe number of shortest paths between the first and second nodes,n jk (i)representing nodesjAndkthrough nodes in the shortest path betweeniThe number of the (c) is greater than the total number of the (c),
Figure 320536DEST_PATH_IMAGE071
to representiNode betweenness of (2);
s3.3.3 calculating elastic space parameters of city infrastructure groupRSP：
Figure 56410DEST_PATH_IMAGE072
Wherein the content of the first and second substances,B m to representmNode betweenness of the infrastructure.
7. The city infrastructure group network elasticity analysis method of claim 6, 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 ability parameter of the single infrastructure to resist disturbance, the process vulnerability parameter, is calculatedPVP：
Figure 599518DEST_PATH_IMAGE073
Wherein the content of the first and second substances,OL j andOL k are respectivelyjAndkin case of overload failureIs the multiple of the overload of (a),ias a root node, the node is a node,SP ij 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),
Figure 330714DEST_PATH_IMAGE074
representjA process vulnerability parameter of (a);
s3.4.2 calculating elastic tree structure parameters of city infrastructure groupRTSP：
Figure 324078DEST_PATH_IMAGE075
S3.4.3 calculating elastic function related parameters of city infrastructure group
Figure 547249DEST_PATH_IMAGE076
：
Figure 127003DEST_PATH_IMAGE077
S3.4.4, providing an elastic recovery efficiency parameter from the perspective of the efficiency of the elastic recovery strategyRREP：
Figure 978285DEST_PATH_IMAGE078
Wherein the content of the first and second substances,FS j representing infrastructurejOverloading the set of infrastructure on the failure path on the cascading failure tree structure,
Figure 876971DEST_PATH_IMAGE079
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.
8. 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 7 when executing the computer program.
9. 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 7.
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