CN117557010A - Spare part quantity optimization method, system, equipment and medium in random degradation system - Google Patents

Spare part quantity optimization method, system, equipment and medium in random degradation system Download PDF

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CN117557010A
CN117557010A CN202410045060.9A CN202410045060A CN117557010A CN 117557010 A CN117557010 A CN 117557010A CN 202410045060 A CN202410045060 A CN 202410045060A CN 117557010 A CN117557010 A CN 117557010A
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张正新
司小胜
张建勋
李天梅
冯磊
杜党波
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Rocket Force University of Engineering of PLA
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Abstract

The invention discloses a method, a system, equipment and a medium for optimizing the number of spare parts in a random degradation system, and relates to the technical field of equipment optimization, wherein the method comprises the following steps: constructing a performance degradation model of a component by adopting a wiener process with linear drift, wherein the component comprises spare parts and working parts; determining the reliability of a single working part system with different spare parts according to the performance degradation model; determining all allocation modes for allocating a plurality of spare parts to a set number of working parts; obtaining service life distribution of a degradation system according to reliability of a single working part system with different spare parts and reliability improvement quantity brought by all distribution modes; constructing a unit time expected cost function of system operation based on the life distribution of the single spare part and the life distribution of the random degradation system; the optimized number of spare parts is obtained by minimizing the expected cost function per unit time of the random degradation system operation. The invention improves the accuracy of the number of spare parts and reduces the resource waste.

Description

Spare part quantity optimization method, system, equipment and medium in random degradation system
Technical Field
The invention relates to the technical field of equipment optimization, in particular to a method, a system, equipment and a medium for optimizing the number of spare parts in a random degradation system.
Background
Predictive and health management (Prognostics and health management, PHM) technology has proven a key technology to ensure efficient, safe, economical operation of systems. PHM technology is a hot spot of basic theory and application research in the reliability field in recent years, and is widely focused by scholars and engineering technicians. Life prediction is one of the core and key of PHM, and is also an important basis for supporting manufacturers to optimize after-sales service strategies and supporting users to optimize the whole life cycle health management activities of equipment such as maintenance, maintenance replacement, spare part management and the like. Therefore, the accurate prediction of the service life of the system is to realize the scientific management of the system health, thereby achieving the aims of reducing the downtime, improving the reliability and saving the running cost. The standby components are stored, so that the waiting time for ordering and maintaining the standby components after the system fails is avoided, the time cost for maintaining the system is greatly reduced by replacing the standby components, and the standby components are common strategies for ensuring the operation reliability of key systems such as aerospace, large weapon platforms and the like.
During long-term storage, the performance of the spare parts is also degraded due to aging of materials and structures, even if the spare parts fail without use, due to the influence of environmental stress and other factors. However, existing approaches have two major problems in predicting the life of such degraded systems with spare parts: first, existing methods generally define the life of the system as the life of the system itself, and do not take into account the life-prolonging efficacy of existing spare parts on the system; secondly, the existing methods generally assume that the spare parts do not degrade during storage, i.e. the performance of the corresponding parts of the system is restored as new after replacement of the spare parts. These problems may shift the life prediction of the system towards conservation on the one hand and may also lead to excessive spare part storage, thereby wasting spare parts and their storage resources on the other hand.
Disclosure of Invention
The invention aims to provide a method, a system, equipment and a medium for optimizing the number of spare parts in a random degradation system, which improve the accuracy of the number of spare parts and reduce the resource waste.
In order to achieve the above object, the present invention provides the following solutions:
a spare part quantity optimization method in a random degradation system, the random degradation system comprising a first set number of spare parts and a second set number of working parts, the spare part quantity optimization method in the random degradation system comprising:
constructing a performance degradation model of the spare part and a performance degradation model of the working part by adopting a wiener process with linear drift;
calculating the service life distribution and reliability of the spare part according to the performance degradation model of the spare part, and calculating the service life distribution and reliability of the working part according to the performance degradation model of the working part;
determining the reliability of a single working component system with different numbers of spare components according to the service life distribution of the spare components and the service life distribution of the working components;
determining all allocation modes for allocating the first set number of spare parts to the second set number of working parts;
obtaining the reliability of the degradation system according to the reliability of the single working part system with different spare parts and the reliability lifting quantity brought by all distribution modes;
determining the life distribution of the random degradation system according to the reliability of the random degradation system;
constructing a unit time expected cost function of random degradation system operation based on a lifetime distribution of the single spare part and a lifetime distribution of the random degradation system;
the optimized spare part count is obtained by minimizing the expected cost function per unit time of operation of the random degradation system.
The invention also discloses a spare part quantity optimizing system in the random degradation system, the random degradation system comprises a first set quantity of spare parts and a second set quantity of working parts, and the spare part quantity optimizing system in the random degradation system comprises:
the component performance degradation model construction module is used for constructing a performance degradation model of the spare component and a performance degradation model of the working component by adopting a wiener process with linear drift;
a life distribution and reliability determination module for calculating the life distribution and reliability of the spare part according to the performance degradation model of the spare part, and calculating the life distribution and reliability of the working part according to the performance degradation model of the working part;
a reliability determination module of the single working part system for determining reliability in the case that the single working part system has different numbers of spare parts according to the life distribution of the spare parts and the life distribution of the working parts;
an allocation mode determining module for determining all allocation modes for allocating the first set number of spare parts to the second set number of working parts;
the reliability lifting amount determining module is used for obtaining the reliability of the degradation system according to the reliability of the single working part system with different spare parts and the reliability lifting amount caused by all the distribution modes;
the service life distribution determining module of the random degradation system is used for determining the service life distribution of the random degradation system according to the reliability of the random degradation system;
a unit time expected cost function construction module for constructing a unit time expected cost function of operation of the random degradation system based on a lifetime distribution of the single spare part and a lifetime distribution of the random degradation system;
and the spare part quantity determining module is used for obtaining the optimized spare part quantity by minimizing a unit time expected cost function of the random degradation system operation.
The invention also discloses an electronic device, which comprises a memory and a processor, wherein the memory is used for storing a computer program, and the processor runs the computer program to enable the electronic device to execute the spare part quantity optimization method in the random degradation system.
The invention also discloses a computer readable storage medium storing a computer program, the computer program is executed by a processor to perform the method for optimizing the number of spare parts in the random degradation system.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention constructs the expected cost function of unit time of random degradation system operation based on the service life distribution of single spare part and the service life distribution of the random degradation system; the optimized number of spare parts is obtained by minimizing the expected cost function in unit time, so that the accuracy of the number of spare parts is improved, and the resource waste is reduced.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a method for optimizing the number of spare parts in a random degradation system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of performance degradation traces for each component in a 2-component 4 spare component system provided by an embodiment of the present invention;
FIG. 3 is a schematic view of a service life distribution PDF of a working part according to an embodiment of the present invention;
FIG. 4 is a schematic view of a spare part life distribution PDF according to an embodiment of the invention;
FIG. 5 is a schematic diagram of a life distribution of a single component system with different numbers of spare components provided by an embodiment of the present invention;
FIG. 6 is a diagram of an embodiment of the present inventionProbability of reliable operation of single components under different numbers of spare components at the moment;
FIG. 7 is a schematic diagram of a life PDF of a system with a different number of spare parts according to an embodiment of the invention;
FIG. 8 is a schematic diagram of expected operating costs per unit time for a system with different numbers of spare parts provided by an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a method, a system, equipment and a medium for optimizing the number of spare parts in a random degradation system, which improve the accuracy of the number of spare parts and reduce the resource waste.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1
As shown in fig. 1, the method for optimizing the number of spare parts in a random degradation system according to the present embodiment includes a first set number of spare parts and a second set number of working parts, where the method for optimizing the number of spare parts in the random degradation system includes the following steps.
Step 101: and constructing a performance degradation model of the spare part and a performance degradation model of the working part by adopting a wiener process with linear drift.
Step 102: the life distribution and reliability of the spare part are calculated from the performance degradation model of the spare part, and the life distribution and reliability of the working part are calculated from the performance degradation model of the working part.
Step 103: based on the life distribution of the spare parts and the life distribution of the working parts, the reliability is determined for a single working part system having different numbers of spare parts.
Step 104: all allocation patterns for allocating the first set number of spare parts to the second set number of working parts are determined.
Step 105: and obtaining the reliability of the degradation system according to the reliability of the single working part system with different spare parts and the reliability improvement quantity caused by all distribution modes.
Step 106: and determining the service life distribution of the random degradation system according to the reliability of the random degradation system.
Step 107: based on the lifetime distribution of the individual spare parts and the lifetime distribution of the random degenerate system, a cost function expected per unit time of the random degenerate system operation is constructed.
Step 108: the optimized spare part count is obtained by minimizing the expected cost function per unit time of operation of the random degradation system.
The working parts refer to parts used in the running process of the system, and the standby parts are stored standby parts, and are short for standby parts. The first set number of spare parts and the second set number of working parts are generic parts of the same type.
The random degradation system is a multi-component serial system, and the work of the random degradation system needs m similar components to operate simultaneously. In order to avoid waiting time of spare part ordering, system downtime is reduced, n spare parts are ordered along with m parts, and after m similar parts are put into use along with the system, the n spare parts are stored for standby. Both the performance of the operational components and spare parts may decrease as the length of service of the system increases, but the rate of degradation of the spare parts is much less than the rate of degradation of the operational components. Since all components are homogeneous, when the system is running at willPerformance degradation to a preset failure thresholdWhen the component is deemed to be failed, and spare parts in storage that have not failed are immediately selected to replace the failed component. The time for component replacement is negligible compared to the life of the system and the performance of components replaced into the system will degrade at the rate of degradation in the operating environment. When the failed component is not replaced by an available spare part, the system is considered to be failed, and the corresponding time is the service life of the system. FIG. 2 shows the performance degradation trace of each component in a random degradation system with 2 working components and 4 spare components +.>For the failure time of the 1 st working part, +.>For the failure time of the 2 nd working part, +.>For the failure time of the 1 st spare part of the 1 st working part, +.>Failure time of 1 st spare part for 2 nd working part, +.>Failure time of the 2 nd spare part for the 1 st working part, +.>The failure time of the 2 nd spare part for the 2 nd working part,is the system failure time.
The step 101 specifically includes:
the performance degradation process of components and spare parts is modeled using Wiener (Wiener) process with linear drift.
（1）
Wherein,a performance degradation model representing the working part at time t, < >>A performance degradation model representing the spare part at time t, < >>Indicating the initial degradation of the working part, +.>Representing the degradation rate of the working part, also called drift coefficient,>representing the diffusion coefficient of the working part,/->Indicating the initial degradation of the spare part, +.>Indicating the degradation rate of the spare part->Diffusion coefficient representing spare part, +.>Representing the standard Brownian motion, the diffusion coefficient is +.>Together characterize the temporal dynamics of the device performance degradation process. The values of the initial degradation amount, drift coefficient, and diffusion coefficient may be determined from a model of the performance degradation mechanism of the component or identified based on degradation monitoring data of the component。
The step 102 specifically includes:
defining the life of a component as its performance first reaching a failure thresholdThe probability density functions (Probability Density Function, PDF) of the working and spare part lives are calculated, respectively.
（2）
（3）
Wherein,probability density function representing the lifetime of the working part at time t, < >>Probability density function representing spare part life at time t, < >>Representing a failure threshold.
And->The corresponding cumulative probability distributions (Cumulative Distribution Function, CDF) are in turn:
wherein,CDF, indicative of a standard normal distribution, +.>Cumulative probability distribution function representing the lifetime of the working part at time t,/->A cumulative probability distribution function representing spare part life at time t.
The reliability of the working part is expressed asThe method comprises the steps of carrying out a first treatment on the surface of the The reliability of the spare part is expressed asWherein->Indicating the reliability of the working part at time t, < >>Indicating the reliability of the spare part at time t.
Step 103 specifically includes: solving the service life distribution and reliability of the corresponding single-component system (a random degradation system formed by 1 working component) under different numbers of spare parts, and the probability of working after the spare parts are replaced for different times in the single-component system. The single working part system in step 103 is a single part system.
The PDF of the life distribution of the single component systems under different numbers of spare parts is calculated in a push-down type recursion mode.
（6）
Wherein,PDF representing the lifetime distribution of the single component system at time t for 1 working component/spare component,PDF, which represents the life distribution of the single-component system for 1 working component l-1 spare part at time t,/->Is a positive integer greater than 0.
Wherein,，/>representing a single component system failure time (spare part replacement time), a method for controlling the same, and a computer program product>Representing a single component single spare part system at +.>Conditional lifetime distribution of replacement->And->Auxiliary symbols employed for simplifying the formula, i.e. +.>And->All are intermediate parameters, and the calculation process is as follows:
（7）
（8）
wherein,PDF with standard normal distribution, +.>、/>、/>、/>、/>Auxiliary symbols employed for simplifying the formula, i.e. +.>、/>、/>、/>、/>Are all intermediate parameters, and the specific calculation method is +.>，/>，/>，/>And->。
Computing spare partsThe number isThe reliability of the time-single component system is as follows:
。
and is also provided withThe time single component system is->The probability of individual component operation is:
（9）
wherein,representation->The time single component system is->Probability of individual component operation->Indicating the number of spare parts as +.>Reliability of time-single-component system, +.>Indicating the number of spare parts as +.>Reliability of the single component system at-1.
Number of spare partsIndicating the number of working parts +.>And (3) representing.
Step 104 is to solve all possible distribution mode lists of spare parts, and solve possible distribution mode matrixes of spare parts according to the number m of working parts forming the random degradation system and the number n of spare parts of the systemThe method specifically comprises the following steps:
is provided withIs +.>Validly set vector (L)>Representation->Spare parts for replacement->No. H of the working parts>Possible allocation, +.>Middle->Individual element->Indicating the number of times the ith working element is replaced,/-)>The number of divisions representing all the allocation patterns. Can be->Constitutes a->Matrix of dimensions->，/>Matrix of allocation patterns representing the number of spare parts n,>the number of spare parts is n+1, which indicates the number of distribution modes. />The following three conditions are satisfied:
①。
(2) initialization ofWherein, represent->Matrix transpose,/->Representation->A rank identity matrix.
③All columns in (1) can pass through at +.>Is obtained by adding 1 to one of the elements of a certain column.
According to the above properties, the method can be based on the following recursive methodSolving->：
(1) The process of the initialization is carried out,，/>，/>represents the allocation matrix when n=1, +.>The number of allocation patterns when n=1 is indicated.
(2) For a pair of，/>Wherein->Representation->Order identity matrix->And will all +.>Composition->。/>Indicating the number of distribution modes when the number of spare parts is n, < >>Representing the distribution pattern matrix when the number of spare parts is n+1.
(3) Deletion ofAnd (3) repeating the columns to obtain an allocation mode matrix.
The method for optimizing the number of spare parts in the random degradation system further comprises the following steps: the reliability and life distribution of the multi-generic component system is calculated taking into account the degradation of the storage spare parts, including in particular the following.
The present embodiment employs a single failed component replacement strategy, i.e., when there is a failure of one working component, reliable spare component replacement failure is immediately selected from the stored spare components. Based on spare part distribution mode and service life distribution conclusion of single-component system, the method comprises the following steps of recursively calculatingBy +.>Reliability of the random degradation system composed of the working components.
（10）
Wherein,indicating that time t has +.>The spare parts are made up of->Reliability of random degenerate system composed of individual working parts,/->Indicating that time t has +.>The spare parts are made up of->Reliability of random degenerate system composed of individual working parts,/->Representing reliability delta. />Represents that at time t there is no spare part, by +.>Reliability of random degenerate system composed of individual working parts,/->，/>Representing the reliability of a random degenerate system of one working element composition at time t,/>The reliability of a random degenerate system consisting of 1 working part with 0 spare parts at time t is indicated. />Indicate->The system reliability improvement amount brought by the spare parts. The reliability improvement amount can be calculated as in equation (9).
The reliability improvement amount is expressed as:
（11）
wherein,indicate->Reliability improvement amount brought by spare parts, < >>Represents the number of distribution modes, m represents the number of working parts,/->Indicate->Probability of reliable operation in the seed allocation mode,indicating the i-th working part replacement in the j-th allocation mode>The system reliability improvement amount brought by the time,represents the (th) in the j-th allocation mode>The number of times the individual working parts are replaced, +.>And (3) calculating according to formulas (2) - (7).
Step 106 specifically includes: and deriving the reliability of the random degradation system to obtain the service life distribution of the random degradation system.
Based on the relation between the service life distribution and the reliability, the reliability of the random degradation system is derived, and the service life of the random degradation system can be calculatedCumulative probability distribution->And probability density function->The calculation formula is as follows:
（12）
（13）
wherein,；
。
wherein,indicating that time t has +.>In the case of spare parts, by->Reliability of the random degradation system composed of the working parts; />PDF representing life distribution of m working parts at time t under the condition that the random degradation system of m working parts has no spare parts;random degradation system representing 1 working element at time t>PDF of lifetime distribution in case of secondary replacement spare parts;indicating 1 working element at time tRandom degenerate system of->PDF of lifetime distribution in case of secondary replacement spare parts; />Indicating that in the j-th allocation mode, the p-th working part is replaced +>The system reliability improvement amount brought by the sub-band, < >>Indicating the number of times the p-th working element is replaced in the j-th allocation.
The expected cost function per unit time for random degenerate system operation is expressed as:
（14）
wherein,representing the desired budget->Indicating the expiration time of the shut-off system>Total number of failed component replacements performed, +.>A desired cost per unit time representing the operation of a randomly degraded system, < >>Representing the expectations of the cost of a random degenerate system over the life cycle,/-, for example>Indicating a life cycle expectation, n being the first set numberQuantity (S)>Representing the cost of a component comprising a spare part and a working part +.>Representing the storage cost of one spare part,representing the replacement cost of a component, +.>Representing other costs including random degenerate system burst failure loss,/for>Indicating the expectations of the life of the system +.>Indicating the desire for the total number of failed work part replacements made at the time of system failure.
；
；
Wherein,representing the probability that the lifetime of a spare part is greater than the lifetime of a random degenerate system with m working parts of i spare parts>A probability density function representing spare part life at time t,random degradation system for representing i-1 spare parts of m working parts at t momentA probability density function of the lifetime of (c) a,a cumulative probability distribution function representing the lifetime of a random degradation system of i spare parts of m working parts at time t.
The calculation can be performed by numerical integration according to the formula (2) and the formula (8).
The invention realizes the life prediction of the random degradation system with a plurality of spare parts, and optimizes the number of the spare parts by minimizing the expected running cost of the random degradation system in unit time based on the life prediction result.
The following describes a method for optimizing the number of spare parts in a random degradation system according to the present invention by using a specific example.
This example employs a random degenerate system of 3 homogeneous working components with different numbers of spare parts. Firstly, determining parameters of a degradation model in the running and storage states of the component through analysis of a performance degradation mechanism of the component or based on historical performance monitoring data of the component, and solving PDF, CDF and reliability of service life distribution of the running component and the storage spare parts; secondly, calculating life distribution and reliability function of single-component random degradation system under different spare parts and the time tProbability of the individual spare parts being reliably operated; thirdly, when solving the given spare part number, all possible combinations of spare part distribution modes of the multi-similar component system are obtained; then, solving the reliability of the system under different spare part distribution modes, and calculating the reliability of the random degradation system through summation; finally, constructing a system life cycle expected operation cost function comprehensively considering the influences of factors such as component unit price, spare part storage cost, component failure replacement cost, system failure loss and the like, and obtaining the optimal spare part number of the system by minimizing the objective function. The method comprises the following specific steps:
A. parameters of the degradation model are determined and life distributions of the operating components and the storage spare parts are solved.
It is assumed that parameters of a degradation model of a component in an operating and storage state obtained by referring to product data or based on component history degradation data are specifically shown in table 1.
Substituting the parameters in table 1 into formulas (1) to (5), and calculating the service life distribution and reliability of the working parts and the storage spare parts. Obtained life PDF results、/>As shown in fig. 3 and 4.
B. Calculating life distribution, reliability and the like of random degradation system of single-component system under different spare partsTime is +.>Probability of the individual spare parts being reliably operated.
Recursively calculating life distribution of single-component random degradation system under different spare parts according to formula (6)Reliability->And calculate +.>The time single-component system is->Probability of reliable operation of individual spare parts +.>。And->The results of (2) are shown in FIGS. 5 and 6, respectively.
C. When solving for a given number of spare parts, all possible combinations of spare part distribution modes of the multi-same-type component system are adopted.
All possible distribution mode matrix of multiple similar spare parts when determining given spare part number according to method presented in invention content C. For example, the possible allocation pattern matrix of 3 similar components for 4 spare parts +.>The method comprises the following steps:
；
wherein each column of the matrix is a specific division, representing the number of 4 spare parts divided into 3 parts. For example, the number of the cells to be processed,column 1 of (c) indicates that the number of spare parts divided into 3 parts is 4, 0 in order.
D. And solving the reliability of the system under different spare part distribution modes, and calculating the service life distribution of the system by summing the reliability of the system.
For matrixThe corresponding spare part distribution mode of each column is calculated and recorded according to the probability of reliable operation of the system under the distribution mode>And then calculating the reliability of the system according to the formula (10), and further calculating the reliability of the system according to the formula (12) and the formulaFormula (13) is a lifetime distribution of the computing system. The results obtained are shown in FIG. 7 below.
E. A desired running cost function of the system is constructed and an optimal number of spare parts is obtained by minimizing the function.
Substituting the price of the components of the system, the cost per unit time of the storage spare parts, the replacement cost of the single component and other costs including the failure loss of the system into the expected operation cost function of the system per unit time as shown in the formula (14) to obtain the expected operation cost of the system per unit time when different spare parts are available. The function is made to obtain the minimum spare part number, namely the optimal spare part number of the system.
Let the costs be shown in table 2 and the expected costs for a system with a different number of spare parts be shown in fig. 8. As can be seen from fig. 8, the running cost per unit time of the system is the lowest when the number of spare parts is 20.
In view of the random dynamic characteristics which are shown in the equipment performance degradation process and the capability of describing a non-monotonic degradation process based on a random degradation model of a Wiener process, the invention firstly establishes a random evolution model of the performance of an operating part and a storage spare part respectively based on the Wiener process with linear drift, defines the failure time of the part as the time when the performance reaches a preset failure threshold value, and gives out the service life distribution and reliability function of the part under the operating and storage conditions; secondly, solving all possible spare part distribution mode lists of the random system when the number of spare parts is given by adopting an integer division method; thirdly, deducing the reliability of the system when the number of spare parts is different from the given number based on a life distribution calculation formula of the single part in stages, further calculating the reliability increment of the system and the reliability of the system caused by the increase of the parts, solving the life distribution of the system based on the relation between the reliability function and the life distribution of the system, and realizing the life prediction of the system; finally, based on the life prediction result, a unit time expected operation cost function comprehensively considering factors such as component unit price, storage cost, replacement cost, system failure loss and the like is constructed, and the optimal equipment number of the system is solved by minimizing the objective function.
Example 2
The embodiment provides a spare part quantity optimizing system in a random degradation system. Wherein the random degradation system comprises a first set number of spare parts and a second set number of working parts, and the spare part number optimizing system in the random degradation system comprises:
and the component performance degradation model construction module is used for constructing a performance degradation model of the spare component and a performance degradation model of the working component by adopting a wiener process with linear drift.
And the service life distribution and reliability determination module is used for calculating the service life distribution and reliability of the spare part according to the performance degradation model of the spare part and calculating the service life distribution and reliability of the working part according to the performance degradation model of the working part.
And a reliability determination module of the single working component system for determining the reliability of the single working component system with different numbers of spare components according to the service life distribution of the spare components and the service life distribution of the working components.
And the allocation mode determining module is used for determining all allocation modes for allocating the first set number of spare parts to the second set number of working parts.
And the reliability lifting amount determining module is used for obtaining the reliability of the degradation system according to the reliability of the single working part system with different spare parts and the reliability lifting amount caused by all the distribution modes.
And the life distribution determining module is used for determining the life distribution of the random degradation system according to the reliability of the random degradation system.
A unit time expected cost function construction module for constructing a unit time expected cost function for operation of the random degradation system based on a lifetime distribution of the individual spare parts and a lifetime distribution of the random degradation system.
And the spare part quantity determining module is used for obtaining the optimized spare part quantity by minimizing a unit time expected cost function of the random degradation system operation.
Example 3
An electronic device provided in this embodiment includes a memory and a processor, where the memory is configured to store a computer program, and the processor runs the computer program to enable the electronic device to execute the method for optimizing the number of spare parts in the random degradation system described in embodiment 1.
The present embodiment also provides a computer-readable storage medium storing a computer program that is executed by a processor to perform the spare part number optimizing method in the random degradation system described in embodiment 1.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.

Claims (10)

1. A method for optimizing the number of spare parts in a random degradation system, wherein the random degradation system comprises a first set number of spare parts and a second set number of working parts, the method for optimizing the number of spare parts in the random degradation system comprising:
constructing a performance degradation model of the spare part and a performance degradation model of the working part by adopting a wiener process with linear drift;
calculating the service life distribution and reliability of the spare part according to the performance degradation model of the spare part, and calculating the service life distribution and reliability of the working part according to the performance degradation model of the working part;
determining the reliability of a single working component system with different numbers of spare components according to the service life distribution of the spare components and the service life distribution of the working components;
determining all allocation modes for allocating the first set number of spare parts to the second set number of working parts;
obtaining the reliability of the degradation system according to the reliability of the single working part system with different spare parts and the reliability lifting quantity brought by all distribution modes;
determining the life distribution of the random degradation system according to the reliability of the random degradation system;
constructing a unit time expected cost function of random degradation system operation based on a lifetime distribution of the single spare part and a lifetime distribution of the random degradation system;
the optimized spare part count is obtained by minimizing the expected cost function per unit time of operation of the random degradation system.
2. The method for optimizing the number of spare parts in a random degradation system according to claim 1, wherein the performance degradation model of the working part is expressed as；
The performance degradation model of the spare part is expressed as；
Wherein,a performance degradation model representing the working part at time t, < >>Indicating the nature of the spare part at time tEnergy degeneration model,/->Indicating the initial degradation of the working part, +.>Representing drift coefficient>Representing the diffusion coefficient of the working member,indicating the initial degradation of the spare part, +.>Indicating the degradation rate of the spare part->Diffusion coefficient representing spare part, +.>Representing a standard brownian motion.
3. The method for optimizing the number of spare parts in a random degradation system according to claim 2, wherein the life distribution of the spare part is expressed as a probability density function and a cumulative probability distribution function of the life of the spare part, and the life distribution of the working part is expressed as a probability density function and a cumulative probability distribution function of the life of the working part;
wherein the probability density function of the working part life is expressed as:
；
the probability density function of spare part life is expressed as:
；
wherein,probability density function representing the lifetime of the working part at time t, < >>Probability density function representing spare part life at time t, < >>Representing a failure threshold;
the reliability of the working part is expressed as:；
the reliability of the spare part is expressed as:；
wherein,indicating the reliability of the working part at time t, < >>Indicating the reliability of the spare part at time t, < >>Cumulative probability distribution function representing the lifetime of the working part at time t,/->A cumulative probability distribution function representing spare part life at time t.
4. The method for optimizing the number of spare parts in a random degenerate system according to claim 1, wherein the reliability of the degenerate system is expressed as:
；
wherein,indicating that time t has +.>The spare parts are made up of->Reliability of random degenerate system composed of individual working parts,/->Indicating that time t has +.>The spare parts are made up of->Reliability of random degenerate system composed of individual working parts,/->Representing reliability increment, +.>Represents that at time t there is no spare part, by +.>Reliability of random degenerate system composed of individual working parts,/->Indicate->System reliability improvement amount caused by spare parts.
5. The method for optimizing the number of spare parts in a random degradation system according to claim 4, wherein the reliability improvement amount is expressed as:
；
wherein,indicate->Reliability improvement amount brought by spare parts, < >>Represents the number of distribution modes, m represents the number of working parts,/->Indicate->Probability of reliable operation in seed allocation mode, +.>Indicating the i-th working part replacement in the j-th allocation mode>The reliability of the system is improved.
6. The method for optimizing the number of spare parts in a random degenerate system according to claim 1, wherein the expected cost function per unit time of the random degenerate system operation is expressed as:
；
wherein,a desired cost per unit time representing the operation of a randomly degraded system, < >>Representing the expectations of the cost of a random degenerate system over the life cycle,/-, for example>Indicating the desire for life cycle ∈>For said first set number, +.>Representing the cost of a component comprising a spare part and a working part +.>Representing the storage costs of a spare part, +.>Representing the replacement cost of a component, +.>Representing other costs including random degenerate system burst failure loss,/for>Representing a desire for a total number of failed work component replacements made at a system failure time;
；
；
wherein,indicating that the spare part has a longer life than with +.>Probability of lifetime of random degenerate system of m working parts of spare parts, +.>Probability density function representing spare part life at time t, < >>Probability density function representing the lifetime of a random degenerate system of m working parts i-1 spare parts at time t,/>A cumulative probability distribution function representing the lifetime of a random degradation system of i spare parts of m working parts at time t.
7. The method for optimizing the number of spare parts in a random degradation system according to claim 1, wherein determining the lifetime distribution of the random degradation system according to the reliability of the random degradation system specifically comprises:
and deriving the reliability of the random degradation system to obtain the service life distribution of the random degradation system.
8. A spare part quantity optimizing system in a random degradation system, wherein the random degradation system includes a first set number of spare parts and a second set number of working parts, the spare part quantity optimizing system in the random degradation system comprising:
the component performance degradation model construction module is used for constructing a performance degradation model of the spare component and a performance degradation model of the working component by adopting a wiener process with linear drift;
a life distribution and reliability determination module for calculating the life distribution and reliability of the spare part according to the performance degradation model of the spare part, and calculating the life distribution and reliability of the working part according to the performance degradation model of the working part;
a reliability determination module of the single working part system for determining reliability in the case that the single working part system has different numbers of spare parts according to the life distribution of the spare parts and the life distribution of the working parts;
an allocation mode determining module for determining all allocation modes for allocating the first set number of spare parts to the second set number of working parts;
the reliability lifting amount determining module is used for obtaining the reliability of the degradation system according to the reliability of the single working part system with different spare parts and the reliability lifting amount caused by all the distribution modes;
the service life distribution determining module of the random degradation system is used for determining the service life distribution of the random degradation system according to the reliability of the random degradation system;
a unit time expected cost function construction module for constructing a unit time expected cost function of operation of the random degradation system based on a lifetime distribution of the single spare part and a lifetime distribution of the random degradation system;
and the spare part quantity determining module is used for obtaining the optimized spare part quantity by minimizing a unit time expected cost function of the random degradation system operation.
9. An electronic device comprising a memory for storing a computer program and a processor that runs the computer program to cause the electronic device to perform the method of optimizing the number of spare parts in a random degradation system according to any one of claims 1 to 7.
10. A computer readable storage medium, characterized in that it stores a computer program which, when executed by a processor, implements the method for optimizing the number of spare parts in a random degenerate system according to any one of claims 1 to 7.
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103632214A (en) * 2013-12-23 2014-03-12 清华大学 Maintenance and spare part supply combined optimization method for use in absence of inventory degradation data
WO2018076475A1 (en) * 2016-10-26 2018-05-03 广东产品质量监督检验研究院 Photovoltaic assembly accelerated degradation model established based on deep approach of learning, and method for predicting photovoltaic assembly lifetime
CN108520152A (en) * 2018-04-13 2018-09-11 中国人民解放军火箭军工程大学 A kind of the service life distribution determination method and system of engineering equipment
CN110737991A (en) * 2019-10-21 2020-01-31 北京航空航天大学 load sharing degradation system reliability evaluation and state switching optimization method
CN111523251A (en) * 2020-06-09 2020-08-11 江苏科技大学 Method for rapidly evaluating service life of product under random environmental stress
CN116384876A (en) * 2023-01-30 2023-07-04 湖南大学 Spare part dynamic inventory-production control method, system and medium based on wiener process
CN116562017A (en) * 2023-05-10 2023-08-08 中国人民解放军火箭军工程大学 Nonlinear storage system life prediction method considering spare part storage degradation

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103632214A (en) * 2013-12-23 2014-03-12 清华大学 Maintenance and spare part supply combined optimization method for use in absence of inventory degradation data
WO2018076475A1 (en) * 2016-10-26 2018-05-03 广东产品质量监督检验研究院 Photovoltaic assembly accelerated degradation model established based on deep approach of learning, and method for predicting photovoltaic assembly lifetime
CN108520152A (en) * 2018-04-13 2018-09-11 中国人民解放军火箭军工程大学 A kind of the service life distribution determination method and system of engineering equipment
CN110737991A (en) * 2019-10-21 2020-01-31 北京航空航天大学 load sharing degradation system reliability evaluation and state switching optimization method
CN111523251A (en) * 2020-06-09 2020-08-11 江苏科技大学 Method for rapidly evaluating service life of product under random environmental stress
CN116384876A (en) * 2023-01-30 2023-07-04 湖南大学 Spare part dynamic inventory-production control method, system and medium based on wiener process
CN116562017A (en) * 2023-05-10 2023-08-08 中国人民解放军火箭军工程大学 Nonlinear storage system life prediction method considering spare part storage degradation

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
CHAO REN 等: "A Remaining Useful Life Prediction Method With Degradation Model Calibration", 《2023 IEEE 12TH DATA DRIVEN CONTROL AND LEARNING SYSTEMS CONFERENCE (DDCLS)》, 7 July 2023 (2023-07-07) *
司小胜;胡昌华;周东华;: "带测量误差的非线性退化过程建模与剩余寿命估计", 自动化学报, no. 05, 15 May 2013 (2013-05-15) *
喻勇;司小胜;胡昌华;崔忠马;李洪鹏;: "数据驱动的可靠性评估与寿命预测研究进展:基于协变量的方法", 自动化学报, no. 02, 11 December 2017 (2017-12-11) *
汪玉: "基于质量信息的多部件退化系统的视情维修", 《中国优秀硕士学位论文全文数据库》, 29 February 2020 (2020-02-29) *
蔡景;肖罗椿;李鑫;: "基于维纳过程的维修决策和备件库存联合优化", 系统工程与电子技术, no. 08, 4 March 2016 (2016-03-04) *
黄亮: "基于随机过程的航空发动机剩余寿命预测及维修决策研究", 《中国优秀硕士学位论文全文数据库》, 29 February 2020 (2020-02-29) *

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