CN112329253A - Workpiece life prediction method and device and storage medium - Google Patents

Workpiece life prediction method and device and storage medium Download PDF

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CN112329253A
CN112329253A CN202011264974.2A CN202011264974A CN112329253A CN 112329253 A CN112329253 A CN 112329253A CN 202011264974 A CN202011264974 A CN 202011264974A CN 112329253 A CN112329253 A CN 112329253A
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王开业
谭启涛
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Chengdu Aerospace Science And Industry Big Data Research Institute Co ltd
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Abstract

The invention discloses a method, a device and a storage medium for predicting the service life of a workpiece, which relate to the field of workpiece prediction and maintenance and comprise the following steps: acquiring degradation data of a workpiece; modeling a linear wiener process by adopting random parameters to obtain prior distribution taking normal gamma distribution as a mean parameter and a drift parameter; combining the prior distribution, and obtaining a posterior estimated value according to the prior distribution which takes the normal gamma distribution as a mean parameter and a drift parameter; combining Bayes theory and posterior estimation value, adopting EM algorithm iteration solution to obtain estimation value; and obtaining a predicted value of the service life of the workpiece and a predicted value of the residual service life of the workpiece according to the estimated value and the failure threshold value of the workpiece. The invention provides a method for quickly and efficiently predicting the service life and the residual service life by combining a Wiener process, a Bayes theory and an EM (effective electromagnetic) algorithm aiming at a degraded and failed product, and further provides a basis for measures such as predictive maintenance, maintenance and replacement of the product.

Description

Workpiece life prediction method and device and storage medium
Technical Field
The invention relates to the field of workpiece prediction and maintenance, in particular to a method and a device for predicting the service life of a workpiece and a storage medium.
Background
For core components such as machine tools, weaponry and the like, the components are generally complex to manufacture and expensive, and once the equipment fails, shutdown and production halt are caused, huge economic loss is caused. Due to the importance of the replacement, the core components are generally replaced periodically in practice, and if the life and the remaining life of the core components can be predicted, the replacement has great significance for predictive maintenance, replacement and the like of the core components.
Since such parts are generally replaced in advance, the failure time of the parts cannot be observed, that is, the 'life' data cannot be observed; however, such a method generally observes that a certain performance index directly related to the lifetime shows a certain trend from the beginning of the product to the end of the lifetime, which is called "degradation data", and is commonly referred to as corrosion strength, wear degree, humidity, and the like.
For degradation data, a degradation track method is generally adopted to describe a degradation process at present, namely a linear curve and a polynomial curve are used for fitting the degradation track, the estimation method is simple, products have certain randomness due to differences of original materials, production procedures, external operating environments and the like in practice, the degradation process has slight difference, the simple degradation curve method cannot meet the actual requirements, the service life and the residual service life are easily subjected to error evaluation, and then wrong decisions are made on predictive maintenance, replacement and the like of the products.
Disclosure of Invention
The invention provides a method, a device and a storage medium for workpiece life prediction, and provides a method for efficiently and quickly estimating the product life and the residual life by combining a Wiener process and an EM (effective electromagnetic) algorithm.
The technical scheme adopted by the invention is as follows:
in a first aspect, the present invention provides a method for predicting a lifetime of a workpiece, comprising the steps of:
acquiring degradation data of a workpiece;
modeling a linear wiener process by adopting random parameters to obtain prior distribution taking normal gamma distribution as a mean parameter and a drift parameter;
combining the prior distribution, and adopting an EM algorithm to carry out iterative solution to obtain an estimated value;
and obtaining a predicted value of the service life of the workpiece and a predicted value of the residual service life of the workpiece according to the estimated value and the failure threshold value of the workpiece.
Further, combining the prior distribution, adopting an EM algorithm to iteratively solve, and obtaining an estimated value comprises the following steps: obtaining a posterior estimated value according to the prior distribution which takes the normal gamma distribution as a mean parameter and a drift parameter; and combining the posterior estimated value and the EM algorithm for iterative solution.
Further, the method of using normal gamma distribution as the prior distribution of the mean parameter and the drift parameter is as follows:
assuming that the number of samples is n, each sample is at an initial time ti0The degradation value y is 0i0＝0，yi1,yi2,…,yimRespectively represents the m times t of the sample ii1,ti2,…,timAmount of degradation, Δ yijDenotes the sample i at time ti(j-1)To time tijDelta of degradation between, Δ yij＝yij-yi(j-1)Wherein j is 1,2, …, m; i is 1,2, …, n, m and n are positive integers, Δ tijRepresenting the sample i at time ti(j-1)To time tijTime interval therebetween, Δ tij＝tij-ti(j-1)；
Let the mean parameter be u and the drift parameter be2(ii) a From the conjugate distribution Bayes equation, assume u and σ2Are both unknown but related; the joint prior distribution is constructed as follows;
the joint distribution consists of two parts:
Figure BDA0002775776450000031
wherein, a, b, c and d are characteristic parameters of the random parameter distribution, which are abbreviated as superparameters, N is positive-Tai distribution, Gamma represents Gamma distribution, and constant z is 1/sigma2Gamma obeying parameters a and bCarrying out Ma distribution; knowing that the distribution of u after z obeys a positive-Tai distribution with parameter c and parameter d/z;
combining prior distribution to obtain normal-gamma distribution N-Ga of z and u obeying parameters (a, b) and (c, d/z), which are abbreviated as:
(z,u)～N-Ga(a,b；c,d/z)，
wherein z is 1/sigma2So that z is 1/σ2Is expressed as a probability density function PDF
Figure BDA0002775776450000032
exp is an exponential function with a natural constant e as a base, and Γ (a) is a gamma function formula;
the probability density function PDF of u under the known z condition is expressed as:
Figure BDA0002775776450000033
when h times of actual degradation data y of one workpiece are obtained, obtaining the actual degradation data y (y ═ y)1,y2,…,yh) Then, the joint posterior estimate can be represented by the conjugate distribution Bayes equation, with the known y the joint posterior density function of u and z being:
Figure BDA0002775776450000034
pi (u, z | y) represents a joint posterior density function with respect to u and z in the case where actual degraded data y is observed, L (y | u, z) represents a maximum likelihood function of a sample with respect to u and z in the case where actual degraded data y is observed, and L (y | u, z) is:
Figure BDA0002775776450000041
pi is the operator of taking product, Δ yr＝yr-yr-1,Δtr＝tr-tr-1,r＝1,2,…,h，yrRepresenting the r-th actual degradation data among the h actual degradation data; t is trRepresenting the time t corresponding to the r-th actual degradation data in the h actual degradation data;
substituting into the posterior density function formula (1) to obtain
Figure BDA0002775776450000042
Pi is the operator of taking product, Δ yr＝yr-yr-1,Δtr＝tr-tr-1,r＝1,2,…,h；
Substituting into the posterior density function formula (1), and calculating by proportional ratio
Figure BDA0002775776450000043
The posterior joint distribution of the random parameter still has the same distribution type as the prior joint distribution, and the difference is only the change of the hyper-parameter, so the joint posterior density depends on the u and z obedience parameters (a) under the condition of knowing y by the property of conjugate distribution*,b*) And parameter (c)*,d*Z) positive gamma distribution, can be obtained
u,z|y～N-Ga(a*,b*；c*,d*/z)，
Wherein, a*,b*,c*,d*Representing a posteriori estimates of said hyper-parameters a, b, c, d, respectively, given the actual degradation data y,
thus, the posterior estimates of the hyper-parameters are:
Figure BDA0002775776450000051
further, the method for obtaining the estimated value by adopting the EM algorithm to carry out iterative solution and combining the prior distribution is as follows,
according to the EM algorithm, the likelihood function for a full sample is:
Figure BDA0002775776450000052
thus, a full log-likelihood function containing Ω ═ (a, b, c, d):
Figure BDA0002775776450000053
obtaining a maximum likelihood estimation value of the hyperparameter by the formula, wherein the maximum likelihood estimation value of a
Figure BDA0002775776450000061
Solved by the following markets:
Figure BDA0002775776450000062
where ψ is a digamma distribution function, ψ (x) ═ ln Γ (x)]',miIs a number m, z of measured values representing a workpiece iiIs the z value representing the workpiece i; (ii) a
Maximum likelihood estimate of b
Figure BDA0002775776450000063
Maximum likelihood estimate of c
Figure BDA0002775776450000064
Maximum likelihood estimate of d
Figure BDA0002775776450000065
The expression of (a) is:
Figure BDA0002775776450000066
randomly giving a group of initial values of the hyper-parameters, and solving by using an EM algorithm, wherein the EM algorithm comprises a step E and a step M;
in step E, it is necessary to determine the posterior including the hidden variable dataExpected values, including E (z)i)，E(lnzi)，E(uizi)，
Figure BDA0002775776450000067
Assuming a value of the hyperparametric parameter of degree l
Figure BDA0002775776450000068
The value of the super parameter is
Figure BDA0002775776450000069
Substituting the expression of the posterior estimated value to obtain the following expression of the posterior expected value
Figure BDA0002775776450000071
In the step M, substituting the expected values into iterative formulas (2) and (3) of the parameters to obtain an estimated value of the iteration in the step l + 1:
Figure BDA0002775776450000072
after m iterations, if
Figure BDA0002775776450000073
And
Figure BDA0002775776450000074
the distance between them reaches a predetermined accuracy
Figure BDA0002775776450000075
I.e. an estimate of the hyper-parameter (a, b, c, d).
Further, a method for obtaining a predicted value of the life of the workpiece based on the estimated value and the failure threshold of the workpiece is as follows,
from the estimated values, the average life can be found to be:
Figure BDA0002775776450000081
wherein: z is 1/sigma2～Gamma(a*,b*),u|z～N(c*,d*/z),
Figure BDA0002775776450000082
Wherein D is the failure threshold.
Further, the method for obtaining the predicted value of the residual life of the workpiece according to the estimated value and the failure threshold value of the workpiece is as follows,
the remaining life at any time t, t >0 is:
Figure BDA0002775776450000083
wherein:
Figure BDA0002775776450000084
Figure BDA0002775776450000085
d is a failure threshold value, and x is a probability density value.
In a second aspect, the present invention provides an apparatus for predicting a lifetime of a workpiece, comprising a degraded data obtaining unit, a prior distribution calculating unit, an estimated value obtaining unit, a predicted value of a lifetime of a workpiece calculating unit, and a predicted value of a remaining lifetime of a workpiece calculating unit,
the degradation data acquisition unit is used for acquiring degradation data of the workpiece;
the prior distribution calculating unit adopts random parameters to model a linear wiener process to obtain prior distribution taking normal gamma distribution as a mean parameter and a drift parameter;
the estimation value acquisition unit is used for combining the prior distribution and adopting an EM algorithm to carry out iterative solution to acquire an estimation value;
the workpiece life predicted value calculating unit obtains a workpiece life predicted value and a workpiece residual life predicted value according to the estimated value and the failure threshold value of the workpiece;
and the predicted value calculation unit of the residual life of the workpiece obtains the predicted value of the residual life of the workpiece according to the estimated value and the failure threshold value of the workpiece.
The system further comprises a posterior estimated value calculation unit, wherein the posterior estimated value calculation unit obtains a posterior estimated value according to the prior distribution which takes the normal gamma distribution as the mean parameter and the drift parameter.
In a third aspect, the present invention provides an apparatus for workpiece life prediction, comprising a memory, a processor and a transceiver connected in sequence, wherein the memory is used for storing a computer program, the transceiver is used for transmitting and receiving messages, and the processor is used for reading the computer program and executing the method according to the first aspect.
In a fourth aspect, the present invention provides a computer readable storage medium having stored thereon instructions which, when run on a computer, perform the method according to the first aspect.
The invention has the following advantages and beneficial effects:
1. the invention provides a method for quickly and efficiently predicting the service life and the residual service life by combining a Wiener process, a Bayes theory and an EM (effective electromagnetic) algorithm aiming at a degraded and failed product, and further provides a basis for measures such as predictive maintenance, maintenance and replacement of the product.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a block diagram of the apparatus of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments of the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises," "comprising," "includes," and/or "including," when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, numbers, steps, operations, elements, components, and/or groups thereof; the term "and/or" herein is merely an association describing an associated object, meaning that three relationships may exist, e.g., a and/or B, may mean: a exists alone, B exists alone, and A and B exist at the same time, and the term "/and" is used herein to describe another association object relationship, which means that two relationships may exist, for example, A/and B, may mean: a alone, and both a and B alone, and further, the character "/" in this document generally means that the former and latter associated objects are in an "or" relationship.
It should also be noted that, in some alternative implementations, the functions/acts noted may occur out of the order noted in the figures. For example, two figures shown in succession may, in fact, be executed substantially concurrently, or the figures may sometimes be executed in the reverse order, depending upon the functionality/acts involved.
It should be understood that specific details are provided in the following description to facilitate a thorough understanding of example embodiments. However, it will be understood by those of ordinary skill in the art that the example embodiments may be practiced without these specific details. For example, systems may be shown in block diagrams in order not to obscure the examples in unnecessary detail. In other instances, well-known processes, structures and techniques may be shown without unnecessary detail in order to avoid obscuring example embodiments.
As shown in fig. 1, the present embodiment provides, in a first aspect, a method for predicting a lifetime of a workpiece, including the steps of:
acquiring degradation data of a workpiece;
modeling a linear wiener process by adopting random parameters to obtain prior distribution taking normal gamma distribution as a mean parameter and a drift parameter;
combining the prior distribution, and adopting an EM algorithm to carry out iterative solution to obtain an estimated value;
and obtaining a predicted value of the service life of the workpiece and a predicted value of the residual service life of the workpiece according to the estimated value and the failure threshold value of the workpiece.
In specific implementation, the prior distribution is combined, an EM algorithm is adopted for iterative solution, and the method for obtaining the estimated value comprises the following steps: obtaining a posterior estimated value according to the prior distribution which takes the normal gamma distribution as a mean parameter and a drift parameter; and combining the posterior estimated value and the EM algorithm for iterative solution.
In specific implementation, the method using normal gamma distribution as the prior distribution of the mean parameter and the drift parameter is as follows:
assuming that the number of samples is n, each sample is at an initial time ti0The degradation value y is 0i0＝0，yi1,yi2,…,yimRespectively represents the m times t of the sample ii1,ti2,…,timAmount of degradation, Δ yijDenotes the sample i at time ti(j-1)To time tijDelta of degradation between, Δ yij＝yij-yi(j-1)Wherein j is 1,2, …, m; i is 1,2, …, n, m and n are positive integers, Δ tijRepresenting the sample i at time ti(j-1)To time tijTime interval therebetween, Δ tij＝tij-ti(j-1)；
Let the mean parameter be u and the drift parameter be2(ii) a From the conjugate distribution Bayes equation, assume u and σ2Are both unknown but related; the joint prior distribution is constructed as follows;
the joint distribution consists of two parts:
Figure BDA0002775776450000111
wherein, a, b, c and d are characteristic parameters of the random parameter distribution, which are abbreviated as superparameters, N is positive-Tai distribution, Gamma represents Gamma distribution, and constant z is 1/sigma2Obeying a gamma distribution with a parameter a and a parameter b; knowing that the distribution of u after z obeys a positive-Tai distribution with parameter c and parameter d/z;
the joint prior distribution is defined as a normal-gamma distribution, abbreviated as:
(z,u)～N-Ga(a,b；c,d/z)，
wherein z is 1/sigma2So that z is 1/σ2Is expressed as a probability density function PDF
Figure BDA0002775776450000121
exp is an exponential function with a natural constant e as a base, and Γ (a) is a gamma function formula;
the probability density function PDF of u under the known z condition is expressed as:
Figure BDA0002775776450000122
when h times of actual degradation data y of one workpiece are obtained, obtaining the actual degradation data y (y ═ y)1,y2,…,yh) Then, the joint posterior estimate can be represented by the conjugate distribution Bayes equation, with the known y the joint posterior density function of u and z being:
Figure BDA0002775776450000123
pi (u, z | y) represents a joint posterior density function with respect to u and z in the case where actual degraded data y is observed, L (y | u, z) represents a maximum likelihood function of a sample with respect to u and z in the case where actual degraded data y is observed, and L (y | u, z) is:
Figure BDA0002775776450000131
pi is the operator of taking product, Δ yr＝yr-yr-1,Δtr＝tr-tr-1,r＝1,2,…,h，yrRepresenting the r-th actual degradation data among the h actual degradation data; t is trRepresenting the time t corresponding to the r-th actual degradation data in the h actual degradation data;
substituting into the posterior density function formula (1) to obtain
Figure BDA0002775776450000132
The posterior joint distribution of the random parameters and the prior joint distribution still have the same distribution type, and the difference is only the change of the hyper-parameters, so that the joint posterior density:
u,z|y～N-Ga(a*,b*；c*,d*/z)，
the posterior estimated values of the hyper-parameters are respectively as follows:
Figure BDA0002775776450000133
in the implementation, the EM algorithm is adopted for iterative solution, the prior distribution is combined, the method for obtaining the estimated value is as follows,
according to the EM algorithm, the likelihood function for a full sample is:
Figure BDA0002775776450000141
thus, a full log-likelihood function containing Ω ═ (a, b, c, d):
Figure BDA0002775776450000142
obtaining a maximum likelihood estimation value of the hyperparameter by the formula, wherein the maximum likelihood estimation value of a
Figure BDA0002775776450000143
Solved by the following markets:
Figure BDA0002775776450000144
where ψ is a digamma distribution function, ψ (x) ═ ln Γ (x)]'，miIs a number m, z of measured values representing a workpiece iiIs the z value representing the workpiece i;
maximum likelihood estimate of b
Figure BDA0002775776450000145
Maximum likelihood estimate of c
Figure BDA0002775776450000146
Maximum likelihood estimate of d
Figure BDA0002775776450000147
The expression of (a) is:
Figure BDA0002775776450000151
randomly giving a group of initial values of the hyper-parameters, and solving by using an EM algorithm, wherein the EM algorithm comprises a step E and a step M;
in step E, it is necessary to find the A posteriori expectation values including the hidden variable data, including E (z)i)，E(lnzi)，E(uizi)，
Figure BDA0002775776450000152
Assuming a value of the hyperparametric parameter of degree l
Figure BDA0002775776450000153
The value of the super parameter is
Figure BDA0002775776450000154
Substituting the expression of the posterior estimated value to obtain the following expression of the posterior expected value
Figure BDA0002775776450000155
In step M, substituting the above expectation values into iterative formulas (2) and (3) of the parameters to obtain an estimate value of the iteration of step l + 1:
Figure BDA0002775776450000161
after m iterations, if
Figure BDA0002775776450000162
And
Figure BDA0002775776450000163
the distance between them reaches a predetermined accuracy
Figure BDA0002775776450000164
I.e. an estimate of the hyper-parameter (a, b, c, d).
In practice, the method for obtaining the predicted value of the service life of the workpiece according to the estimated value and the failure threshold value of the workpiece is as follows,
from the estimated values, the average life can be found to be:
Figure BDA0002775776450000165
wherein z is 1/sigma2～Gamma(a*,b*),u|z～N(c*,d*/z),
Figure BDA0002775776450000166
Wherein D is the failure threshold.
Further, the method for obtaining the predicted value of the residual life of the workpiece according to the estimated value and the failure threshold value of the workpiece is as follows,
the remaining life at any time t, t >0 is:
Figure BDA0002775776450000171
wherein:
Figure BDA0002775776450000172
Figure BDA0002775776450000173
d is a failure threshold value, and x is a probability density value.
In a second aspect, as shown in fig. 2, the present embodiment provides an apparatus for predicting a life of a workpiece, comprising a degradation data obtaining unit, a prior distribution calculating unit, an estimated value obtaining unit, a predicted value of a life of a workpiece calculating unit, and a predicted value of a remaining life of a workpiece calculating unit, wherein,
the degradation data acquisition unit is used for acquiring degradation data of the workpiece;
the prior distribution calculating unit adopts random parameters to model a linear wiener process to obtain prior distribution taking normal gamma distribution as a mean parameter and a drift parameter;
the estimation value acquisition unit is used for combining the prior distribution and adopting an EM algorithm to carry out iterative solution to acquire an estimation value;
the workpiece life predicted value calculating unit obtains a workpiece life predicted value and a workpiece residual life predicted value according to the estimated value and the failure threshold value of the workpiece;
and the predicted value calculation unit of the residual life of the workpiece obtains the predicted value of the residual life of the workpiece according to the estimated value and the failure threshold value of the workpiece.
When the method is implemented, the method further comprises a posterior estimated value calculation unit, and the posterior estimated value calculation unit obtains the posterior estimated value according to the prior distribution which takes the normal gamma distribution as the mean parameter and the drift parameter.
In a third aspect, the present embodiment provides an apparatus for workpiece life prediction, comprising a memory, a processor and a transceiver connected in sequence, wherein the memory is used for storing a computer program, the transceiver is used for sending and receiving messages, and the processor is used for reading the computer program and executing the method according to the first aspect.
For example, the Memory may include, but is not limited to, a Random Access Memory (RAM), a Read Only Memory (ROM), a Flash Memory (Flash Memory), a First In First Out (FIFO) Memory, and/or a First In Last Out (FILO) Memory, and the like; the processor may not be limited to the use of a microprocessor model number STM32F105 family; the transceiver may be, but is not limited to, a Wireless Fidelity (WiFi) Wireless transceiver, a bluetooth Wireless transceiver, a General Packet Radio Service (GPRS) Wireless transceiver, a ZigBee protocol (ZigBee) Wireless transceiver, and/or the like. In addition, the device may include, but is not limited to, a power module, a display screen, and other necessary components.
In a fourth aspect, the present invention provides a computer readable storage medium having stored thereon instructions which, when run on a computer, perform the method according to the first aspect.
A fifth aspect of the present embodiment provides a computer-readable storage medium, on which instructions are stored, and when the instructions are executed on a computer, the method for generating data of a jira system according to the first aspect or any one of the possible designs of the first aspect is executed. The computer-readable storage medium refers to a carrier for storing data, and may include, but is not limited to, floppy disks, optical disks, hard disks, flash memories, flash disks and/or Memory sticks (Memory sticks), etc., and the computer may be a general purpose computer, special purpose computer, computer network, or other programmable device.
For the working process, the working details, and the technical effects of the computer-readable storage medium provided in this embodiment, reference may be made to the first aspect of the embodiment, which is not described herein again.
The present invention provides a computer program product comprising instructions which, when run on a computer, cause the computer to perform the secure encryption method of the multimedia control system according to the first aspect of the embodiments or the second aspect of the embodiments, wherein the computer may be a general purpose computer, a special purpose computer, a computer network, or other programmable device.
The embodiments described above are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device to perform the methods described in the embodiments or some portions of the embodiments.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A method of workpiece life prediction, comprising the steps of:
acquiring degradation data of a workpiece;
modeling a linear wiener process by adopting random parameters to obtain prior distribution taking normal gamma distribution as a mean parameter and a drift parameter;
combining the prior distribution, and adopting an EM algorithm to carry out iterative solution to obtain an estimated value;
and obtaining a predicted value of the service life of the workpiece and a predicted value of the residual service life of the workpiece according to the estimated value and the failure threshold value of the workpiece.
2. The method of claim 1, wherein the prior distribution is combined and iteratively solved by using an EM algorithm, and the method of obtaining the estimated value is: obtaining a posterior estimated value according to the prior distribution which takes the normal gamma distribution as a mean parameter and a drift parameter; and combining the posterior estimated value and the EM algorithm for iterative solution.
3. The method of claim 2, wherein the linear wiener process is modeled by random parameters, and the normal gamma distribution is used as the prior distribution of the mean parameter and the drift parameter, and the method comprises the following steps:
assuming that the number of samples is n, each sample is at an initial time ti0The degradation value y is 0i0＝0，yi1,yi2,…,yimRespectively represents the m times t of the sample ii1,ti2,…,timAmount of degradation, Δ yijDenotes the sample i at time ti(j-1)To time tijDelta of degradation between, Δ yij＝yij-yi(j-1)Wherein j is 1,2, …, m; i is 1,2, …, n, m and n are positive integers, Δ tijRepresenting the sample i at time ti(j-1)To time tijTime interval therebetween, Δ tij＝tij-ti(j-1)；
Let the mean parameter be u and the drift parameter be2(ii) a From the conjugate distribution Bayes equation, assume u and σ2Are both unknown but related; the joint prior distribution is constructed by;
the joint distribution consists of two parts:
Figure FDA0002775776440000021
a, b, c and d are characteristic parameters of the random parameter distribution, which are abbreviated as hyper-parameters, N is positive-Tai distribution, Gamma represents Gamma distribution, and constant z is 1/sigma2Obeying a gamma distribution with a parameter a and a parameter b; knowing that the distribution of u after z obeys a positive-Tai distribution with parameter c and parameter d/z;
combining prior distribution to obtain normal-gamma distribution N-Ga of z and u obeying parameters (a, b) and (c, d/z), which are abbreviated as:
(z,u)～N-Ga(a,b；c,d/z)，
wherein z is 1/sigma2So that z is 1/σ2Is expressed as a probability density function PDF
Figure FDA0002775776440000022
exp is an exponential function with a natural constant e as a base, and Γ (a) is a gamma function formula;
the probability density function PDF of u under the known z condition is expressed as:
Figure FDA0002775776440000023
when h times of actual degradation data y of one workpiece are obtained, the actual degradation data y is equal to (y)1,y2,…,yh) Wherein the joint posterior estimate may be represented by the conjugate distribution Bayes formula, where the joint posterior density function of u and z given y is:
Figure FDA0002775776440000024
pi (u, z | y) represents a joint posterior density function with respect to u and z in the case where actual degraded data y is observed, L (y | u, z) represents a maximum likelihood function of a sample with respect to u and z in the case where actual degraded data y is observed, and L (y | u, z) is:
Figure FDA0002775776440000031
pi is the operator of taking product, Δ yr＝yr-yr-1,Δtr＝tr-tr-1,r＝1,2,…,h，yrRepresenting the r-th actual degradation data among the h actual degradation data; t is trRepresenting the time t corresponding to the r-th actual degradation data in the h actual degradation data;
substituting into the posterior density function formula (1), and calculating by proportional ratio
Figure FDA0002775776440000032
The posterior joint distribution of the random parameter still has the same distribution type as the prior joint distribution, and the difference is only the change of the hyper-parameter, so the joint posterior density depends on the u and z obedience parameters (a) under the condition of knowing y by the property of conjugate distribution*,b*) And parameter (c)*,d*Z) positive gamma distribution, can be obtained
u,z|y～N-Ga(a*,b*；c*,d*/z)，
Wherein, a*,b*,c*,d*Representing a posteriori estimates of said hyper-parameters a, b, c, d, respectively, given the actual degradation data y,
thus, the posterior estimates of the hyper-parameters are:
Figure FDA0002775776440000041
4. the method for predicting the service life of the workpiece as set forth in claim 3, wherein the EM algorithm is adopted for iterative solution, and the estimation value is obtained by combining the prior distribution,
according to the EM algorithm, the likelihood function for a full sample is:
Figure FDA0002775776440000042
thus, a full log-likelihood function containing Ω ═ (a, b, c, d):
Figure FDA0002775776440000043
obtaining a maximum likelihood estimation value of the hyperparameter by the formula, wherein the maximum likelihood estimation value of a
Figure FDA0002775776440000044
Is solved by the formula (2):
Figure FDA0002775776440000045
where ψ is a digamma distribution function, ψ (x) ═ ln Γ (x)]',miIs a number m, z of measured values representing a workpiece iiIs the z value representing the workpiece i; (ii) a
Maximum likelihood estimate of b
Figure FDA0002775776440000051
Maximum likelihood estimate of c
Figure FDA0002775776440000052
Maximum likelihood estimate of d
Figure FDA0002775776440000053
The expression of (a) is:
Figure FDA0002775776440000054
randomly giving a group of initial values of the hyper-parameters, and solving by using an EM algorithm, wherein the EM algorithm comprises a step E and a step M;
in step E, it is necessary to find the A posteriori expectation values including the hidden variable data, including E (z)i)，E(lnzi)，E(uizi)，
Figure FDA0002775776440000055
Assuming a value of the hyperparametric parameter of degree l
Figure FDA0002775776440000056
The value of the super parameter is
Figure FDA0002775776440000057
Substituting the expression of the posterior estimated value to obtain the following expression of the posterior expected value
Figure FDA0002775776440000058
In step M, substituting the above expectation values into iterative formulas (2) and (3) of the parameters to obtain an estimate value of the iteration of step l + 1:
Figure FDA0002775776440000061
after m iterations, if
Figure FDA0002775776440000062
And
Figure FDA0002775776440000063
the distance between them reaches a predetermined accuracy
Figure FDA0002775776440000064
I.e. an estimate of the hyper-parameter (a, b, c, d).
5. The method of claim 4, wherein the predicted value of the life of the workpiece is obtained based on the estimated value and the failure threshold of the workpiece by,
from the estimated values, the average life can be found to be:
Figure FDA0002775776440000065
wherein z is 1/sigma2～Gamma(a*,b*),u|z～N(c*,d*/z),
Figure FDA0002775776440000066
Wherein D is the failure threshold.
6. The method of claim 5, wherein the predicted value of the remaining life of the workpiece is obtained based on the estimated value and the failure threshold of the workpiece,
the remaining life at any time t, t >0 is:
Figure FDA0002775776440000071
wherein:
Figure FDA0002775776440000072
Figure FDA0002775776440000073
d is a failure threshold value, and x is a probability density value.
7. A device for predicting the service life of a workpiece is characterized by comprising a degradation data acquisition unit, a prior distribution calculation unit, an estimation value acquisition unit, a predicted workpiece service life value calculation unit and a predicted workpiece residual service life value calculation unit,
the degradation data acquisition unit is used for acquiring degradation data of the workpiece;
the prior distribution calculating unit adopts random parameters to model a linear wiener process to obtain prior distribution taking normal gamma distribution as a mean parameter and a drift parameter;
the estimation value acquisition unit is used for combining the prior distribution and adopting an EM algorithm to carry out iterative solution to acquire an estimation value;
the workpiece life predicted value calculating unit obtains a workpiece life predicted value and a workpiece residual life predicted value according to the estimated value and the failure threshold value of the workpiece;
and the predicted value calculation unit of the residual life of the workpiece obtains the predicted value of the residual life of the workpiece according to the estimated value and the failure threshold value of the workpiece.
8. The apparatus of claim 6, further comprising a posterior estimate calculation unit, wherein the posterior estimate calculation unit obtains the posterior estimate according to the prior distribution using the normal gamma distribution as the mean parameter and the drift parameter.
9. An apparatus for predicting a life of a workpiece, comprising: the system comprises a memory, a processor and a transceiver which are connected in sequence, wherein the memory is used for storing a computer program, the transceiver is used for transmitting and receiving messages, and the processor is used for reading the computer program and executing the method according to any one of claims 1 to 6.
10. A computer-readable storage medium characterized by: the computer-readable storage medium having stored thereon instructions which, when executed on a computer, perform the method of any of claims 1-6.
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