JP7464481B2 - Method, program, and device for predicting metal loss - Google Patents

Description

The present invention relates to a method, program, and device for predicting the amount of thinning in the thickness of components of equipment installed in a facility.

It is known that the thickness (hereafter referred to as wall thickness) of the components of equipment in facilities such as waste-to-energy plants gradually thins over time due to abrasion and erosion caused by high-temperature, high-pressure water flow, wear caused by mechanical sliding, and chemical corrosion. For this reason, for the purpose of maintaining and managing the components of equipment in the plant, wall thickness is periodically detected to check whether it has become too thin. In addition, wall thickness is periodically measured and future wall thickness is linearly predicted from the thinning trend of past wall thickness data to identify areas that require repair or replacement.

However, there can be variation in the tendency for metal thinning to occur in components. For example, the tendency for metal thinning to occur in components can vary due to variations in the thickness of the components during manufacturing or measurement errors in measuring instruments. In addition, there can be variation in the tendency for metal thinning to occur due to differences in various environmental factors in the usage environment of each component, such as temperature and pressure, the flow rate of the fluid around the component, the chemical composition of the fluid, and the adhesion of abrasive and corrosive substances to the component. For this reason, with conventional methods of linearly predicting the tendency for metal thinning to occur, it was difficult to predict the tendency for metal thinning to occur in components while taking these uncertain factors into account.

In addition, based on past trends in thickness data, it is known empirically that the thickness of a component may change at a certain point, and may change suddenly midway. However, the conventional method of predicting thinning trends linearly was not able to predict thinning that takes into account the change at the point in time when the thinning trend exists.

The present invention has been made in view of the above points, and one aspect of the present disclosure is a method executed by a processor for constructing a wall-thinning model that expresses a time-dependent change in a physical quantity that represents a wall-thinning tendency of a component arranged in a facility in order to predict wall-thinning of the component, the method comprising:
Setting a prior distribution of hyperparameters used to adjust the probability distribution of parameters included in the wall-thinning model;
A step of setting a likelihood equation for calculating the likelihood of the measurement value based on the value of the hyperparameter and the measurement value of a physical quantity representing a wall-thinning tendency of the component;
A step of applying Bayes' theorem to the likelihood equation to calculate a posterior distribution of the hyperparameter from a prior distribution of the hyperparameter and a measured value of a physical quantity representing a wall-thinning tendency of the component;
and constructing the metal loss model from a posterior distribution of the calculated hyper-parameters.

The present invention has been made in view of the above points. Another aspect of the present disclosure is an apparatus for constructing a wall-thinning model for predicting wall-thinning of a component arranged in a facility, comprising:
a wall-reduction model setting unit that sets a prior distribution of a hyperparameter used to adjust a probability distribution of a parameter included in the wall-reduction model;
a hierarchical Bayesian model setting unit that sets a likelihood equation for calculating the likelihood of the measurement value based on the value of the hyperparameter and a measurement value of a physical quantity that represents a wall-thinning tendency of the component, applies Bayes' theorem to the likelihood equation, and calculates a posterior distribution of the hyperparameter from a prior distribution of the hyperparameter and the measurement value of the physical quantity that represents a wall-thinning tendency of the component;
and a metal-reduction model construction unit that constructs the metal-reduction model from the calculated posterior distribution of the hyper-parameters.

1 shows an overview of a process flow executed in a prediction device that predicts thinning of components of equipment in a facility according to an embodiment of the present disclosure. 2 shows an example of a hardware configuration of a prediction device that performs the process flow for predicting thinning of a component shown in FIG. 1 . FIG. 3 is a block diagram showing a functional configuration of the prediction device shown in FIG. 2 . 13 illustrates a processing flow of a method executed in a prediction device according to an embodiment of the present disclosure. 1 illustrates an example of a broken line model representing a metal loss trend according to an embodiment of the present disclosure. This is a conceptual diagram of the hierarchical Bayes model. 1 illustrates an example of a broken line model that statistically represents a tendency for thinning of a component according to an embodiment of the present disclosure. 13 illustrates an example of a linear curve model that statistically represents the tendency of thinning of a component according to another embodiment of the present disclosure. 13 illustrates a quadratic curve model that statistically represents the tendency of thinning of a component according to another embodiment of the present disclosure.

[Description of the embodiments of the present disclosure]
First, the contents of the embodiment of the present disclosure will be listed and described. One embodiment of the present disclosure has the following configuration.
(Item 1) A method executed by a processor for constructing a wall-thinning model that expresses a change over time in a physical quantity that represents a wall-thinning tendency of a component arranged in a facility in order to predict wall-thinning of the component, comprising:
Setting a prior distribution of hyperparameters used to adjust the probability distribution of parameters included in the wall-thinning model;
A step of setting a likelihood equation for calculating the likelihood of the measurement value based on the value of the hyperparameter and the measurement value of a physical quantity representing a wall-thinning tendency of the component;
A step of applying Bayes' theorem to the likelihood equation to calculate a posterior distribution of the hyperparameter from a prior distribution of the hyperparameter and a measured value of a physical quantity representing a wall-thinning tendency of the component;
and constructing the metal loss model from a posterior distribution of the calculated hyper-parameters.

(Item 2) The method according to item 1, wherein the parameters include at least one of the initial thickness of the member and a measurement error that occurs in the measurement result of the thickness.

(Item 3) The method according to item 2,
The method of claim 1, wherein the probability distribution of the initial wall thickness is a normal distribution, the probability distribution of the measurement error is a normal distribution, and the hyperparameters include a mean value of the initial wall thickness, a standard deviation of the initial wall thickness, a mean value of the measurement error, and a standard deviation of the measurement error.

(Item 4) A method according to any one of items 1 to 3, in which the metal loss model is composed of two or more phases, and the parameters include the elapsed time at which the phases switch.

(Item 5) The method according to item 4, wherein the probability distribution of the elapsed time is a Poisson distribution, and the hyperparameter includes an expected number of occurrences of an event occurring within a given interval.

(Item 6) The method according to Item 5, wherein in each of the phases, the thinning trend of the component is approximated by a straight line with respect to time, and the parameters include a first thinning rate that is the slope of the straight line in the first phase, and a second thinning rate that is the slope of the straight line in the second phase.

(Item 7) The method according to item 6, comprising:
the probability distribution of the first wall-loss rate and the probability distribution of the second wall-loss rate are gamma distributions, and the hyperparameters include a shape parameter of the first wall-loss rate, a scale parameter of the first wall-loss rate, a shape parameter of the second wall-loss rate, and a scale parameter of the second wall-loss rate.

ここで、μ_εは前記測定誤差εの平均値、
σ_εは前記測定誤差εの標準偏差、
λは所与の区間内で発生する事象の期待発生回数、
α_１は前記第１減肉速度の形状母数、
β_１は前記第１減肉速度の尺度母数、
α_２は前記第２減肉速度の形状母数、
β_２は前記第２減肉速度の尺度母数、
μ_ｗｏは前記初期肉厚ｗ_ｏの平均値、
σ_ｗｏは前記初期肉厚ｗ_ｏの標準偏差、
Ｌ_ｔｐ（μ_ε,σ_ε,λ,α_１,β_１,α_２,β_２, μ_ｗ０,σ_ｗ０)は各前記ハイパーパラメータ（μ_ε,σ_ε,λ,α_１,β_１,α_２,β_２, μ_ｗ０,σ_ｗ０)が与えられたもとでの時刻ｔにおける測定点ｐにおける肉厚の測定値ｙ_ｔｐの尤度、
ｗ_ｔｐは真の肉厚値、

は前記測定誤差εの確率分布、
ｔ_ｏｐは測定点ｐにおける経過時間、
ｖ_１ｐは測定点ｐにおける前記第１減肉速度、
ｖ_２ｐは測定点ｐにおける前記第２減肉速度、
Ｐ_ｐｏｉｓ（ｔ₀｜λ）は経過時間ｔ₀の確率分布、
Ｐ_γ（ｖ_１ｐ｜α_１，β_１）は測定点ｐにおける第１減肉速度ｖ_１ｐの確率分布、
Ｐ_γ（ｖ_２｜α_２，β_２）は測定点ｐにおける第２減肉速度ｖ_２ｐの確率分布、
Ｐ_Ｎ（ｗ_０ｐ｜μ_ｗ０,σ_ｗ０）は測定点ｐにおける初期肉厚ｗ_０ｐの確率分布である方法。 (Item 8) In the method according to item 7, the likelihood is expressed by a mathematical model of the following formula (1):

where μ _ε is the average value of the measurement error ε,
σ _ε is the standard deviation of the measurement error ε,
λ is the expected number of occurrences of an event in a given interval,
α ₁ is a geometric parameter of the first thinning rate,
β ₁ is a scale parameter of the first thinning rate,
_α2 is a geometric parameter of the second thinning rate,
β ₂ is a scale parameter of the second thinning rate,
μ _wo is the average value of the initial thickness _wo ,
σ _wo is the standard deviation of the initial thickness _wo ,
L _tp (μ _ε , σ _ε , λ, α ₁ , β ₁ , α ₂ , β ₂ , μ _w0 , σ _w0 ) is the likelihood of the thickness measurement value y tp at the measurement point p at time t given _the hyperparameters (μ _ε , σ _ε , λ, α ₁ , β ₁ , α ₂ , β ₂ , μ _w0 , σ _w0 );
w _tp is the true wall thickness value,

is the probability distribution of the measurement error ε,
t _op is the elapsed time at measurement point p,
v _1p is the first thinning rate at the measurement point p,
v _2p is the second thinning rate at the measurement point p,
P _pois (t ₀ |λ) is the probability distribution of elapsed time t ₀ ,
P _γ (v _1p |α ₁ , β ₁ ) is the probability distribution of the first thinning rate v _1p at the measurement point p,
P _γ (v ₂ |α ₂ , β ₂ ) is the probability distribution of the second thinning rate v _2p at the measurement point p,
A method in which P _N (w _0p |μ _w0 ,σ _w0 ) is the probability distribution of the initial thickness w _0p at the measurement point p.

(Item 9) The method according to any one of items 1 to 8, wherein the step of calculating the posterior distribution of the hyperparameters includes a step of calculating the posterior distribution of the hyperparameters by applying a Markov chain Monte Carlo method to the prior distribution of the hyperparameters and a measured value of a physical quantity representing a wall-thinning tendency of the component.

(Item 10) The method according to any one of items 1 to 9,
The method further includes a step of specifying a prediction time for the constructed thinning model, and acquiring a probability distribution of a physical quantity representing a thinning tendency of the component at the prediction time.

(Item 11) A program for causing a processor installed in the facility to execute the method according to any one of items 1 to 10.

(Item 12) An apparatus for constructing a thinning model for predicting thinning of a component disposed within a facility, comprising:
a wall-reduction model setting unit that sets a prior distribution of a hyperparameter used to adjust a probability distribution of a parameter included in the wall-reduction model;
a hierarchical Bayesian model setting unit that sets a likelihood equation for calculating the likelihood of the measurement value based on the value of the hyperparameter and a measurement value of a physical quantity that represents a wall-thinning tendency of the component, applies Bayes' theorem to the likelihood equation, and calculates a posterior distribution of the hyperparameter from a prior distribution of the hyperparameter and the measurement value of the physical quantity that represents a wall-thinning tendency of the component;
and a metal-reduction model construction unit that constructs the metal-reduction model from the calculated posterior distribution of the hyperparameters.

[Details of the embodiment of the present disclosure]
Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In the drawings, identical or similar elements are given identical or similar reference symbols, and duplicate descriptions of identical or similar elements may be omitted in the description of each embodiment. In addition, the features shown in each embodiment can be applied to other embodiments as long as they are not mutually inconsistent. However, the embodiments of the present disclosure are not necessarily limited to such aspects. It will be apparent to those skilled in the art that the embodiments of the present disclosure can take various aspects within the scope defined in the claims.

According to the present disclosure, a statistical model showing the future thickness of a component (e.g., pipes such as boiler water tubes and superheater tubes, scrapers and rails of conveyors, refractories in incinerators, etc.) constituting equipment used in facilities such as waste-to-energy plants is constructed from measurement data such as the thickness of the component. The material of the component is general mechanical material such as metal, inorganic material, organic material, composite material, etc. The components constituting equipment (boilers, incinerators, turbines, conveyors, etc.) used in facilities such as waste-to-energy plants become thinner over time due to corrosion, wear, etc. Based on the constructed statistical model, a prediction is made of the thinning tendency of the component, which is the gradual thinning of the thickness. Below, a method for predicting the future thinning of a component of equipment used in a facility according to one embodiment of the present disclosure will be described with reference to the drawings. Note that the components for which the amount of thinning is predicted according to the present disclosure are not limited to components used in waste-to-energy plants, but may be any components that gradually become thinner due to aging deterioration caused by corrosion, wear, etc., and therefore require inspection or replacement, etc., and may be components used in large-scale facilities such as power generation facilities, building structures (e.g., structural materials such as steel frames, piping), and components inside vehicles (e.g., engine exhaust system components). In the following, the components are defined as components that make up equipment used in facilities such as waste-to-energy plants.

First, an overview of the processing according to one embodiment of the present disclosure will be described with reference to FIG. 1. FIG. 1 shows an overview of a processing flow 100 executed in a prediction device 200 that predicts thinning of a component. The prediction device 200 can be realized by an information processing device with a well-known configuration, which will be described later in FIG. 2.

First, in step 102, the prediction device 200 acquires measurement data of a physical quantity that indicates a tendency for thinning of a component, such as the thickness or weight of the component, obtained from a measuring device that measures the thickness or weight of the component.

Next, in step 104, the prediction device 200 accepts the selection of a metal-thinning model 244 (FIG. 3) that expresses the change over time in the physical quantity (thickness and weight of the component) that represents the metal-thinning tendency of the component with respect to the elapsed time from the start of use of the component or the duration of use. The metal-thinning model 244 is a model that is selected from the time-varying trend of the measurement data of the physical quantity that represents the past metal-thinning tendency of the component, and that fits well to that trend. The prediction device 200 accepts the metal-thinning model 244 that has been selected in advance by a designer or the like.

Furthermore, in step 104, the prediction device 200 sets each parameter included in the acquired metal-reduction model 244, the probability distribution that each parameter follows, and hyperparameters for adjusting the probability distribution that each parameter follows. For each metal-reduction model 244, each parameter used to represent the model is determined in advance, and when a metal-reduction model 244 is selected, each parameter corresponding to the selected metal-reduction model 244 is set. In addition, the probability distribution that each parameter representing the metal-reduction model 244 follows, and the hyperparameters for adjusting the probability distribution are determined in advance by a designer, etc.

As mentioned above, the tendency for metal thinning of the target components varies due to differences in various environmental factors, such as the temperature, pressure, moisture content, and corrosive gas concentration in the usage environment of each component, as well as the state of adhesion of corrosive substances to the components. For this reason, it is not preferable to treat the parameters included in the metal thinning model 244 as deterministic. The prediction device 200 of the present invention is configured to predict the tendency for metal thinning by expressing the parameters included in the metal thinning model 244 as a probability model and reducing the problem to one of estimating the probability model.

In addition, there may be cases where the amount and quality of measurement data of physical quantities (thickness and weight of components) that indicate metal thinning trends, which is used to construct a probabilistic model that expresses the parameters included in the metal thinning model 244, is limited. Even in such cases, in order to efficiently estimate the parameters included in the metal thinning model 244, the prediction device 200 employs a parametric probability model as the probability model that each parameter follows. This makes it possible to change the values of the parameters (hyperparameters) included in the parameter probabilistic model, and accurately adjust the probability distribution that each parameter follows.

For example, when the parameter included in the metal-thinning model 244 includes the value of the initial thickness _w0 , which is the thickness at the time of manufacturing the member, a normal distribution can be set as a parametric probability distribution (statistical distribution) that the initial thickness _w0 of the member follows. In this case, the average μ _w0 and the standard deviation σ _w0 , which are parameters included in a function that analytically expresses the normal distribution, are hyperparameters corresponding to the parameter _w0 included in the metal-thinning model 244. The prediction device 200 acquires these hyperparameters. By changing the values of the average μ _w0 and the standard deviation σ _w0 , the distribution shape of the normal distribution can be adjusted to match the actual probability distribution of the value of the initial thickness _w0 . Note that, when the metal-thinning model 244 is acquired (step 104), the values of the parameters included in the metal-thinning model 244 and the values of the hyperparameters for adjusting the probability distributions are unknown.

Next, in step 106, a hierarchical Bayesian model formula is set based on each parameter set in step 104 and the corresponding hyperparameters. The hierarchical Bayesian model formula is a likelihood formula set hierarchically based on the parameters included in the metal-reduction model 244 and the hyperparameters for adjusting the probability distribution of these parameters. In the present disclosure, the likelihood formula is set based on the hierarchical relationship between the probability distribution of each parameter and the hyperparameters for adjusting these distributions. As a result, the metal-reduction model 244 is
Even if the probability distribution that each parameter included in 44 follows differs for each parameter, or the value of a certain parameter (e.g., the initial thickness _w0 or the measurement error ε) differs depending on the location of the component, the installation environment, the measurement method, etc., it is possible to construct an accurate likelihood equation that reflects these influences, etc.

Next, processing is performed using Bayes' theorem. Processing using Bayes' theorem (finding causes and their probabilities from results) includes setting a prior distribution, modifying the prior distribution based on the values of new data (Bayesian update), and deriving a posterior distribution. By using Bayes' theorem, it is possible to accurately estimate the values of each parameter and/or hyperparameter based on information and knowledge obtained in advance (a priori information) about each parameter and/or hyperparameter and information contained in the data actually obtained.

The values (statistical distribution) of the hyperparameters included in the metal-reduction model obtained in step 104 are unknown. In step 108, the prediction device 200 estimates the probability distribution of these hyperparameters and sets a prior distribution for the hyperparameters to be estimated.

Next, in step 110, the MCMC method (Markov Chain Monte Carlo method) is applied to the prior distribution of the hyperparameters set in step 108 based on Bayes' theorem. Note that the method is not limited to the MCMC method, and other methods for approximating the probability density function with an analytical function to obtain the posterior distribution, such as the sequential Monte Carlo method and the maximum likelihood estimation method, may be applied. When the maximum likelihood estimation method is used, the maximum likelihood point can be determined by various optimization methods such as the gradient method and the simplex method. The maximum likelihood point may also be determined by applying the simulated annealing method, the genetic algorithm, the evolutionary optimization method, the particle swarm optimization (PSO) method, etc. Furthermore, it is also possible to solve the posterior probability density function of the estimation target by an approach of fitting a parametric probability model such as a mixed normal distribution. In this case, it is preferable to identify the parameters of the probability density function by a method such as the least squares method.

The MCMC method numerically simulates the posterior distribution of parameters to examine the distribution of their estimates. By applying the MCMC method, in step 112, the posterior distribution of the hyperparameters whose values are unknown is numerically derived.

Once the posterior distribution of the hyperparameters whose values are unknown is obtained, a probability distribution is obtained for all parameters to be estimated. In step 114, the prediction device 200 constructs a metal-thinning model 244 based on the posterior distribution of the hyperparameters and the probability distribution of all parameters included in the metal-thinning model obtained based on them. Furthermore, in step 114, a probability distribution of the metal-thinning tendency of components in the facility at the prediction time is obtained based on the constructed metal-thinning model 244. By predicting the metal-thinning tendency, it is possible to predict changes in physical quantities (e.g., thickness and weight) that represent the metal-thinning tendency of the components.

Furthermore, in step 116, the posterior distribution of the hyperparameters predicted in step 112 is given as the prior distribution of the hyperparameters in other facilities, so that the posterior distribution of the hyperparameters in other facilities can be derived based on Bayes' theorem. This makes it possible to use the constructed wall-thickness reduction model 244 to predict future wall-thickness of components in other facilities where past wall-thickness measurement data of components is not available or where the amount of wall-thickness data of components measured in the past is insufficient.

Fig. 2 shows an example of the hardware configuration of a prediction device 200 as an information processing device that performs the process flow 100 for predicting thinning of a component shown in Fig. 1. The prediction device 200 is configured, for example, by a personal computer, a workstation, a tablet terminal, or any other arbitrary information processing device.

The prediction device 200 may be configured with two or more terminals. For example, a terminal for constructing the metal-reduction model 244 and a terminal for calculating a predicted value of future wall thickness using the metal-reduction model 244 may be configured separately, or may be configured on the cloud. As shown in the figure, the prediction device 200 has, as main hardware elements, a processor 202, a memory 204, a user input interface (IF) 206, and a display 208. Each of these elements is connected to each other so as to be able to communicate with each other via a bus (not shown).

The memory 204 temporarily and permanently stores programs and data. Programs stored in the memory 204 include an operating system program and a wall-reduction model construction program. The operating system is a computer program for controlling the overall operation of the prediction device 200. The wall-reduction model construction program is a computer program for the prediction device 200 to realize each process for model construction described below. The memory 204 can also temporarily or permanently store data generated by the operation of the prediction device 200. Specific examples of the memory 204 include a ROM (Read Only Memory), a RAM (Random Access Memory), a hard disk, a flash memory, an optical disk, and any other storage device. A part of the memory 204 may be provided as a separate unit outside the main body of the prediction device 200. In this case, the program and data are stored in a separate external memory (not shown).

The processor 202 is configured to read out a program stored in the memory 204 and execute processing in accordance with the program. For example, the processor 202 executes a metal-reduction model construction program stored in the memory 204 to realize various processes for constructing various models, which will be described later. The processor 202 includes a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit).

The user input interface 206 is configured to receive input from a user for operating the prediction device 200. Examples of the user input interface 206 include a keyboard, a mouse, a touchpad, etc.

The display 208 is configured to provide visual information to a user of the prediction device 200. For example, the display 208 displays a plurality of icons for launching various applications on a home screen or desktop screen of an operating system stored in the memory 204. As an example, a liquid crystal display or an organic EL display can be used for the display 208.

Figure 3 is a block diagram showing the functional configuration of the prediction device 200 shown in Figure 2. The prediction device 200 includes a processing unit 220 and a storage unit 240. The processing unit 220 corresponds to the processor 202 shown in Figure 2. The storage unit 240 corresponds to the memory 204 shown in Figure 2. Each of the units 222 to 232 represents a function realized by the processor 202 shown in Figure 2 reading and executing a program in the memory 204.

The processing unit 220 may include a data acquisition unit 222 for acquiring measurement data of the thickness of a member, an initial condition setting unit 224 for setting initial conditions for measuring the thickness of a member and predicting the thickness, a wall-thinning model setting unit 226 for acquiring a selected wall-thinning model 244 from the wall-thinning tendency of past wall-thinning measurement data of the member and setting various parameters defining the wall-thinning model 244 and hyperparameters for adjusting their probability distributions, a hierarchical Bayesian model setting unit 228 for setting a hierarchical Bayesian model hierarchically configured by each parameter constituting the wall-thinning model 244 and the hyperparameters, a wall-thinning model construction unit 230 for setting a prior distribution of the hyperparameters, applying Bayes' theorem to the prior distribution to derive a posterior distribution, and constructing the wall-thinning model 244 from the derived posterior distribution, and a wall-thinning prediction unit 232 for predicting the wall-thinning based on the constructed wall-thinning model 244. A detailed description of the processes performed by each unit 222 to 232 will be described later with reference to FIG. 4.

Note that the various components included in the processing unit 220 in FIG. 3 are merely one example of a module representing the functions executed by the processor 202. The functions of multiple components may be realized by a single component. The processor 202 may be configured to execute the functions of all the components.

The storage unit 240 may be configured to store various information. In one example, the storage unit 240 stores wall thickness measurement data 242 that is composed of a history of wall thickness measurement data of components measured by a measuring device. The wall thickness measurement data 242 is past historical data of wall thickness measurement results of components at a certain location. The wall thickness measurement data 242 may include wall thickness measurement results intermittently measured multiple times at different times by an inspector or the like, or may include wall thickness measurement results obtained multiple times at different times from wall thickness measurements continuously measured over a certain period of time. The wall thickness measurement data 242 may include historical data of wall thickness measurement results of components at different locations in a facility, the positions of the measurement points, and the number of measurement points. In another example, the storage unit 240 may store a wall thickness reduction model 244. The wall thickness reduction model 244 is initially composed of parameters whose values (statistical distribution) are unknown, and is therefore shown by a dotted line in FIG. 3. FIG. 5 illustrates a wall thickness reduction model 244 composed of parameters and hyperparameters whose values are unknown. By implementing the model construction flow of this disclosure, the values (statistical distributions) of the parameters and hyperparameters are obtained and the final metal loss model 244 is constructed (Figure 7).

Next, referring to FIG. 4, a process flow 400 of a method executed in the processing unit 220 shown in FIG. 3 according to one embodiment of the present disclosure will be described. The process flow 400 shown in FIG. 4 is a detailed description of the process flow 100 shown in FIG. 1.

First, in step 402 (step 102 in FIG. 1), the prediction device 200 (data acquisition unit 222) acquires component thickness measurement data 242 previously measured in the target facility for which thickness prediction is to be performed, and stores it in the memory unit 240. The measurement points for the component thickness may be the same location or different locations. By measuring at the same location, a thinning model 244 can be constructed that represents the thinning trend over time at that measurement point. By measuring at different locations, a thinning model 244 can be constructed that represents the thinning trend of the components of the equipment in the facility over a wide range.

Next, in step 404, the prediction device 200 (initial condition setting unit 224) acquires and sets initial conditions for measuring and predicting the thickness of a component input by a designer or the like via the user input IF 206. As an example, the prediction device 200 includes a number of measurement points N _p1 , a number of measurements per unit time N _t1 (e.g., once a year), and a number of predictions N _t2 . The number of measurement points N _p1 , the number of measurements per unit time N _t1 , and the number of predictions N _t2 can be set to any value.

Next, in step 406 (step 104 in FIG. 1 ), the prediction device 200 (thinning model setting unit 226) accepts the thinning model 244 selected by the designer or the like via the user input IF 206. The thinning model 244 is a model that is estimated from the thinning tendency of the past thickness measurement data 242 of the component and that fits well to the thickness measurement data 242. Specifically, the thinning model 244 is expressed as a mathematical expression that expresses the change over time in the physical quantity (thickness and weight of the component) that represents the thinning tendency of the component with respect to the elapsed time from the start of use of the component or the duration of use. Various thinning models 244 are prepared in advance in the prediction device 200 (thinning model setting unit 226), and the selection of one of them is accepted.

In this embodiment, the selected thinning model 244 is a broken line model consisting of two phases in which an increase in the thinning rate occurs at a certain elapsed time t _0. In the case of a broken line model, parameters required to express this thinning model 244 include at least the elapsed time t ₀ from the start of measurement until the increase in the thinning rate occurs, the thinning rate v ₁ before the increase in the thinning rate, and the thinning rate v ₂ after the increase in the thinning rate. By using such a broken line model, it is possible to accurately predict the thinning trend even in a case where the thinning trend changes suddenly at the elapsed time t _0. In addition, the parameters required to express the thinning model 244 may include the initial thickness w ₀ , which is the thickness of the member at the time of manufacture, and the measurement error ε of the thickness occurring in the measurement result. By including the initial thickness w ₀ and the measurement error ε of the thickness, it is possible to accurately predict the thinning trend taking into account the influence of the variation in the initial thickness of the member and the measurement error of the measuring device. FIG. 5 illustrates the thinning model 244. As shown in Fig. 5, the metal-thinning model 244 is composed of a first phase before the elapsed time _t0 and a second phase after the elapsed time _t0 . In each phase, the metal-thinning tendency of the component is approximated by a straight line with respect to time. The metal-thinning model 244 will be described in detail later. In step 406, the values of each parameter required to express the metal-thinning model 244 are unknown.

The thinning model 244 is not limited to a broken line model in which the thinning rate changes once. The thinning model 244 may be a model that best represents the thinning tendency of the wall thickness estimated from the wall thickness measurement data 242 including the wall thickness history of the past member. The thinning model 244 may be composed of three or more phases in which the elapsed time t ₀ at which each phase switches occurs multiple times. The thinning model 244 may be, for example, a linear curve model in which the thinning rate is constant, a quadratic curve model in which the thinning rate increases with time, a parabolic law (1/2 power) model in which the thinning rate decreases with time, a logistic curve model in which the thinning rate increases significantly in the initial stage but eventually converges, or a bathtub curve model in which the thinning rate decreases with time and then increases again after a period in which it becomes constant. The thinning model 244 may be a model in which the thinning rate decreases after a certain elapsed time, or a model having different approximation models before and after a certain elapsed time, for example, a model having a linear curve model before the elapsed time and a quadratic curve model after the elapsed time. Hereinafter, the wall-thinning model 244 will be described as a broken line model.

Next, in step 408 (step 104 in FIG. 1), the prediction device 200 (metal-reduction model setting unit 226) sets a probability distribution for each parameter included in the metal-reduction model 244. The designer predetermines for each parameter the distribution that best fits each parameter included in the metal-reduction model 244. The prediction device 200 sets the probability distribution for each parameter that has been predetermined by the designer.

The values that each parameter included in the wall-thinning model 244 can take vary depending on the configuration of the facility, the environment in which the component is placed, the measurement location, the material that constitutes the component, and the like. That is, the values that each parameter can take vary. For example, the initial wall thickness w ₀ of the component at the time of manufacture and the measurement accuracy (measurement error ε) of the measuring device vary. In addition, the elapsed time t ₀ until the wall-thinning rate increases varies from facility to facility, and also varies depending on the measurement location even in the same facility. Therefore, for the five parameters (initial wall thickness w ₀ , measurement error ε of the measuring device, elapsed time t ₀ until the wall-thinning rate increases, wall-thinning rate v ₁ , and wall-thinning rate v ₂ ) that represent the broken line model shown in FIG. 5 , the statistical probability distributions that these parameters follow are each previously determined.

The probability distribution of each parameter included in the wall-thinning model 244 is selected to be the best fit according to the distribution of values that each parameter can take. The distribution of values that each parameter can take can be selected taking into consideration the time-dependent trends of past data of the values of each parameter, the properties of each parameter, and the like. For example, a normal distribution is selected as the distribution to which the initial wall thickness w ₀ and the measurement error ε follow. This is because the normal distribution is often used as an error distribution because it is symmetrical. In addition, a Poisson distribution is selected for the elapsed time t _0. This is because the Poisson distribution is often used for phenomena that rarely occur. In addition, a gamma distribution is selected for the wall-thinning rates v ₁ and v _2. This is because the gamma distribution is a distribution that does not become negative.

The probability distributions selected as the distributions that various parameters follow are not limited to those described above. For example, the distribution that the initial wall thickness w ₀ follows may be a continuous univariate distribution that is supported on the entire positive number line, and may be, for example, a stable distribution such as a Cauchy distribution or a Holzmark distribution, a Laplace distribution, or a logistic distribution. The distribution that the measurement error ε follows may be a continuous univariate distribution that is supported on the entire real number line, and may be, for example, a stable distribution such as a Cauchy distribution or a Holzmark distribution, a Laplace distribution, or a logistic distribution. The distributions that the wall-thinning rate v ₁ and the wall-thinning rate v ₂ follow are not likely to be less than 0 in terms of the phenomenon, so they may be continuous univariate distributions that are supported within a semi-infinite period, and may be, for example, a normal distribution with a non-negative condition, a semi-Cauchy distribution, a chi-square distribution, an inverse Gaussian distribution, or a Levy distribution. The distribution that the elapsed time _t follows may be a continuous univariate non-negative probability distribution supported within a semi-infinite period, or a probability distribution that expresses the probability of occurrence per unit time, and may be a normal distribution with non-negativity conditions, a gamma distribution, a semi-Cauchy distribution, a categorical distribution, or the like.

Figure 5 illustrates a broken line model in which the x-axis represents the number of years elapsed and the y-axis represents the wall thickness, and the wall thinning rate increases after _t0 hours has elapsed. Figure 5 conceptually illustrates the statistical distribution that each parameter representing the broken line model can take. The probability distribution of each parameter is expressed by the following formula.

The probability distribution of the initial thickness _w0 expressed as a normal distribution is represented as P _N ( _w0 | _μw0 , _σw0 ). Here, the notation P _N ( _w0 | _μw0 , _σw0 ) indicates that the initial thickness _w0 follows a normal distribution with a mean value _μw0 and a standard deviation _σw0 . _μw0 is the mean value of the initial thickness, and _σw0 is the standard deviation of the initial thickness. In other words, _μw0 and _σw0 are hyperparameters corresponding to the parameter _w0 .

When the measurement error ε is expressed as a normal distribution, its probability distribution is represented as P _N (ε|μ _ε , σ _ε ), where μ _ε is the mean value of the measurement error, and σ _ε is the standard deviation of the measurement error. In other words, μ _ε and σ _ε are hyperparameters corresponding to the parameter ε.

The probability distribution of the wall-thinning rate _v1 expressed by the gamma distribution is expressed as _Pγ ( _v1 | _α1 , _β1 ), where _α1 is the shape parameter ( _α1 >0) of the wall-thinning rate _v1 , and _β1 is the scale parameter ( _β1 >0). In other words, _α1 and _β1 are hyperparameters corresponding to the parameter _v1 .

The probability distribution of the wall-thinning rate _v2 expressed by the gamma distribution is expressed as _Pγ ( _v2 | _α2 , _β2 ), where _α2 is the shape parameter ( _α2 >0) of the wall-thinning rate _v2 , and _β2 is the scale parameter ( _β2 >0). In other words, _α2 and _β2 are hyperparameters corresponding to the parameter _v2 .

When the elapsed time _t0 until the rate of wall thinning increases is expressed by a Poisson distribution, the probability distribution is represented as P _pois ( _t0 |λ), where λ is the parameter of the Poisson distribution. In other words, λ is a hyperparameter corresponding to the parameter _t0 .

The wall-thickness reduction model 244 (broken line model) shown in Fig. 5 can be expressed by the following equation using the above parameters: If the wall-thickness measurement error ε follows a normal distribution P _N (ε|μ _ε , σ _ε ), the wall-thickness measurement value Y1 also follows a normal distribution P _N (μ _w +μ _ε , σ _ε ). The wall-thickness measurement value Y1 is expressed by the following equation (1).

Measured wall thickness values Y1 to P _N (μ _w + μ _ε , σ _ε ) where μ _w = w ₀ - v ₁ × T1 when the measurement time T1 is 0≦T1≦t ₀
When the measurement time T1 is _t0 <T1, _μw = _w0 - _v1 ×t0 _{- v2} ×(T1- _t0 ) (1)

Here, μ _w is the average value of the true wall thickness at the measurement time T1, μ _ε is the average value of the measurement error, w ₀ is the true initial wall thickness, v ₁ is the wall thinning rate up to time t ₀ , and v ₂ is the wall thinning rate after time t _0. The true wall thickness value is not an actual measurement value including a measurement error, but an actual wall thickness value. Here, the true wall thickness value is an estimated value, and the measurement error ε is added to this to obtain the measured wall thickness value Y1. The measured value Y1 is the measured wall thickness value at time T1, and both time T1 and the measured value Y1 are known values obtained from the wall thickness measurement data 242.

If the predicted value Y2 of the wall thickness also follows a normal distribution P _N (μ _w + μ _ε , σ _ε ) like the measured value Y1 of the wall thickness, it can be expressed by the following formula (2). The predicted value Y2 of the wall thickness is the true wall thickness value plus the measurement error ε.

Predicted wall thickness Y2 to P _N (μ _w + μ _ε , σ _ε ) where, when the predicted time T2 is 0≦T2≦t ₀ , μ _w = w ₀ - v ₁ × T2 + μ _ε
When the predicted time T2 is _t0 <T2, _μw = _w0 - _v1 ×T2- _v2 ×(T2- _t0 )+ _με (2)

Here, the predicted value Y2 is a predicted value of the wall thickness at the predicted time T2, and is unknown. The predicted time T2 is obtained from the number of measurements _Nt1 per unit time and the predicted number _Nt2 , which are set in step 404. For example, if _Nt1 is once a year and _Nt2 is 20, the predictions are set from the 0th year to every other year up to 20 years later.

According to the present disclosure, from the relationship between the measurement time T1 and the measured thickness value Y1 described above, a predicted thickness value Y2 at the predicted time T2 arbitrarily set in step 404 can be obtained using the posterior distribution of each parameter obtained by Bayesian estimation.

Next, in step 410 (step 106 in FIG. 1), the prediction device 200 (hierarchical Bayes model setting unit 228) sets a hierarchical Bayes model formula based on hyperparameters for adjusting each probability distribution to which the five parameters (ε, t ₀ , v ₁ , v ₂ , w ₀ ) included in the broken line model follow, i.e., the above-mentioned nine hyperparameters (μ _ε , σ _ε , λ, α ₁ , β ₁ , α ₂ , β ₂ , μ _w0 , σ _w0 ). The hierarchical Bayes model formula is a formula that expresses, as a function, a numerical value (likelihood) that indicates the likelihood of inferring that the precondition was "something" from the measurement result when a result appears according to a certain precondition. The hierarchical Bayes model formula is expressed as the following formula (3).

は測定誤差の確率分布である。ｗ_ｔｐは時刻ｔにおける測定点ｐと同じ場所における真の肉厚値である。肉厚の測定誤差εは肉厚の実際の測定値ｙ_ｔｐから真の肉厚値ｗ_ｔｐを減算することによって導出され、ｙ_ｔｐ－ｗ_ｔｐ（ｔ_０ｐ，ｖ_１，ｖ_２）と表される。
また、Ｐ_ｐｏｉｓ（ｔ_0ｐ｜λ）は測定点ｐにおける減肉速度増大までの経過時間ｔ_0ｐの確率分布、
Ｐ_γ（ｖ_１ｐ｜α_１，β_１）は測定点ｐにおける第１フェーズの減肉速度ｖ_１ｐの確率分布、
Ｐ_γ（ｖ_２ｐ｜α_２，β_２）は測定点ｐにおける第２フェーズの減肉速度ｖ_２ｐの確率分布、
Ｐ_Ｎ（ｗ_０ｐ｜μ_ｗ０,σ_ｗ０）は測定点ｐにおける初期肉厚ｗ_０ｐの確率分布である。添え字ｐは測定点ｐにおける値を指す。 Here, L _tp (μ _ε , σ _ε , λ, α ₁ , β ₁ , α ₂ , β ₂ , μ _w0 , σ _w0 ) is the likelihood of the measured thickness y _tp at the measurement point p at time t given each hyperparameter to be estimated, and y _tp is the measured thickness

is the probability distribution of the measurement error. _wtp is the true wall thickness value at the same location as the measurement point p at time t. The wall thickness measurement error ε is derived by subtracting the true wall thickness value _wtp from the actual measured wall thickness value ytp, and is expressed as _{ytp - wtp( t0p,} v1 _, v2 ₎ .
P _pois (t _0p |λ) is the probability distribution of the elapsed time t _0p until the thinning rate increases at the measurement point p,
P _γ (v _1p |α ₁ , β ₁ ) is the probability distribution of the first phase thinning rate v _1p at the measurement point p,
P _γ (v _2p |α ₂ , β ₂ ) is the probability distribution of the second phase thinning rate v _2p at the measurement point p,
P _N (w _0p |μ _w0 , σ _w0 ) is the probability distribution of the initial thickness w _0p at the measurement point p, where the subscript p refers to the value at the measurement point p.

Fig. 6 conceptually illustrates the above-mentioned hierarchical Bayes model formula. In the hierarchical Bayes model, the probability distribution of five parameters (ε, t ₀ , v ₁ , v ₂ , w ₀ ) representing the broken line model and nine hyperparameters (μ _ε , σ _ε , λ, α ₁ , β ₁ , α ₂ , β ₂ , μ _w0 , σ _w0 ) for adjusting the probability distribution of these five parameters are hierarchically represented. If the hierarchical Bayes model shown in Fig. 6 can be expressed, the posterior distribution of each hyperparameter can be obtained from the past thickness measurement data 242 according to Bayes' theorem, a thinning model 244 can be constructed according to this posterior distribution, and the wall thickness of the component in a desired prediction interval can be predicted from the constructed thinning model 244.

<Application of Bayes'Theorem>
The prediction device 200 executes processing using Bayes' theorem based on the hierarchical Bayes model formula. Processing using Bayes' theorem (obtaining a cause and its probability from a result) includes setting a prior distribution, correcting the prior distribution based on the value of new data (Bayes update), and deriving a posterior distribution. Therefore, first, predictions (prior distributions) of how plausible each of the nine parameters is set.

Therefore, in step 412 (step 108 in FIG. 1 ), the prediction device 200 (hierarchical Bayesian model setting unit 228) sets a prior distribution in a Bayesian statistical model for each hyperparameter (μ _ε , σ _ε , λ, α ₁ , β ₁ , α ₂ , β ₂ , μ _w0 , σ _w0 ) of the metal-reduction model 244 to be estimated. A prior distribution determined in advance by a designer or the like is applied as the prior distribution. The prior distribution can be set from information on frequency distribution held in advance. However, when there is no prior information such as the average value and standard deviation of each hyperparameter to be estimated, a non-informative prior distribution can be adopted. Known non-informative prior distributions include a uniform distribution and a non-regular distribution.

In one example, as the non-informative prior distribution, the probability distribution of the mean value (the mean value of the initial wall thickness μ _w0 , the mean value of the measurement error μ _ε , and the parameter λ of the Poisson distribution) is given as a uniform distribution in a certain interval. When giving as a uniform distribution, the range of the possible values is also set. For example, for the mean value of the initial wall thickness μ _w0 , an appropriate range is set in consideration of the tolerance of the component to be estimated. That is, for a component with a nominal wall thickness of 5 mm and a tolerance of ±1 mm, a uniform distribution with equal probability in a sufficiently wide interval including at least an interval from 4 mm to 6 mm is given as the prior distribution of the initial wall thickness. Also, for example, the mean value of the measurement error μ _ε is set in an appropriate range in consideration of the measurement accuracy of the measuring device used. That is, if the measurement accuracy of the measuring device is ±0.1 mm,
m, the prior distribution of the measurement accuracy is a uniform distribution with equal probability in a sufficiently wide interval including at least the interval from -0.1 mm to +0.1 mm. If the average value of the measurement error of the thickness measuring device is approximately zero, the hyperparameter μ _ε corresponding to the average value of the measurement error can be set to 0, and therefore can be excluded from the hyperparameters to be estimated.

As another example, since the standard deviation always takes a positive value, a non-negative probability distribution, such as a gamma distribution or a semi-Cauchy distribution, is given to the probability distribution of the standard deviation (the standard deviation of the initial thickness σ _w0 and the standard deviation of the measurement error σ _ε ) as a non-informative prior distribution.

<Parameter estimation based on the MCMC (Markov Chain Monte Carlo) method>
The MCMC method is a method for obtaining an optimal solution by repeatedly performing sampling. When the number of hyperparameters or parameters to be estimated increases, it is generally not easy to calculate the posterior distribution, but the MCMC method is a method that makes this possible. According to the present disclosure, the prediction device 200 derives the posterior distribution by the MCMC method using the prior distribution defined in step 412 and the known wall thickness measurement data 242. Therefore, the Bayesian estimation method can be applied to problems with a large number of hyperparameters or parameters to be estimated.

First, in step 414, the prediction device 200 (hierarchical Bayesian model setting unit 228) applies the MCMC method to numerically obtain a posterior distribution from the above-mentioned prior distribution. The MCMC method is a method in which some model is determined in advance and the distribution of parameters that best fit the actual data is mathematically calculated inversely. The MCMC method obtains the posterior distribution from the prior distribution for all nine hyperparameters ( _με , _σε , λ, _α1 , _β1 , _α2 , _β2 , _μw0 , _σw0 ) to be estimated. The MCMC method numerically derives the probability distribution (posterior distribution) of each hyperparameter to be estimated that best fits the past wall thickness measurement data 242 of the equipment components to be predicted in the facility.

Specifically, first, the initial values of the nine hyperparameters to be estimated ( _με , _σε , λ, _α1 , _β1 , _α2 , _β2 , _μw0 , _σw0 ) are set. The initial values are values required for calculations using the MCMC method, and any value can be set. In order to speed up the convergence of the calculations, it is preferable to set the initial values to values that are consistent with the actual values, for example, values close to the actual values.

Next, for each of the nine hyperparameters ( _με , _σε , λ, _α1 , _β1 , _α2 , _β2 , _μw0 , _σw0 ) to be estimated, a joint posterior probability density function is calculated by repeating sampling from the posterior probability density function. By repeating sampling a sufficient number of times, each hyperparameter ( _με , _σε , λ, _α1 , _β1 , _α2 , _β2 , _μw0 , _σw0 ) reaches a stationary state of the Markov chain, and the sample θ after the number of samples that reach the stationary state becomes equal to the sample from the joint posterior probability density function.

Next, in step 416 (step 114 in FIG. 1), the prediction device 200 (metal-thinning model construction unit 230) constructs a metal-thinning model 244 that represents the statistical characteristics of the broken line model that represents the metal-thinning tendency of the component from the posterior distribution of the nine hyperparameters that have been found. The metal-thinning model 244 is composed of formula (2) that calculates the probability distribution of the estimated value Y2 of the wall thickness at any time point T2 using the nine hyperparameters, and a data set of sampling results using the MCMC method that corresponds to the posterior distribution of the nine hyperparameters.

Next, in step 418 (step 114 in FIG. 1), the prediction device 200 (wall thickness prediction unit 232) calculates a wall thickness prediction value Y2 in an arbitrarily designated prediction interval using the constructed wall thickness reduction model 244 (illustrated in FIG. 7). Specifically, the prediction time T2 in the prediction interval is specified by the number of measurement points N _p1 , the number of measurements per unit time N _t1 , and the number of predictions N _t2 set in step 404. Next, the wall thickness prediction value Y2 at the specified prediction time T2 is obtained from the wall thickness reduction model 244 expressed by the mathematical formula (2). From the probability distribution of the wall thickness prediction value Y2, the upper limit, lower limit, and median of the wall thickness prediction value Y2 may be obtained based on the percentile value. For example, when the prediction interval is 95%, the 97.5th percentile is set as the upper limit and the 2.5th percentile is set as the lower limit. FIG. 7 illustrates an example of a prediction result of the wall thickness prediction value based on a broken line model that statistically represents the wall thickness reduction tendency of the component of the target device obtained in this step. As shown in Fig. 7, the broken line model results in a band-like distribution, and the wall thickness prediction value has a range from a lower limit value to an upper limit value at a certain time. In this way, according to the present disclosure, it is possible to mathematically predict the future wall thinning tendency of the components of the target equipment in the facility based on the constructed statistical model.

According to the present disclosure, it is possible to mathematically express a wall-thinning model 244 that expresses the wall-thinning tendency of a component. In particular, it is possible to construct a wall-thinning model 244 that takes into account the initial wall thickness wo and the variation in the measurement error ε. This makes it possible to predict the future wall thickness of a component, taking into account uncertain factors such as the initial wall thickness wo and the variation in the measurement error ε.

Furthermore, according to the present disclosure, even if the thinning rate of a component increases midway, the time elapsed until the thinning rate increases and the thinning rate before and after the increase can be expressed as a statistical distribution. Therefore, even for components whose thinning rate increases midway, future predictions of the wall thickness can be made with high accuracy. As a result, it is possible to manage the wall thickness of components in the short, medium, and long term.

Furthermore, according to the present disclosure, although the thinning model 244 is constructed based on the wall thickness trend of the actually measured components, the thinning model 244 constructed can also be applied to components other than the actually measured components to predict the thinning trend. Therefore, for example, it is possible to predict the thinning trend of other components of the same equipment in the same facility without measuring the wall thickness or with a small number of measurements.

Returning to FIG. 4, further, in step 420, the posterior distribution of each hyperparameter obtained in step 414 may be given as a prior distribution for other facilities or a prior distribution for other equipment components of the same design in the same facility. That is, instead of giving an uninformative prior distribution as a prior distribution, the posterior distribution of the parameters obtained in step 414 may be given as an initial value of the prior distribution for the other facilities. Specifically, the medians of the posterior distributions of the nine hyperparameters calculated in step 414 are set as the initial values of the prior distributions of the nine hyperparameters set for the other facilities. For example, when the initial thickness w ₀ of the components in the other facilities follows a normal distribution, the mean value μ _w0 and standard deviation σ _w0 of the posterior distribution (sampling result) of the initial thickness w ₀ obtained in step 414 are calculated, and the normal distribution expressed by the mean value μ _w0 and standard deviation σ _w0 is used as the prior distribution of the hyperparameters (mean value μ _w0′ and standard deviation σ _w0′ ) to be estimated in the other facilities. Next, the posterior distribution is numerically obtained from the prior distribution of the hyperparameters to be estimated in the set other facilities by applying the MCMC method, and processing corresponding to step 414 is performed for the other facilities. Similarly, by performing processing corresponding to steps 416 and 418 for the other facilities, predicted values of the wall thickness in the other facilities can be obtained. In this way, according to the present disclosure, it is possible to mathematically predict the wall thickness of the parts of the target equipment in other facilities where there is no information at all or little information about the wall thickness of the parts of the target equipment.

The past thickness measurement data 242 used to calculate the posterior distribution may be classified in advance by the type of component, the location where the component is located, etc. This makes it possible to construct a thinning model 244 that represents the thinning tendency for each type and location where the component is located.

Furthermore, according to the present disclosure, the prediction device 200 can perform evaluations related to facility operation, maintenance, and facility design from the wall thickness prediction value obtained in step 418.

As an example, it is possible to determine whether or not repairs are required for components of the target equipment based on the wall thickness prediction value. For example, the prediction device 200 determines that repairs are required when there is a time when the lower limit value of the predicted wall thickness in the wall thickness prediction interval falls below the desired wall thickness value. Furthermore, when there is a time when the value falls below the limit, the prediction device 200 displays this time on the display 208.

As another example, it is possible to determine whether or not the next thickness measurement needs to be performed. For example, the prediction device 200 determines that the next (next) thickness measurement needs to be performed when the predicted thickness value at the next measurement opportunity is lower than the desired thickness value. In addition, the prediction device 200 can display a notification on the display 208 indicating that the next thickness measurement needs to be performed.

As another example, by understanding the thinning trend, it is possible to determine optimal initial wall thickness values and repair frequencies from the perspective of minimizing life cycle costs, and to reflect these in the design of facilities and components. Specifically, the amount of thinning of components from completion to the end of use of the facility can be calculated from the predicted thinning trend, and a sufficient initial wall thickness can be set so that repairs will not be necessary during the use of the facility. Furthermore, if making the initial wall thickness too thick would make the component too heavy, the optimal initial wall thickness and repair frequency can be set by taking into account the increased cost due to the increased weight and the reduced cost due to minimizing the repair frequency of the component.

In the second embodiment of the present disclosure, the thinning model 244A selected in step 406 is a linear curve model. There are three parameters required to express the linear curve model (initial thickness w ₀ , measurement error ε of the measuring device, thinning rate v ₁ ). The statistical probability distributions to which these parameters follow are, for example, a normal distribution P _N (w ₀ |μ _w0 , σ _w0 ) for the initial thickness w ₀ , a normal distribution P _N (ε|μ _ε , σ _ε ) for the measurement error ε, and a gamma distribution P _γ (v ₁ |α ₁ , β ₁ ) for the thinning rate v ₁ . The linear curve model can be constructed by a process similar to the process when the thinning model 244 is a broken line model, which has already been described. Therefore, the same process as the process already described will not be described below. FIG. 8A illustrates a linear curve model 244A constructed by a model construction process according to the present disclosure.

When the thinning model 244A (linear curve model) is expressed by an equation using the above parameters, it becomes as shown in the following equation (4).
Measured wall thickness values Y1 to P _N (μ _w + μ _ε , σ _ε ), where μ _w = w ₀ - v ₁ × T1 (4)

Here, μ _w is the average value of the true thickness at the measurement time T1, μ _ε is the average value of the measurement error, w ₀ is the true initial thickness, and v ₁ is the thinning rate. Similarly, the predicted value Y2 of the thickness can be expressed by the following equation (5).

Predicted wall thickness values Y2 to P _N (μ _w + μ _ε , σ _ε ), where μ _w = w ₀ - v ₁ × T2 (5) at the predicted time T2

Furthermore, when the wall-thinning model 244A is a linear curve model, the likelihood equation is expressed by the following equation (6).

According to the present disclosure, from the relationship between the measurement time T1 and the measured thickness value Y1 described above, a predicted thickness value Y2 at the predicted time T2 arbitrarily set in step 404 can be obtained using the posterior distribution of each parameter obtained by Bayesian estimation.

In the third embodiment of the present disclosure, the thinning model 244B selected in step 406 is a quadratic curve model. The parameters required to express the quadratic curve model are four: the initial wall thickness w ₀ , the measurement error ε of the measuring device, the thinning rate coefficient a ₁ , and the thinning rate coefficient a ₂ . The statistical probability distributions to which these parameters follow are, for example, a normal distribution P _N (w ₀ |μ _w0 , σ _w0 ) for the initial wall thickness w ₀ , a normal distribution P _N (ε|μ _ε , σ _ε ) for the measurement error ε, a gamma distribution P _γ (a ₁ |α ₁ , β ₁ ) for the thinning rate coefficient a ₁ , and a gamma distribution P _γ (a ₂ |α ₂ , β ₂ ) for the thinning rate coefficient a ₂ . The thinning rate coefficient a ₁ and the thinning rate coefficient a ₂ may adopt other distributions such as a normal distribution. The quadratic curve can also be constructed by the same process as the thinning models 244 and 244A. Therefore, the following description will be omitted for the same processes as those already described. Fig. 8B illustrates a quadratic curve model 244B constructed by the model construction process according to the present disclosure.

When the thinning model 244B (quadratic curve model) is expressed by an equation using the above parameters, it becomes as shown in the following equation (7).
Measured wall thickness values Y1 to P _N (μ _w + μ _ε , σ _ε ), where μ _w = w ₀ - a ₁ × T1 - a ₂ × T1 ² (7)

Here, μ _w is the average value of the true thickness at the measurement time T1, μ _ε is the average value of the measurement error, w ₀ is the true initial thickness, and a ₁ and a ₂ are parameters corresponding to the thinning rate. Similarly, the predicted value Y2 of the thickness can be expressed by the following equation (8).

Predicted wall thickness values Y2 to P _N (μ _w + μ _ε , σ _ε ) where μ _w = w ₀ - a ₁ × T2 - a ₂ × T2 ² (8)

Furthermore, when the wall-thinning model 244B is a quadratic curve model, the likelihood equation is expressed by the following equation (9).

According to the present disclosure, a statistical model indicating the future thickness of components can be constructed from measurement data such as the thickness of components constituting equipment used in facilities such as waste-to-energy plants. By constructing a statistical model appropriately selected according to the thinning tendency of the component, the thinning tendency of the component can be predicted with high accuracy.

Although the embodiments of the present invention have been described above, the embodiments are intended to facilitate understanding of the present invention and do not limit the present invention. The present invention may be modified or improved without departing from its spirit, and the present invention naturally includes equivalents. Furthermore, any combination of the embodiments and modifications is possible within the scope of solving at least part of the above-mentioned problems or achieving at least part of the effects, and any combination or omission of each component described in the claims and specification is possible.

Reference Signs List 200 Prediction device 202 Processor 204 Memory 206 User input interface 208 Display 220 Processing unit 222 Data acquisition unit 224 Initial condition setting unit 226 Thinning model acquisition unit 228 Hierarchical Bayesian model setting unit 230 Thinning model construction unit 232 Wall thickness prediction unit 240 Storage unit 242 Wall thickness measurement data

Claims (13)

A method executed by a processor for constructing a wall-thinning model that represents a time-dependent change in a physical quantity that represents a wall-thinning tendency of a component arranged in a facility in order to predict wall-thinning of the component, the method comprising:
Setting a prior distribution of hyperparameters used to adjust the probability distribution of parameters included in the wall-thinning model;
A step of setting a likelihood equation for calculating the likelihood of the measurement value based on the value of the hyperparameter and the measurement value of a physical quantity representing a wall-thinning tendency of the component;
A step of applying Bayes' theorem to the likelihood equation to calculate a posterior distribution of the hyperparameter from a prior distribution of the hyperparameter and a measured value of a physical quantity representing a wall-thinning tendency of the component;
and constructing the metal loss model from the posterior distribution of the calculated hyperparameters ;
The method , wherein the parameters include at least one of an initial thickness of the component and a measurement error occurring in a measurement result of the thickness . 2. The method of claim 1 ,
The method of claim 1, wherein the probability distribution of the initial wall thickness is a normal distribution, the probability distribution of the measurement error is a normal distribution, and the hyperparameters include a mean value of the initial wall thickness, a standard deviation of the initial wall thickness, a mean value of the measurement error, and a standard deviation of the measurement error. In order to predict thinning of components installed in a facility, the time course of physical quantities that indicate the thinning tendency of the components is
1. A processor-implemented method for constructing a metal loss model that represents a time-dependent change in a metal loss profile, comprising:
Setting a prior distribution of hyperparameters used to adjust the probability distribution of parameters included in the wall-thinning model;
A step of setting a likelihood equation for calculating the likelihood of the measurement value based on the value of the hyperparameter and the measurement value of a physical quantity representing a wall-thinning tendency of the component;
A step of applying Bayes' theorem to the likelihood equation to calculate a posterior distribution of the hyperparameter from a prior distribution of the hyperparameter and a measured value of a physical quantity representing a wall-thinning tendency of the component;
constructing the wall-thinning model from the calculated posterior distribution of the hyperparameters;
Including,
The wall-thinning model is composed of two or more phases, and the parameters include an elapsed time at which the phase switches,
a metal loss trend of the component in each of the phases is approximated by a straight line versus time, and the parameters include a first metal loss rate that is a slope of the straight line in a first phase, and a second metal loss rate that is a slope of the straight line in a second phase. The method of claim 3 , wherein the parameters include at least one of an initial thickness of the member and a measurement error occurring in a measurement result of the thickness. 5. The method of claim 4,
The method of claim 1, wherein the probability distribution of the initial wall thickness is a normal distribution, the probability distribution of the measurement error is a normal distribution, and the hyperparameters include a mean value of the initial wall thickness, a standard deviation of the initial wall thickness, a mean value of the measurement error, and a standard deviation of the measurement error. 4. The method of claim 3 , wherein the probability distribution of elapsed time is a Poisson distribution and the hyperparameters include an expected number of occurrences of an event occurring within a given interval. 4. The method of claim 3 ,
the probability distribution of the first wall-loss rate and the probability distribution of the second wall-loss rate are gamma distributions, and the hyperparameters include a shape parameter of the first wall-loss rate, a scale parameter of the first wall-loss rate, a shape parameter of the second wall-loss rate, and a scale parameter of the second wall-loss rate. 4. The method according to claim 3, wherein the parameter includes at least one of an initial thickness of the member and a measurement error occurring in a measurement result of the thickness,
The probability distribution of the initial wall thickness is a normal distribution, the probability distribution of the measurement error is a normal distribution, and the hyperparameters include a mean value of the initial wall thickness, a standard deviation of the initial wall thickness, a mean value of the measurement error, and a standard deviation of the measurement error;
the probability distribution of the elapsed time is a Poisson distribution, and the hyperparameters include an expected number of occurrences of an event occurring within a given interval;
the probability distribution of the first wall-loss rate and the probability distribution of the second wall-loss rate are gamma distributions, and the hyperparameters include a shape parameter of the first wall-loss rate, a scale parameter of the first wall-loss rate, a shape parameter of the second wall-loss rate, and a scale parameter of the second wall-loss rate. 9. The method according to claim 8 , wherein the likelihood is expressed by a mathematical model of the following formula (1):
where μ _ε is the average value of the measurement error ε,
σ _ε is the standard deviation of the measurement error ε,
λ is the expected number of occurrences of an event in a given interval,
α ₁ is a geometric parameter of the first thinning rate,
β ₁ is a scale parameter of the first thinning rate,
_α2 is a geometric parameter of the second thinning rate,
β ₂ is a scale parameter of the second thinning rate,
μ _wo is the average value of the initial thickness _wo ,
σ _wo is the standard deviation of the initial thickness _wo ,
L _tp (μ _ε , σ _ε , λ, α ₁ , β ₁ , α ₂ , β ₂ , μ _w0 , σ _w0 ) is the likelihood of the thickness measurement value y tp at the measurement point p at time t given _the hyperparameters (μ _ε , σ _ε , λ, α ₁ , β ₁ , α ₂ , β ₂ , μ _w0 , σ _w0 );
w _tp is the true wall thickness value,
is the probability distribution of the measurement error ε,
t _op is the elapsed time at measurement point p,
v _1p is the first thinning rate at the measurement point p,
v _2p is the second thinning rate at the measurement point p,
P _pois (t ₀ |λ) is the probability distribution of elapsed time t ₀ ,
P _γ (v _1p |α ₁ , β ₁ ) is the probability distribution of the first thinning rate v _1p at the measurement point p,
P _γ (v ₂ |α ₂ , β ₂ ) is the probability distribution of the second thinning rate v _2p at the measurement point p,
A method in which P _N (w _0p |μ _w0 ,σ _w0 ) is the probability distribution of the initial thickness w _0p at the measurement point p. 10. The method according to claim 1 , wherein the step of calculating the posterior distribution of the hyperparameters includes a step of calculating the posterior distribution of the hyperparameters by applying a Markov chain Monte Carlo method to the prior distribution of the hyperparameters and a measured value of a physical quantity representing a wall-thinning tendency of the component. 11. The method according to any one of claims 1 to 10 ,
The method further includes a step of specifying a prediction time for the constructed thinning model, and acquiring a probability distribution of a physical quantity representing a thinning tendency of the component at the prediction time. A program for causing a processor provided in the facility to execute the method according to any one of claims 1 to 11 . An apparatus for constructing a thinning model for predicting thinning of components arranged in a facility, comprising:
a wall-reduction model setting unit that sets a prior distribution of a hyperparameter used to adjust a probability distribution of a parameter included in the wall-reduction model;
a hierarchical Bayesian model setting unit that sets a likelihood equation for calculating the likelihood of the measurement value based on the value of the hyperparameter and a measurement value of a physical quantity that represents a wall-thinning tendency of the component, applies Bayes' theorem to the likelihood equation, and calculates a posterior distribution of the hyperparameter from a prior distribution of the hyperparameter and the measurement value of the physical quantity that represents a wall-thinning tendency of the component;
and a metal-reduction model construction unit that constructs the metal-reduction model from the calculated posterior distribution of the hyperparameters,
The parameters include at least one of an initial thickness of the member and a measurement error occurring in a measurement result of the thickness, or
The metal-thinning model is composed of two or more phases, the parameters include an elapsed time at which the phases are switched, and in each of the phases, a metal-thinning tendency of the component is approximated by a straight line with respect to time, and the parameters include a first metal-thinning rate which is a slope of the straight line in a first phase, and a second metal-thinning rate which is a slope of the straight line in a second phase.
Device.

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