JP4885008B2 - Maintenance planning method - Google Patents

Description

  The present invention relates to a maintenance planning method for various plants and products such as nuclear plants, petroleum plants, and chemical plants that require maintenance over a long period of time. Especially, whether or not an accident occurs or whether inspection is necessary, etc. The present invention relates to a maintenance planning method in which the probability in the vicinity of an important state in the maintenance plan can be obtained in more detail than before and can be obtained without performing a large amount of computation.

  Various plants such as nuclear power plants, petroleum plants, chemical plants, and some large-scale products such as aircraft that have a long depreciation period have a large influence on the surroundings at the time of failure, and thus appropriate maintenance is essential. For this reason, it is common to perform periodic maintenance and inspections during the depreciation period, and to perform inspections, repairs, replacements, etc. while considering the life and fatigue level of the parts and units that make up the plant and product. Has been done. However, since such conventional periodic maintenance inspections were performed by simply deciding that they would be performed every fixed year, such as one year, three years, or five years, parts that must be replaced soon. Even if there are units or units, the replacement was carried over until the next periodic inspection, and during that time a failure occurred, causing a large amount of money to be repaired or restored, and lost credit. Conversely, even if there are parts or units that have reached the end of their life and have been replaced, inspections may be performed, or parts or units that do not need to be replaced may be replaced, resulting in unnecessary costs. .

  For this reason, conventionally, it has been studied how it is effective to perform maintenance during a long depreciation period, which is disclosed in Patent Documents 1 and 2, for example. Patent Document 1 relates to a maintenance plan in which a maintenance plan over the entire depreciation period of a plant or product can be planned quantitatively from the viewpoint of cost, and the depreciation period of the plant or product is divided into short-term maintenance periods. For each short-term maintenance period, calculate the state of the units and parts that make up the plant and product based on the damage probability at the end of the period, and perform inspection and repair at the start of the short-term maintenance period based on the calculation result A maintenance plan that selects the units and parts to be performed and calculates the inspection costs and repair costs by the calculation means, and repeats them until the depreciation year, thereby selecting the maintenance units and parts and calculating the maintenance costs. Is.

  Patent Document 2 relates to a maintenance plan that predicts the risk cost due to damage, performance degradation, and function stop of equipment constituting the plant, and selects and supports the optimal operation method while comparing with the gain from operation. An event simulation means for calculating an unreliability corresponding to an operation parameter according to an event tree of a plant device based on a failure statistics database stored in advance by associating an event tree of the device and an unreliability with respect to a failure event, and an event tree Therefore, the risk cost calculation means for calculating the risk cost by accumulating the product of the unreliability and the recovery cost, and the operation method determination means for determining the suitability of the operation condition from the comparison between the risk cost and the gain planned to continue operation And the operation method is a plant according to the operation method determined by the fixed means. It relates maintenance plan which includes the operation method instruction means for instructing a specified operating conditions vessel.

JP 2003-99119 A JP 200494663 A

  However, although both the technique disclosed in Patent Document 1 and the technique disclosed in Patent Document 2 can perform a maintenance plan for a plant or equipment, for example, does it lead to an accident or is inspection necessary? Even if you want to find out only the probabilities of states that are important in the maintenance plan, such as whether or not, in detail, random numbers must be generated uniformly. Because it requires a lot of random numbers and therefore requires a large amount of random numbers, resulting in a heavy load on the calculation process, it takes a long time to calculate and requires the use of a high-performance calculation means, so that a maintenance plan is made. The cost of In particular, when Monte Carlo simulation is used for the calculation, since the error is inversely proportional to the square root of the number of samples, the convergence time is extremely slow. The problem cannot be ignored.

  Therefore, in view of the problems of the prior art, the present invention can determine the probability of the vicinity of an important state in the maintenance plan, such as whether inspection is necessary, in more detail than before, and without performing a large amount of calculations. The purpose is to provide a maintenance planning method.

In order to solve the above problems, in the present invention,
Calculate the damage status of the parts and units that make up the plant and product based on the data of the probability of damage status related to the parts and units that make up the plant and product, and perform inspection and repair based on the calculation results A maintenance planning method for selecting parts and units, which is a weighted probability density that gives weight to damaged conditions that require inspection and repair based on demonstration data on the damaged conditions of parts and units that make up a plant or product A first step of obtaining a function w, and generating a uniform random number u _n or a super uniform random number u * _n (hereinafter referred to as a uniform random number or the like) of 0 or more and 1 or less, The cumulative probability of the cumulative distribution function of the weighted probability density function w, the second step of obtaining a random variable z _n corresponding to the uniform random number, etc., and the parts and units constituting the plant and product Data relating to the probability of damage state relating to the damage state is stored in the storage means, and from the data relating to the probability of damage state, the weight probability of damage state of the parts and units constituting the plant and product is determined by Monte Carlo simulation using z _n as a random number A component that constitutes a plant or a product from the third step to calculate and a weighted restoration value W based on the weighted probability density function w, and from the restoration value W and the weighted probability of the damage state obtained in the third step And a fifth step of calculating the probability of the damage state of the unit, and the damage state of the part or unit constituting the plant or product based on the probability of the damage state of the component or unit calculated in the fifth step. It is characterized by selecting parts and units to be inspected and repaired based on the calculation results.

In this first step, a weighted probability density function w that gives weight to a damaged state that requires inspection / repair is obtained based on the verification data on the damaged state of parts and units constituting the plant or product. To generate a uniform random number of 0 or more and 1 or less, and the uniform random number or the like as the cumulative probability of the cumulative distribution function of the weighted probability density function w, and a random variable z _n corresponding to the uniform random number or the like As a result, the random variable z _n has a distribution weighted to a damaged state that requires inspection and repair. In the third step, the weighting probability of the damage state of the parts and units constituting the plant and product can be calculated from the data relating to the probability of the damage state by using Monte Carlo simulation with z _n as a random number. By calculating the damage state probability of the parts and units constituting the plant and product from the restoration value W in the fourth step and the weighted probability of the damage state obtained in the third step, the first and second It is possible to restore the weights given to z _n obtained in the above step to the correct probability. In this way, after performing weighting using the weighted probability density function w, the calculation is performed by Monte Carlo simulation, and finally the weight is restored without generating a large amount of uniform random numbers or the like, that is, without performing a large amount of calculation. The damage probability in the vicinity of the important part in the maintenance plan can be obtained in detail.

  As described above, the maintenance planning method of the present invention has the advantage that the probability of the vicinity of an important state in the maintenance plan, such as whether inspection is necessary, can be obtained in more detail than before, and without performing a large amount of computation. There is.

  Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the drawings. However, the dimensions, materials, shapes, relative arrangements, and the like of the components described in this embodiment are not intended to limit the scope of the present invention unless otherwise specified, but are merely illustrative examples. Not too much.

FIG. 1 is a block diagram illustrating a maintenance planning method according to the first embodiment. 1 is a weighted probability density function determining means for determining a weighted probability density function w that gives a weight to a desired damage state based on demonstration data on the damage state of parts and units constituting the plant or product. Based on a weighted probability density function w, a weighted random variable generator that generates a weighted random variable z _n that is a random number weighted to the desired damage state, 3 is the weighted random variable z _n as a random number, Weighting for calculating the weighting probability of the damage state of the parts or units constituting the plant or product weighted to the desired damage state by the Monte Carlo simulation from the data regarding the damage state probability of the plant or product previously stored in the database 6 4 is based on the weighted probability density function w. Damage probability calculation means for calculating a restoration value W for restoring weighting, and calculating a damage state probability of a part or unit constituting a plant or product from the restoration value W and the weighting probability of the damage state; It is a maintenance planning means that calculates and calculates the damage status of parts and units that make up the plant and product from the probability of damage status of the components and units, and selects the parts and units to be inspected and repaired based on the calculation results .
Hereinafter, it will be described in detail along the flow of the block diagram shown in FIG.

  First, the weighted probability density function determining means 1 determines the weighted probability density function w. FIG. 2 is a flowchart showing a flow for obtaining the weighted probability density function w. In FIG. 2, first, a temporary weighted probability density function w ′ is appropriately set in step S11. In the next step S12, a probability density function I is obtained from the provisional weighted probability density function w ′ set in step S11 by using Monte Carlo simulation.

In the next step S13, the probability variable at the peak of the probability density function I is compared with a probability variable important in the maintenance plan to determine whether or not they match. Here, the coincidence may be a complete coincidence, but an appropriate range may be provided and the coincidence may be determined within the range.
If YES is determined in the step S13, the process proceeds to a step S14. In the step S14, the provisional weighting probability density function w ′ at the determination time is determined as the weighting density function w. If NO is determined in step S13, the process proceeds to step S15 described later.
Here, a random variable important in the maintenance plan is a random variable corresponding to a damage state of a part or unit constituting a plant or product that needs to be examined in detail. Depending on the product, part or unit and the purpose of use, for example, if the part is cracked, the crack depth that requires inspection, the crack depth that requires repair, the crack depth that leads to the occurrence of an accident, etc. Determined based on empirical data. Damage conditions that need to be examined in particular in this way are determined based on demonstration data, so a lot of demonstration data is collected, for example, crack depth that requires inspection, crack depth that requires repair, etc. Is preferably used.

Next, in step S15, it is determined whether or not the peak random variable of the probability density function I is larger than the random variable important in the maintenance plan. If YES is determined in step S15, the probability variable of the probability density function I has a large probability variable. Therefore, in step S16, the temporary weighting variable w ′ is changed so that the probability variable of the peak of the probability density function I decreases. Return to S12. On the other hand, if NO is determined in step S15, the peak probability variable of the probability density function I is small. Therefore, in step S17, the temporary weighted probability variable w ′ is changed so that the peak probability variable of the probability density function I decreases. The process returns to step S12 again.
Thus, the weighting density function w is determined by repeating Steps S11 to S17.

Then weighting random variable generator 2 generates a weighted random variable z _n. FIG. 3A is a graph showing an example of the weighted random variable w, where the vertical axis represents the probability and the horizontal axis represents the random variable. FIG. 3B is a graph showing the cumulative distribution function of the weighted probability variable w shown in FIG. 3A. The vertical axis represents the cumulative probability, and the horizontal axis represents the random variable.

In the weighted random variable generator 2, first, the weighted probability density function w determined by the weighted probability density function determining means 1 as shown in FIG. 3A is accumulated as shown in FIG. 3B. Convert to distribution function. Then generates a 0 or more and 1 or less of n uniform random number u _n or ultra uniform random number u * n _(hereinafter represented by uniform random numbers or the like as called u _n), shown respectively in FIG. 3 (B) To the cumulative probability of the cumulative distribution function. FIG. 3B shows only u _i which is one of _n uni. Thus the random variable z _n corresponding to the u _n which fit the cumulative probability obtained from the cumulative distribution function. FIG. 3B shows only a random variable z _i corresponding to u _i .
Z _n obtained in this way is defined as a weighted random variable.

Next, the weighting probability calculating means 3 calculates and calculates the weighting probability. The weighted random variable z _n generated by the weighted random variable generating device 2 is used as a substitute for a random number, and the probability variable x _n (w _{n) is determined} from the probability of damage states related to parts and units constituting the plant and product stored in the database 6. ) And calculating and calculating the weighting probability of the damage state of the parts and units constituting the plant or product by Monte Carlo simulation.

Here, the random variable x _n (w _n ) is generated as follows. FIG. 4A is a graph showing an example of a probability density function of damage states related to parts and units constituting a plant or a product, where the vertical axis represents probability and the horizontal axis represents random variables. FIG. 4B is a graph showing the cumulative distribution function of the probability density function shown in FIG. 4A, where the vertical axis represents the cumulative probability and the horizontal axis represents the random variable. Each of the weighted random variables z _n is applied to the cumulative probability of the cumulative distribution function shown in FIG. FIG. 4B shows only z _i which is one of _n z _n . In this way, the random variable x _n (w _n ) can be generated by determining the random variable corresponding to z _n fitted to the cumulative probability from the cumulative distribution function.

In addition, here, the probability of the damage state regarding the parts and units constituting the plant or product stored in the database 6 is, for example, the probability of occurrence of damage, the probability of occurrence of the damage that has occurred, the probability of detecting the damage that has occurred, etc. Of which one or more probabilities are used.
Further, the weighting probability of the damage state of the parts or units constituting the plant or product calculated by the weighting probability calculating means 3 is the weighting probability that requires inspection, the weighting probability that requires repair, or an accident. The weighting probability is given.

However, the weighted probability of the damage state of the parts and units constituting the plant and product obtained by the weighted probability calculation means 3 by the Monte Carlo simulation using the weighted random variable z _n which is a biased variable in this way as a substitute for the random number. Does not represent the probability of damage of the parts and units constituting the plant or product. Therefore, the damage state probability calculation device 4 calculates the probability of damage states of the parts and units constituting the plant and product by restoring the weights from the weighted damage state probabilities of the parts and units constituting the plant and product. calculate.

  The damage state probability calculating device 4 restores the weights as follows and calculates and calculates the damage state probability of the parts and units constituting the plant and product. Here, as an example of the probability of damage states of parts and units constituting a plant or product, an example of calculating the probability of occurrence of an accident by calculating the depth of cracks occurring in the parts is given.

また、ｎ個の重み付け確率変数ｚ_ｎを数２で表すことができる。

この時、全体（ｘ_１、ｘ_２、・・・ｘ_ｎ）の重みを復元するための復元値をＷとすると、Ｗは数３で表すことができる。

First, n random variables to be used in the Monte Carlo simulation can be expressed by Equation 1.

Further, n weighting probability variables z _n can be expressed by Equation 2.

At this time, if the restoration value for restoring the weight of the whole (x ₁ , x ₂ ,... X _n ) is W, W can be expressed by Equation 3.

亀裂深さＬ_０以上で事故が発生する、つまり亀裂深さＬ_０が事故発生に至る境界深さである場合、事故が発生するシミュレーション結果数Ω^Ｘと、事故が発生しないシミュレーション結果数Ω^０はそれぞれ数５及び数６を用いて求めることができる。

従って、事故発生確率Ｐ^Ｘは前記Ω^Ｘ及びΩ^０を復元値Ｗで復元して数７を用いて求めることができる。

Moreover, the crack depth L of the simulation result can be expressed by Equation 4,

When an accident occurs at a crack depth L ₀ or more, that is, when the crack depth L ₀ is a boundary depth leading to the occurrence of the accident, the number of simulation results Ω ^X where the accident occurs and the number of simulation results Ω ⁰ where no accident occurs Can be obtained using Equation 5 and Equation 6, respectively.

Therefore, the accident occurrence probability P ^X can be obtained by using Equation 7 after restoring the Ω ^X and Ω ⁰ with the restoration value W.

  Next, the maintenance plan means 5 calculates the damage state probability calculation means 4 and calculates the damage state of the parts and units constituting the plant and product from the damage state probability of the parts and units constituting the plant and product. And a part or unit to be inspected / repaired is selected based on the calculation result.

  The maintenance planning method of the first embodiment can be applied to any part or unit as long as it is a maintenance plan for parts and units constituting a plant or product. It is preferable to use for parts and units that are connected to each other and have a large recovery cost when damage is caused, and the repair criteria can be adjusted. The repair criteria can be adjusted, for example, when there are multiple inspection methods, and when repairs are made according to the crack length found in the inspection, it is possible to determine the criteria for the crack length that the repair is deemed necessary. .

  As such a preferable specific example, for example, crack inspection of a tail cylinder of an incinerator of a gas turbine can be given. In the inspection of cracks in the incinerator of a gas turbine, how long is the crack depending on the inspection method, and what is the error between the actual crack length and the crack length detected in the inspection? The basic data of the relationship is organized, and the criteria for the depth of cracks detected in inspections that require repair are determined. Therefore, it is effective to perform simulations on a plurality of inspection methods and repair methods, and to select effective inspection / repair measures by giving weights in the vicinity of an important state in terms of maintenance management whether or not serious damage will occur.

FIG. 5 is a block diagram showing the maintenance planning method according to the second embodiment. 11 is a classification means for classifying parts and units constituting a plant or product into parts and units having similar structures and grouping them, and 12 is a damaged state by extracting a part of the parts and units for each of the classified groups. Is an inspection means for inspecting the distribution L * of the gas, and reference numeral 13 denotes a plurality of damage states created based on the damage state distribution L * and verification data of parts and units constituting the plant and product stored in the storage means 14. Is a selection means for determining the degree of coincidence with the distribution L ′ _{n of} L * _n and selecting L ′ _n having the highest degree of coincidence with L *, and 15 is based on L ′ _n selected by the selection means 14. Computation means for computing the damage state of the parts and units that are in the same group as the parts and units extracted by the inspection means 12 and not extracted by the inspection means 12; A means for selecting the components and units to inspect and repair based on the wound state.
Hereinafter, a detailed description will be given along the flow of the block diagram shown in FIG.

  First, the classification means 11 classifies the parts and units constituting the plant and products into parts and units having similar structures.

Next, the inspection unit 12 extracts a part or part of each unit classified by the classification unit 11 and obtains a damage state distribution L * by inspection. The number of samples to be extracted is not particularly limited, but if it is too large, the cost of extraction and inspection will increase, and if it is too small, L' _n having the highest degree of coincidence with L *, which will be described later, cannot be selected accurately. Since the management accuracy is lowered, it is preferable to determine the number of sampling according to the required cost and the maintenance management accuracy.

Next, a plurality of damages created by the selection means 13 based on the verification data of the unit of the parts constituting the plant and the product are stored in the storage means 14 with the damage state distribution L * obtained by the inspection means 12. The degree of coincidence is determined by comparison with the state distribution L ′ _n . Kolmogorov-Smirnov test, which is a kind of hypothesis test, is used to determine the degree of coincidence.

Here, the damage state distribution L ′ _n created based on the verification data of the parts and units constituting the plant and product stored in the storage means 14 will be described. FIG. 6 is a conceptual diagram of L ′ _n stored in the storage means 4. As shown in FIG. 6, M types of data (1) to (M) are stored in the storage unit 14, and each has different damage occurrence time probability distributions and occurrence frequencies. And wherein (1) ~ (M) of the M types of data, each said damage occurring timing probability and frequency related parameter _{(m i, σ i) (} i integer from 1 to M) and the parameter _{(m i,} σ _i ) having a distribution function L ′ (m _i , σ _i ) corresponding to a damaged state, and L ′ (m _i , σ _i ) corresponds to L ′ _n .

Moreover, the damage occurrence probability distribution and occurrence frequency shown in FIG. 6 are determined on the basis of demonstration data. For example, in the case of a product part, the part design data, delivery quality data, production lot, use condition Etc.
Further, in FIG. 6, in order to obtain the parameters (m _i , σ _i ) and the damage state distribution L ′ (m _i , σ _i ), the damage occurrence time probability distribution and the occurrence frequency are used. Alternatively, for example, a probability distribution of damage progress may be added to obtain parameters and damage state distributions from three or more types of data.
Further, the distribution of the parameters and the damage state may be obtained based on the damage state probability of the parts and units constituting the plant or product obtained by the damage state probability calculation means 4 shown in FIG.

Next, the calculation means 15 is in the same group as the parts and units extracted by the inspection means 12 based on L ′ _n selected by the selection means 14 and is damaged by the inspection means 12 and has not been extracted. The state is calculated by calculation, and the maintenance plan means 16 selects a part or unit to be inspected / repaired based on the damage state of the part or unit calculated by the calculation means.

The maintenance planning method of the second embodiment can be used for any part or unit as long as it is a maintenance plan for parts and units constituting a plant or product. A hole is mentioned. Usually, there are dozens of cooling holes in the incinerator tail tube, and cracks may occur from each hole. When the maintenance planning method of the second embodiment is not applied, 100% inspection will be performed, but the ease of crack generation and growth varies depending on the state where the incinerator is placed, that is, the positional relationship between the incinerator and the cooling hole. There is a track record. Therefore, by preparing a plurality of L ′ _n corresponding to the results and inspecting some cracks in the cooling holes, it is possible to calculate and calculate cracks in other cooling holes. In addition, since it is also known what kind of positional relationship between the incinerator and the cooling holes, cracks are likely to grow, so by inspecting the cooling holes where cracks are likely to grow, the cracks in the remaining cooling holes Can model from the actual data what kind of dispersion corresponds to the inspection result. By performing simulation using the modeled model, the growth rate to the depth corresponding to the crack damage is compared according to the sampling rate, and the simulation is used for selecting the optimal rate, selecting the interest rate, and selecting the sampling site. It becomes possible.

  Probability in the vicinity of important states in maintenance plans, such as whether inspection is necessary, can be determined in more detail than before, and without requiring a large amount of computation, so it can be used for maintenance management plans for parts and units of plants and products. Can be used.

The maintenance plan method in Example 1 is shown with the block diagram. It is the flowchart which showed the flow which calculates | requires the weighted probability density function w. FIG. 3A is a graph showing an example of the weighted probability variable w, and FIG. 3B is a graph showing the cumulative distribution function of the weighted probability variable w shown in FIG. FIG. 4A is a graph showing an example of a probability density function of a damage state related to parts and units constituting a plant or a product, and FIG. 4B is an accumulation of probability density functions shown in FIG. It is a graph showing a distribution function. The maintenance plan method in Example 2 is shown with the block diagram. It is a conceptual diagram of L' _n accommodated in the memory | storage means.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Weighted probability density determination means 2 Weighted random variable generator 3 Weighted probability calculation means 4 Damage state probability calculation means 5 Maintenance plan means 11 Classification means 12 Inspection means 13 Selection means 14 Storage means 15 Calculation means 16 Maintenance plan means

Claims (1)

Calculate the damage status of the parts and units that make up the plant and product based on the data of the probability of damage status related to the parts and units that make up the plant and product, and perform inspection and repair based on the calculation results A maintenance planning method for selecting parts and units,
A first step of obtaining a weighted probability density function w weighted to a damaged state that requires inspection / repair based on demonstration data on a damaged state of a part or unit constituting a plant or product;
A uniform random number u _n or super uniform random number u * _n (hereinafter referred to as a uniform random number) of 0 or more and 1 or less is generated, and the uniform random number or the like is represented by a cumulative distribution function of the weighted probability density function w. A second step for determining a random variable z _n corresponding to the uniform random number, etc., as a cumulative probability;
Data relating to the probability of damage state relating to the parts and units constituting the plant and product is stored in a storage means, and the plant and product are constituted by Monte Carlo simulation using z _n as a random number from the data relating to the probability of damage state. A third step of calculating a weighted probability of the damage state of the part or unit;
The weighted restoration value W is obtained based on the weighted probability density function w, and the probability of the damage state of the parts and units constituting the plant or product is determined from the restoration value W and the weighting probability of the damage state obtained in the third step. A fifth step of calculating,
The damage state of the parts and units constituting the plant and product is calculated based on the damage state probability of the parts and units calculated in the fifth step, and inspection and repair are performed based on the calculation results. A maintenance planning method characterized by selecting parts and units.

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