JP2019008637A - Parameter estimating device, device-failure predicting device, optimal measures searching device, method, and program - Google Patents

Abstract

To enable estimation of a parameter relating to a failure of a device in consideration of an influence on a speed of deterioration of an external environment.SOLUTION: Based on failure time data 22, external environmental data 24, and maintenance data 26, a parameter estimating unit 34 calculates an estimation parameter including a parameter used in an aged deterioration function with a virtual age of a device being an argument and a degradation rate for each of discretized external environmental values. At this time, the virtual age of the device is expressed by using the deterioration rate for each of the discretized external environmental values, the external environmental data, and the maintenance data. When a failure rate of the device is obtained by multiplying the value of the aged deterioration function by a time corresponding to the virtual age of the device, the estimation parameter is estimated so as to maximize a posterior probability of the estimation parameter including a likelihood function of the estimation parameter expressed by using the time of failure and the failure rate of the device.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a parameter estimation device, an equipment failure prediction device, an optimum measure search device, a method, and a program.

  There are many techniques for modeling a state in which the failure probability of a device increases / decreases in accordance with the aging since the device is installed as a conventional technology related to modeling of aging deterioration. For example, there is a technique using a Weibull hazard function (Non-Patent Document 1).

  As a conventional technique related to modeling of a maintenance effect, there is a technique for modeling a state in which a failure probability of a device is reduced by maintenance. This is a technology that considers the elapsed time from the installation as the age of the device and thinks that the substantial age = Virtual Age is rejuvenated by maintenance, and is called Virtual Age Model (Non-Patent Document 2). In the Virtual Age Model, aging is given as a function of Virtual Age. An example of the Virtual Age Model is shown in FIG. As shown in FIG. 7, the virtual age is rejuvenated by γ (<1) times due to the maintenance effect. Model parameters can be estimated from equipment failure data.

As a conventional technique related to the optimization of a maintenance plan, a future cost is predicted or a predicted value by taking a period Ω from installation to replacement and a maintenance implementation timing (v ₁ , v ₂ ,..., V _n ) as measures. There is a conventional technique for finding a measure for minimizing the above. The function that expresses the cost varies depending on the situation assumed by each operator, but a typical example is shown below (Non-patent Document 3).

However, C _r is the expected value of the replacement cost, C _P is maintenance once the cost, C _f the repair once the cost, the total number of failures in the N _f the period. The optimal maintenance plan can be found by the trade-off between maintenance cost and repair cost.

Cassady et al., “A generic model of equipment availability under imperfect maintenance”, IEEE Transactions on Reliability, 54, pp.564-571, 2005. Kijima, “Some results for repairable systems with general repair”, Journal of Applied Probability, pp.89-102, 1989. Nakagawa, “Sequential imperfect preventive maintenance policies”, IEEE Transactions on Reliability, 37, pp.295-298, 1988. MacKay, “Introduction to Gaussian processes”, NATO ASI Series F Computer and Systems Sciences, 168, pp.133-166, 1998.

  In the prior art (Non-Patent Documents 1, 2, and 3), the influence of the deterioration rate of the device from the external environment has been ignored. Non-Patent Document 2 considers the immediate influence of the external environment on the failure probability, but does not consider the cumulative (accumulative) influence caused by increasing the deterioration rate. For example, if a device is temporarily exposed to a poor external environment, the failure probability will return to its original value when the environment is normalized in the former. It is high. By ignoring the influence on the deterioration rate of the external environment, the following problems are considered to occur.

  First, the estimation and prediction of the deterioration status of each device is inaccurate. Moreover, as a result, extra costs are generated by performing maintenance more than necessary, and conversely, there is a great failure risk due to insufficient maintenance. For example, consider a case where the external environment is air temperature, and the deterioration rate of the device increases when the air temperature is high. Deterioration progresses in the year when the heat wave continues, and the failure probability of equipment should be high in the following year, but if the effect of temperature is ignored, the number of failures in the following year will be estimated less than the actual, and as a result, more than expected It will cause a failure. Moreover, by analyzing a plurality of devices under different temperatures as exhibiting the same behavior, there is a possibility of overlooking devices that should be preferentially maintained.

  Secondly, it is not possible to discover optimal measures including the external environment. For example, if the equipment is installed in a room where the room temperature can be controlled, should the deterioration rate be reduced at the expense of the air conditioning cost and the replacement period be extended, or the air conditioning cost should be kept low even if the replacement period is advanced, I cannot answer such a problem.

  The present invention has been made in view of the above circumstances, and provides a parameter estimation apparatus, method, and program capable of estimating parameters related to equipment failure in consideration of the influence on the deterioration rate of the external environment. With the goal.

  It is another object of the present invention to provide an apparatus failure prediction apparatus, method, and program capable of accurately predicting information related to an apparatus failure or Virtual Age.

  It is another object of the present invention to provide an optimum measure searching apparatus, method, and program capable of searching for an optimum measure in consideration of the influence on the deterioration rate of the external environment.

  In order to achieve the above object, a parameter estimation apparatus according to the present invention includes failure time data of an analysis target device, external environment data representing an external environment value at each time when the device was exposed, and the device. Based on maintenance data representing a time series of maintenance performed on the device, a parameter used in an aged deterioration function using the virtual age of the device as an argument, and a discretized external environment A parameter estimation unit for estimating an estimation parameter including a degradation rate for each of the values, wherein the virtual age of the device is a degradation rate for each of the discretized external environment values, the external environment data, and the Maintenance data, and the failure rate of the device is converted to the value of the aging function to the virtual value of the device. maximizing the posterior probability of the estimated parameter, including a likelihood function of the estimated parameter expressed using the time of failure of the device and the failure rate, when determined by multiplying the time corresponding to l Age As described above, a parameter estimation unit for estimating the estimation parameter is included.

  Further, in the parameter estimation method according to the present invention, the parameter estimation unit includes a failure time data of a device to be analyzed, external environment data representing an external environment value at each time when the device was exposed, and the device. Maintenance data representing a time series of maintenance carried out on the basis of the parameters used in the aged deterioration function using the virtual age of the device as an argument, and a discretized external environment value A virtual age of the device, wherein the virtual age of the device is a degradation rate for each of the discretized external environment values, the external environment data, the maintenance data, The failure rate of the device is represented by the value of the aging function and the virtual age of the device. So as to maximize the posterior probability of the estimated parameter, including the likelihood function of the estimated parameter expressed using the failure time of the device and the failure rate, when multiplied by the corresponding time , Estimating the estimation parameter.

  The device failure prediction apparatus according to the present invention represents a sequence of external environment information representing external environment values at each time when the device to be analyzed is scheduled to be exposed and a time of maintenance scheduled to be performed on the device. Based on the maintenance plan, the parameters used in the aging degradation function using the virtual age of the device as an argument, estimated by the parameter estimation device, and the degradation rate for each of the discretized external environment values The apparatus includes a failure prediction unit that predicts information related to a failure of the device or a virtual age using the estimated parameter.

  In addition, in the device failure prediction method according to the present invention, the failure prediction unit is scheduled to be performed on the device and the external environment information representing the external environment value at each time when the device to be analyzed is scheduled to be exposed. Based on a maintenance plan representing a maintenance time series, parameters used in an aging function using the virtual age of the device as an argument, estimated by the parameter estimation method, and discretized external environment values Information regarding the failure of the device, or Virtual Age, is estimated using estimated parameters including the degradation rate for each of the two.

  Further, the optimum measure searching apparatus according to the present invention includes a sequence of external environment information representing external environment values at each time when the device to be analyzed is scheduled to be exposed, and a maintenance time scheduled for the device. And a maintenance plan that represents an optimization measure as an optimization target measure, and for each of the measure candidates for the optimization target measure, the device Estimated by the parameter estimation device based on the external environment information representing the external environment value at each time scheduled to be exposed and the maintenance plan representing the maintenance time series scheduled to be performed on the device. Further, a parameter used in an aging deterioration function using the virtual age of the device as an argument, a deterioration rate for each of the discretized external environment values, and A failure prediction unit that predicts information related to the failure of the device using an estimation parameter that includes the information about the failure of the device predicted by the failure prediction unit for each of the candidate measures As a measure for minimizing a predetermined cost function including information relating to a failure, an optimum measure search unit for determining any of the measure candidates is configured.

  The optimum measure searching method according to the present invention represents a sequence of external environment information representing the external environment value at each time when the device to be analyzed is exposed and the time of maintenance scheduled to be performed on the device. An optimum measure searching method in an optimum measure searching apparatus that searches for an optimum measure using at least one of the maintenance plan as a measure to be optimized, wherein the failure prediction unit is a measure candidate for the measure to be optimized For each of the above, based on external environment information representing the external environment value at each time the device is scheduled to be exposed, and a maintenance plan representing a series of maintenance times scheduled for the device, The parameters used in the aging degradation function using the virtual age of the device as an argument, estimated by the parameter estimation method, and the discretized external Information about failure of the device is predicted using an estimation parameter including a deterioration rate for each of the environmental values, and the device for which the optimum measure search unit is predicted for each of the measure candidates by the failure prediction unit Based on the information on the failure of the device, any of the measure candidates is determined as a measure for minimizing a predetermined cost function including information on the failure of the device.

  The program which concerns on this invention is a program for functioning a computer as each part which comprises said parameter estimation apparatus, said apparatus failure prediction apparatus, or said optimal measure search apparatus.

  According to the parameter estimation apparatus, method, and program of the present invention, the virtual age of a device is represented using the degradation rate, external environment data, and maintenance data for each of the discretized external environment values. Is calculated by multiplying the value of the aging function by the time corresponding to the virtual age of the device, the likelihood function of the estimated parameter expressed using the failure time and the failure rate of the device. By estimating the estimated parameter so that the posterior probability of the estimated parameter is maximized, it is possible to estimate the parameter relating to the failure of the device in consideration of the influence on the deterioration rate of the external environment. .

  In addition, according to the apparatus failure prediction apparatus, method, and program of the present invention, by using the parameter related to the device failure estimated in consideration of the influence on the deterioration rate of the external environment, the information about the device failure, or the Virtual The effect that Age can be predicted with high accuracy is obtained.

  In addition, according to the optimum measure searching apparatus, method, and program of the present invention, by using parameters related to equipment failure estimated in consideration of the influence on the deterioration rate of the external environment, the influence on the deterioration speed of the external environment is obtained. The effect that it is possible to search for the optimum measure in consideration is obtained.

It is a block diagram which shows the structure of the parameter estimation apparatus which concerns on the 1st, 2nd embodiment of this invention. It is a block diagram which shows the structure of the apparatus failure prediction apparatus which concerns on the 1st Embodiment of this invention. It is a flowchart which shows the parameter estimation processing routine in the parameter estimation apparatus which concerns on the 1st, 2nd embodiment of this invention. It is a flowchart which shows the equipment failure prediction process routine in the equipment failure prediction apparatus which concerns on the 1st Embodiment of this invention. It is a block diagram which shows the structure of the optimal measure search apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows the optimal measure search process routine in the optimal measure search apparatus which concerns on the 2nd Embodiment of this invention. It is a figure for demonstrating Virtual Age.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Overview according to the first embodiment of the present invention>
First, an outline of the first embodiment of the present invention will be described.

(1) In the conventional Virtual Age Model (Non-Patent Document 2), the progress rate of Virtual Age (that is, the degradation rate) was constant, but a new one that allowed the progress rate to be proportional to the nonlinear function of the external environment. Introduce Virtual Age and use a new model that can take into account the impact on the external environment degradation rate.

(2) By modeling a function representing the nonlinear relationship between the external environment and the degradation rate using a stochastic process (eg, Gaussian process (Non-Patent Document 4)), the nonlinear function can be made non-parametric from data. That is, the function shape is estimated without making a strong assumption. The estimated nonlinear function is continuous with respect to the value of the external environment and does not require ad hoc quadrant division.

  In the first embodiment of the present invention, a parameter estimation device that estimates from a data a parameter indicating how a failure probability changes with time and the external environment after the device is installed, a future external environment, and maintenance The present invention is applied to an equipment failure prediction apparatus that takes a plan as an input and outputs a predicted value such as the future failure probability and the number of failures or the resulting cost / risk to each equipment based on the estimated parameters. An example will be described. Details of each device will be described below.

[First Embodiment]
<Configuration of Parameter Estimation Device According to First Embodiment of the Present Invention>
Next, the configuration of the parameter estimation apparatus according to the first embodiment of the present invention will be described. As shown in FIG. 1, a parameter estimation apparatus 100 according to the first embodiment of the present invention includes a CPU, a RAM, a ROM that stores a program and various data for executing a parameter estimation processing routine described later, and , Can be configured with a computer including. Functionally, the parameter estimation apparatus 100 includes an input unit 10, a calculation unit 20, and an output unit 40 as shown in FIG.

<Failure time data>
The input unit 10 receives data on the period from the installation of each device to be analyzed to the end of observation, and failure time data generated during the observation period, and stores the data in the failure time data 22.

Failure time data 22, the device ID (u hereinafter), the total number of devices (U hereinafter), the length of time to observe completion of the installation of equipment u (T ^u hereinafter), the failure observed with devices u Number of times (denoted as N ^u ), time series of failures observed in the equipment u (

). However, the failure time is given by the elapsed time from the installation time of each device.

<External environmental data>
The input unit 10 receives external environment data to which each device to be analyzed was exposed during the observation period, and stores it in the external environment data 24. The external environment data 24 includes a device ID u, the number of times when the external environment value is given to the device u (denoted as I ^u ), and a time series (when the external environment value is given)

), A series of external environmental values at each time (

). External environment values are generally given in multiple dimensions (temperature, humidity, pressure, etc.). However, the time sequence {t ^u _i } is given by the elapsed time from the installation time of each device. In each device, the value of the external environment is given at least by the installation time, observation end time, and failure time.

<Maintenance data>
The input unit 10 accepts a series of maintenance times performed during the observation period for each device to be analyzed, and stores it in the maintenance data 26. Here, maintenance means a measure that may reduce the failure probability of the device. Maintenance data 26, the instrument u, (referred to as M ^u) maintenance total number of devices u, the maintenance is carried out in equipment u time series (

). However, the maintenance time series {v ^u _n } is given by the elapsed time from the installation time of each device, and v ^u ₀ = 0 for convenience of calculation. If no maintenance is performed, M ^u = 0 is given as an input.

<Aging function>
The input unit 10 accepts designation of an aging deterioration function indicating a state in which the failure probability varies with respect to Virtual Age, that is, aged deterioration, and stores it in the aging deterioration function storage unit 28. The elapsed time from the installation time is t, the failure probability per unit time for each elapsed time (hereinafter referred to as failure rate) is λ ^u (t), the virtual age of the device u is τ ^u (t), and aging degradation When the function is expressed as f (τ | θ), the failure rate of the device u is defined as follows.

... (1)

However, the failure rate is the probability that a failure event occurs per unit time, θ is a parameter of an aging deterioration function, dt is a minute time interval, and dτ ^u (t) is a minute interval of Virtual Age. Although the aging deterioration function f (τ | θ) needs to be non-negative, this embodiment does not impose any other conditions on the aging deterioration function. Examples of the aging function include the following Weibull hazard function.

... (2)

<Discrete method>

In the parameter estimation of the parameter estimation unit 34 described later, there is an operation for discretizing the value of the external environment for convenience of calculation processing. Therefore, the input unit 10 accepts designation of a method for discretizing the value of the external environment and stores it in the discretization method storage unit 30. The discretization method is specified by the number of values that the external environment can take (denoted as L), a sequence of possible values (denoted as {z _l } ≡ (z ₁ , z ₂ , ..., z _L )), A rule that converts an arbitrary value y in the external environment into an index of any value of {z _l } (

). As an example of conversion rule, conversion to closest point

... (3)

However, it is not limited to this.

  It is desirable that the number L of discretization is larger because it improves the estimation accuracy of the parameter estimator 34, but the calculation time of the parameter estimator 34 is increased. Therefore, it is necessary to set a moderate value. is there.

<Kernel function in Gaussian process>
In this embodiment, since a Gaussian process is used as an example of a non-linear function stochastic process, the input unit 10 accepts specification of a function called a kernel function that determines the smoothness of a function to be modeled. Stored in the function storage unit 32. In the present embodiment, the function to be modeled is a function representing a non-linear relationship (deterioration rate) between the external environment and the deterioration rate.

  An example of a kernel function is a Gaussian kernel. When the degradation rate in the external environment value is expressed as G (y) and the kernel function for any two external environment values (y ′, y) is expressed as k (y ′, y), the Gaussian kernel is given as follows.

... (4)

  However, the selection of the kernel function is not limited to the Gaussian kernel. For example, when a Poisson process is used as an example of a stochastic process of a nonlinear function, a kernel function corresponding to the Poisson process is selected.

  The computing unit 20 includes failure time data 22, external environment data 24, maintenance data 26, aged deterioration function storage unit 28, discretization method storage unit 30, kernel function storage unit 32, parameter estimation unit 34, and parameter value storage unit 36. It is comprised including.

  The parameter estimation unit 34 includes failure time data 22 of the device to be analyzed, external environment data 24 representing the external environment value at each time when the device was exposed, and a series of times of maintenance performed on the device. Is stored in the kernel function storage unit 32, the aging deterioration function stored in the aging deterioration function storage unit 28, the discretization method stored in the discretization method storage unit 30, and the kernel function storage unit 32. Based on the kernel function, an estimation parameter including a parameter used in an aging deterioration function using the virtual age of the device as an argument and a deterioration rate for each of the discretized external environment values is estimated. Here, the virtual age of the device is represented by using the degradation rate for each of the discretized external environment values, the external environment data 24, and the maintenance data 26. In addition, when the failure rate of the device is obtained by multiplying the value of the aging degradation function by the time corresponding to the virtual age of the device, the likelihood of the estimated parameter expressed using the failure time and the failure rate of the device. The estimation parameter is estimated so as to maximize the posterior probability of the estimation parameter including the degree function. Further, the deterioration rate for each of the discretized external environment values is estimated according to a Gaussian process.

  A specific calculation method performed by the parameter estimation unit 34 will be described in detail below.

  The failure time data 22 of the device to be analyzed, the external environment data 24 representing the external environment value at each time when the device was exposed, and the maintenance data 26 representing the time series of maintenance performed on the device Based on the aging deterioration function stored in the aging deterioration function storage unit 28, the discretization method stored in the discretization method storage unit 30, and the kernel function stored in the kernel function storage unit 32, The deterioration function parameter θ and the deterioration rate parameter G (y) for the external environment y are estimated. The parameter estimation is performed by maximizing the posterior probability of the parameter.

First, assuming that the external environment value ^yu (t) is given to the elapsed time t from the installation time of the device u, the virtual age τ ^u (t) of the device u uses the deterioration rate parameter G (y). The

···(Five)

Given in. However, γ (0 ≦ γ ≦ 1) is the rate at which Virtual Age decreases (rejuvenates) due to maintenance, γ = 1 indicates that the initial installation state is reset by maintenance, and y = O indicates the effect of maintenance. Indicates that it cannot be seen. Since Virtual Age τ ^u (t) decreases discontinuously immediately after maintenance time v ^u _m , Virtual Age τ ^u (v ^u _m ) immediately before maintenance time v ^u _m and Virtual Age ⁺ τ ^u (v ^u immediately after maintenance time v ^u _m ) _m ) takes different values. As will be described later, the calculation of the posterior probability of the parameter is performed by calculating Virtual Age τ ^u (s ^u _n ) at each failure time, Virtual Age τ ^u (T ^u ) at the observation end time, and Virtual Age τ ^u ( Although the value of v ^u _m ) is necessary, it is difficult to analytically execute the integration of Equation (5), and therefore each Virtual Age is obtained by the approximate integration calculation as follows. Considering that the external environment value ^yu (t) is discretized as specified by the discretization method stored in the discretization method storage unit 30, now, Virtual Age τ ^u (t) at time t is

... (6)

Can be written down.

Where G≡ (G (z ₁ ),..., G (z _L )), A'B represents the inner product, and Δ (t), Φ (t), and ⁺ Φ (t) are defined below. Is done.

... (7)

δ _{a, b} represents the Kronecker delta. At this time, the degradation rate parameter to be estimated is a vector G having the discretized number L as the number of dimensions.

Next, input data of all devices

The likelihood function of the parameter for is derived. In general, given the failure rate λ ^u (t), the parameter likelihood function is written as

... (8)

  When formula (8) is written down using formula (1) and formula (5),

(9)

Further, considering that the value of the external environment ^yu (t) is discretized as specified by the discretization method stored in the discretization method storage unit 30, the equations (5) to (7) are used. The logarithm of the parameter likelihood function is calculated as follows.

··· (Ten)

  Finally, the posterior probabilities of the parameters for the input data D of all devices are calculated. Assuming that the degradation rate parameter G follows a Gaussian process in which each element has a vector I of 1 as an average, the prior distribution of the degradation rate parameter is obtained by using a kernel function stored in the kernel function storage unit 32.

(11)

It is expressed. Assuming that the prior distribution of the parameter θ and the maintenance effect γ of the aging function f (τ | θ) is a uniform distribution, the logarithm of the posterior probability of the parameter is calculated as follows.

(12)

  However, Const. Represents a constant term that does not depend on parameters.

  The parameter estimation unit 34 outputs the estimated value of the parameter (θ, γ, G) as the parameter value that maximizes the posterior probability of Expression (12).

···(13)

Since the posterior probability of equation (12) can be calculated explicitly with the first and second derivatives of the parameters (θ, γ, G), standard optimization algorithms such as Newton and quasi-Newton methods can be used. Can be used to easily execute equation (14). In addition,

Is calculated only from the input data D, and by previously calculating and storing it once, the posterior probabilities for various parameters (θ, γ, G) can be evaluated efficiently.

The parameter value storage unit 36 stores the parameter value estimated by the parameter estimation unit 34 together with a sequence of values {z _l } that can be taken by the external environment and the used kernel function k (y, y ′). Further, the output unit 40 outputs the parameter values stored in the parameter value storage unit 36, a sequence of values {z _l } that can be taken by the external environment, and the used kernel function k (y, y ′).

  An output example is shown in Table 1.

  Table 1 shows an output example when the aging function is Weibull hazard fuction, the kernel function is Gaussian kernel, and L = 5.

It should be noted that the sequence of values that can be taken by the external environment and the used kernel function are added and output by the device failure prediction apparatus 200, which will be described later, to calculate the degradation rate parameter G (y) for any external environment value y. Because they need them to do. Specifically, an estimate of G (y) for L points

Is given, the estimate for any point y of G (y) following a Gaussian process is

(14)

Given in.

<Configuration of equipment failure prediction apparatus according to first embodiment of the present invention>
Next, the configuration of the equipment failure prediction apparatus according to the first embodiment of the present invention will be described. As shown in FIG. 2, the device failure prediction apparatus 200 according to the first embodiment of the present invention stores a CPU, a RAM, a program for executing a device failure prediction processing routine described later, and various data. It can be composed of a computer including a ROM. Functionally, the device failure prediction apparatus 200 includes an input unit 50, a calculation unit 60, and an output unit 90 as shown in FIG. The device failure prediction apparatus 200 outputs a predicted value such as a future failure probability, the number of failures, or a cost / risk as a result thereof for each device uε {1, 2,..., U}.

<Estimated parameter value>
The input unit 50 receives input of the parameter value estimated by the parameter estimation device 100, a sequence of values {z _l } that can be taken by the external environment, and the kernel function k (y, y ′), and enters the parameter value storage unit 62. Store.

<Aging function>
The input unit 50 receives designation of the same aging deterioration function as the parameter estimation device 100 and stores it in the aging deterioration function storage unit 64.

<Designation of prediction target>
The input unit 50 receives designation of the amount to be predicted and stores it in the prediction target storage unit 66. Hereinafter, examples of amounts to be predicted are listed, but are not limited thereto.

(1) The expected value and variance of the number of failures in a specific period in the future are accepted as designation of the amount to be predicted. At this time, the device ID u and the future specific period for the device u (denoted as [Q ^u ₀ , Q ^u ₁ ]) are accepted as the prediction target designation.

(2) The probability that a failure will occur within a specific period in the future is accepted as the designation of the amount to be predicted. At this time, the device ID u and the future specific period for the device u (denoted as [Q ^u ₀ , Q ^u ₁ ]) are accepted as the prediction target designation.

(3) The expected value and variance of the time when a failure occurs for the first time since a specific time in the future are accepted as designation of the amount to be predicted. At this time, the device ID u and a specific time point (denoted as Q ^u ₀ ) for each device u are accepted as the prediction target designation.

(4) The virtual age at a specific time in the future is accepted as the designation of the amount to be predicted. At this time, the device ID u and a specific time point (denoted as Q ^u ₀ ) for each device u are accepted as the prediction target designation.

(5) The deterioration rate G (y) with respect to the external environment y is accepted as the designation of the amount to be predicted. At this time, a set of external environment values (denoted as Y = {y _i }) for outputting the deterioration rate is further accepted as a prediction target specification.

<External environment information until the forecast period>
The input unit 50 receives the value of the external environment scheduled to be exposed from the installation to the prediction period for each device, and stores it in the external environment information storage unit 68. As external environment information, device IDu, the number of times when external environment values are given to device u (

), A series of times when external environment values are given (

), A series of external environmental values at each time (

). However, time series

Is given by the elapsed time from the installation time of each device. In each device, the first time of the external environment value shall be the same as the installation time (

). The superscript horizontal line used in the notation here is for distinguishing from the input data of the parameter estimation unit 34.

<Maintenance plan until the forecast period>
The input unit 50 receives a maintenance plan that is a series of maintenance times planned from the installation to the prediction period for each device, and stores the maintenance plan in the maintenance plan storage unit 70. In addition, the maintenance plan, the input unit 50, for each device, the total number of maintenance of the device u (

), A series of maintenance times scheduled for equipment u (

). However, maintenance time series

Is given by the elapsed time from the installation time of each device.

And

  The calculation unit 60 includes a parameter value storage unit 62, an aging deterioration function storage unit 64, a prediction target storage unit 66, an external environment information storage unit 68, a maintenance plan storage unit 70, a failure prediction unit 72, and a prediction value storage unit 74. It consists of

  The failure predicting unit 72 is stored in the external environment information storage unit 68 and is stored in the maintenance plan storage unit 70 and external environment information representing the external environment value at each time when the device to be analyzed is scheduled to be exposed. A maintenance plan representing a time series of maintenance scheduled to be performed on the device, an aging deterioration function stored in the aging deterioration function storage unit 28, and a device stored in the parameter value storage unit 62. Based on the parameters used in the aging degradation function having the virtual age of the virtual age as an argument and the degradation rate for each of the discretized external environment values, information on the failure of the device, or the virtual age is predicted.

  Specifically, the failure prediction unit 72 uses the parameter value output by the parameter estimation device 100 and the aging deterioration function stored in the aging deterioration function storage unit 64 for each device, and specifies the specified prediction. Calculate the predicted value of the target quantity. Here, a calculation method is presented for each example of the amount of the prediction target.

(1) Calculate the expected value E ^u [N] and the variance V ^u [N] of the number of failures in the future specific period [Q ^u ₀ , Q ^u ₁ ] as the amount to be predicted according to the following equation (15). To do.

(15)

(2) As a quantity to be predicted, the probability P ^u that a failure will occur within a specific period [Q ^u ₀ , Q ^u ₁ ] in the future is calculated according to the following equation (16).

(16)

(3) As an amount to be predicted, an expected value E ^u [t] at the time when a failure occurs for the first time since a certain future time point Q ^u ₀ is calculated according to the following equation (17).

(17)

(4) As a quantity to be predicted, Virtual Age τ ^u (Q ^u ₀ ) at a specific future time point Q ^u ₀ is calculated according to equation (15).

(5) As a quantity to be predicted, the degradation rate G (y) for the external environment y is calculated according to the above equation (14) for each value y _i ∈Y of the external environment that outputs the degradation rate.

<Predicted value>
The predicted value calculated by the failure prediction unit 72 is stored in the predicted value storage unit 74. Then, the predicted value stored in the predicted value storage unit 74 is output by the output unit 90. An output example is shown in Table 3.

  The above example is an output example in the case of the example (1) of the amount to be predicted.

<Operation of Parameter Estimation Device According to First Embodiment of the Present Invention>
Next, the operation of the parameter estimation device 100 according to the first embodiment of the present invention will be described. When the input unit 10 receives data from the installation of each device to be analyzed to the end of observation and failure time data generated during the observation period, the parameter estimation apparatus 100 stores the failure time data 22 in the failure time data 22. Further, when the input unit 10 receives external environment data to which each device to be analyzed is exposed during the observation period, the parameter estimation device 100 stores the external environment data 24 in the external environment data 24. In addition, when the input unit 10 receives a series of times of maintenance performed during the observation period for each device to be analyzed, the parameter estimation apparatus 100 stores it in the maintenance data 26. In addition, when the input unit 10 receives designation of an aging deterioration function, the parameter estimation device 100 stores the aging deterioration function storage unit 28. In addition, when the input unit 10 receives designation of a method for discretization of values of the external environment, the parameter estimation device 100 stores the discretization method storage unit 30. In addition, when the input unit 10 receives the specification of the kernel function, the parameter estimation device 100 stores it in the kernel function storage unit 32. And the parameter estimation apparatus 100 performs the parameter estimation process routine shown in FIG.

  First, in step S100, the input data D of all devices including the failure time data 22, the external environment data 24, the maintenance data 26, and the specification of the discretization method of the values of the external environment received by the input unit 10, and the aging. Get the specification of the degradation function and the specification of the kernel function.

Next, in step S102, the parameter estimation unit 34, based on the input data D of all devices,

Is pre-calculated.

  In step S104, the calculation result of step S102, the failure time data 22 of the device to be analyzed, the external environment data 24 representing the external environment value at each time the device was exposed, and the device are executed. Maintenance data 26 representing a series of maintenance times, an aging deterioration function stored in an aging deterioration function storage unit 28, a discretization method stored in a discretization method storage unit 30, and a kernel function storage unit Based on the kernel function stored in 32, an estimation parameter including a parameter used in an aging deterioration function using the virtual age of the device as an argument and a deterioration rate for each of the discretized external environment values is estimated. .

In step S106, the parameter value estimated in step S104, a sequence of values {z _l } that can be taken by the external environment, and the kernel function k (y, y ′) are output by the output unit 40, and a parameter estimation processing routine is performed. Exit.

<Operation of the equipment failure prediction apparatus according to the first embodiment of the present invention>
Next, the operation of the device failure prediction apparatus 200 according to the first embodiment of the present invention will be described. When the input unit 50 receives input of the parameter value estimated by the parameter estimation device 100, a sequence of values {z _l } that can be taken by the external environment, and the kernel function k (y, y ′), the device failure prediction device 200 Is stored in the parameter value storage unit 62. When the input unit 50 receives the specification of the same aging deterioration function as that of the parameter estimation device 100, the equipment failure prediction device 200 stores it in the aging deterioration function storage unit 64. In addition, when the input unit 50 receives designation of the amount to be predicted, the device failure prediction apparatus 200 stores the prediction target storage unit 66. In addition, when the input unit 50 receives a value of the external environment scheduled to be exposed from the installation to the prediction period for each device, the device failure prediction apparatus 200 stores the value in the external environment information storage unit 68. When the input unit 50 receives a maintenance plan that is a series of maintenance times planned from the installation to the prediction period for each device, the device failure prediction apparatus 200 stores the maintenance plan in the maintenance plan storage unit 70. And the equipment failure prediction apparatus 200 performs the prediction process routine shown in FIG.

In step S150, the estimated parameter value received by the input unit 50, a sequence of values {z _l } that can be taken by the external environment, the kernel function k (y, y ′), the specification of the aging deterioration function, and the prediction Specify the quantity to be covered, the value of the external environment that is expected to be exposed from installation to the forecast period for each device, and the maintenance time planned for each device from the installation to the forecast period. Get series and.

  In step S152, the failure prediction unit 72 predicts the value of the amount to be predicted based on the data acquired in step S150.

  In step S154, the output unit 90 outputs the prediction value obtained in step S152 as a result, and ends the prediction processing routine.

  As described above, according to the parameter estimation apparatus according to the first embodiment, the virtual age of the device includes the deterioration rate, the external environment data, and the maintenance data for each of the discretized external environment values. The device failure rate is obtained by multiplying the value of the aging function by the time corresponding to the device's Virtual Age, and the device failure time and the failure rate. By estimating the estimated parameters so as to maximize the posterior probability of the estimated parameters including the parameter likelihood function, it is possible to estimate the parameters related to the failure of the equipment in consideration of the influence on the deterioration rate of the external environment. .

  In addition, according to the device failure prediction apparatus according to the first embodiment, by using the parameter related to the device failure estimated by the parameter estimation device in consideration of the influence on the deterioration rate of the external environment, Information or Virtual Age can be predicted with high accuracy.

  Moreover, the following effects can be acquired by predicting the failure probability according to the external environmental conditions to which the device is exposed and the maintenance plan. For example, by predicting the failure time, it is possible to prevent the system and service from being down. For example, it is possible to calculate the remaining life of a device, that is, the remaining life of the device, and perform maintenance immediately before that.

  In addition, in the equipment maintenance plan, it is possible to reduce the investment cost by targeting the equipment having a higher failure probability.

  Also, measures against the external environment can be examined by estimating the degree of influence of the deterioration rate of the equipment on the external environment (the degree of tolerance of the equipment). For example, it can be considered to set the room temperature to an appropriate temperature.

  In addition, by estimating the degree of influence of the deterioration rate of equipment on the external environment, it is possible to find a facility with an appropriate external environment. For example, when equipment is installed in a building, the deterioration rate of the equipment calculated from the room temperature and humidity of each room in the building can be evaluated, and each room can be scored based on the evaluation value. .

[Second Embodiment]
explain about. In addition, about the part which becomes the structure similar to 1st Embodiment, the same code | symbol is attached | subjected and description is abbreviate | omitted.

  The second embodiment is different from the first embodiment in that an optimum measure for minimizing cost and risk is searched from various external environments and maintenance plans.

<Overview>
As described in the first embodiment, a function representing a nonlinear relationship between the external environment and the deterioration rate is modeled using a Gaussian process (Non-Patent Document 4), so that a nonlinear function can be obtained from data. Estimate non-parametrically, ie without strongly assuming the shape of the function. The estimated nonlinear function is continuous with respect to the value of the external environment and does not require ad hoc quadrant division.

  With the above implementation, it is possible to predict the number of future failures and the associated repair costs as a function of the external environment. We propose a new cost function that adds the result and the cost generated from the control of the external environment to the conventional cost. By minimizing this cost function, optimization of measures including the set values of the external environment is realized.

<Configuration of Parameter Estimation Device According to Second Embodiment of the Present Invention>
As described in the first embodiment, the parameter estimation apparatus 100 according to the second embodiment includes parameters used in an aging function having an argument of the virtual age of the device, and a discretized external environment. Estimate the estimated parameters including the degradation rate for each of the values, and output the estimated parameter values, a sequence of values {z _l } that the external environment can take, and the kernel function k (y, y ′) used.

<Configuration of optimum measure searching apparatus according to second embodiment of the present invention>
As shown in FIG. 5, the optimum measure searching apparatus 300 according to the second embodiment includes an input unit 250, a calculation unit 260, and an output unit 90. The optimum measure searching apparatus 300 includes external environment information representing external environment values at each time when the device to be analyzed is scheduled to be exposed, a maintenance plan representing a series of maintenance times scheduled to be performed on the devices, At least one of these is searched for the optimum measure as a measure to be optimized.

<Estimated parameter value>
The input unit 250 receives input of the parameter value estimated by the parameter estimation device 100, a sequence of values {z _l } that can be taken by the external environment, and the kernel function k (y, y ′), and enters the parameter value storage unit 62. Store.

<Aging function>
The input unit 250 receives the same aging deterioration function designation as that of the parameter estimation device 100 and stores it in the aging deterioration function storage unit 64.

<Cost function specification>
The input unit 250 receives designation of a function that expresses the cost to be minimized, and stores it in the cost function storage unit 266. Functions that express costs vary depending on the situation assumed by each operator. Here, as an example, a case where the room temperature that is kept constant by air conditioning is the external environment, and the maintenance cost for a certain period of the device u is assumed as a cost function is given. C _p is the cost of one maintenance, C _f is the cost of one repair, C _α (y) is the air conditioning cost when the room temperature is kept y for a certain period,

Assuming that the number of maintenances in a certain period and N ^u _f is the expected value of the total number of failures in a certain period of equipment u, the maintenance cost for a certain period of equipment u is

... (18)

It is expressed. The expected value N ^u _f of the total number of failures varies depending on the maintenance plan (number of times and execution time) or the set temperature of the air conditioning, and the value can be calculated from the output of the parameter estimation device 100 (in the device failure prediction device 200). Example of quantity to be predicted (see expected value E ^u [N] in (1)). As a result, the maintenance cost of equation (18) is a complex function of the maintenance plan and the set air conditioning temperature. By searching for the maintenance plan that minimizes the maintenance cost of Equation (18) and the set air conditioning temperature as external environment information according to the designation of the measure to be optimized, which will be described later, the optimum measure can be found. .

<Designation of measures to optimize and setting of other measures>
The input unit 250 receives designation of a measure to be optimized (indicated as ρ ^u ) among measures that affect the cost function stored in the cost function storage unit 266, and stores it in the measure storage unit 268. In the above cost function example, the measures that affect the cost function are the maintenance plan (number of times and execution time) and the air conditioning setting temperature as external environment information, and the options for the optimization measures are the maintenance plan and air conditioning settings. Temperature and / or temperature. If only one of the targets is to be optimized, the value of the other measure is input as the setting value for the other measure.

  The calculation unit 260 includes a parameter value storage unit 62, an aged deterioration function storage unit 64, a cost function storage unit 266, a measure storage unit 268, a failure prediction unit 272, an optimum measure search unit 274, and a minimum cost value and optimum measure storage unit. 276.

The failure prediction unit 272 is scheduled to be performed on the external environment information indicating the external environment value at each time when the device is exposed to each measure candidate for the measure to be optimized, and on the device. Each of the parameters used in the aging degradation function using the virtual age of the device as an argument, estimated by the parameter estimation device 100 based on the maintenance plan representing the maintenance time series, and the discretized external environment value The information about the failure of the equipment is predicted using the estimation parameters including the deterioration rate with respect to. For example, the expected value E ^u [N] of the number of failures in a specific period [Q ^u ₀ , Q ^u ₁ ] in the future is predicted as the expected value N ^u _f of the total number of failures. Here, the external environment information representing the external environment value at each time when the device is to be exposed is external environment information determined for the measure candidate or set as another measure. In addition, the maintenance plan representing the maintenance time series scheduled for the device is a maintenance plan determined for the measure candidate or set as another measure.

  The optimum measure searching unit 274 is a measure for minimizing a predetermined cost function including information related to device failure based on information related to device failure predicted by the failure prediction unit 272 for each of the measure candidates. Determine any of the candidate measures.

  Specifically, as shown in the following formula (19), a policy candidate that minimizes the cost function stored in the cost function storage unit 266 is searched from the policy candidates for the policy to be optimized. Measures are searched for each device u ∈ {1, 2, ..., U}.

... (19)

<Minimum cost value and optimal measures>
The minimum cost value and optimum measure storage unit 276 stores the minimum cost value COST ^u (ρ _u ^* ) searched for each device by the optimum measure search unit 274 and the measure ρ _u ^* that realizes the minimum cost value COST ^u (ρ _u ^* ). The minimum cost value COST ^u (ρ _u ^* ) stored in the value and optimum measure storage unit 276 and the measure ρ _u ^* that realizes the minimum cost value are output by the output unit 90. Table 4 shows an output example.

  The above example is an output example when the optimization target measure is room temperature.

<Operation of Parameter Estimation Device According to Second Embodiment of the Present Invention>
Next, the parameter estimation apparatus 100 according to the second embodiment of the present invention executes the parameter estimation processing routine shown in FIG. 3 as in the first embodiment.

<Operation of the optimum measure searching apparatus according to the second embodiment of the present invention>
Next, the operation of the optimum measure searching apparatus 300 according to the second embodiment of the present invention will be described. When the input unit 250 receives input of the parameter value estimated by the parameter estimation device 100, the sequence of values {z _l } that the external environment can take, and the kernel function k (y, y ′), the optimal measure search device 300 is received. Is stored in the parameter value storage unit 62. When the input unit 250 receives the specification of the same aging deterioration function as that of the parameter estimation device 100, the optimum measure searching device 300 stores it in the aging deterioration function storage unit 64. In addition, when the input unit 250 receives the specification of the cost function, the optimum measure searching apparatus 300 stores the cost function in the cost function storage unit 266. In addition, when the input unit 250 receives designation of a measure to be optimized and setting of another measure, the optimum measure searching apparatus 300 stores the measure in the measure storage unit 268. And the optimal measure search apparatus 300 performs the optimal measure search process routine shown in FIG.

In step S250, the estimated parameter value received by the input unit 250, a sequence of values {z _l } that can be taken by the external environment, the kernel function k (y, y ′), the specification of the aging function, and the cost Get function specification, specification of measures to optimize, and setting of other measures.

  In step S252, the failure prediction unit 272 predicts information related to a device failure for each of the measure candidates for the measure to be optimized based on the data acquired in step S250.

  In step S254, using the predicted value predicted for each measure candidate in step S252, one of the measure candidates is determined as a measure that minimizes the designated cost function.

  In step S256, the output unit 90 outputs the measure for minimizing the cost function determined in step S254 and the cost value as a result, and ends the optimum measure search processing routine.

  As described above, according to the optimum measure searching apparatus according to the second embodiment, by using the parameter relating to the failure of the equipment estimated by the parameter estimation apparatus 100 in consideration of the influence on the deterioration rate of the external environment. Since it is possible to accurately predict information related to device failure for each measure candidate, it is possible to search for the optimum measure in consideration of the influence on the deterioration rate of the external environment.

  In addition, for example, maintenance that maximizes cost control and risk avoidance for equipment installed at places where travel costs are high, such as islands and mountainous areas, or where emergency driving is difficult It can be expected to determine the timing.

  The present invention is not limited to the above-described embodiment, and various modifications and applications can be made without departing from the gist of the present invention.

  For example, although the case where the parameter estimation apparatus 100 and the equipment failure prediction apparatus 200 are configured as separate apparatuses has been described as an example in the first embodiment, the parameter estimation apparatus 100 and the equipment failure prediction apparatus 200 are set to 1 You may comprise as one apparatus.

  Moreover, although the case where the parameter estimation device 100 and the optimum measure searching device 300 are configured as separate devices has been described as an example in the second embodiment, the parameter estimating device 100 and the optimum measure searching device 300 are set to one. You may comprise as one apparatus.

  Moreover, although the parameter estimation apparatus 100, the equipment failure prediction apparatus 200, and the optimum measure search apparatus 300 described above have a computer system therein, the “computer system” may be a case where a WWW system is used. For example, the homepage provision environment (or display environment) is also included.

  In the present specification, the embodiment has been described in which the program is installed in advance. However, the program can be provided by being stored in a computer-readable recording medium.

10, 50, 250 Input unit 20, 60, 260 Calculation unit 22 Failure time data 24 External environment data 26 Maintenance data 28, 64 Aged deterioration function storage unit 30 Discretization method storage unit 32 Kernel function storage unit 34 Parameter estimation unit 36, 62 Parameter value storage unit 40, 90 Output unit 66 Prediction target storage unit 68 External environment information storage unit 70 Maintenance plan storage unit 72, 272 Failure prediction unit 74 Prediction value storage unit 100 Parameter estimation device 200 Equipment failure prediction device 266 Cost function storage Unit 268 Measure storage unit 274 Optimal measure search unit 276 Optimal measure storage unit 300 Optimal measure search device

Claims (8)

Failure time data of the device to be analyzed, external environment data representing the external environment value at each time the device was exposed, maintenance data representing a sequence of maintenance times performed on the device, A parameter estimation unit for estimating an estimation parameter including a predetermined parameter used in an aging degradation function using the virtual age of the device as an argument and a degradation rate for each of the discretized external environment values Because
The virtual age of the device is expressed using the degradation rate for each of the discretized external environment values, the external environment data, and the maintenance data.
When the failure rate of the device is obtained by multiplying the value of the aging function by a time corresponding to the virtual age of the device, the failure rate of the device is represented using the failure time and the failure rate. A parameter estimation device including a parameter estimation unit that estimates the estimated parameter so as to maximize the posterior probability of the estimated parameter including the likelihood function of the estimated parameter.   The parameter estimation device according to claim 1, wherein the parameter estimation unit estimates a deterioration rate for each of the discretized external environment values according to a stochastic process of a nonlinear regression function. Claimed on the basis of external environment information representing the external environment value at each time when the device to be analyzed is scheduled to be exposed, and a maintenance plan representing a series of maintenance times scheduled for the device. Using estimation parameters including parameters used in an aging degradation function using the virtual age of the device as an argument, estimated by the parameter estimation device according to 1 or 2, and degradation rates for each of the discretized external environment values A device failure prediction apparatus including a failure prediction unit that predicts information related to device failure or Virtual Age. Optimizing at least one of external environment information representing the external environment value at each time when the device to be analyzed is scheduled to be exposed and a maintenance plan representing a series of maintenance times scheduled for the device. As a measure to be optimized, it is an optimum measure search device that searches for an optimum measure,
A series of external environment information representing the external environment value at each time when the device is to be exposed to each of the measure candidates for the measure to be optimized, and the time of maintenance scheduled to be performed on the device And a parameter used in an aging function using the virtual age of the device as an argument, estimated by the parameter estimation device according to claim 1, and a discretized external environment value A failure prediction unit that predicts information related to the failure of the device using an estimation parameter including a degradation rate for each of the
The measure candidate as a measure for minimizing a predetermined cost function including information related to the failure of the device based on information related to the failure of the device predicted for each of the measure candidates by the failure prediction unit An optimum measure searching device including an optimum measure searching unit for determining any of the above. A parameter estimation unit includes a failure time data of a device to be analyzed, external environment data representing an external environment value at each time when the device was exposed, and a series of times of maintenance performed on the device. And an estimated parameter including a parameter used in a predetermined aging deterioration function using the virtual age of the device as an argument and a deterioration rate for each of the discretized external environment values based on the maintenance data to be expressed. To estimate,
The virtual age of the device is expressed using the degradation rate for each of the discretized external environment values, the external environment data, and the maintenance data.
When the failure rate of the device is obtained by multiplying the value of the aging function by a time corresponding to the virtual age of the device, the failure rate of the device is represented using the failure time and the failure rate. A parameter estimation method comprising: estimating the estimation parameter so as to maximize the posterior probability of the estimation parameter including a likelihood function of the estimation parameter. The failure prediction unit includes external environment information representing the external environment value at each time when the device to be analyzed is scheduled to be exposed, and a maintenance plan representing a series of maintenance times scheduled for the device. Based on the parameter estimation method according to claim 5, the estimation includes a parameter used in an aging degradation function using the virtual age of the device as an argument, and a degradation rate for each of the discretized external environment values. A device failure prediction method for predicting information on a failure of the device or a virtual age using a parameter. Optimizing at least one of external environment information representing the external environment value at each time when the device to be analyzed is scheduled to be exposed and a maintenance plan representing a series of maintenance times scheduled for the device. As a measure to be optimized, it is an optimum measure search method in an optimum measure search device that searches for an optimum measure,
The failure prediction unit is scheduled to be implemented on the device with external environment information representing the external environment value at each time the device is scheduled to be exposed to each measure candidate for the measure to be optimized. Based on a maintenance plan representing a maintenance time series, parameters used in an aged deterioration function using the virtual age of the device as an argument, estimated by the parameter estimation method according to claim 5, and discretized Predict information about the equipment failure using estimated parameters including degradation rates for each of the external environmental values,
The optimum measure searching unit minimizes a predetermined cost function including information related to the device failure based on the information related to the device failure predicted for each of the measure candidates by the failure prediction unit. As a measure, an optimal measure search method that determines any of the candidate measures.   A program for causing a computer to function as each part constituting the parameter estimation device according to claim 1, the device failure prediction device according to claim 3, or the optimum measure searching device according to claim 4.