CN110197288A - The remaining life prediction technique of equipment under the influence of failure - Google Patents
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Abstract
The invention discloses a kind of remaining life prediction techniques of equipment under the influence of failure, specifically include: 1) degradation model for determining equipment there are failure；2) the remaining life distribution function of equipment under the influence of failure is determined；3) unknown parameter of model is determined；4) the equipment life prediction model of multi-parameter is determined.The present invention establishes the degradation model of equipment using Wiener process, calculate the life distribution function based on first-hitting time, pass through the EM algorithm unknown parameter that degradation estimation unknown-model parameter and failure generation moment are distributed simultaneously, it is finally completed predicting residual useful life of equipment under the influence of failure, the invention can effectively predict the equipment remaining life under complex environment, be conducive to carry out maintenance to equipment, it is ensured that equipment safety reliably works.
Description
Technical Field
The invention relates to the field of residual service life prediction of equipment, in particular to a residual service life prediction method of equipment under the influence of faults.
Background
Residual life has been widely used in aerospace, military and large complex equipment fields as an important component of prediction and health management technology (PHM). The residual life prediction technology is the key for ensuring the reliability and safety of equipment and is an important means for reducing the maintenance cost of the equipment. Therefore, the method for predicting the residual service life of the research equipment has very important practical significance.
Since the performance degradation data of the device is directly related to the health state of the device, a device life prediction method based on the degradation data becomes mainstream. However, because the working environments of most of the devices are very complex, such as the aviation engine, the rotary bearing, the large fan and other devices can be subjected to the environments of abrasion, overload operation, high temperature, high pressure and the like among the devices, the devices can cause certain faults in the performance degradation process, the continuous operation of the devices is not affected by the faults, but the original degradation trend can be changed, the failure of the devices is accelerated, and the residual service life of the devices is finally shortened. Fig. 1 shows a plant degradation curve in which a fault occurs during degradation. For example, a defect is generated in a certain blade of the fan, and the defect does not affect the continuous operation of the fan, but the generation of the fault affects the service life of the whole system.
Most of the existing methods for predicting the service life of the equipment consider that the whole service life cycle of the equipment is in a normal degradation state, but do not consider that faults possibly occur in the degradation process, so that the accuracy of service life prediction is reduced. In recent years, many studies have shown that the degradation trajectory of the device changes at a certain time or even at a plurality of times (regime switching). But this moment is often considered as definite and the number of transitions is known. Depending on the uncertainty of the fault, the moment of occurrence of the fault is not observable and unknown. The failure may occur at any time, the probability of which increases as the operating time of the device increases. This results in a great difference between the predicted life and the actual life obtained by the general method, and a limited reference value. Considering that the fault affects the degradation process of the equipment is a difficult point for researching the service life prediction of the equipment.
Disclosure of Invention
In view of the above, the present invention provides a method for predicting the remaining service life of a device under the influence of a fault. In view of the above, the present invention provides a method for considering the remaining life of a device under the influence of a fault. Establishing a degradation model under the influence of a fault by utilizing a Wiener process, wherein a drift coefficient of the degradation model is used for describing the change of a degradation track, and a diffusion coefficient is used for describing the stability of the degradation process; then, assuming that the fault occurrence time is a random variable, obeying certain distribution, thereby obtaining the residual life distribution based on the first arrival time; due to the uncertainty of the fault, the occurrence time of the fault cannot be observed, so that a missing value exists in an observation interval, and the problem of parameter estimation under the condition of missing data is solved by using an EM (effective magnetic field) algorithm; the occurrence of the fault can simultaneously influence the change of a plurality of performance parameters, strong correlation exists between the parameters in a degradation process chapter, and the service life prediction of the equipment with the parameters under the influence of the fault is obtained through a Copula function, so that the residual service life prediction of the equipment under the influence of the fault is realized, the accuracy of the service life prediction can be effectively improved, the maintenance and the repair of the equipment are facilitated, and the safe and reliable work of the equipment is ensured.
The purpose of the invention is realized by the following technical scheme:
in a first aspect, the method for predicting the remaining service life of equipment under the influence of a fault, provided by the invention, comprises the following steps:
step S1: determining an equipment degradation model, and changing a drift coefficient by using the characteristic of a Wiener process to describe a degradation track influenced by a fault;
step S2: determining the relationship between the degradation rate and the degradation rate before and after the fault occurs by taking the degradation model obtained in the step S1 as a known condition, and respectively obtaining a residual life distribution expression of the normal degradation state and the fault degradation state;
step S3: taking the service life distribution of the two states obtained in the step S2 as a known condition, and regarding the fault occurrence time as a random variable, thereby obtaining a service life distribution function under the condition of uncertain faults;
step S4: taking the service life distribution function of the equipment under the influence of the fault obtained in the step S3 as a known condition, regarding the fault occurrence time in the whole detection interval as missing data, and solving the parameter estimation problem of the missing data in the detection data by using an EM (effective electromagnetic radiation) algorithm;
step S5: obtaining the service life distribution function determined in the step 3 by taking the unknown parameters obtained in the step S4 as known conditions, and calculating an expectation value, wherein the obtained expectation value is a predicted residual service life value, so that the service life prediction of a single performance parameter of the equipment under the influence of faults is realized;
step S6: and describing the correlation among the multiple parameters by using the Copula function under the known condition of the service life distribution of the single parameter under the influence of the fault obtained in the step S5, and obtaining the combined service life distribution of the multiple parameters under the influence of the fault, thereby completing the residual service life prediction of the equipment.
Specifically, in step S1, the degradation model is:
wherein X (t) represents a degradation performance characteristic value of the device, λ1 and λ2Is the rate of degradation before and after the occurrence of the fault; b (t) is the standard brownian motion, which obeys N (0, t), τ being the moment when the fault occurs;
considering the detection value as a discrete quantity, the corresponding degradation model is:
wherein ,ΔXi,jIn increments of Xi,j+1-Xi,j，Δti,j＝ti,j+1-ti,j。
Specifically, in step S2, the occurrence time of the failure is known, and the life distribution function thereof is expressed as
wherein ,is at ti,jLifetime probability density function of time, w being a failure threshold set by the device, Zi,jThe performance degradation amount at the current moment;
the corresponding cumulative distribution function of remaining life is:
where Φ (·) is the normal distribution.
Specifically, in step S3, the life distribution function obtained by considering the occurrence time of the failure as a random variable is expressed as:
wherein ,fτ(τ,θτ) and Fτ(t,θτ) Probability density function and cumulative distribution function, theta, respectively, of the time of occurrence of the faultτShowing unknown ginsengAnd (4) counting.
In particular, the parameter estimation problem under missing data is solved in step S4 by using the EM algorithm, and its complete data likelihood function can be expressed as:
wherein m is the number of experimental devices, niFor the observed number of the tested devices I, I {. is an indicator function;
the incremental probability density function of the fault occurrence time at three incremental different positions is expressed as follows:
wherein { k ═ 1,2,3} is represented by τ, respectively>ti,j+1,ti<τ<ti,j+1 and τ<ti,j。
In particular, the lifetime distribution of the plurality of parameters under the influence of the fault in step S6 can be divided into two cases of independence and correlation between the parameters, which can be expressed as:
wherein ,the remaining life of the c-th performance characteristic;
when there is a correlation among the performance parameters in step S6, the joint lifetime distribution function and the joint probability density function can be expressed as:
where C (-) is the Copula function.
In a second aspect, an electronic device of the present invention includes: a processor, a memory, and a bus, wherein,
the processor and the memory are communicated with each other through the bus;
the memory stores program instructions executable by the processor, which when invoked by the processor are capable of performing a method as previously described.
In a third aspect, the invention provides a non-transitory computer readable storage medium storing computer instructions that cause the computer to perform the method as described above.
The invention has the beneficial effects that:
1. the service life prediction method is provided, the fault influence is introduced into the service life prediction method for the first time, and the reliability and the accuracy of service life prediction are improved.
2. And taking the fault occurrence time as a random variable, and acquiring a life distribution function based on first-arrival time.
3. And simultaneously estimating unknown parameters of the degradation model and the fault occurrence time distribution function by using an EM (effective electromagnetic) algorithm.
4. Multiple performance parameters are simultaneously considered in the life prediction under the influence of a fault.
5. Under the condition that a plurality of degradation parameters are strongly correlated, the Copula function is used for describing the quantitative correlation among the parameters, and a multi-parameter life prediction model of the equipment under the influence of faults is obtained.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof.
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In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings, in which:
FIG. 1 is a schematic diagram of the degradation curves for a normal state and a fault state of the present invention;
FIG. 2 is a schematic diagram of a degradation trajectory for a plurality of performance parameters under the influence of a fault;
FIG. 3 is a schematic diagram of a remaining useful life prediction result of the device;
FIG. 4 is a flow chart of the present invention.
Detailed Description
Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be understood that the preferred embodiments are illustrative of the invention only and are not limiting upon the scope of the invention.
The implementation process of the invention comprises the following steps: 1) determining a degradation model under the influence of a fault; 2) determining various performance parameters capable of characterizing the equipment; 3) determining the service life distribution under the influence of faults; 4) determining unknown parameters; 5) and determining a multi-parameter life prediction model under the influence of the fault, wherein the flow of the whole invention is shown in FIG. 4. Specifically, the method comprises the following steps:
step S1: determining a device degradation model, and changing a drift coefficient by using the characteristics of a Wiener process to describe a degradation track under the influence of the fault as shown in FIG. 1;
the degradation model expression of the equipment under the normal condition is as follows:
6.X(t)＝X(0)+λt+σB(t)
then under the influence of the fault, the degradation model of the device is:
wherein X (t) represents a degradation performance characteristic value of the device, λ1 and λ2Is the rate of degradation before and after the occurrence of the fault; b (t) is the standard brownian motion, which obeys N (0, t), τ being the moment when the fault occurs;
considering the detection value as a discrete quantity, the corresponding degradation model is:
wherein ,ΔXi,jIn increments of Xi,j+1-Xi,j，Δti,j＝ti,j+1-ti,j。
Step S2: determining the relationship between the degradation rate and the degradation rate before and after the fault occurs by taking the degradation model obtained in the step S1 as a known condition, and respectively obtaining a residual life distribution expression of the normal degradation state and the fault degradation state;
specifically, the remaining useful life of the device based on the first arrival time may be expressed as:
T＝inf{t:X(t)≥w|X(0)<w}
further, expressing the remaining useful life of the device at the present time may be expressed as:
Li,j＝inf{l:X(ti,j+l)≥w|Xi,j<w}
wherein l is the remaining service life.
Since the remaining lifetime distribution in the normal case follows a gaussian distribution, the expressions of the probability density function and the cumulative distribution function are respectively:
considering that the fault occurrence time is known, the degradation rates before and after the fault occurs change, so the expressions of the probability density function and the cumulative distribution function of the remaining service life distribution corresponding to the fixed fault occurrence time can be respectively expressed as:
where Φ (·) is the normal distribution.
Since the moment of occurrence of a fault is not detectable, it is considered as a random variable, and the remaining life distribution of the device can be expressed as:
wherein ,fτ(τ,θτ)，Fτ(t,θτ) A probability density function and a cumulative probability density function, respectively, obeying a certain distribution as random variables at the moment of occurrence of the fault.
Step S3: taking the service life distribution of the two states obtained in the step S2 as a known condition, and regarding the fault occurrence time as a random variable, thereby obtaining a service life distribution function under the condition of uncertain faults;
specifically, the time when the fault occurs is taken as the missing data, and the joint probability density function at this time is:
wherein, A (Δ X)i)，B(ΔXi,j) and C(ΔXi) The probability density functions are respectively combined for the increment of the fault before the whole detection interval, in the detection interval and after the whole detection interval. They can be represented as:
step S4: taking the service life distribution function of the equipment under the influence of the fault obtained in the step S3 as a known condition, regarding the fault occurrence time in the whole detection interval as missing data, and solving the parameter estimation problem of the missing data in the detection data by using an EM (effective electromagnetic radiation) algorithm;
specifically, in the present embodiment, when there are m devices to perform the lifetime test, each device corresponds to a different failure occurrence time { τ } for each device1,τ2,…,τmThe full data likelihood function can be expressed as:
wherein ,δk,i,jOne indicator variable is { k is equal to 1,2,3} and the fault occurrence time tau is corresponding to the increment delta Xi,jThree cases in between. Based on this, the full data likelihood log function can be expressed as:
since the objective of the step E of the EM algorithm is to calculate the conditional expectation of the likelihood function of the complete data under the missing data, the expression can be expressed as:
wherein , θp＝λ1,λ2,σ2。
the EM algorithm works only when the full data likelihood function is linearly divisible. The conditional expectation expression can be expressed as:
where v consists of missing data and m consists of an unknown parameter θp and θτAnd (4) forming. Whereby the two parts have a logarithmic function ofDue to the presence of the second portion increment, then Q is1 and Q2Can be expressed as:
e step of EM algorithm obtains condition expectation of fault occurrence time under observation data and observation time, and condition expectation Q of first item of complete data log-likelihood function1Can be expressed as:
second term Q of log-likelihood function due to complete data2The property of the constant integral can be divided into three parts, relating to the conditional expectation between increments:
a)
b)ti,j<τ<ti,j+1
c)τ≤ti,j＝τ<ti,1+ti,1≤τ≤ti,j
wherein ,
m steps in the EM algorithm solve the partial derivative of the complete data likelihood function on the basis of obtaining the condition expectation of the missing data, and the calculation expression is as follows:
step S5: obtaining the service life distribution function determined in the step 3 by taking the unknown parameters obtained in the step S4 as known conditions, and obtaining an expectation value of the function, wherein the obtained expectation value is a predicted residual service life value, so as to realize service life prediction of a single performance parameter of the equipment under consideration of fault influence, and obtain a service life prediction curve shown in fig. 3;
step S6: and describing the correlation among the multiple parameters by using the Copula function under the known condition of the service life distribution of the single parameter under the influence of the fault obtained in the step S5, and obtaining the combined service life distribution of the multiple parameters under the influence of the fault, thereby completing the residual service life prediction of the equipment.
In the present embodiment, assuming that the device has n performance degradation characteristics, the occurrence of a fault will simultaneously affect the change of n parameter degradation trajectories, as shown in fig. 2. Life distribution function of each performance characteristic under fault influenceThe remaining useful life of the target device can be expressed as:
in the case that a plurality of performance parameters of the device may not affect each other during the degradation process, i.e. are independent of each other, the joint distribution function of the remaining service life of the device may be represented as:
in the degradation process of most equipment, the component parts of the equipment are mutually influenced, so that a plurality of performance parameters of the equipment have strong correlation, the strong correlation between the parameters can be described by using a Copula function, the Clayton function is suitable for describing tail-related multiparameters, and the expression is as follows:
α is a Copula parameter, and the corresponding calculation formula istau is the correlation coefficient.
The multi-parameter life prediction model of the equipment under the influence of the fault can be expressed as follows:
wherein, the corresponding probability density function is:
it should be recognized that embodiments of the present invention can be realized and implemented by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The methods may be implemented in a computer program using standard programming techniques, including a non-transitory computer-readable storage medium configured with the computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner, according to the methods and figures described in the detailed description. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language. Furthermore, the program can be run on a programmed application specific integrated circuit for this purpose.
Further, the operations of processes described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and/or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) collectively executed on one or more processors, by hardware, or combinations thereof. The computer program includes a plurality of instructions executable by one or more processors.
Further, the method may be implemented in any type of computing platform operatively connected to a suitable interface, including but not limited to a personal computer, mini computer, mainframe, workstation, networked or distributed computing environment, separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, and the like. Aspects of the invention may be embodied in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optically read and/or write storage medium, RAM, ROM, or the like, such that it may be read by a programmable computer, which when read by the storage medium or device, is operative to configure and operate the computer to perform the procedures described herein. Further, the machine-readable code, or portions thereof, may be transmitted over a wired or wireless network. The invention described herein includes these and other different types of non-transitory computer-readable storage media when such media include instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor. When the website intrusion detection method and the technology based on big data log analysis are programmed, the invention also comprises the computer.
A computer program can be applied to input data to perform the functions described herein to transform the input data to generate output data that is stored to non-volatile memory. The output information may also be applied to one or more output devices, such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including particular visual depictions of physical and tangible objects produced on a display.
In practical application, when complex equipment such as a turbine engine, a rolling bearing, a large fan and the like works in a complex working environment, faults can be generated to shorten the residual service life of the equipment, and the residual service life of the equipment can be predicted by executing the method provided by the invention.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.
Claims (8)
1. The method for predicting the residual service life of the equipment under the influence of the fault is characterized by comprising the following steps: the method comprises the following steps:
step S1: determining an equipment degradation model, and changing a drift coefficient by using the characteristic of a Wiener process to describe a degradation track influenced by a fault;
step S2: determining the relationship between the degradation rate and the degradation rate before and after the fault occurs by taking the degradation model obtained in the step S1 as a known condition, and respectively obtaining a residual life distribution expression of the normal degradation state and the fault degradation state;
step S3: taking the service life distribution of the two states obtained in the step S2 as a known condition, and regarding the fault occurrence time as a random variable, thereby obtaining a service life distribution function under the condition of uncertain faults;
step S4: taking the service life distribution function of the equipment under the influence of the fault obtained in the step S3 as a known condition, regarding the fault occurrence time in the whole detection interval as missing data, and solving the parameter estimation problem of the missing data in the detection data by using an EM (effective electromagnetic radiation) algorithm;
step S5: obtaining the service life distribution function determined in the step S3 by taking the unknown parameters obtained in the step S4 as known conditions, and calculating an expectation value, wherein the obtained expectation value is a predicted residual service life value, so that the service life prediction of a single performance parameter of the equipment under the influence of faults is considered;
step S6: and describing the correlation among the multiple parameters by using the Copula function under the known condition of the service life distribution of the single parameter under the influence of the fault obtained in the step S5, and obtaining the combined service life distribution of the multiple parameters under the influence of the fault, thereby completing the residual service life prediction of the equipment.
2. The method of claim 1, wherein the method comprises the steps of: in step S1, the degradation model is:
wherein X (t) represents a degradation performance characteristic value of the device, λ1 and λ2Is the rate of degradation before and after the occurrence of the fault; b (t) is the standard brownian motion, which obeys N (0, t), τ being the moment when the fault occurs;
considering the detection value as a discrete quantity, the corresponding degradation model is:
wherein ,ΔXi，jIn increments of Xi，j+1-Xi，j，Δti，j＝ti，j+1-ti，j。
3. The method of claim 1, wherein the method comprises the steps of: in step S2, the time of occurrence of the fault is known, and the probability density function expression of the life distribution is
wherein ,is at ti，jLifetime probability density function of time, w being a failure threshold set by the device, Zi，jThe performance degradation amount at the current moment;
the corresponding cumulative distribution function of remaining life is:
where Φ (·) is the normal distribution.
4. The method of claim 1, wherein the method comprises the steps of: in step S3, the life distribution function obtained by considering the occurrence time of the failure as a random variable is expressed as:
wherein ,fτ(τ，θτ) and Fτ(t，θt) Probability density function and cumulative distribution of the time of occurrence of a fault τ, respectivelyFunction, thetaτRepresenting an unknown parameter.
5. The method of claim 1, wherein the method comprises the steps of: in step S4, the parameter estimation problem under missing data is solved using the EM algorithm, and its complete data likelihood function can be expressed as:
wherein m is the number of experimental devices, niFor the observed number of the tested devices I, I {. is an indicator function;
the incremental probability density function of the fault occurrence time at three incremental different positions is expressed as follows:
wherein { k ═ 1,2,3} is represented by τ > t, respectivelyi，j+1，ti＜τ＜ti，j+1 and τ＜ti，j。
6. The method of claim 1, wherein the method comprises the steps of: the life distribution of the plurality of parameters under the influence of the fault in step S6 can be divided into two cases, independent and related between the parameters, which can be expressed as:
wherein ,the remaining life of the c-th performance characteristic;
when there is a correlation among the performance parameters in step S6, the joint lifetime distribution function and the joint probability density function can be expressed as:
where C (-) is the Copula function.
7. An electronic device, comprising: a processor, a memory, and a bus, wherein,
the processor and the memory are communicated with each other through the bus;
the memory stores program instructions executable by the processor, the processor invoking the program instructions to perform the method of any of claims 1-6.
8. A non-transitory computer-readable storage medium storing computer instructions that cause a computer to perform the method of any one of claims 1-6.
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| CN111046564A (en) * | 2019-12-16 | 2020-04-21 | 重庆大学 | Method for predicting residual life of two-stage degraded product |
| CN111814331A (en) * | 2020-07-08 | 2020-10-23 | 重庆大学 | Method for predicting residual service life of equipment with multiple variable points under complex conditions |
| CN112101662A (en) * | 2020-09-16 | 2020-12-18 | 珠海格力电器股份有限公司 | Equipment health condition and life cycle detection method, storage medium and electronic equipment |
| CN112505568A (en) * | 2020-11-11 | 2021-03-16 | 电子科技大学 | Multi-stack solid oxide fuel cell system service life prediction method |
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| CN112505568B (en) * | 2020-11-11 | 2022-03-15 | 电子科技大学 | Multi-stack solid oxide fuel cell system service life prediction method |
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| CN112560234A (en) * | 2020-12-01 | 2021-03-26 | 江苏南高智能装备创新中心有限公司 | Method and device for calculating residual life estimation probability of numerical control machine tool and network side server |
| CN112836380A (en) * | 2021-02-15 | 2021-05-25 | 苏州优它科技有限公司 | Fault estimation and maintenance method for intelligent manufacturing production line |
| CN114429249A (en) * | 2022-04-06 | 2022-05-03 | 杭州未名信科科技有限公司 | Method, system, equipment and storage medium for predicting service life of steel pipe bundle production equipment |
| CN116756881B (en) * | 2023-08-21 | 2024-01-05 | 人工智能与数字经济广东省实验室(广州) | Bearing residual service life prediction method, device and storage medium |
| CN116756881A (en) * | 2023-08-21 | 2023-09-15 | 人工智能与数字经济广东省实验室(广州) | Bearing residual service life prediction method, device and storage medium |
| CN117114352A (en) * | 2023-09-15 | 2023-11-24 | 北京阿帕科蓝科技有限公司 | Vehicle maintenance method, device, computer equipment and storage medium |
| CN117114352B (en) * | 2023-09-15 | 2024-04-09 | 北京阿帕科蓝科技有限公司 | Vehicle maintenance method, device, computer equipment and storage medium |
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