CN106462908B - Maintenance management index calculation device and maintenance management index calculation method - Google Patents
Maintenance management index calculation device and maintenance management index calculation method Download PDFInfo
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Abstract
A maintenance management index calculation device is provided with: a data acquisition unit that acquires inspection result data including an inspection result obtained by evaluating the presence or absence of abnormality of the civil structure for a plurality of inspection items; a maintenance management index calculation unit that calculates a maintenance management index relating to maintenance management of the civil structure including a priority index, assuming that the priority index indicating a priority of maintenance management for each predetermined section of the civil structure follows a gamma distribution, by applying a model based on an item reaction theory to the inspection result data; and an output unit that outputs the maintenance management index calculated by the maintenance management index calculation unit.
Description
Technical Field
The present invention relates to a maintenance management index calculation device and a maintenance management index calculation method for a civil structure.
Background
Civil engineering structures such as underground tunnels of urban railways are subjected to maintenance and management based on the results of inspections performed periodically. The inspection result is managed using a database system or the like (see, for example, patent document 1). In addition, when a plan for performing maintenance management is prepared, it is common to evaluate each abnormality by performing comparison with a past inspection result, comparison of inspection results of a plurality of items, or the like, and prepare a maintenance management plan such as repair.
Documents of the prior art
Patent document
Patent document 1: JP 2002-288180 publication
Disclosure of Invention
Problems to be solved by the invention
However, the inspection items related to the general civil engineering structure include inspection items in which evaluation may be diverged if the inspector is different, as in the case of visual inspection. Further, the inspection results may include inspection results with different inspection conditions such as different inspection times. Therefore, simply comparing the inspection results with each other may not accurately determine whether the civil structure is actually problematic. In addition, since it has been conventionally determined whether or not various measures such as repair are necessary after evaluating the abnormality alone, there is room for improvement in evaluation in consideration of the soundness of the civil engineering structure itself.
The present invention has been made in view of the above circumstances, and an object thereof is to provide a maintenance management index calculation device and a maintenance management index calculation method that calculate a maintenance management index that can be used as an index for maintenance management of a civil structure based on an inspection result.
Means for solving the problems
In order to achieve the above object, a maintenance management index calculation device according to an aspect of the present invention includes: a data acquisition unit that acquires inspection result data including an inspection result obtained by evaluating the presence or absence of abnormality of the civil structure for a plurality of inspection items; a maintenance management index calculation unit that calculates a maintenance management index relating to maintenance management of the civil structure including a priority index, assuming that the priority index indicating a priority of maintenance management for each predetermined section of the civil structure follows a gamma distribution, by applying a model based on an item reaction theory to the inspection result data; and an output unit that outputs the maintenance management index calculated by the maintenance management index calculation unit.
In addition, a maintenance management index calculation method according to an aspect of the present invention includes: a data acquisition step of acquiring inspection result data composed of inspection results obtained by evaluating the presence or absence of abnormality of the civil structure with respect to a plurality of inspection items; a maintenance management index calculation step of calculating a maintenance management index relating to maintenance management of the civil structure including a priority index, assuming that the priority index indicating a priority of maintenance management for each predetermined section of the civil structure follows a gamma distribution, by applying a model based on a project reaction theory to the inspection result data; and an output step of outputting the maintenance management index calculated in the maintenance management index calculation step.
According to the maintenance management index calculation device and the maintenance management index calculation method described above, it is possible to calculate the maintenance management index including the priority index indicating the priority of maintenance management for each predetermined section of the civil structure by separating the information derived from the "inspection state" and the information derived from the "soundness of the civil structure" included in the inspection result data by applying the model based on the project reaction theory to the inspection result data on the assumption that the priority index indicating the priority of maintenance management for each predetermined section of the civil structure follows the gamma distribution. Therefore, a more appropriate maintenance management index can be calculated as an index relating to maintenance management of the civil structure.
Here, the following manner can be adopted: the model based on the project reaction theory is an inspection project reaction model, and the inspection project reaction model is a model for calculating a maintenance management index on the assumption that the inspection result is abnormal.
In the case of using the inspection item reaction model, the maintenance management index is calculated based on the presence or absence of the abnormality of the inspection result, and therefore, a maintenance management index more appropriate as an index relating to maintenance management of the civil engineering structure can be calculated by relatively simple calculation.
Further, the following manner can be adopted: the model based on the project reaction theory is a stage inspection reaction model for calculating a maintenance management index so that the inspection result belongs to any one of 3 or more stages assigned according to the level of abnormality.
In the case of using the stage inspection reaction model, the maintenance management index is calculated on the basis that the inspection result belongs to any one of stages of 3 or more assigned according to the level of the anomaly, and therefore, the priority of the maintenance management can be considered in more detail.
Further, the following manner can be adopted: the stage to which the inspection result belongs in the stage inspection reaction model is 4 or less.
By setting the stage to which the inspection result belongs to 4 or less, it is possible to calculate the maintenance management index that more accurately indicates the priority of maintenance management of the civil engineering structure without excessively increasing the load for calculation of the maintenance management index.
Effects of the invention
According to the present invention, a maintenance management index calculation device and a maintenance management index calculation method are provided that calculate a maintenance management index that can be used as an index relating to maintenance management of a civil structure based on an inspection result.
Drawings
Fig. 1 is a functional block diagram of a maintenance management index calculation device according to an embodiment of the present invention.
Fig. 2 is a flowchart illustrating a maintenance management index calculation method of the maintenance management index calculation device.
Fig. 3 is a diagram showing an example of the examination item reaction function.
Fig. 4 is a diagram showing a method of converting inspection result data when the inspection item reaction model is applied.
Fig. 5 is a diagram showing a method of converting inspection result data when the inspection item reaction model is applied.
Fig. 6(a) and 6(B) are diagrams illustrating a method of converting inspection result data when the inspection item reaction model is applied.
Fig. 7 is a diagram showing a method of converting inspection result data when the inspection item reaction model is applied.
Fig. 8 is a diagram showing a part of the priority index obtained by applying the examination item reaction model.
Fig. 9 is a histogram of the priority index obtained by applying the examination item reaction model.
Fig. 10 is a distribution diagram of the priority index obtained by applying the examination item reaction model.
Fig. 11 is a diagram showing the recognition power a and the difficulty level b obtained by applying the test item reaction model.
Fig. 12(a) is a diagram showing an inspection item response function obtained by applying the inspection item response model to the inspection item on the left side, and fig. 12(B) is a diagram showing an inspection item response function obtained by applying the inspection item response model to the inspection item on the right side.
Fig. 13(a) is a diagram showing an inspection item reaction function obtained by applying the inspection item reaction model to the upper inspection item, and fig. 13(B) is a diagram showing an inspection item reaction function obtained by applying the inspection item reaction model to another inspection item.
Fig. 14 is a diagram showing an example of the examination-type reaction function.
Fig. 15 is a diagram showing a method of converting inspection result data when the stage inspection reaction model is applied.
Fig. 16(a) and 16(B) are diagrams showing a method of converting inspection result data when the stage inspection reaction model is applied.
Fig. 17 is a diagram showing a method of converting inspection result data when the stage inspection reaction model is applied.
Fig. 18 is a diagram showing a part of the priority index obtained by applying the phase inspection reaction model.
Fig. 19 is a histogram of the priority index obtained by applying the phase check reaction model.
Fig. 20 is a distribution diagram of the priority index obtained by applying the phase inspection reaction model.
Fig. 21(a) is a diagram showing an inspection type reaction function obtained by inspecting the reaction model at the crack application stage with respect to the left side surface, and fig. 21(B) is a diagram showing an inspection type reaction function obtained by inspecting the reaction model at the water leakage application stage with respect to the left side surface.
Fig. 22(a) is a view showing an inspection type reaction function obtained by inspecting the reaction model at the stage of application of floating/peeling on the left side surface, and fig. 22(B) is a view showing an inspection type reaction function obtained by inspecting the reaction model at the stage of application of degradation of the steel material on the left side surface.
Detailed Description
Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted.
Fig. 1 is a functional block diagram of a maintenance management index calculation device according to an embodiment of the present invention. The maintenance management index calculation device 1 according to the present embodiment is a device that calculates a maintenance management index that can be used as an index in maintenance management of a civil structure, particularly when a maintenance management plan such as repair/monitoring is made.
The "maintenance management index" calculated by the maintenance management index calculation device 1 is an index for making a plan of maintenance management relating to the civil structure for each predetermined section based on the inspection result when a plurality of items relating to the presence or absence of abnormality in the civil structure are inspected. The plurality of inspection items are types of abnormal shapes related to the respective evaluations in the inspection in which the evaluations are performed for each different type of abnormal shape. Even when the same point of view evaluation is performed in the same section, if the measurement target positions are different from each other, they may be handled as a plurality of inspection items individually. The maintenance management priority of the civil structure means a priority of executing various measures for maintenance management (continuous observation, repair/reinforcement, use restriction, and the like) within a range that can be grasped from the inspection result of the civil structure. In other words, the maintenance management priority may also be referred to as an index indicating a degree of possibility (risk) that the civil engineering structure is in a situation in which some measure needs to be implemented.
As will be described in detail later, the inspection result for maintenance management of the civil engineering structure includes an element that the inspection result changes depending on the inspection state (inspector, inspection date and time). Therefore, it is difficult to directly determine the maintenance management priority of the civil engineering structure from the inspection result. The "maintenance management index" processed by the maintenance management index calculation device 1 according to the present embodiment is an index that indicates the priority of maintenance management of the civil structure to be inspected regardless of the inspection state, and is calculated based on the inspection result.
The term "abnormal shape" means a state in which the performance of the civil engineering structure is degraded from the state of soundness that it should be. Here, the civil engineering structure refers to "a structure except for a building" represented by a tunnel, a bridge, a dam, or the like. In order to detect abnormalities such as damage and deterioration, these structures are inspected regularly or irregularly for the presence or absence of abnormalities. The maintenance management index calculated by the maintenance management index calculation device 1 is used when the priority of maintenance management of the civil engineering structure is evaluated based on the result of the inspection repeatedly performed in this manner.
In the following embodiments, a case where the civil engineering structure is an underground tunnel of an urban railway will be described. Abnormal conditions in an underground tunnel refer to a condition in which the performance of the underground tunnel has been degraded from a proper sound condition. Further, the inspection related to the presence or absence of abnormality in the underground tunnel of the urban railway includes, for example, regular inspection, that is, regular overall inspection and special overall inspection, which are performed based on "maintenance management standards such as a railway structure" and which are used to grasp the presence or absence of abnormality of the structure of the underground tunnel and the state of the progressivity thereof. The examination for the presence or absence of abnormality is not limited to the above examination. The abnormal shape of the underground tunnel is generally generated on the surface of the lining (body) as a phenomenon that can be visually confirmed, for example, cracking, water leakage, or the like. Therefore, the inspection related to the presence or absence of abnormality includes visual inspection. Note that tap sound investigation for investigating the state of a lining (body) such as floating/peeling that cannot be visually confirmed is also included.
In addition, when the maintenance management index calculation device 1 is applied to the inspection result of another type of civil structure, the data structure of the inspection item and the inspection result changes depending on the target civil structure, and the specific processing is appropriately changed depending on the data structure of the inspection result.
The maintenance management index calculation device 1 described in the present embodiment is a device that acquires a data group including inspection results regarding a plurality of inspection items at each position of an underground tunnel (hereinafter, this data is referred to as "inspection result data"), and calculates a maintenance management index related to the underground tunnel for each predetermined section from the inspection result data.
As shown in fig. 1, the maintenance management index calculation device 1 has the following functions: the inspection result data is acquired from an external device 2 such as a mobile terminal or a server device, and the maintenance management index calculated from the inspection result is transmitted to the external device 2. Examples of the external device 2 include a terminal device carried by a person who performs an inspection for the abnormality of the underground tunnel, and a server that manages information on a railroad including the underground tunnel. The device that transmits the inspection result data to the maintenance management index calculation device 1 and the device that is the target of transmission of the maintenance management index calculated by the maintenance management index calculation device 1 need not be the same device, but may be different from each other.
The maintenance management index calculation device 1 is configured as a computer including hardware such as a CPU (Central Processing Unit), a RAM (Random Access Memory) and a ROM (Read only Memory) as main storage devices, a communication module for performing communication, and an auxiliary storage device such as a hard disk. These components operate to function as each part.
Next, the functions of each part of the maintenance management index calculation device 1 will be described. As shown in fig. 1, the maintenance management index calculation device 1 includes a data acquisition unit 11 (data acquisition means), a maintenance management index calculation unit 12 (calculation means), an algorithm storage unit 13, and a result output unit 14 (output means).
The data acquisition unit 11 functions as data acquisition means for acquiring the inspection result data from the external device 2. The inspection result data acquired by the data acquisition unit 11 is sent to the maintenance management index calculation unit 12, and the process related to the calculation of the maintenance management index is performed.
The maintenance management index calculation unit 12 functions as a maintenance management index calculation means for calculating a maintenance management index from the inspection result data. The maintenance management index calculation unit 12 calculates a maintenance management index by applying a model based on a project reaction theory to the inspection result, assuming that the index to be calculated follows a Gamma (Gamma) distribution. As a model based on the project reaction theory, 2 types of models, that is, "inspection project reaction model" and "stage inspection reaction model" can be applied. In order to apply these models, processing such as numerical conversion may be performed on the inspection result data together. The explanation of the 2 models described above and the method of calculating the maintenance management index when these models are applied will be described later.
The algorithm storage unit 13 functions as a storage means for storing a model and an algorithm for calculating the maintenance management index. The model and the algorithm stored in the algorithm storage unit 13 are transmitted to the maintenance management index calculation unit 12 based on an instruction from the maintenance management index calculation unit 12 and executed.
The result output unit 14 functions as an output means for outputting the maintenance management index calculated by the maintenance management index calculation unit 12 to the external device 2.
The maintenance management index calculation method of the maintenance management index calculation device 1 will be described with reference to the flowchart of fig. 2.
First, the data acquiring unit 11 acquires the inspection result data from the external device 2 (S01: data acquiring step). Next, a maintenance management index is calculated from the inspection result data (S02: maintenance management index calculating step). Here, the maintenance management index is calculated by applying a model based on the project reaction theory to the inspection result data on the assumption that the maintenance management index follows the gamma distribution using the algorithm stored in the algorithm storage unit 13. When the maintenance management index calculation device 1 holds a plurality of models based on the project reaction theory, the maintenance management index may be calculated by applying a model for calculating the maintenance management index specified by the user. In this case, the maintenance management index is calculated by selecting and executing an algorithm used for calculation of the maintenance management index from among the algorithms corresponding to the respective models stored in the algorithm storage unit 13.
Finally, the result output unit 14 outputs the calculation result to the external device 2 (S03: output step). Through the above processing, the processing pertaining to the maintenance management index calculation method ends.
Next, a specific method of calculating the maintenance management index in the maintenance management index calculation device 1 will be described. As described above, in the calculation of the maintenance management index, assuming that the maintenance management index follows the gamma distribution, the maintenance management index is calculated by applying, as a model based on the project reaction theory, an "inspection project reaction model" which is a model indicating a possibility that a difference in inspection results is observed, or a "stage inspection reaction model" which is a model indicating which stage the inspection results belong to among 3 or more stages to the inspection result data. A method of calculating the maintenance management index using the 2 models will be described.
(1) Examination item reaction model
As described above, the inspection result data is originally data reflecting the current state of the underground tunnel to be inspected, and the inspection result is preferably constituted by information derived from "the degree of soundness of the civil structure", that is, information indicating whether or not the civil structure actually satisfies the performance required for the structure. In the case where the inspection result is composed of only information derived from "the degree of soundness of civil engineering structure", the inspection result at a place where the necessity of measures is high should be a result with a high degree of abnormality. Therefore, the inspection result should directly show the maintenance management priority of the underground tunnel.
However, the inspection result data includes an element that the inspection result changes depending on the inspection state (inspector/inspection date and time). For example, inspection of an underground tunnel includes inspection in which an inspector makes a judgment based on a predetermined judgment criterion, such as visual inspection. Here, when the examination is performed in a state where the understandings of the judgment criteria between the examiners at different dates and times are slightly different from each other, it is considered that there is a situation where the examination results differ between the examiners. In this manner, the inspection result data is data of a state including information indicating the "inspection state" and information derived from the "soundness of civil structure". That is, the inspection result data has "soundness of civil structure", and has "situation dependency" depending on the inspection situation. On the other hand, the maintenance management index calculation device 1 calculates an index that can separate "situation dependency" from the data of the inspection result as a maintenance management index. The maintenance management index calculation device 1 is intended to calculate "an index indicating the priority of maintenance management for each predetermined section", but also calculates "an index indicating the characteristic of an inspection item" that affects the calculation of the index indicating the priority of maintenance management. The "index indicating the characteristic of the inspection item" is an index that changes depending on the inspection state (inspector, date and time, and type).
Here, it is assumed that a priority index indicating the maintenance management priority in a predetermined section of the underground tunnel to be inspected is θ. The priority index θ indicates a maintenance management priority of the underground tunnel as the civil structure, and is an index in which the probability of observing a strange state (observation probability) is high when the priority index θ is large, and the probability of observing a strange state is low when the priority index θ is small.
In the examination item reaction model, the priority index θ indicates the possibility that a place requiring a remedy or the like is included in a predetermined section, and the degree of abnormality is not considered. Therefore, the inspection result data for each section is evaluated after being converted into 2 values of 0 (no measure required) or 1 (measure required).
When the inspection item is j, the priority index θ and the observation probability P of the abnormal state are setjThe relationship of (θ) satisfies a 2-parameter logic (Logistic) function represented by the following equation (1).
[ equation 1]
Here, ajIs an item identification parameter, bjIs an item difficulty parameter.
Fig. 3 shows the force parameter a among the 2 parametersjTheta and P shown by the numerical expression (1) in the case of changej(θ). In FIG. 3, a is shownj0.3 and bjCase of 8, and aj1.5 and bjThe case is 8. So-called item identification force parameter ajThe parameter is a parameter indicating how the observation probability of the anomaly changes with respect to the change in the maintenance management priority. As shown in FIG. 3, at ajWhen the theta is 1.5, the P is in the vicinity of 6-8jLargely changed, whereas in ajWhen theta is equal to 0.3, P in the vicinity of theta is 6-8jDoes not change much from the changes in the other priority indices theta. Namely, represents ajThe smaller items of examination are such that the variation in the priority index θ is hardly reflected in PjWhereas, ajThere is a clear threshold value for the larger check items that sensitively reflects the variation of the priority index θ.
In addition, the item difficulty level parameter bjIs shown in the graph P shown in FIG. 3jThe number of positions where the change occurs greatly. As shown in fig. 3, the priority index θ has a value of 0 or more, and therefore, b is a valuejAt a larger value, PjThe position where the change is large is shifted to the right side of the figure, and indicates that P is not a significant value of the priority index θjNo change occurred, i.e., it was difficult to observe the anomaly. On the other hand, in bjAt a smaller value, PjThe position of the large change is shifted to the left side of the figure, and indicates P from the stage where the priority index θ is smalljChanges occur, i.e., easy to observe.
Thus, the observation probability P of the abnormal state is expressed by the equation (1)j(θ) how the priority index θ fluctuates. The case where θ follows the gamma distribution in the Model represented by equation (1) is defined as "Inspection Item Response Model (IIRM)" which is one of the models using the Item Response theory. Furthermore, the item identification force parameter a in equation (1) will be determinedjAnd a project difficulty level parameter bjThe Function of (2) is defined as "Inspection Item Response Function (IIRF)".
The examination item reaction function defined above is obtained when examination of a predetermined item is performed in a section where the priority index θ is a specific valueThe probability of observing a anomaly (determined to be anomalous) is taken as a function. The examination item reaction function comprises a priority index theta and an item identification force parameter ajAnd a project difficulty level parameter bjThese 3 parameters. In addition, since the priority index θ is divided for each section, the priority index for each section can be defined as θi(I1, 2.. said., I, where I is the number of intervals of the underground tunnel). In addition, the item identification force parameter ajAnd a project difficulty level parameter bjJ included in (a) can be defined as J1, 2.
The maintenance management index calculation device 1 calculates the priority index θ based on the inspection result dataiItem identification force parameter ajAnd a project difficulty level parameter bjIn this case, each parameter is assumed to satisfy the condition of the following expression (2).
[ equation 2]
The above expression (2) assumes a probability distribution satisfied by each parameter, and indicates the priority index θiAnd a project difficulty level parameter bjThe gamma distribution specified by the shape parameter shape and the scale parameter scale is satisfied. Furthermore, an item identification force parameter a is shownjSatisfies the equation of mean mu and variance sigma2A prescribed lognormal distribution. These are selected based on the characteristics of the parameters. That is, the priority index θ is assumediAnd a project difficulty level parameter bjThe distribution is similar to a gamma distribution in a case where, for example, the lifetime of an electronic device in reliability engineering is used as a probability variable. On the other hand, assume an item identification force parameter ajThe distribution follows a lognormal distribution in which a limit is imposed as if the value becomes 0 or more. In addition, the item identification force parameter a may be assumedjA truncated normal distribution is followed instead of a log normal distribution.
The test item reaction model can be described by the numerical expressions (1) and (2). In addition, in the actual analysis, it is necessary toThe priority index theta is calculated assuming that the inspection data of each inspection item is applied to the inspection item reaction modeliItem identification force parameter ajAnd a project difficulty level parameter bj. For the estimation of the parameter, Markov Chain Monte Carlo (MCMC), which is a well-known method, is used. The markov chain monte carlo method is a method for numerically simulating the posterior distribution of parameters to examine the distribution of the estimated quantity. The model relating to the project reaction theory is generally a maximum likelihood estimation method or the like, but the examination project reaction model includes a parameter (priority index θ) conforming to the gamma distributioniAnd a project difficulty level parameter bj) Therefore, instead of using the maximum likelihood estimation method, MCMC is used.
Here, analysis data for applying the test item reaction model will be described. As described above, in the examination item reaction model, the examination result data is estimated after being converted into 2 values of 0 (no measure required) or 1 (measure required). Therefore, the inspection result data is first converted into 2 values.
Fig. 4 shows an example of the inspection result data acquired by the data acquiring unit 11. Fig. 4 shows an example of an inspection result in a case where the lining (body) of the underground tunnel is made of concrete. In the inspection result data, the kilometer number (キロ th) corresponding to the position information in the underground tunnel and the inspection results of the plurality of inspection items (in fig. 4, lower left crack, left … …) at the kilometer number are associated with each other. In the inspection result data shown in fig. 4, when some state change (state other than the normal state) relating to the crack is observed as a result of the visual inspection, any one of "AA, a1, a2, and B, C, S" is assigned (in fig. 4, AA is not included) depending on the observed state.
In the inspection result data of fig. 4, AA, a1, a2 represent abnormal conditions or the like that threaten or possibly threaten the safety of the driver, passengers, the public, and the like, and the guarantee of the normal operation of the train, and AA, a1, a2 are assigned according to the severity thereof. B indicates that a state transition to AA, A1, or A2 is possible in the future. C indicates the presence of a slight abnormality, etc. Further, S indicates soundness (the result of measures (repair, etc.), and is determined to be soundness). Moreover, the blank column indicates that no state change was observed.
Next, as shown in fig. 5, in each inspection result, the result of "presence of abnormality (required measure)" is converted into "1", and the result of "absence of abnormality (not required measure)" is converted into "0". In the inspection result data in the present embodiment, the columns described as AA, a1, a2, and B are converted to "1", and the columns described as S or C and the empty column are converted to "0". Thereafter, the test pieces are divided into predetermined sections (every 5m in the present embodiment), and the numbers described in the respective columns are added for each test item. The result is shown in FIG. 6 (A). However, in the example shown in fig. 6(a), the columns having different observation positions at the lower left, upper left, and lower left are counted up to the left. Similarly, for each anomaly, the 3 positions divided into left, upper and right positions are summed up (the sum is calculated).
Next, in the table shown in fig. 6(a), the number of the column in which the number of 1 or more is described is converted to "1" again, and as a result, the table shown in fig. 6(B) is obtained. By performing the conversion as shown in fig. 6B, when 1 or more "presence of abnormality (measure required)" results are obtained in the predetermined inspection items in the predetermined section, the inspection result data in which "1" is described in the corresponding column can be obtained.
Similar processing is performed for other inspection items, and as a result, data as shown in fig. 7 is obtained. This data is used for analysis for applying an examination item reaction model.
In analysis using a test item reaction model, a priority index θ is obtainediItem identification force parameter ajAnd a project difficulty level parameter bjWhen a matrix is used. Specifically, the analysis data shown in fig. 7 can be described as a matrix X of I rows (the number of sections) × J columns (the number of inspection items). In addition, the priority index θ vector can be expressed as (θ)1、θ2、……、θI). Similarly, the item identification force vector a can be expressed as (a)1、a2、……、aJ) Difficulty and ease of projectThe vector b can be represented as (b)1、b2、……、bJ)。
In the inspection result of the inspection item j in the section i, the probability of observing a different shape is represented by Pij(θi) In the case of (1), the observation probability P of the abnormal state is determined as described aboveij(θi) The following equation (3) can be used to obtain the target. In this case, in the inspection result of the inspection item j in the section i, the probability that no anomaly is observed is represented as Qij(θi) In the case of (2), Qij(θi) The following equation (4) can be used to obtain the target.
[ equation 3]
Qij(θi)＝1-Pij(θi) (4)
In this case, the probability p of obtaining the matrix X corresponding to the analysis data corresponds to the product of the probabilities of obtaining the results of the respective examination items in the respective sections, and therefore, the probability p can be derived by the following equation (5).
[ equation 4]
In addition, p (X | θ) indicates a probability (distribution) of obtaining the result X when the priority index θ is a predetermined value. However, the priority index θ is actually unknown, and what is desired to be calculated as the maintenance management index is the priority index θ when the result X becomes a predetermined value, which corresponds to the probability (distribution) p (θ | X). That is, it is necessary to calculate a posterior probability distribution p (θ | X) (posterior distribution).
When bayesian theorem is used, the two satisfy the following relation of equation (6). Since p (x) included in the numerical formula (6) is a constant, the numerical formula (6) can be described as the numerical formula (7).
[ equation 5]
p(θ|X)∝p(X|θ)p(θ) (7)
In equation (7), it is shown that the posterior distribution p (θ | X) is a product of the probability (distribution) p (X | θ) as likelihood and p (θ) as prior distribution (prior probability distribution). Therefore, by assuming a distribution that θ should satisfy as an a priori distribution, that is, a gamma distribution, calculation of the posterior distribution p (θ | X) becomes possible.
The parameters estimated by the test item reaction model according to the present embodiment include not only θ but also 2 item identification force vectors a ═ a (a)1、a2、……、aJ) And the item difficulty vector b ═ b (b)1、b2、……、bJ) Therefore, the posterior probability distribution is described by the following expressions (8) to (10).
[ equation 6]
p(θ|a，b，X)∝p(X|θ，a，b)p(θ) (8)
p(a|θ，b，X)∝p(X|θ，a，b)p(a) (9)
p(b|θ，a，X)∝p(X|θ，a，b)p(b) (10)
At this time, a gamma distribution is assumed among the prior distributions p (θ) and p (b). In addition, a log-normal distribution is assumed in p (a).
The equations (8) to (10) can be calculated for each parameter by applying MCMC, which is a known method. For calculating each parameter, a known algorithm such as Gibbs Sampling (Gibbs Sampling) and Metropolis-Hastings (MH) algorithm, which are typical methods of MCMC, is used in combination. The MCMC algorithm used in calculating the parameters may be appropriately selected as needed. The estimation of the MCMC involved in the calculation of the parameters may be performed by using known statistical analysis software that can execute the MCMC in the maintenance management index calculation device 1.
With the above method, the priority index θ is calculated (θ) corresponding to each section1、θ2、……、θI). In addition, the itemThe object identification force parameter a is calculated corresponding to each inspection item (a)1、a2、……、aJ). In addition, the item difficulty level parameter b is also calculated for each inspection item (b)1、b2、……、bJ)。
Fig. 8 to 13 show an example of the results of the above calculation. Fig. 8 to 13 show results of analyzing inspection results of a plurality of items related to one underground tunnel in a certain year by the above-described method, that is, results of calculating a maintenance management index. The result of the examination to be analyzed is when the number of sections (I) is about 3000 and the number of examination items (J) in each section is 15. In addition, the number of examination items includes a case where examination positions (left/top/right) are different even for the same examination content, and the number of examination items is counted as another item. Fig. 8 shows a part of the result of estimating and calculating the priority index θ in a predetermined section (kilometers per 5m) obtained as a result of the analysis by the above-described method. Fig. 9 is a diagram showing a result of estimating and calculating the priority index θ in all the sections as a histogram. Fig. 10 is a graph in which priority index θ is plotted in association with the number of kilometers, where the horizontal axis represents the number of kilometers (unit: m) and the vertical axis represents priority index θ. Table 1 below shows statistics on the priority index θ.
[ Table 1]
| Minimum value | Center value | Mean value of | Maximum value | Standard of meritDeviation of |
| 1.13 | 1.28 | 1.98 | 9.23 | 1.29 |
Fig. 11 is a table showing the results of calculating the item identification force parameter a and the item difficulty level parameter b for each test item. The estimated value and the standard deviation are calculated for the item identification force parameter a and the item difficulty parameter b, respectively. Fig. 12 and 13 are diagrams each showing an examination item reaction function for each examination position. Fig. 12(a) shows the reaction function of the inspection items concerning cracking, water leakage, floating/peeling, and deterioration of the steel material on the left side surface. Fig. 12(B) shows the reaction function of the inspection items relating to the cracks, water leakage, floating/peeling, and steel material deterioration on the right side surface, and fig. 13(a) shows the reaction function of the inspection items relating to the cracks, water leakage, floating/peeling, and steel material deterioration on the upper surface. In addition, fig. 13(B) shows an inspection item reaction function related to CJ (cold joint), initial deterioration, and other abnormal shapes. Comparing fig. 12(a) and fig. 13(B), it can be confirmed that the general tendency is small, for example, the degree of difficulty of deterioration of the steel material is small (a different shape is easily observed from the stage where the priority index θ is small) compared with other inspection items, but it is confirmed that the inspection item reaction function differs for each measurement position even in the same inspection. Therefore, it is conceivable that the evaluation is performed by using the maintenance management index shown in the present embodiment instead of directly evaluating the soundness of the civil engineering structure based on the inspection result, and the comparison between the inspection results can be performed with higher accuracy.
(2) Phase check reaction model
In the inspection item reaction model, the priority index θ indicates the possibility of including a place requiring measures in a predetermined section, and since the degree of observed abnormality or the like is not taken into consideration, the inspection result data of each section is evaluated after being converted into 2 values of 0 (unnecessary measures) or 1 (necessary measures). However, a location where many irregularities are observed and the degree of irregularity is determined to be a serious location, and the maintenance management priority is considered to be higher than a location where irregularities are observed sporadically. Therefore, the "phase check reaction model" is a model in which the following is considered: the inspection result data for each section is 3-valued, that is, is assigned to any one of stages (categories) of 1, 2, and 3 as an assignment including a weight relating to an anomaly. Therefore, the inspection result data is also converted into 3 values of any one of 1, 2, and 3, and then evaluated.
In the inspection reaction model at this stage, the priority index θ is also defined in the same manner as the inspection item reaction model, but the observation probability of the abnormal state is defined as Pjc(θ), this is different. In this case, j is a value indicating an examination item, and c is a category number (any one of 1, 2, and 3 as a realized value). In the case of such setting, the observation probability P of the abnormal state can be defined as follows, for examplejc(θ)。
P11(θ): probability of crack (left) being evaluated as 1
P12(θ): probability of crack (left) being evaluated as 2
P13(θ): probability of crack (left) being evaluated as 3
P21(θ): probability of cracking (upper) being evaluated as 1
Here, based on the project reaction theory, the priority index in the section i is θ, as in the inspection project reaction modeliIn the case of (2), the probability P that the result of the inspection item is determined to be not less than the category c* jc(θi) The following logic function (11) is satisfied. The reaction function to each category (correspondence relationship between categories) can be obtained by using the following expression (12). In addition, the priority index θ is similar to the examination item reaction modeliThe calculation is performed for each interval. In addition, the item identification force parameter ajCalculated for each examination item, but item difficultyParameter bjcCalculated per examination item and per category.
[ equation 7]
In addition, the priority index θ and the item identification force parameter ajAnd a project difficulty level parameter bj(bjc) The following probability distribution is assumed to be satisfied as in the examination item reaction model. In addition, the item identification force parameter ajInstead of a lognormal distribution, it may also be assumed to follow a truncated normal distribution.
[ equation 8]
In the case of 3-value data, the observation probability P of an abnormal shape is expressed using models represented by expressions (11) to (13)jc(θ) corresponds to how the priority index θ varies. The models represented by the numerical expressions (11) to (13) are referred to as "step Inspection reaction Model (GIRM)" which is one of the models using the project reaction theory. Furthermore, the items in equation (11) are identified as force parameter ajAnd a project difficulty level parameter bj(bjc) The determined Function is defined as "Inspection Category Response Function (Inspection Category Response Function; ICRF) ".
An example of the inspection category reaction function in the case of 3-value data is shown in fig. 14. Here, the abnormal state is an example in which the abnormal state is worsened as the category c becomes larger. In the 3-value test class response function, a curve with c equal to 1, a curve with c equal to 3, and a curve with c equal to 2 are generated. In the stage inspection reaction model, by estimating each parameter using the MCMC, a curve of a function such as that shown in fig. 14 can be drawn for each inspection item.
Specifically, data for analysis of an application phase inspection reaction model is described. As described above, in the stage inspection reaction model, the inspection result data is converted into values corresponding to 3 categories (1, 2, 3: inspection result data with a higher priority with the measure of 3) according to the degree of the inspection result data, and then the inspection result data is estimated. Therefore, the inspection result data is first converted into the above-mentioned 3 values. In this embodiment, a processing example using the same data as shown in fig. 4 as the test item reaction model will be described.
First, as shown in fig. 15, each inspection result is converted into any one of 1 to 3. Specifically, "AA, a1, a 2" is converted to "3". "B, S" is converted to "2". Further, "C" is converted to "1". The blank column is changed to "0" (fig. 15 shows a state where the change to "0" is not performed).
Thereafter, the test pieces are divided into predetermined sections (every 5m in the present embodiment), and the numbers shown in the columns are added for each test item. The result is shown in FIG. 16 (A). However, in the example shown in fig. 16(a), the observation positions of different shapes are set to the left from the lower left, the upper left, and the total to the upper left. Similarly, the total of the 3 positions divided into left, upper and right is added for each abnormal shape.
Next, in the table shown in fig. 16(a), 0 point is converted to "1", 1 to 3 points are converted to "2", and 4 or more points are converted to "3". The result of the conversion again is a table shown in fig. 16 (B). By performing conversion as shown in fig. 16(B), a "3" is input for the inspection items and sections for which many different shapes are confirmed, and inspection result data for which a "1" is input for the inspection items and sections for which no different shape is confirmed is obtained.
Similar processing is performed for other inspection items, and as a result, data as shown in fig. 17 is obtained. This data becomes analysis data for the application phase inspection reaction model.
The analysis data generated by the above method is calculated for each parameter by applying MCMC in the same manner as in the case of inspecting the project reaction model. For calculating each parameter, a known algorithm such as Gibbs Sampling (Gibbs Sampling) and Metropolis-Hastings: MH (Meropolis-Hastings) algorithm, which are typical methods for MCMC, is used in combination.
With the above method, the priority index θ is calculated (θ) corresponding to each section1、θ2、……、θI). Further, the item identification force parameter a is calculated in association with each inspection item (a)1、a2、……、aJ). The item difficulty level parameter b is also calculated in correspondence with the boundary of the category in each inspection item (b)11、b12、b21、b22、……、bJ1、bJ2)。
Fig. 18 to 22 show an example of the results of the above calculation. Fig. 18 to 22 are results of analyzing, by the above-described method, inspection result data similar to the calculation of the maintenance management index using the inspection item reaction model, that is, inspection results of a plurality of items related to one underground tunnel in a certain year. The result of the examination to be analyzed is about 3000 intervals (I), and the number of examination items in each interval (J) is 15. In addition, the number of examination items includes a case where examination positions (left/top/right) are different even for the same examination content, and the number of examination items is counted as another item. Fig. 18 shows a part of the results of estimating and calculating the priority index θ in a predetermined section (kilometers per 5m) obtained as a result of the analysis by the above-described method. Fig. 19 is a diagram showing a result of estimating and calculating the priority index θ in all the sections as a histogram. Fig. 20 is a graph in which priority index θ is plotted in association with the number of kilometers, where the horizontal axis represents the number of kilometers (unit: m) and the vertical axis represents priority index θ. Table 2 below shows statistics on the priority index θ.
[ Table 2]
| Minimum value | Center value | Mean value of | Maximum value | Standard deviation of |
| 0.88 | 1.39 | 1.97 | 8.88 | 1.38 |
Fig. 21 and 22 are diagrams each depicting an examination type reaction function for each examination item. Fig. 21(a) shows an inspection type reaction function relating to a crack on the left side surface. Fig. 21(B) shows an inspection type reaction function relating to water leakage from the left side surface, fig. 22(a) shows an inspection type reaction function relating to floating/peeling of the left side surface, and fig. 22(B) shows an inspection type reaction function relating to deterioration of the steel material from the left side surface. Thus, the examination type response function differs for each examination item. Although not shown, the test type response function may be different for each measurement position even in the same test. Therefore, it is conceivable that the health of the civil engineering structure is not directly evaluated from the inspection results of the inspection items, but the evaluation is performed by using the maintenance management index shown in the present embodiment, so that the comparison between the inspection results can be performed with higher accuracy.
In the present embodiment, the case where the stage examination reaction model is assigned to any one of stages 1, 2, and 3 (class: c) as the assignment including the weight relating to the anomaly has been described, but the number of stages (classes) is not particularly limited. However, since the parameter increases by increasing the stage as described above, the processing load for the numerical calculation using the MCMC increases by increasing the stage. Therefore, when the reaction model is examined in the application stage, it is preferable to set the reaction model to 4 stages or less.
As described above, according to the maintenance management index calculation device 1 and the maintenance management index calculation method of the present embodiment, it is assumed that the priority index θ indicating the priority of the maintenance management for each predetermined section of the civil structure follows the gamma distribution, and a model based on the project reaction theory is applied to the inspection result data. Accordingly, since the information indicating the "inspection state" and the information derived from the "soundness of civil structure" included in the inspection result data can be separated, the information derived from the "soundness of civil structure" including the priority index indicating the priority of maintenance management can be used to calculate the maintenance management index relating to the maintenance management of the civil structure. Therefore, according to the maintenance management index calculation device 1 and the maintenance management index calculation method according to the present embodiment, it is possible to calculate a maintenance management index that can be used as an index for maintenance management of a civil engineering structure. The maintenance management index is calculated for each predetermined section of the civil engineering structure. Therefore, as compared with a case where a maintenance management plan is created based on the cause, prediction, and the like of the observed abnormality, the maintenance management plan for each section can be created in consideration of soundness as the civil engineering structure.
The maintenance management index including the priority index shown in the above embodiment can be used in common even for civil engineering structures of the same kind including the same inspection item, and therefore evaluation of the inspection result can be performed with higher accuracy using the maintenance management index. That is, the maintenance management index calculated by the maintenance management index calculation device 1 and the maintenance management index calculation method according to the present embodiment is suitable for use in comparing the inspection results of civil engineering structures of the same type (other underground tunnels in urban railways). In particular, the priority index θ among the maintenance management indexes is an index for extracting only an element depending on "soundness of civil structure" from the inspection result of the inspection item which is determined to be likely to change depending on the inspection state, and therefore is an index for realizing a pure calculation of the maintenance management priority for each section of the civil structure. Therefore, the method can be applied to evaluation of the inspection result. Further, since the priority index θ is a value in which "situation dependency" depending on the examination situation is eliminated, it is also possible to perform annual comparison and route comparison of the estimated priority indexes θ with each other.
Further, in the case where the inspection item reaction model is applied as a model based on the item reaction theory, the maintenance management index is calculated on the basis of the presence or absence of any abnormality in the inspection result, and therefore, the maintenance management index more suitably indicating the priority of maintenance management relating to the civil engineering structure can be calculated by a simpler calculation.
Further, in the case where the stage inspection reaction model is applied as a model based on the project reaction theory, the maintenance management index is calculated assuming that the inspection result belongs to any one of stages of 3 or more assigned according to the level of the anomaly, and therefore, for example, the calculation of the maintenance management index after the weight based on the number of observations of the anomaly, the degree thereof, and the like is reflected can be performed.
When the application stage inspection reaction model is used, the stage to which the inspection result belongs is set to 4 or less, whereby the maintenance management index that more preferably indicates the priority of maintenance management for the civil engineering structure can be calculated without excessively increasing the load for calculation of the maintenance management index.
The maintenance management index calculation device and the maintenance management index calculation method according to the embodiment of the present invention have been described above, but the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the scope of the invention.
For example, the inspection items to be calculated as the maintenance management index of the maintenance management index calculation device 1 are not limited to the items described in the above embodiment. In the above embodiment, the case where the maintenance management index relating to the inspection result of the underground tunnel is calculated has been described, but when the object of calculation of the maintenance management index is another civil structure, the maintenance management index calculation device 1 and the maintenance management index calculation method can be applied to the inspection item corresponding to the civil structure.
The method of generating the analysis data can be appropriately changed according to the specification, data format, and the like of the inspection result of the inspection item. For example, in the generation of the analysis data, a part of the summation processing is performed in consideration of the observation sites of different shapes, but how the analysis data is generated can be appropriately changed. Further, the classification method and the like of the categories in the case of using the stage inspection reaction model can be appropriately changed.
In the above-described embodiment, the description has been given of the case where the priority index θ, the item recognition ability parameter a, and the item difficulty level parameter b are included in the maintenance management index calculated by the maintenance management index calculation device 1, but there is a case where a parameter different from the item recognition ability parameter a and the item difficulty level parameter b is used as a parameter used when the model based on the item reaction theory is applied. In this manner, the parameters used in the model to which the model based on the project reaction theory is applied are not limited to the parameters described in the above embodiment.
In the above-described embodiment, the case where the maintenance management index calculation device 1 is implemented by 1 device has been described, but the maintenance management index calculation device 1 may be configured by a plurality of devices.
Description of the reference symbols
1 … maintenance management index calculation device, 11 … data acquisition unit, 12 … maintenance management index calculation unit, 13 … algorithm storage unit, and 14 … result output unit.
Claims (2)
1. A maintenance management index calculation device is provided with:
a data acquisition unit that acquires inspection result data including an inspection result obtained by evaluating the presence or absence of abnormality of the civil structure for a plurality of inspection items at each position of the civil structure;
a maintenance management index calculation unit that calculates a maintenance management index relating to maintenance management of the civil structure including a priority index, assuming that the priority index indicating a priority of maintenance management for each predetermined section of the civil structure follows a gamma distribution, by applying a model based on an item reaction theory to the inspection result data; and
an output unit that outputs the maintenance management index calculated by the maintenance management index calculation unit,
the model based on the project reaction theory is a stage inspection reaction model that calculates the maintenance management index so that the inspection result belongs to any one of stages of 3 or more and 4 or less assigned according to the level of abnormality.
2. A maintenance management index calculation method comprises the following steps:
a data acquisition step of acquiring inspection result data composed of inspection results obtained by evaluating the presence or absence of abnormality of the civil structure for a plurality of inspection items at each position of the civil structure;
a maintenance management index calculation step of calculating a maintenance management index relating to maintenance management of the civil structure including a priority index, assuming that the priority index indicating a priority of maintenance management for each predetermined section of the civil structure follows a gamma distribution, by applying a model based on a project reaction theory to the inspection result data; and
an output step of outputting the maintenance management index calculated in the maintenance management index calculation step,
the model based on the project reaction theory is a stage inspection reaction model that calculates the maintenance management index so that the inspection result belongs to any one of stages of 3 or more and 4 or less assigned according to the level of abnormality.
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