KR102081377B1 - Determination method and system of optimal performance threshold for short and middle span bridge network - Google Patents

Abstract

The present invention relates to a method and a system for determining an optimal performance target for maintenance of a small and medium bridge network. The method according to the present invention comprises the following steps of: modeling a plurality of individual small and medium bridges located in a target area of a small and medium bridge network into a small and medium bridge network consisting of a plurality of bridge groups which are grouped according to a predetermined standard; and calculating a solution of a multi-purpose optimization problem consisting of a plurality of purpose functions corresponding to a plurality of performance indicators for evaluating performance of the modeled small and medium bridge network and variables for designing target performance for maintenance of the bridge groups. According to the present invention, effect and efficiency of maintenance targeting a small and medium bridge can be maximized through maintenance of a small and medium bridge network level, and an asset management system of a small and medium bridge can be established.

Description

Determination method and system of optimal performance threshold for short and middle span bridge network

The present invention relates to a method and system for determining optimal performance target for maintenance of small and medium bridge networks.

Construction structures including large bridges, such as more than 1,800 civil facilities over 30 years nationwide, are aging, but the budget for maintenance is not increasing accordingly.

Class 1 bridges are active in the system and implementation for maintenance, while small and medium bridges managed by local governments lack active maintenance due to limited budget and manpower.

Currently, the bridge maintenance techniques and systems currently used are mostly DB level systems for grasping the status of maintenance. In addition, currently applied bridge maintenance techniques and systems are centered on individual bridges as in Korean Patent Registration No. 10-0795967, and maintenance is applied by prioritizing the grade and size of bridges, taking into account the importance on the network of bridges. It is not.

Therefore, it is necessary to develop differentiated maintenance techniques for small and medium sized bridges for efficient application of limited budget and manpower in the midst of the increase of small and medium sized bridges for maintenance.

Korea Patent Registration No. 10-0795967 (Registration Date: 2008.01.11)

Therefore, the technical problem to be solved by the present invention is to provide a method and system for grouping a plurality of bridges on the small and medium bridge network, to determine the maintenance performance target for each bridge group, and thus to optimize the maintenance performance target of small and medium individual bridges It aims to do it.

In order to solve the above technical problem, a method for determining optimal performance target for maintenance of a small and medium bridge network according to the present invention includes a plurality of bridge groups in which a plurality of small and medium individual bridges located in a target area of a small and medium bridge network are grouped according to a predetermined criterion. Modeling the small and medium bridge network comprising: a plurality of objective functions corresponding to a plurality of performance indicators for evaluating the performance of the modeled small and medium bridge network, and a target performance of maintenance of the plurality of bridge groups. Calculating a solution of the multipurpose optimization problem.

The modeling of the small and medium bridge network may include determining a plurality of connection paths connecting the first point and the second point in the target area of the small bridge network, and for each of the plurality of links constituting the determined plurality of connection paths. Grouping the small and medium individual bridges may be included.

The plurality of objective functions corresponding to the plurality of performance indicators are based on the network performance indicator (P _c ) based on the connection reliability of the small and medium bridge network, the network performance indicator (R _c ) based on the margin, and the user cost. Equation 1, Equation 3, Equation 7 and Equation 8 corresponding to the network performance indicator (U _c ) and the network performance indicator (M _c ) based on the maintenance cost can be represented.

[Equation 1]

개의 경우의 수에서 네트워크 연결가능 총 경우의 수이고, N_b는 교량그룹의 총 개수이며, P_b,i는 N_c에서 i번째 경우가 발생할 확률로서 아래 수학식 2에 의해 계산될 수 있다.Where N _c is the total number of bridge groups

Is the total number of network connectable cases in the number of cases, N _b is the total number of bridge groups, and P _{b, i} is the probability of occurrence of the i th case in N _c and can be calculated by Equation 2 below.

[Equation 2]

는 연결가능한 교량그룹의 집합이며, N_s는

의 요소개수로 연결 가능한 교량그룹의 개수이고,

는 연결이 불가능한 교량의 집합이며, N_f는

의 요소개수로 연결 불가능한 교량그룹의 개 수를 나타낼 수 있다.Where P _{s, i} is the connectable probability of the jth bridge group,

Is the set of connectable bridge groups, and N _s is

The number of bridge groups that can be connected by the number of elements of

Is the set of bridges that are not reachable, and N _f is

The number of elements in the bridge can represent the number of bridge groups that cannot be connected.

[Equation 3]

Here, N _b is the total number of the bridge _group, P _{oc, i} is the i-th bridge group only chance of a connection failure, and RI _i is also free due to connection loss of the i-th bridge group _indices, P _{oc, i} Is calculated by Equation 4 below, and RI _i may be calculated by Equation 5 below.

[Equation 4]

[Equation 5]

Β _c is a reliability index corresponding to P _c of Equation 1, which is obtained by Equation 6 below, and β _{c, i} may be a reliability index corresponding to network performance index due to loss of connection of the i-th bridge group. .

[Equation 6]

Φ ⁻¹ may be a normal inverse cumulative distribution function.

[Equation 7]

Here, U _{ct, i} may represent the cost for the time required for the route movement in the i th case of N _c , and U _{cv, i} may represent the cost for the fuel required for the i th route.

[Equation 8]

Here, Si may be the sum of the lengths of the individual bridges included in the i-th bridge group.

The multi-purpose optimization problem may include maximizing an average value of the network performance indicator (P _c ) based on the connection reliability, maximizing an average value of the network performance indicator (R _c ) based on the margin, and network performance based on the user cost. It may be aimed at minimizing the average value of the indicator U _c and minimizing the average value of the network performance indicator M _c based on the maintenance cost.

The number of design variables is equal to the number of bridge groups and may be expressed by Equation 9 below.

[Equation 9]

Pall and i are design variables corresponding to the i th bridge group, P _{s and i} are probable probabilities of the i th bridge group, and the limit condition of P _{s and i} can be limited from the lower limit 0.9 to the upper limit 0.9999.

The calculating of the multipurpose optimization problem may include: obtaining a Pareto optimal set, which is a plurality of solutions of the multipurpose optimization problem, calculating weights for the plurality of objective functions, and calculating the weighted values. And selecting and applying a predetermined multi-attribute decision making method to select one solution from the Pareto solution.

The maintenance target performance of the small and medium individual bridges may be determined by the maintenance target performance of the bridge group to which the small and medium individual bridge belongs.

In order to solve the above technical problem, a computer-readable recording medium may include a program for performing a method for determining a maintenance optimal performance target for a small and medium bridge network according to the present invention.

The program includes a command set for performing a step of modeling a plurality of small and medium individual bridges located in a target area of a small and small bridge network according to a predetermined criterion into a small and small bridge network comprising a plurality of bridge groups, and the modeled small and medium bridge. A set of instructions for calculating a solution of a multipurpose optimization problem consisting of a plurality of objective functions corresponding to a plurality of performance indicators for evaluating the performance of the network and a maintenance target performance of the plurality of bridge groups is a design variable. It may include.

In order to solve the above technical problem, a system for determining an optimal performance target for maintenance of a small and medium bridge network according to the present invention includes a plurality of bridge groups in which a plurality of small and medium individual bridges located in a target area of a small and medium bridge network are grouped according to predetermined criteria. The modeling unit for modeling the small and medium bridge network, and a plurality of objective functions corresponding to a plurality of performance indicators for evaluating the performance of the modeled small and medium bridge network and the target performance management of the plurality of bridge groups as design variables It includes a calculation unit for calculating a solution of the multi-purpose optimization problem is composed.

According to the present invention, it is possible to maximize the effectiveness and efficiency of small and medium bridge maintenance through the maintenance of the small and medium bridge network level, and contribute to establishing the asset management system of the small and medium bridge.

1 is a block diagram of a system for determining an optimal performance target for maintenance of a small and medium bridge network according to an embodiment of the present invention.
2 is an operation flowchart of a system for determining an optimal performance target for maintenance of a small and medium bridge network according to an exemplary embodiment of the present invention.
3 is a view provided to explain the small and medium bridge network modeling according to the present invention.
4 is a flowchart illustrating a process of determining maintenance target performance of a bridge group according to an embodiment of the present invention.
FIG. 5 illustrates a Pareto solution for determining maintenance target performance of a multipurpose optimization problem corresponding to the bridge network of FIG. 3.

DETAILED DESCRIPTION Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art may easily implement the present invention.

1 is a block diagram of a system for determining an optimal performance target for maintenance of a small and medium bridge network according to an embodiment of the present invention.

Referring to FIG. 1, a system for determining optimal performance target for maintenance of a small and medium bridge network according to the present invention may include a modeling unit 110, an input data processing unit 120, a calculation unit 130, and a determination unit 140. have.

The modeling unit 110 may model the small and medium bridge network including a plurality of bridge groups in which a plurality of small and medium individual bridges located in the small and medium bridge network target area are grouped according to a predetermined criterion.

The input data processor 120 may include the number and length of bridge groups, the number of connection paths included in the modeled network, the sum of the lengths of the individual bridges included in each bridge group, and the vehicle speed limit of each connection path included in the modeled network. For example, the fuel cost per distance, vehicle fuel economy, and the average labor cost per hour of the user may be input as input data. The input data may be input as random variables.

The calculation unit 130 receives the input data, and consists of a plurality of objective functions corresponding to a plurality of performance indicators for evaluating the performance of the modeled small and medium bridge network and the target performance of maintenance of the plurality of bridge groups as design variables. Compute the solution of the multipurpose optimization problem.

The determination unit 140 may determine the maintenance target performance of the small and medium individual bridges based on the maintenance target performance of the bridge group to which the small and medium individual bridge belongs.

2 is an operation flowchart of a system for determining an optimal performance target for maintenance of a small and medium bridge network according to an exemplary embodiment of the present invention.

Referring to FIGS. 1 and 2, first, when the small and medium bridge network target region is determined, the modeling unit 110 may perform the small and medium bridge network modeling to group small and medium individual bridges into a plurality of bridge groups in the target region (S210). ).

3 is a view provided to explain the small and medium bridge network modeling according to the present invention.

For example, as illustrated in FIG. 3, when a region including Gwangju and Yeosu is selected as a small and medium bridge network target area, the modeling unit 110 first connects both Gwangju and Yeosu points, and includes a plurality of individual bridges including small and medium individual bridges. The connection path can be determined. There may be multiple paths connecting both points. Therefore, the modeling unit 110 may include the small and medium individual bridges, but determine a plurality of connection paths by a predetermined number in the order of short distance. When determining the route, it is possible to include only roads such as national roads and local roads, and exclude highways.

1) Gwangju-1-2-3-4-5-Yeosu, 2) Gwangju-1-2-9-8-5-Yeosu, 3) Gwangju-1-2-3-7-8-5-Yeosu, 4) Gwangju-6-2-3-4-5-Yeosu, 5) Gwangju-6-2-9-8-5-Yeosu, 6) Gwangju-6-2-3-7-8-5-Yeosu, etc. Explain that the six connection paths of are determined. In FIG. 3, the number indicated by the arrow indicates a bridge group corresponding to each link constituting six connection paths. Bridge group can be created by grouping small and medium individual bridges located in the link. Meanwhile, in the present invention, the small and medium bridge may be defined as a bridge belonging to a predetermined bridge length range. Criteria for defining small and medium bridges may vary depending on the embodiment.

As illustrated in FIG. 3, the modeling unit 110 may connect a plurality of bridge groups in series-parallel to model a bridge network of a small and medium bridge network target region.

The number, location, type and length of bridges in each bridge group can be grasped. In addition, it is possible to grasp the current status of the bridge groups included in the connection paths for the plurality of connection paths.

Referring back to FIG. 2, when the small and medium bridge network modeling is completed (S210), a plurality of objective functions corresponding to a plurality of performance indicators for evaluating the performance of the modeled small and medium bridge network and the maintenance target performance of the plurality of bridge groups are performed. The solution of the multipurpose optimization problem consisting of the design variables can be calculated (S220).

In operation S220, the maintenance target performance of the plurality of bridge groups may be determined through a multipurpose optimization and decision making process.

4 is a flowchart illustrating a process of determining maintenance target performance of a bridge group according to an embodiment of the present invention.

Referring to FIG. 4, a multipurpose optimization problem for determining the maintenance target performance of the bridge group may be configured (S221).

First, a plurality of performance indicators for evaluating the performance of a modeled small and medium bridge network will be described first. A plurality of performance indicators for evaluating the performance of a modeled small and medium bridge network are network performance indicators based on connection reliability of the small and medium bridge network. (P _c ), network performance indicator (R _c ) based on margin, network performance indicator (U _c ) based on user cost, and network performance indicator (M _c ) based on maintenance cost. Can be.

Network performance index (P _c ) based on the connection reliability of the small and medium bridge network can be represented by Equation 1 below.

[Equation 1]

개의 경우의 수에서 네트워크 연결가능 총 경우의 수이고, N_b는 교량그룹의 총 개수이며, P_b,i는 N_c에서 i번째 경우가 발생할 확률로서 아래 수학식 2에 의해 계산된다.Where N _c is the total number of bridge groups

Is the total number of network connectable cases in the number of cases, N _b is the total number of bridge groups, and P _{b, i} is the probability that the i th case in N _c will be calculated by Equation 2 below.

[Equation 2]

는 연결가능한 교량그룹의 집합이며, N_s는

의 요소개수로 연결 가능한 교량그룹의 개수이고,

는 연결이 불가능한 교량의 집합이며, N_f는

의 요소개수로 연결 불가능한 교량그룹의 개 수를 나타낸다. 예를 들어, 도 3에서 9개의 교량그룹의 연결 유무에 따라 총 2⁹ = 512개의 경우의 수가 존재한다. 이 경우의 수 중에서 1, 7, 8, 9번째 교량그룹이 연결불가이고, 2, 3, 4, 5, 6번째 교량그룹이 연결 가능할 경우, 전체 교량네트워크는 연결이 가능하다. 즉 도 3에서 4번째 연결경로인 '광주-6-2-3-4-5-여수'로 교량네트워크 연결이 가능하다. 이때

= {2, 3, 4, 5, 6},

= {1, 7, 8, 9}이고, N_s는 5, N_f는 4이며, 이에 해당하는 P_b,i는 아래와 같이 계산할 수 있다.Where P _{s, i} is the connectable probability of the jth bridge group,

Is the set of connectable bridge groups, and N _s is

The number of bridge groups that can be connected by the number of elements of

Is the set of bridges that are not reachable, and N _f is

The number of bridge groups that cannot be connected by the number of elements of. For example, in FIG. 3, there are a total of 2 ⁹ = 512 cases depending on whether nine bridge groups are connected. In this case, if the 1st, 7th, 8th, and 9th bridge groups are not connectable, and the 2nd, 3rd, 4th, 5th, 6th bridge groups can be connected, the entire bridge network can be connected. That is, the bridge network can be connected to the fourth connection path 'Gwangju-6-2-3-4-5-Yeosu' in FIG. 3. At this time

= {2, 3, 4, 5, 6},

= {1, 7, 8, 9}, N _s is 5, N _f is 4, and corresponding P _{b, i} can be calculated as follows.

The network performance index R _c based on the margin may be represented by Equation 3 below.

[Equation 3]

Where N _b is the total number of bridge groups, P _{oc, i} is the probability that only the i-th bridge group will lose its linkage function, and RI _i is the margin indicator due to the loss of connection of the i-th bridge group. P _{oc, i} is calculated by Equation 4 below. In Equation 3, RI _{i, which} is a margin indicator due to loss of connection of the i-th bridge group, may be calculated by Equation 5 below.

[Equation 4]

[Equation 5]

Β _c is a reliability index corresponding to P _c of Equation 1, and is obtained by Equation 6 below, and β _{c, i} is a reliability index corresponding to a network performance index due to loss of connection of the i-th bridge group.

[Equation 6]

Φ ⁻¹ is the normal inverse cumulative distribution function.

The network performance index U _c based on the user cost can be obtained by Equation 7 below.

[Equation 7]

Here, U _{ct, i} represents the cost for the time required for the route movement in the i-th case of N _c , U _{cv, i} represents the cost for the fuel required for the use of the i-th route. P _{b, i} may be defined by Equation 2 above.

Network performance indicator (M _c ) based on the maintenance cost can be represented by Equation 8 below. The total maintenance cost of the bridge network is the sum of the maintenance costs of the entire bridge group, and the maintenance cost of each bridge group is considered to be proportional to the bridge group connectability and the length of the bridge group.

[Equation 8]

Where Si is the sum of the lengths of the individual bridges included in the i-th bridge group.

Network performance indicator (P _c ) based on connection reliability of small and medium bridge network, network performance indicator (R _c ) based on margin, network performance indicator (U _c ) based on user cost, and maintenance Design variables for maintenance objective performance of a plurality of objective functions and a plurality of bridge groups represented by equations (1), (3), (7) and (8) corresponding to the cost-based network performance indicator (M _c ) It is possible to construct a multipurpose optimization problem consisting of:

In the multi-purpose optimization problem, the objectives are four and are as follows. Network Performance Indicator (P _c) the average value E (P _c) to maximize, the network performance metrics that are based on the margin (R _c) an average value E (R _c) the network performance metrics to the maximum, based on the user's cost of the ( U _c) is the minimum of the average value E (U _c) minimize and maintain network performance indicators that are based on the cost (M _c) the average value E (M _c) of the.

In the multipurpose optimization problem, the design variable is equal to the number of bridge groups and may be expressed by Equation 9 below.

[Equation 9]

P _{all, i} is a design variable corresponding to the i-th bridge group, P _{s, i} is the connectable probability of the i-th bridge group, and the constraint condition of P _{s, i} can be limited from the lower limit 0.9 to the upper limit 0.9999.

For example, in the bridge network modeled as nine bridge groups in FIG. 3, the design variable of the multipurpose optimization problem has nine design variables as follows.

P _all = {P _{all, 1} , P _{all, 2} , P _{all, 3} , P _{all, 4} , P _{all, 5} , P _{all, 6} , P _{all, 7} , P _{all, 8} , P _{all, 9} }

In the multipurpose optimization problem, the input data includes the number and length of bridge groups as described above, the number of connection paths included in the modeled network, the sum of the lengths of the individual bridges included in each bridge group, and each connection path included in the modeled network. The speed limit of the vehicle, the fuel cost per distance, the fuel economy of the vehicle, the average labor cost per hour of the user, etc., the input data may be input as a random variable. In addition, according to the exemplary embodiment, 100,000 samples of random variables, which are input data, may be generated, and Monte Carlo simulation may be applied.

Next, the Pareto optimal set for the multipurpose optimization problem configured in step S221 may be calculated by applying the multipurpose optimization technique (S223).

FIG. 5 illustrates a Pareto solution for determining maintenance target performance of a multipurpose optimization problem corresponding to the bridge network of FIG. 3.

Next, the following procedure may be performed to select one solution among a plurality of Pareto solutions calculated in step S223.

A plurality of objective functions, weights are calculated for the four objective functions presented above (S225). To this end, one of Standard Deviation (SD), Criteria Importance Through Inter-Criteria Correlation (CRITIC), and Correlation Coefficient and Standard Deviation (CCSD) can be selected and applied.

Subsequently, one solution may be selected from the Pareto solution by applying the weight calculated in step S225 by selecting a predetermined multi-property decision method (S227). In step S227, the Simple Additive Weighting (SAW) method, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, and the ELimination and Choice Expressing The Reality (ELECTRE) method You can choose to apply one. From this, one solution is selected from the multiple optimal sets.

In FIG. 5, the weight was calculated by applying the CRITIC method, and the O _{S was selected} by using the SAW method, the O _T by applying the TOPSIS method, and the O _E by applying the ELECTRE method.

FIG. 6 is a table showing bridge group maintenance target performance which is a design variable corresponding to the solution selected in FIG. 5.

In FIG. 6, the target performance of nine bridge groups maintenance, which is a design variable corresponding to the optimal solution selected from FIG. 5, O _S , O _T , and O _E , may be confirmed.

The optimal solution of each design variable selected in step S227 may be determined as the maintenance target performance of the bridge group.

Referring back to FIG. 2, the determination unit 140 may determine the maintenance target performance of the small and medium individual bridges belonging to the bridge group based on the maintenance target performance of each bridge group calculated in step S227 (S230). ). For example, assuming that each individual bridge included in the bridge group is connected in series and is completely correlated between the individual bridges, the maintenance target performance of each bridge is compared with the maintenance target performance of the bridge group to which the bridge belongs. The same decision can be made. Therefore, even when the optimum maintenance target performance of the second group of bridges illustrated in six defined as 0.9960 by O _S, to maintain the target performance of the individual bridges belonging to a bridge group 2 also determined by 0.9960.

The embodiments described above may be implemented as hardware components, software components, and / or combinations of hardware components and software components. For example, the devices, methods, and components described in the embodiments may include, for example, processors, controllers, arithmetic logic units (ALUs), digital signal processors, microcomputers, field programmable gates (FPGAs). It may be implemented using one or more general purpose or special purpose computers, such as an array, a programmable logic unit (PLU), a microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to the execution of the software. For convenience of explanation, one processing device may be described as being used, but one of ordinary skill in the art will appreciate that the processing device includes a plurality of processing elements and / or a plurality of types of processing elements. It can be seen that it may include. For example, the processing device may include a plurality of processors or one processor and one controller. In addition, other processing configurations are possible, such as parallel processors.

The software may include a computer program, code, instructions, or a combination of one or more of the above, and may configure the processing device to operate as desired, or process independently or collectively. You can command the device. Software and / or data may be any type of machine, component, physical device, virtual equipment, computer storage medium or device in order to be interpreted by or to provide instructions or data to the processing device. Or may be permanently or temporarily embodied in a signal wave to be transmitted. The software may be distributed over networked computer systems so that they may be stored or executed in a distributed manner. The software and data may be stored on one or more computer readable recording media.

The method according to the embodiment may be embodied in the form of program instructions that can be executed by various computer means and recorded in a computer readable medium. The computer readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions recorded on the media may be those specially designed and constructed for the purposes of the embodiments, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tape, optical media such as CD-ROMs, DVDs, and magnetic disks, such as floppy disks. Magneto-optical media, and hardware devices specifically configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

Although the embodiments have been described with reference to the accompanying drawings, those skilled in the art may apply various technical modifications and variations based on the above. For example, the described techniques may be performed in a different order than the described method, and / or components of the described systems, structures, devices, circuits, etc. may be combined or combined in a different form than the described method, or other components. Or, even if replaced or substituted by equivalents, an appropriate result can be achieved.

110: modeling unit
120: input data processing unit
130: calculation unit
140: decision

Claims (10)

delete delete Modeling unit modeling a plurality of small and medium individual bridges located in the target area of the small and medium bridge network into a small and medium bridge network composed of a plurality of bridge groups grouped according to a predetermined criterion; and
A calculation unit calculates a solution of a multipurpose optimization problem consisting of a plurality of objective functions corresponding to a plurality of performance indicators for evaluating the performance of the modeled small and medium bridge network and a maintenance target performance of the plurality of bridge groups. step
Including,
Modeling with the small and medium bridge network,
Determining a plurality of connection paths connecting the first point and the second point in the target area of the small and medium bridge network; and
Grouping small and medium individual bridges for each of a plurality of links constituting the determined plurality of connection paths;
Including;
The plurality of objective functions corresponding to the plurality of performance indicators are based on the network performance indicator (P _c ) based on the connection reliability of the small and medium bridge network, the network performance indicator (R _c ) based on the margin, and the user cost. Equation 1, Equation 3, Equation 7 and Equation 8 corresponding to the network performance indicator (M _c ) based on the network performance indicator (U _c ) and maintenance cost to
[Equation 1]

Where N _c is the total number of bridge groups

Is the total number of network connectable cases in the number of cases, N _b is the total number of bridge groups, P _{b, i} is the probability of occurrence of the i th case in N _c , and is calculated by Equation 2 below.
[Equation 2]

Where P _{s, i} is the connectable probability of the jth bridge group,

Is the set of connectable bridge groups, and N _s is

The number of bridge groups that can be connected by the number of elements of

Is the set of bridges that are not reachable, and N _f is

Represents the number of bridge groups that cannot be connected by the number of elements of
[Equation 3]

Here, N _b is the total number of the bridge _group, P _{oc, i} is the i-th bridge group only chance of a connection failure, and RI _i is also free due to connection loss of the i-th bridge group _indices, P _{oc, i} Is calculated by Equation 4 below, RI _i is calculated by Equation 5 below,
[Equation 4]

[Equation 5]

Β _c is a reliability index corresponding to P _c of Equation 1, and is obtained by Equation 6 below. Β _{c, i} is a reliability index corresponding to network performance index due to loss of connection of the i th bridge group.
[Equation 6]

Φ ^-1 is the normal inverse cumulative distribution function,
[Equation 7]

Where U _{ct, i} represents the cost for the time required to travel the route in the i th case of N _c , and U _{cv, i} represents the cost for the fuel required to use the i th route,
[Equation 8]

Where Si is the sum of the lengths of the individual bridges included in the i-th bridge group. In claim 3,
The multi-purpose optimization problem may include maximizing an average value of the network performance indicator (P _c ) based on the connection reliability, maximizing an average value of the network performance indicator (R _c ) based on the margin, and network performance based on the user cost. A method for determining the optimal performance target for maintenance of small and medium bridge networks aimed at minimizing the average value of the indicator U _c and minimizing the average value of the network performance indicator M _c based on the maintenance cost. In claim 4,
The number of design variables is equal to the number of bridge groups and is represented by Equation 9 below.
[Equation 9]

Pall, i is the design variable corresponding to the i-th bridge group, P _{s, i} is the probability of connection of the i-th bridge group, and the constraint condition of P _{s, i} is the small and medium bridge network that limits from the lower limit 0.9 to the upper limit 0.9999. To determine optimal performance objectives In claim 5,
Computing the multipurpose optimization problem,
Obtaining a Pareto optimal set, which is a plurality of solutions of the multipurpose optimization problem,
Calculating weights for the plurality of objective functions, and
Selecting one solution from the Pareto solution by applying the calculated weight by selecting a predetermined multi-property decision method;
Method for determining the optimal performance maintenance of small and medium bridge network comprising a. In claim 3,
The maintenance target performance of the small and medium individual bridge is determined by the maintenance target performance of the bridge group to which the small and medium individual bridge belongs. delete delete Modeling unit for modeling a small and medium bridge network consisting of a plurality of bridge groups grouping a plurality of small and medium individual bridges located in the target area of the small and medium bridge network according to a predetermined standard, and
A calculation unit for calculating a solution of the multi-purpose optimization problem consisting of a plurality of objective functions corresponding to a plurality of performance indicators for evaluating the performance of the modeled small and medium bridge network and the maintenance target performance of the plurality of bridge groups as a design variable
Including,
The modeling unit,
Determining a plurality of connection paths connecting the first point and the second point in the target area of the small bridge network, grouping the small and medium individual bridges for each of the plurality of links constituting the determined plurality of connection paths;
The plurality of objective functions corresponding to the plurality of performance indicators are based on the network performance indicator (P _c ) based on the connection reliability of the small and medium bridge network, the network performance indicator (R _c ) based on the margin, and the user cost. Equation 1, Equation 3, Equation 7 and Equation 8 corresponding to the network performance indicator (M _c ) based on the network performance indicator (U _c ) and maintenance cost to
[Equation 1]

Where N _c is the total number of bridge groups

Is the total number of network connectable cases in the number of cases, N _b is the total number of bridge groups, P _{b, i} is the probability of occurrence of the i th case in N _c , and is calculated by Equation 2 below.
[Equation 2]

Where P _{s, i} is the connectable probability of the jth bridge group,

Is the set of connectable bridge groups, and N _s is

The number of bridge groups that can be connected by the number of elements of

Is the set of bridges that are not reachable, and N _f is

Represents the number of bridge groups that cannot be connected by the number of elements of
[Equation 3]

Here, N _b is the total number of the bridge _group, P _{oc, i} is the i-th bridge group only chance of a connection failure, and RI _i is also free due to connection loss of the i-th bridge group _indices, P _{oc, i} Is calculated by Equation 4 below, RI _i is calculated by Equation 5 below,
[Equation 4]

[Equation 5]

Β _c is a reliability index corresponding to P _c of Equation 1, and is obtained by Equation 6 below. Β _{c, i} is a reliability index corresponding to network performance index due to loss of connection of the i th bridge group.
[Equation 6]

Φ ^-1 is the normal inverse cumulative distribution function,
[Equation 7]

Where U _{ct, i} represents the cost for the time required to travel the route in the i th case of N _c , and U _{cv, i} represents the cost for the fuel required to use the i th route,
[Equation 8]

Where Si is the sum of the lengths of the individual bridges in the i-th bridge group,
The multi-purpose optimization problem may include: maximizing an average value of the network performance indicator (P _c ) based on the connection reliability, maximizing an average value of the network performance indicator (R _c ) based on the margin, and network performance based on the user cost To minimize the average value of the indicator (U _c ) and to minimize the average value of the network performance indicator (M _c ) based on the maintenance cost,
The number of design variables is equal to the number of bridge groups and is represented by Equation 9 below.
[Equation 9]

Pall, i is a design variable corresponding to the i-th bridge group, P _{s, i} is the connectable probability of the i-th bridge group _, the constraint condition of the P _{s, i} is limited from the lower limit 0.9 to the upper limit 0.9999,
The calculator calculates a Pareto optimal set, which is a plurality of solutions of the multipurpose optimization problem, calculates weights for the plurality of objective functions, and calculates the weighted values to calculate the solution of the multipurpose optimization problem. Select and apply a predetermined multi-property decision method to select one solution from the Pareto solution,
The determination unit for determining the maintenance target performance of the small and medium individual bridges is determined by the maintenance target performance of the bridge group to which the small and medium individual bridge belongs
Maintenance optimal performance target determination system of small and medium bridge network further comprising.

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