CN115130193B - City infrastructure group elasticity analysis method, electronic device, and storage medium - Google Patents

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

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CN115130193B
CN115130193B CN202211028738.XA CN202211028738A CN115130193B CN 115130193 B CN115130193 B CN 115130193B CN 202211028738 A CN202211028738 A CN 202211028738A CN 115130193 B CN115130193 B CN 115130193B
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周子益
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

An urban infrastructure group elasticity analysis method, electronic equipment and a storage medium belong to the technical field of evaluation analysis. In order to solve the technical problems that the existing urban infrastructure analysis method is too simple, breaks away from the analysis of actual conditions and the like, the method for constructing the cascade failure model of the urban infrastructure group network comprises the steps of counting the operation data of urban infrastructures, and converting the operation data of the urban infrastructures into the operation function values of the urban infrastructures; establishing a city infrastructure group as an analysis basic unit based on the operation function value of the city infrastructure, and performing primary division on the city infrastructure group; performing secondary division on the primarily divided urban infrastructure group by adopting a DBSCAN algorithm to obtain a final urban infrastructure group; establishing a cascade failure model of the urban infrastructure group; and performing elasticity analysis on infrastructures in the urban infrastructure group and the urban infrastructure group. The elasticity analysis of the invention is more comprehensive, and the elasticity capability measurement of the actual system is more reasonable.

Description

City infrastructure group elasticity analysis method, electronic device, and storage medium
Technical Field
The invention relates to a city infrastructure group analysis method, in particular to a city infrastructure group 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, important 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 breakdowns. 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 the 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 actual disturbance to the local is analyzed, and then the disturbance gradually expands to a part along with the relevance of the system structure and function and finally 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 is a problem to be solved at present.
The 'evaluation research of urban infrastructure toughness under cascading failure based on complex network theory' article divides urban infrastructure networks into six types, but the analysis is independently carried out, and uniform indexes and conclusions cannot be obtained after the analysis. Therefore, the method is not very meaningful for practical guidance. The article utilizes the seepage theory for analysis, but only simple node removal is applied in the actual process, the difference and the load condition among all actual nodes are not considered, and meanwhile, the propagation process of disturbance in the system is not depicted, so that all analysis is separated from the actual condition, and the elasticity of the system cannot be effectively measured. The final conclusions drawn are therefore not persuasive. The network quoted by the case analysis of the article has small scale, and the fracture performance of the single-layer network based on single nodes and connected edges can not achieve the analysis effect on the actual situation. The article of comprehensive evaluation of the toughness of the Chinese city is insufficient in application of city operation data, and the effectiveness of practical application is difficult to explain, and the article analyzes the city elasticity by using an analytic hierarchy process, but cannot effectively measure the coupling special effect among multiple functions; in the process of analyzing the article, the subjectivity is too high by using a weight distribution method, and the problem also exists in subsequent analysis. The final conclusion is without effective theory and data support, and secondly, the analysis process is simpler, and no effective contrast analysis and no accidental factor removal treatment are performed.
Disclosure of Invention
The invention provides a city infrastructure group elasticity analysis method, electronic equipment and a storage medium, aiming at the technical problems that the existing city infrastructure analysis method in the prior art is not strong in relevance, is separated from the actual condition analysis and the like.
A method for elastic analysis of urban infrastructure group comprises the following steps:
s1, constructing a cascading failure model of an urban infrastructure group network;
s1, the specific implementation method for constructing the cascade failure model of the urban infrastructure group network comprises the following steps:
s1.1, counting the operation data of the urban infrastructure, and converting the operation data of the urban infrastructure into an operation function value of the urban infrastructure;
s1.2, establishing an urban infrastructure group as an analysis basic unit based on the running function value of the urban infrastructure, and performing primary division on the urban infrastructure group;
the specific implementation method of the step S1.2 comprises the following steps:
s1.2.1, extracting a facility corresponding to the attribute of the urban infrastructure as a core infrastructure based on the running function value of the urban infrastructure, and setting the maximum radius according to the urban scaleD max In aD max Computing spatial correlations between infrastructures in a city infrastructure group within rangeC(r)Comprises the following steps:
Figure 779354DEST_PATH_IMAGE001
iin order to be a core infrastructure of the system,jis an infrastructure and is characterized by that in the system,FV i is a core infrastructureiThe value of the operating function of (c),FV j as an infrastructurejThe value of the operating function of (c),
Figure 299156DEST_PATH_IMAGE002
is the average of the operating function values of the infrastructure, H isD max The set of all the infrastructure in the scope,
Figure 78893DEST_PATH_IMAGE003
the variance is represented as a function of time,r ij is composed ofiAndjthe euclidean distance between them,ris a distance;
Figure 333157DEST_PATH_IMAGE004
the function is used to screen distances ofrWhen a node pair is reachediAndjhas an Euclidean distance ofrWhen the utility model is used, the water is discharged,
Figure 147529DEST_PATH_IMAGE005
the function value is 1, otherwise 0, according toC(r)Distribution selection maximum interval as core infrastructureiActual range of influence ofD i ；
S1.2.2 calculationD max Sequence of infrastructure operational function values and in-range city infrastructure groupsiPearson correlation coefficient between:
Figure 863123DEST_PATH_IMAGE007
PPMCC i，j is composed ofjSequence of infrastructure operational function values andipearson's correlation coefficient therebetween, cov (i，j) Is composed ofiAndjthe covariance of the running function value sequence of (a),
Figure 186657DEST_PATH_IMAGE008
is composed ofiThe standard deviation of (a) is determined,
Figure 855536DEST_PATH_IMAGE009
is composed ofjStandard deviation of (d);
s1.2.3, obtained from Pearson's correlation coefficient
Figure 707955DEST_PATH_IMAGE010
Carrying out primary division on the urban infrastructure group;
Figure 462284DEST_PATH_IMAGE011
Figure 825394DEST_PATH_IMAGE012
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, carrying out secondary division on the primarily divided urban infrastructure group by adopting a DBSCAN algorithm to obtain a final urban infrastructure group;
s1.4, establishing a cascading failure model of the urban infrastructure group;
s2, elastic analysis of infrastructures in the urban infrastructure group;
and S3, elastic analysis of the city infrastructure group.
Further, the step S1.3 is realized by the following steps:
s1.3.1, collecting operation function value data of the urban infrastructure, merging the areas of the primarily divided urban infrastructure group with the non-coincident and blank conditions as a point, and carrying out operationAdding the row function values to obtain a core infrastructure groupgNumber of pointsP(g)：
Figure 348780DEST_PATH_IMAGE013
L 0 A set of infrastructures within a core infrastructure community;
s1.3.2, setting r'For reference to a neighborhood radius, minPts is the number of preset infrastructures in the core infrastructure community;
s1.3.3, applying DBSCAN algorithm, according tor'And attributes of the MinPts judgment points, and finally dividing the urban infrastructure group.
Further, the step S1.4 is realized by the following steps:
s1.4.1, defining initial disturbance as increasing load value of infrastructure based on definition of cascade failure model, for urban infrastructurejComprises the following steps:
Figure 903258DEST_PATH_IMAGE014
Figure 144883DEST_PATH_IMAGE015
as an infrastructurejThe maximum capacity of the battery pack is set,TP j as an infrastructurejThe tolerance parameter(s) of (a) is (are),
Figure 780526DEST_PATH_IMAGE016
as an infrastructurejInitial load of (2):
s1.4.2, removing overloaded infrastructure after cascade failure has occurredjInfrastructure, infrastructurejWill be assigned to first-order neighbors according to connection strengthskThe distribution ratio is as follows:
Figure 423997DEST_PATH_IMAGE017
Figure 883797DEST_PATH_IMAGE018
is composed ofjAndkthe normalized strength of the connection therebetween and,
Figure 612719DEST_PATH_IMAGE019
is composed ofjAndkthe strength of the connection between the two parts,
Figure 317632DEST_PATH_IMAGE020
is composed ofjAndmthe strength of the connection between the two parts,mis composed ofQAny one of the above-mentioned (a) and (b),Qfor all and infrastructurejA connected first-order neighbor set;
S1.4.3、kdistributed load andkthe intensity after normalization is proportional, as follows:
Figure 815609DEST_PATH_IMAGE021
Figure 446311DEST_PATH_IMAGE022
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 396949DEST_PATH_IMAGE023
Comprises the following steps:
Figure 436712DEST_PATH_IMAGE024
s1.4.4, comparisonkUpdate load of andkdetermines whether further removal is requiredk：
Figure 117092DEST_PATH_IMAGE025
Figure 856378DEST_PATH_IMAGE026
Is composed ofkIs set to a value of (a) in (b),MC k is composed ofk0 for removal and 1 for retention;
s1.4.5, repeating S1.4.1-S1.4.4, removing the connections and connection strengths of the affected infrastructure, and normalizing again until the city infrastructure group returns to equilibrium.
Further, step S2 is a specific implementation method of elasticity analysis of infrastructure in the city infrastructure group, including the following steps:
s2.1, setting the fault propagation time as follows based on the cascade failure model of the urban infrastructure group:
Figure 294312DEST_PATH_IMAGE027
Figure 714929DEST_PATH_IMAGE028
is composed ofjIs propagated tokThe time of (2) is greater than the time of (c),
Figure 548018DEST_PATH_IMAGE029
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 of the urban infrastructure groupSCPElastic time parameter of city infrastructure groupRTPComprises the following steps:
Figure 661468DEST_PATH_IMAGE030
wherein, the first and the second end of the pipe are connected with each other,t 0 which represents the starting moment of the elastic triangle,t 1 which represents the end time of the elastic triangle,Ythe number of stages in which the overload occurs in total,
Figure 976912DEST_PATH_IMAGE031
is composed ofkIs propagated tomThe time of (2) is greater than the time of (c),
Figure 201220DEST_PATH_IMAGE032
expressing a maximum function;
s2.3, analyzing the elastic propagation process of the urban infrastructure group from the space propagation angle, and establishing elastic space parametersRSPComprises the following steps:
Figure 154394DEST_PATH_IMAGE033
N k the number of first-order neighbors for a k-order cascade failure,
Figure 235483DEST_PATH_IMAGE034
is composed ofkTomThe spatial distance of (a);
s2.4, constructing maximum elastic recovery parameters of infrastructureMRRPFor the infrastructurejAndjthe infrastructure group isMRRP(j) Under the condition of the infrastructurejOverload occurs and causes a global crash:
Figure 710326DEST_PATH_IMAGE035
Figure 770949DEST_PATH_IMAGE036
is at leastMRRP（j) Under the conditions ofjElastic time parameter of (d);
s2.5, analyzing elastic zero value parameter of overload direct blocking for initial disturbanceRZPThat is, in this case, cascade failure does not occur, and the elastic delta area of the urban infrastructure group system is 0, the same applies tojFor example, there are:
Figure 952531DEST_PATH_IMAGE037
RZP(j) Is composed ofjThe elastic zero-value parameter of (a),RTP（j，RZP(j) Is atRZP(j) Under the conditions ofjElastic time parameter of (d);
RZP(j) In the case of 0, that is to sayjThe redundancy upper bound of the first-order neighbor after the load effectively assumesjFor measuring the elasticity capability of the city infrastructure group.
Further, step S3 is a specific implementation method of elasticity analysis of the city infrastructure group, including the following steps:
s3.1, considering the strategy of elastic maintenance of the urban infrastructure group, improving the redundancy upper limit performance of the infrastructure except the initial disturbance, recalculating new elastic parameters under the multiplication condition, analyzing the effectiveness of strategy implementation, and providing the elastic maintenance efficiency of the urban infrastructure group systemRME：
Figure 266838DEST_PATH_IMAGE038
Wherein the content of the first and second substances,lindicates the factor by which the upper redundancy limit is increased, wherein,lwhen the value is more than 1, the performance is improved, and when the value is less than 1, the performance is degraded;
RME(l)for redundancy the upper limit is increased tolThe elasticity under the double condition keeps the efficiency,RSP(l)for redundancy the upper limit is increased tolThe elastic space parameter under the double condition,RTP(l)for redundancy upper limit is increased tolElastic time parameter under double conditions;
s3.2, constructing an analysis mode of multi-point disturbance: setting 5% of infrastructure to generate initial disturbance and overload failure, and calculating according to the probability of generating infrastructure failure to obtain group elasticity parameters of the urban infrastructure group systemRGP：
Figure 166661DEST_PATH_IMAGE039
Figure 93291DEST_PATH_IMAGE040
Wherein, N FIG1 Representing the number of infrastructures in the infrastructure group FIG1,X k denotes the firstkThe set of infrastructures in a respective permutation combination,ais composed ofX k Any one of the above-mentioned (a) and (b),P a to representaThe probability value of the occurrence of failure;
RGP(5%) is the population elasticity parameter under overload failure conditions with initial disturbances at 5% of the infrastructure,RTP k (5%)as an infrastructurekElastic time parameter under overload failure condition with initial disturbance at 5% infrastructure;RSP k (5%)as an infrastructurekElastic space parameters under overload failure conditions with initial disturbances at 5% of infrastructure;RGP k (5%)as an infrastructurekPopulation elasticity parameters under overload failure conditions with initial disturbances at 5% of infrastructure;
s3.3, analyzing the group elasticity keeping efficiency of the urban infrastructure group system aiming at the condition of multipoint initial disturbanceRGME：
Figure 394959DEST_PATH_IMAGE041
RGME（5%，l) Initial disturbances occur for 5% of the infrastructure and the upper redundancy limit is increased tolMaintaining the group elasticity efficiency under the doubling condition;RSP i (5%)as an infrastructureiElastic space parameters under overload failure conditions with initial disturbances at 5% of infrastructure;RSP i (5%，l)as an infrastructureiInitial disturbances occurred at 5% of the infrastructure and the upper redundancy limit increased tolMultiple elastic space parameters;RTP i (5%)as an infrastructureiElastic time parameter under overload failure condition with initial disturbance at 5% infrastructure;RTP i (5%，l)as an infrastructureiInitial disturbances occurred at 5% of the infrastructure and the upper redundancy limit increased tolTime of elasticity parameter.
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 elasticity analysis method when executing the computer program.
A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements a method for resilient analysis of urban infrastructure groups as described.
The invention has the beneficial effects that:
the method constructs an urban infrastructure group elasticity analysis system based on the established urban infrastructure, the cascade failure model and the elasticity analysis theory from the aspects of the establishment of the urban infrastructure group cascade failure model and the elasticity analysis of the infrastructure group. The main contents are as follows:
1. from the point of view of establishing a cascading failure model of 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 all parts of the whole system needs to be analyzed in detail for the black swan event, and the influence of initial disturbance on the whole system at the beginning of analysis and the overall evaluation in the subsequent system recovery process are necessary, so that the influence mode among all units 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. Further, some areas that overlap each other and are a nuisance are obtained according to the above division. Therefore, it is necessary to use a clustering method to change the divided region into a large point, and then use the clustering method together with other overlapped and blank points to make the division more reasonable. Thus, the division of the urban infrastructure group is obtained. 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.
2. 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 triangle, simulates the whole process of initial disturbance occurrence, fault accelerated propagation stage, system recovery stage and system recovery balance state in the whole process, and defines the system state parameter value of the infrastructure. Meanwhile, according to the existing load redundancy upper limit value and the distribution quantity of the infrastructure in the actual load distribution process, the elastic time parameter of the infrastructure is calculated by combining the fault propagation time. And then, establishing elastic space parameters by combining the structural connection relation and the geographical relative position of the infrastructures in the facility group so as to measure the elastic value of the actual infrastructures for fault propagation in the space range under the initial disturbance condition. Then, in response to the huge practical challenges faced by the actual infrastructure, the present invention aims to analyze the maximum disturbance value that the infrastructure in the facility group can endure in the extreme state, which mainly provides effective support for assessing the disaster risk level. Specifically, a maximum elastic recovery parameter of the system is provided; and finally, analyzing the maximum disturbance bearing capacity of the system under the condition that cascade failure does not occur, namely, the elastic zero-value parameter.
3. From an elasticity analysis perspective of the entire infrastructure group: the analysis from the viewpoint of an infrastructure group mainly analyzes the process of fault propagation of initial disturbance in the infrastructure group and the elastic recovery process of the system. The method mainly carries out performance improvement on the first-order neighbor nodes directly according to the influence of initial disturbance on the first-order neighbor nodes, namely, the maximum redundancy value is improved, and the cascade failure process caused by load distribution caused by the initial disturbance is avoided. At the same time, the elasticity preserving parameters of the system are defined based on this idea. And based on the definition of the elastic maintenance parameters and the recovery strategy of the system in the recovery process, providing the elastic maintenance efficiency parameters of the system, and then finding the infrastructure with the maximum elastic maintenance efficiency parameters, thereby formulating a targeted elastic recovery strategy. Furthermore, in order to describe more accurately and realistically the actual elastic recovery process for a single infrastructure group, the initial external disturbance of the system is upgraded from the ideal case of a single point to a larger, wider and more realistic external disturbance due to the failure of a group of infrastructures. And defining and obtaining the group elasticity parameters of the infrastructure group according to the combination relation of the generated infrastructures and the probability value of the actual fault of each infrastructure. And the combination relation of the first 5% in the group elasticity parameter composition is carried out to obtain the fault combination with the maximum elasticity influence of the system. Similarly, in the group fault attack mode, the performance of the whole infrastructure without faults is considered to be improved, and then the group elasticity maintaining efficiency parameter of the infrastructure group is calculated.
The urban infrastructure group elasticity analysis method provided by the invention in combination with the three aspects has the following advantages:
1. according to the urban infrastructure group constructed by the method, the key infrastructure is taken as a core according to the propagation characteristic of the disturbance in the real area and the effectiveness of the actual recovery process, and a method of spatial correlation and threshold screening is introduced to establish urban infrastructure group division. Meanwhile, a cascading failure model of the infrastructure group is established based on the cascading failure method. The model meets the actual analysis requirements, 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 dealing with natural disasters, extreme weather, artificial damage and attacks, 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;
2. the method firstly analyzes the elasticity analysis of the infrastructure in the infrastructure group, and is based on the classical elasticity trigonometric theory, the analysis process and the index rational basis. Meanwhile, the elasticity of the system in time and space is comprehensively considered, so that the elasticity analysis is more comprehensive, and the elasticity capability measurement of the actual system is more reasonable;
3. the elasticity analysis of a single infrastructure group layer of the invention considers more practical disturbances with high frequency and low energy, considers the self-recovery elasticity capability in the infrastructure group and provides effective support for analyzing the disturbances. Meanwhile, for the mode analysis of multi-point disturbance in a single infrastructure group, the key nodes influencing elasticity in the infrastructure group are analyzed and excavated at the same time in a fitting manner;
4. by integrating the elastic analysis of the macro level and the micro level, the invention comprehensively considers the fault propagation process of the micro level, the influence range of the macro level and the research of the recovery strategy, and establishes an elastic analysis system of the urban infrastructure group by means of an effective analysis model and theory from the disturbance energy bearing capacity of the urban infrastructure, the sensitivity of disturbance change, the propagation process and the breadth range calculation of the disturbance in the system and the process analysis of the elastic recovery of the system, thereby providing effective support for researching and improving the elasticity of the urban infrastructure.
Drawings
Fig. 1 is a schematic flow diagram of a DBSCAN process of an urban infrastructure group elasticity analysis method according to the present invention;
FIG. 2 is a flowchart illustrating cascading failures of an infrastructure group of the method for resilient analysis of an urban infrastructure group according to the present invention;
fig. 3 is a process diagram of an elastic triangle model of the urban infrastructure group elasticity analysis method according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and the detailed description. It is to be understood that the embodiments described herein are illustrative only and are not limiting, i.e., that the embodiments described are only a few embodiments, rather than all, of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations, and the present invention may have other embodiments.
Thus, the following detailed description of specific embodiments of the present invention presented in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the detailed description of the invention without inventive step, are within the scope of protection of the invention.
For further understanding of the contents, features and effects of the present invention, the following embodiments are exemplified in conjunction with the accompanying drawings and the following detailed description:
the first embodiment is as follows:
a method for analyzing elasticity of urban infrastructure groups comprises the following steps:
s1, constructing a cascading failure model of an urban infrastructure group network;
the specific implementation method for constructing the cascade failure model of the urban infrastructure group network in the step S1 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;
the city infrastructure attributes of the step S1.1 comprise residence, service, water supply, culture and education, heating, gas, electric power and traffic, wherein the electric power, the water supply and the power supply are converted according to per-capita consumption, and other types are converted according to annual service customer number;
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. And then, secondarily solving the areas which are subjected to superposition and blank in the primary division according to a clustering method, so as to obtain the division of the urban infrastructure group. And then, establishing a cascading failure model of the urban infrastructure group based on the theory of cascading failure.
According to the definition of the infrastructure: the system is a material engineering facility for providing public services for social production and resident life, is a public service system for ensuring normal progress of national or regional social and economic activities, is a general material condition on which the 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 the urban development and the daily activities of urban residents. The actual control was transformed in eight ways as shown in table 1, the comparison was transformed in terms of consumption per person per day:
TABLE 1 Attribute Table for Key infrastructure
Figure 880167DEST_PATH_IMAGE043
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, extracting a facility corresponding to the attribute of the urban infrastructure as a core infrastructure based on the running function value of the urban infrastructure, and setting the maximum radius according to the urban scaleD max In aD max Computing spatial correlations between infrastructures in a city infrastructure group within rangeC(r)Comprises the following steps:
Figure 267286DEST_PATH_IMAGE044
iis a core infrastructure and is provided with a plurality of network nodes,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 infrastructurejThe value of the operating function of (c),
Figure 263186DEST_PATH_IMAGE045
is the average of the operating function values of the infrastructure, H isD max The set of all the infrastructure in the scope,
Figure 153782DEST_PATH_IMAGE046
the variance is represented as a function of time,r ij is composed ofiAndjthe Euclidean distance between the two electrodes,ris a distance;
Figure 809891DEST_PATH_IMAGE047
the function is used to screen distances ofrWhen a node pair is reachediAndjhas an Euclidean distance ofrWhen the temperature of the water is higher than the set temperature,
Figure 418727DEST_PATH_IMAGE048
the function value is 1, otherwise 0, according toC(r)Distribution selection maximum interval as core infrastructureiActual range of influence ofD i ；
S1.2.2 calculationD max Sequence of infrastructure operational function values and in-range city infrastructure groupsiPearson correlation coefficient between:
Figure 727534DEST_PATH_IMAGE049
PPMCC i，j is composed ofjSequence of infrastructure operational function values andipearson's correlation coefficient therebetween, cov (i，j) Is composed ofiAndjthe covariance of the running function value sequence of (a),
Figure 695490DEST_PATH_IMAGE050
is composed ofiThe standard deviation of (a) is determined,
Figure 417721DEST_PATH_IMAGE051
is composed ofjStandard deviation of (d);
s1.2.3, obtained from Pearson's correlation coefficient
Figure 129325DEST_PATH_IMAGE052
Carrying out primary division on the urban infrastructure group;
Figure 853568DEST_PATH_IMAGE053
Figure 992425DEST_PATH_IMAGE054
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.
Further, the operations are carried out on other core infrastructures, and the initial division of the urban infrastructure group is completed.
S1.3, carrying out secondary division on the primarily divided urban infrastructure group by adopting a DBSCAN algorithm to obtain a final urban infrastructure group; for two cases, namely coincidence and blank, with problems in the primary division, a clustering method is used for adjustment, as shown in FIG. 1;
further, the step S1.3 is realized by the following steps:
s1.3.1, collecting operation function value data of urban infrastructure, merging the areas of the primarily divided urban infrastructure groups with the conditions of misalignment and blank as a point, and adding the operation function values to obtain a core infrastructure groupgNumber of pointsP(g)：
Figure 201952DEST_PATH_IMAGE055
L 0 A set of infrastructures within a core infrastructure community;
s1.3.2, setting r'For reference to a neighborhood radius, minPts is the number of preset infrastructures in the core infrastructure group;
at the same time, set upD max The radius of the minimum field is set as 5km for a common city, and the larger scale of the city can be selected as 8km;
s1.3.3, applying DBSCAN algorithm, based onr'And attributes of MinPts judgment points, and finally dividing the urban infrastructure group;
s1.4, establishing a cascading failure model of the urban infrastructure group, wherein a cascading failure flow chart of the infrastructure group is shown in a figure 2;
further, the step S1.4 is implemented by the following steps:
s1.4.1, definition based on cascading failure model, defining initial disturbance as increasing load value of infrastructure for urban infrastructurejComprises the following steps:
Figure 451667DEST_PATH_IMAGE056
Figure 561575DEST_PATH_IMAGE057
being the maximum capacity of the infrastructure j,TP j for the tolerance parameters of the infrastructure j,
Figure 871333DEST_PATH_IMAGE058
for the initial load of infrastructure j:
s1.4.2, removing overloaded infrastructure after cascade failure has occurredjInfrastructure, infrastructurejWill be assigned to first-order neighbors according to connection strengthskThe distribution ratio is as follows:
Figure 568156DEST_PATH_IMAGE059
Figure 621563DEST_PATH_IMAGE060
is composed ofjAndkthe normalized strength of the connection therebetween and,
Figure 320397DEST_PATH_IMAGE061
is composed ofjAndkthe strength of the connection between the two parts,
Figure 801057DEST_PATH_IMAGE062
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;
S1.4.3、kdispensingTo the load andkthe intensity after normalization is proportional, as follows:
Figure 719597DEST_PATH_IMAGE063
Figure 576694DEST_PATH_IMAGE064
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 270981DEST_PATH_IMAGE065
Comprises the following steps:
Figure 47176DEST_PATH_IMAGE066
；
s1.4.4, comparisonkUpdate load of andkthe relationship of maximum capacity to determine whether further removal of k:
Figure 453012DEST_PATH_IMAGE067
Figure 848221DEST_PATH_IMAGE068
is a value of the state of k,MC k is composed ofk0 for removal and 1 for retention;
s1.4.5, repeating S1.4.1-S1.4.4, removing the connections and connection strengths of the affected infrastructure, and normalizing again until the city infrastructure group returns to equilibrium.
S2, elasticity analysis of infrastructures in the urban infrastructure group: based on the obtained cascade failure model of the urban infrastructure group, elastic analysis is carried out from two aspects of time and space based on the theory and model of the classical elastic triangle;
further, the step S2 includes the following steps:
because the actual fault propagation time is difficult to find a definite corresponding quantitative index in reality, the fault propagation time is considered to be set based on the cascade failure model;
s2.1, setting the fault propagation time as follows based on the cascade failure model of the urban infrastructure group:
Figure 256069DEST_PATH_IMAGE069
Figure 344110DEST_PATH_IMAGE070
is composed ofjIs propagated tokThe time of the above-mentioned (c) is,
Figure 73180DEST_PATH_IMAGE071
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 of the urban infrastructure groupSCPAs shown in fig. 3, as shown in elastic trigonometric theory, of the systemSCPIs initially 0, then gradually increases, and finally returns to 0, the elastic time parameter of the city infrastructure groupRTPComprises the following steps:
Figure 272080DEST_PATH_IMAGE072
wherein the content of the first and second substances,t 0 which represents the starting moment of the elastic triangle,t 1 which represents the end time of the elastic triangle,Ythe number of stages in which the overload occurs in total,
Figure 800013DEST_PATH_IMAGE073
is composed ofkIs propagated tomThe time of (2) is greater than the time of (c),
Figure 58956DEST_PATH_IMAGE074
expressing a maximum function;
as indicated above, the continuous integration becomes a discrete addition.
Figure 173805DEST_PATH_IMAGE075
To representkThe longest load transfer object is the load transfer object, because other load transfers are all carried out at the same time, the maximum value is considered;
s2.3, analyzing the elastic propagation process of the urban infrastructure group from the space propagation angle, and establishing elastic space parametersRSPComprises the following steps:
Figure 910817DEST_PATH_IMAGE076
N k is composed ofkThe number of first order neighbors to which the order cascade fails,
Figure 558836DEST_PATH_IMAGE077
is composed ofkTomThe spatial distance of (a);
elastic space parameterRSPThe primary measure is the elastic propagation process of the initial disturbance through the system. The elasticity is inversely proportional to the area of the elastic triangle, so the result takes a negative value;
again, consider the impact of a single infrastructure on the entire infrastructure group, i.e., the propagation of an overload of a single infrastructure through cascading failures results in a crash of the overall system. Thus introducing maximum elastic recovery parameters for the infrastructureMRRP。
S2.4, constructing maximum elastic recovery parameters of infrastructureMRRPFor the infrastructurejAndjin the infrastructure group ofMRRP(j) Under the condition of the infrastructurejOverload occurs and causes a global crash:
Figure 988680DEST_PATH_IMAGE078
Figure 590825DEST_PATH_IMAGE079
is at the same timeMRRP（j) Under the conditions ofjElastic time parameter of (d);
s2.5, analyzing elastic zero value parameter of overload direct blocking for initial disturbanceRZPThat is, in this case, cascade failure does not occur, and the elastic delta area of the urban infrastructure group system is 0, the same applies tojFor example, there are:
Figure 131528DEST_PATH_IMAGE080
RZP(j) Is composed ofjThe elastic zero-value parameter of (a),RTP（j，RZP(j) Is atRZP(j) Under the conditions ofjElastic time parameter of (d);
RZP(j) In the case of 0, that is to sayjThe redundancy upper bound of the first-order neighbor after the load effectively assumesjFor measuring the elasticity capability of the city infrastructure group.
And S3, elasticity analysis of the urban infrastructure group, wherein the elasticity capability of the single infrastructure group for disturbance occurrence is mainly analyzed in a hierarchical manner by considering the external disturbance condition which is high in occurrence frequency, small in influence and concentrated in a certain range. Respectively exploring key infrastructures with the largest influence from the elastic maintaining efficiency of single disturbance and the elastic maintaining efficiency when multipoint disturbance occurs;
further, step S3 is a specific implementation method of elasticity analysis of the city infrastructure group, including the following steps:
s3.1, considering the strategy of elastic maintenance of the urban infrastructure group, improving the redundancy upper limit performance of the infrastructure except the initial disturbance, recalculating new elastic parameters under the multiplication condition, analyzing the effectiveness of strategy implementation, and providing the elastic maintenance efficiency of the urban infrastructure group systemRME：
Figure 634053DEST_PATH_IMAGE081
Wherein the content of the first and second substances,lrepresents the factor by which the redundancy upper limit is increased, wherein,lwhen the value is more than 1, the performance is improved, and when the value is less than 1, the performance is degraded;
RME(l)for redundancy the upper limit is increased tolThe system elasticity under the double condition keeps the efficiency,RSP(l)for redundancy upper limit is increased tolThe elastic space parameter under the double condition,RTP(l)for redundancy the upper limit is increased tolElastic time parameter under double conditions;
in order to satisfy the analysis of the real situation, an analysis mode of multi-point disturbance is introduced. Here for FIG1, 5% of the infrastructure is set to have initial disturbances and overload failures. Wherein, 5% of the sets can be calculated according to a permutation and combination mode, and then the group elasticity parameters of the system are calculated according to the probability of the occurrence of the infrastructure failureRGPThe specific method comprises the following steps:
s3.2, constructing an analysis mode of multipoint disturbance: setting 5% of infrastructure to generate initial disturbance and overload failure, and calculating according to the probability of generating infrastructure failure to obtain group elasticity parameters of the urban infrastructure group systemRGP：
Figure 969220DEST_PATH_IMAGE082
Wherein N is FIG1 Representing the number of infrastructures in the infrastructure group FIG1,X k is shown askThe set of infrastructures in a respective permutation combination,ais composed ofX k Any one of the above-mentioned (a) and (b),P a to representaThe probability value of the occurrence of failure;
RGP(5%) is the population elasticity parameter under overload failure conditions with initial disturbances at 5% of the infrastructure,RTP k (5%)as an infrastructurekInitial disturbance at 5% infrastructure and overload failure barAn elastic time parameter under the part;RSP k (5%)as an infrastructurekElastic space parameters under overload failure conditions with initial disturbances at 5% of infrastructure;RGP k (5%)as an infrastructurekPopulation elasticity parameters under overload failure conditions with initial disturbances at 5% of infrastructure;
s3.3, analyzing the group elasticity keeping efficiency of the urban infrastructure group system aiming at the condition of multipoint initial disturbanceRGME：
Figure 589819DEST_PATH_IMAGE083
RGME（5%，l) Initial disturbance occurred for 5% of the infrastructure and the upper redundancy limit was increased tolMaintaining the group elasticity efficiency under the doubling condition;RSP i (5%)as an infrastructureiElastic space parameters under overload failure conditions with initial disturbances at 5% of infrastructure;RSP i (5%，l)as an infrastructureiInitial disturbances occurred at 5% of the infrastructure and the upper redundancy limit increased tolA multiple elastic space parameter;RTP i (5%)as an infrastructureiElastic time parameter under overload failure condition with initial disturbance at 5% infrastructure;RTP i (5%，l)as an infrastructureiInitial disturbances occurred at 5% of the infrastructure and the upper redundancy limit increased tolTime of elasticity parameter.
Furthermore, 5% of the urban elasticity analysis method is only aimed at general urban elasticity analysis, and can be adjusted according to actual needs for urban elasticity analysis of a specific scale.
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 elasticity analysis method according to the embodiment when executing the computer program.
Further, the computer device of the present invention may be a device including a processor, a memory, and the like, for example, a single chip microcomputer including a central processing unit, and the like. And the processor is used for implementing the steps of the recommendation method capable of modifying the relationship-driven recommendation data based on the CREO software when executing the computer program stored in the memory.
The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a sound playing function, an image playing function, etc.), and the like; the storage data area may store data (such as audio data, a phonebook, etc.) created according to the use of the cellular phone, 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 city infrastructure group elasticity analysis method according to one of the embodiments.
Further, the computer readable storage medium of the present invention may be any form of storage medium read by the processor of the 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 processor of the computer device reads and executes the computer program stored in the memory, the steps of the above-mentioned 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 an elasticity model-based urban infrastructure group network elasticity analysis system, which has the following advantages: 1. according to the urban infrastructure group constructed by the method, the key infrastructure is taken as a core according to the propagation characteristic of the disturbance in the real area and the effectiveness of the actual recovery process, and a method of spatial correlation and threshold screening is introduced to establish urban infrastructure group division. Meanwhile, a cascading failure model of the infrastructure group is established based on the cascading failure method. The model meets the actual analysis requirements, and meanwhile, the established minimum analysis unit, namely the urban infrastructure group, aims at that the urban infrastructure group actually plays a supporting role in urban operation when coping with natural disasters, extreme weather and artificial damage and attack, and is based on the reality of a resource allocation strategy after the disasters happen. 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; 2. the invention firstly analyzes the elasticity analysis of the infrastructure in the infrastructure group, and is based on the classical elastic triangle theory, the analysis process and the index rational data. Meanwhile, the system elasticity of time and space is comprehensively considered, so that the elasticity analysis is more comprehensive, and the elasticity capability measurement of an actual system is more reasonable; 3. the elasticity analysis of a single infrastructure group layer of the invention considers more practical disturbances with high frequency and low energy, considers the self-recovery elasticity capability in the infrastructure group and provides effective support for analyzing the disturbances. Meanwhile, for the mode analysis of multi-point disturbance in a single infrastructure group, the key nodes influencing elasticity in the infrastructure group are analyzed and excavated at the same time according to the actual condition; 4. by integrating the elastic analysis of the macro level and the micro level, the invention comprehensively considers the fault propagation process of the micro level, the influence range of the macro level and the research of the recovery strategy, and establishes an elastic analysis system of the urban infrastructure group by means of an effective analysis model and theory from the disturbance energy bearing capacity of the urban infrastructure, the sensitivity of disturbance change, the propagation process and the breadth range calculation of the disturbance in the system and the process analysis of the elastic recovery of the system, thereby providing effective support 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 cascade failure model of the urban infrastructure group network (aiming at high-frequency and low-intensity disturbance) and the modified version thereof (aiming at low-frequency and low-intensity and high-disturbance).
2. Elastic analysis of the micro level, namely the infrastructure level in the infrastructure group, establishes fault propagation time and then elastic parameters from the system performance degradation stage based on the elastic trigonometric theory.
3. And macroscopical level-elastic analysis of the whole infrastructure group, introducing a multipoint disturbance mode to fit the actual situation, and establishing a system elastic retention efficiency parameter system.
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 Resilence Index: RNI, network resilience indicator.
It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.
While the application has been described above with reference to specific embodiments, various modifications may be made and equivalents may be substituted for elements thereof without departing from the scope of the application. In particular, the various features of the embodiments disclosed herein may be used in any combination that is not inconsistent with the structure, and the failure to exhaustively describe such combinations in this specification is merely for brevity and resource conservation. Therefore, it is intended that the application not be limited to the particular embodiments disclosed, but that the application will include all embodiments falling within the scope of the appended claims.

Claims (4)

1. A method for elastic analysis of urban infrastructure group is characterized by comprising the following steps: the method comprises the following steps:
s1, constructing a cascading failure model of an urban infrastructure group network;
s1, the specific implementation method for constructing the cascade failure model of the urban infrastructure group network comprises the following steps:
s1.1, counting the operation data of the urban infrastructure, and converting the operation data of the urban infrastructure into an operation function value of the urban infrastructure;
s1.2, establishing an urban infrastructure group as an analysis basic unit based on the running function value of the urban infrastructure, and performing primary division on the urban infrastructure group;
the specific implementation method of the step S1.2 comprises the following steps:
s1.2.1, extracting a facility corresponding to the attribute of the urban infrastructure as a core infrastructure based on the running function value of the urban infrastructure, and setting a maximum radius D according to the urban scale max At D max Spatial correlations C (r) between infrastructures in a city infrastructure group are computed in-range as:
Figure FDA0003890244940000011
i as core infrastructure, j as infrastructure, FV i Is the operating function value, FV, of the core infrastructure i j For the value of the operational function of infrastructure j,
Figure FDA0003890244940000012
is the average of the functional values of the infrastructure, H is D max Set of all infrastructures within range, σ 2 Represents the variance, r ij Is the Euclidean distance between i and j, and r is the distance;
δ(r ij -r) function is used to screen node pairs with distance rWhen the Euclidean distance between i and j is r, δ (r) ij -r) a function value of 1, otherwise 0, and selecting the interval in which the maximum value lies as the actual range of influence D of the core infrastructure i according to the C (r) distribution i ；
S1.2.2, calculate D max Pearson's correlation coefficient between the infrastructure operating function value sequences in the city infrastructure group and i within the range:
Figure FDA0003890244940000013
PPMCC i，j for Pearson's correlation coefficient between the j infrastructure running function value sequence and i, cov (i, j) is the covariance of the running function value sequences of i and j, σ i Is the standard deviation of i, σ j Is the standard deviation of j;
s1.2.3 from Pearson's correlation coefficient, F i (j) Carrying out primary division on the urban infrastructure group;
Figure FDA0003890244940000014
F i (j) Indicates whether j is within its centered infrastructure group for core infrastructure i, a value of 1 indicates within it, and a value of 0 is outside it;
s1.3, carrying out secondary division on the primarily divided urban infrastructure group by adopting a DBSCAN algorithm to obtain a final urban infrastructure group;
s1.4, establishing a cascading failure model of the urban infrastructure group;
the specific implementation method of the step S1.4 comprises the following steps:
s1.4.1, the definition of a cascade-based failure model, defining an initial disturbance as an increased load value of the infrastructure, for city infrastructure j:
MC j ＝(1+TP j )·IL j
MC j is the maximum capacity of infrastructure j, TP j As an infrastructureTolerance parameter of j, IL j For the initial load of infrastructure j:
s1.4.2, after cascade failure occurs, deleting the overloaded infrastructure j, and distributing the load of the infrastructure j to the first-order neighbor k according to the connection strength, where the distribution ratio is:
Figure FDA0003890244940000021
L' j,k is the normalized connection strength between j and k, L j,k Is the strength of the connection between j and k, L j,m Is the connection strength between j and m, m is any one of Q, Q is a first-order neighbor set connected with the infrastructure j;
s1.4.3, k the load assigned is proportional to the intensity after k normalization, as follows:
FV j2k ＝FV j ·L' j,k
FV j2k operating function value, FV, of the load assigned to k j Is the operating function value of infrastructure j;
then the updated load FV 'on k' k Comprises the following steps:
FV' k ＝FV k +FV j2k ＝FV k +FV j ·L' j,k
s1.4.4, comparing the relationship of the update load of k to the maximum capacity of k, and determining if further removal of k:
Figure FDA0003890244940000022
e (k) is the state value of k, MC k Maximum capacity of k, 0 for removal, 1 for retention;
s1.4.5, repeating S1.4.1-S1.4.4, removing the connections and connection strengths of the affected infrastructures, and normalizing again until the urban infrastructure group returns to the balance state;
s2, elastic analysis of infrastructures in the urban infrastructure group;
s2, the specific implementation method of the elasticity analysis of the infrastructure in the urban infrastructure group comprises the following steps:
s2.1, setting the fault propagation time as follows based on the cascade failure model of the urban infrastructure group:
Figure FDA0003890244940000031
T j2k time for the load of j to propagate on k, t j2k The time taken for the distance j to k in ohms;
s2.2, setting the state parameter of the urban infrastructure group as the total overload load SCP of the urban infrastructure group, and then setting the elastic time parameter RTP of the urban infrastructure group as follows:
Figure FDA0003890244940000032
wherein, t 0 Denotes the starting time, t, of the elastic triangle 1 Indicating the ending time of the elastic triangle, Y is the total number of overload stages, T k2m Max represents the function of the maximum value, which is the time for the load of k to propagate on m;
s2.3, analyzing the elastic propagation process of the urban infrastructure group from the perspective of space propagation, and establishing an elastic space parameter RSP as follows:
Figure FDA0003890244940000033
N k number of first-order neighbors for k-order cascading failures, r km A spatial distance of k to m;
s2.4, constructing the maximum elastic recovery parameter MRRP of the infrastructure, and for the infrastructure j and the infrastructure group where the infrastructure j is located, under the condition of MRRP (j), overloading the infrastructure j and causing global collapse:
Figure FDA0003890244940000034
RTP (j, MRRP (j)) is the elastic time parameter of infrastructure j under MRRP (j);
s2.5, analyzing an elastic zero-value parameter RZP for directly blocking overload generated by initial disturbance, namely that cascade failure does not occur under the condition, wherein the elastic triangular area of the urban infrastructure group system is 0, and similarly for j, the following parameters are:
Figure FDA0003890244940000035
RZP (j) is an elasticity zero parameter of j, and RTP (j, RZP (j)) is an elasticity time parameter of j under the condition of the RZP (j);
under the condition that RZP (j) is 0, namely the redundancy upper limit of a first-order neighbor behind the j load effectively bears the transfer load of j, the method is used for measuring the elasticity capability of the urban infrastructure group;
s3, elastic analysis of the urban infrastructure group;
s3, the specific implementation method of the elasticity analysis of the urban infrastructure group comprises the following steps:
s3.1, considering a strategy of elastic maintenance of the urban infrastructure group, improving the redundancy upper limit performance of the infrastructure except for the initial disturbance, recalculating a new elastic parameter under the condition of multiplication, analyzing the effectiveness of strategy implementation, and providing the elastic maintenance efficiency RME of the urban infrastructure group system:
Figure FDA0003890244940000041
wherein l represents the times of the improvement of the redundancy upper limit, wherein when l is larger than 1, the situation of performance improvement is represented, and when l is smaller than 1, the situation of performance degradation is represented;
RME (l) is the elastic retention efficiency under the condition that the redundancy upper limit is increased by l times, RSP (l) is the elastic space parameter under the condition that the redundancy upper limit is increased by l times, and RTP (l) is the elastic time parameter under the condition that the redundancy upper limit is increased by l times;
s3.2, constructing an analysis mode of multipoint disturbance: setting 5% of infrastructure to generate initial disturbance and overload failure, and calculating according to the probability of generating infrastructure failure to obtain a group elasticity parameter RGP of the urban infrastructure group system:
Figure FDA0003890244940000042
wherein N is FIG1 Representing the number of infrastructures in the infrastructure group FIG1, X k Denotes the set of infrastructures in the k-th permutation and a is X k Any one of (1), P a Representing the probability value of the failure of a;
RGP (5%) is the population elastic parameter under overload failure conditions with initial perturbations at 5% of the infrastructure, RTP k (5%) is the elastic time parameter of infrastructure k under 5% infrastructure initial disturbance with overload failure; RSP k (5%) elastic space parameters for infrastructure k under overload failure conditions with initial disturbance of 5% of infrastructure; RGP k (5%) is the population elasticity parameter for infrastructure k under overload failure conditions with initial disturbance of 5% of infrastructure;
s3.3, analyzing the group elasticity maintenance efficiency RGME of the urban infrastructure group system aiming at the condition of multipoint initial disturbance:
Figure FDA0003890244940000043
RGME (5%, l) is the population elastic retention efficiency under the condition that 5% of infrastructure is initially disturbed and the upper redundancy limit is increased by a factor of l; RSP i (5%) elastic space parameters for infrastructure i under overload failure conditions with initial disturbance of 5% of infrastructure; RSP i (5%, l) initial perturbations at 5% of infrastructure for infrastructure i and redundancyThe residual upper limit is increased to be l times of elastic space parameters; RTP i (5%) is the elastic time parameter for infrastructure i under 5% infrastructure initial disturbance with overload failure; RTP i (5%, l) is the elastic time parameter for which the infrastructure i experiences an initial disturbance at 5% of the infrastructure and the upper redundancy limit is increased by a factor of l.
2. The city infrastructure group elasticity analysis method of claim 1, wherein: the specific implementation method of the step S1.3 comprises the following steps:
s1.3.1, collecting operation function value data of the city infrastructure, merging the areas of the primarily divided city infrastructure group with the non-coincident and blank conditions as a point, and adding the operation function values to obtain the point number P (g) of the core infrastructure group g:
Figure FDA0003890244940000051
L 0 a set of infrastructures within a core infrastructure community;
s1.3.2, setting r' as a reference neighborhood radius, and MinPts as a number of preset infrastructures in the core infrastructure community;
s1.3.3, applying DBSCAN algorithm, according to r' and attributes of MinPts decision points, making final city infrastructure group division.
3. Electronic device, comprising a memory storing a computer program and a processor implementing the steps of a city infrastructure group elasticity analysis method according to any one of claims 1-2 when executing said computer program.
4. Computer-readable storage medium, on which a computer program is stored, wherein the computer program, when being executed by a processor, implements a city infrastructure group elasticity analysis method as claimed in any one of claims 1-2.
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