CN110197288B - Method for predicting residual service life of equipment under influence of faults - Google Patents
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Abstract
The invention discloses a method for predicting the residual service life of equipment under the influence of faults, which specifically comprises the following steps: 1) Determination device presence of a degradation model of the fault; 2) Determining a residual life distribution function of the equipment under the influence of the fault; 3) Determining unknown parameters of the model; 4) A multiparameter device life prediction model is determined. According to the invention, a degradation model of the equipment is established by utilizing a Wiener process, a life distribution function based on the first time is calculated, unknown parameters of the degradation model and unknown parameters distributed at the occurrence time of the fault are estimated through an EM algorithm, and finally, the residual life prediction of the equipment under the influence of the fault is completed.
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
The remaining life has been widely used in the field of aerospace, military and large complex equipment as an important component of predictive and health management technology (PHM). Residual life prediction techniques are critical to ensuring device reliability and safety, and is an important means for reducing the maintenance cost of the equipment. Therefore, the method for predicting the residual life of the equipment is studied, and has very important practical significance.
Since performance degradation data of a device is directly related to the health state of the device, a device lifetime prediction method based on the degradation data is becoming the mainstream. However, as the working environments of most devices are very complex, such as aeroengines, rotating bearings, large fans and other devices, the devices are subjected to abrasion, overload operation, high temperature, high pressure and other environments, the devices can cause certain faults in the performance degradation process, the faults do not affect the continuous operation of the devices, the original degradation trend is 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 for a fault occurring in a degradation process. 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 occurrence 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 period of the equipment is in a normal degradation state, and do not consider that faults possibly occur in the degradation process, so that the accuracy of the service life prediction is reduced. There have also been many studies in recent years that the degradation trajectory of a device changes at a certain time or even at a plurality of times (operating mode switching). But this moment is often considered to be deterministic and the number of transitions is known. The moment of occurrence of the fault is not observable and unknown, depending on the uncertainty of the fault. The fault may occur at any time and its probability of occurrence increases as the operating time of the device increases. This results in a large difference between the life prediction result and the actual life obtained by the general method, and a limited reference value. Considering the degradation process of equipment affected by faults is a difficulty in equipment life prediction research.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a method for predicting the remaining service life of a device under the influence of a fault. It is therefore an object of the present invention to provide a method for the remaining life of a device taking into account the effects of a fault. Establishing a degradation model under the influence of faults by utilizing a Wiener process, wherein a drift coefficient 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 the fault occurrence time as a random variable, obeying a certain distribution, and obtaining the residual life distribution based on the first arrival time; because of uncertainty of the fault, the occurrence time of the fault is not observable, so that a missing value exists in an observation interval, and the problem of parameter estimation under missing data is solved by using an EM algorithm; the occurrence of faults can influence the change of a plurality of performance parameters at the same time, and strong correlation exists between the parameters in the degradation process chapter, and the life prediction of the equipment with the plurality of parameters under the influence of the faults is obtained through a Copula function, so that the residual life prediction of the equipment under the influence of the faults is realized, the accuracy of the life prediction can be effectively improved, the maintenance and the maintenance of the equipment are facilitated, and the safe and reliable work of the equipment is ensured.
The invention aims at realizing the following technical scheme:
in a first aspect, the method for predicting the remaining service life of equipment under the influence of faults of the invention comprises the following steps:
step S1: determining a degradation model of the equipment, and changing a drift coefficient by utilizing the characteristics of a Wiener process to describe a degradation track influenced by faults;
step S2: determining the relation between the front and rear of the fault occurrence and the degradation rate by taking the degradation model obtained in the step S1 as a known condition, and respectively obtaining a normal degradation state and a residual life distribution expression of the fault degradation state;
step S3: taking the life distribution of the two states obtained in the step S2 as a known condition, and regarding the occurrence time of the fault as a random variable, thereby obtaining a life distribution function under uncertain faults;
step S4: taking the equipment life distribution function under the influence of the faults obtained in the step S3 as a known condition, regarding the occurrence time of the faults as missing data in the whole detection interval, the EM algorithm is utilized to solve the problem of parameter estimation of missing data in the detection data;
step S5: taking the unknown parameters obtained in the step S4 as known conditions, obtaining the life distribution function determined in the step 3, and obtaining an expected value of the life distribution function, wherein the obtained expected value is a predicted residual life value, so that the life prediction of a single performance parameter of the equipment under the influence of a fault is realized;
step S6: and (3) describing the correlation among the plurality of parameters by using a Copula function by taking the life distribution of the single parameter under the influence of the fault obtained in the step S5 as a known condition, and obtaining the joint life distribution of the plurality of parameters under the influence of the fault, thereby completing the residual life prediction of the equipment.
In particular, in the step S1, the degradation model is:
wherein X (t) represents a degraded performance characteristic value of the device, lambda 1 and λ2 Is the degradation rate before and after failure occurs; b (t) is the standard Brownian motion, which obeys N (0, t), τ is the moment of failure;
considering the detection value as a discrete quantity, the corresponding degradation model is:
wherein ,ΔXi,j To be in increment X i,j+1 -X i,j ，Δt i,j ＝t i,j+1 -t i,j 。
In particular, in step S2, the occurrence time of the fault is known, and the lifetime distribution function expression thereof is
wherein ,
at t i,j A life probability density function at the moment, w is a failure threshold value set by equipment, Z i,j The performance degradation quantity at the current moment;
the corresponding cumulative distribution function of remaining life is:
where Φ (·) is the normal distribution of the standard.
In particular, in step S3, the life distribution function obtained by regarding the failure occurrence time as a random variable is expressed as:
wherein ,fτ (τ,θ τ) and Fτ (t,θ τ ) Probability density function and cumulative distribution function, θ, respectively, of failure occurrence time τ τ Representing unknown parameters.
In particular, the EM algorithm is used in step S4 to solve the parameter estimation problem under missing data, and its complete data likelihood function can be expressed as:
wherein m is the number of experimental facilities, n i I { · } is an indication function for the observed number of devices I under test;
Wherein { k=1, 2,3} is denoted as τ, respectively>t i,j+1 ,t i <τ<t i,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 in the case of independent parameters:
wherein ,
remaining life for the c-th performance feature;
when there is a correlation between the performance parameters in step S6, the joint lifetime distribution function and the joint probability density function thereof can be expressed as:
wherein C (.cndot.) 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 complete communication with each other through the bus;
the memory stores program instructions executable by the processor, which are called by the processor to perform the method as described above.
In a third aspect, the present invention provides a non-transitory computer readable storage medium, the non-transitory computer readable storage medium stores computer instructions that cause the computer to perform the method as described previously.
The beneficial effects of the invention are as follows:
1. the life prediction method is provided, the fault influence is introduced into the life prediction method for the first time, and the reliability and the accuracy of life prediction are improved.
2. And regarding the fault occurrence time as a random variable, and acquiring a life distribution function based on the first time.
3. And simultaneously estimating unknown parameters of the degradation model and the fault occurrence moment distribution function by using an EM algorithm.
4. While considering a plurality of performance parameters into life predictions under the influence of faults.
5. Describing the amount correlation among the parameters through a Copula function under the condition that strong correlation exists for a plurality of degradation parameters, and obtaining a multi-parameter life prediction model of the equipment under the influence of faults.
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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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings, in which:
FIG. 1 is a schematic diagram of degradation curves for normal and fault conditions of the present invention;
FIG. 2 is a schematic diagram of degradation trajectories for a plurality of performance parameters under the influence of a fault;
FIG. 3 is a schematic diagram of a residual life prediction result of a 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 presented by way of illustration only and not by way of limitation.
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 device; 3) Determining a lifetime distribution under the influence of a fault; 4) Determining unknown parameters; 5) And determining a multi-parameter life prediction model under the influence of faults, wherein the flow of the whole method is shown in figure 4. Specifically, the method comprises the following steps:
step S1: determining a degradation model of equipment, and changing a drift coefficient by utilizing the characteristics of a Wiener process to describe a degradation track under the influence of faults as shown in fig. 1;
the degradation model expression of the device under normal conditions is:
6.X(t)＝X(0)+λt+σB(t)
the degradation model of the device under the influence of the fault is:
wherein X (t) represents a degraded performance characteristic value of the device, lambda 1 and λ2 Is the degradation rate before and after failure occurs; b (t) is the standard Brownian motion, which obeys N (0, t), τ is the moment of failure;
considering the detection value as a discrete quantity, the corresponding degradation model is:
wherein ,ΔXi,j To be in increment X i,j+1 -X i,j ，Δt i,j ＝t i,j+1 -t i,j 。
Step S2: determining the relation between the front and rear of the fault occurrence and the degradation rate by taking the degradation model obtained in the step S1 as a known condition, and respectively obtaining a normal degradation state and a residual life distribution expression of the fault degradation state;
in particular, the remaining lifetime of the device based on the time of arrival can be expressed as:
T＝inf{t:X(t)≥w|X(0)<w}
further, expressing the remaining lifetime of the device at the current time may be expressed as:
L i,j ＝inf{l:X(t i,j +l)≥w|X i,j <w}
wherein l is the remaining service life.
Since the remaining life distribution under normal conditions follows gaussian distribution, the probability density function and the cumulative distribution function are expressed as:
considering that the fault occurrence time is known, the degradation rate before and after the fault occurrence changes, so the probability density function and the expression of the cumulative distribution function of the remaining service life distribution corresponding to the fixed fault occurrence time can be expressed as:
where Φ (·) is the normal distribution of the standard.
Since the moment of occurrence of the fault is not detectable, it is regarded as a random variable, and the remaining lifetime distribution of the device can be expressed as:
wherein ,fτ (τ,θ τ )，F τ (t,θ τ ) Probability density functions and cumulative probability density functions, which obey a certain distribution as random variables, respectively, for the occurrence timings of faults.
Step S3: taking the life distribution of the two states obtained in the step S2 as a known condition, and regarding the occurrence time of the fault as a random variable, thereby obtaining a life distribution function under uncertain faults;
specifically, the failure occurrence time is taken as missing data, and the joint probability density function is:
wherein A (DeltaX) i )，B(ΔX i,j) and C(ΔXi ) The incremental joint probability density functions before the fault occurs in the whole detection interval, within the detection interval and after the whole detection interval, respectively. They can be expressed as:
step S4: taking the equipment life distribution function under the influence of the faults obtained in the step S3 as a known condition, regarding the occurrence time of the faults as missing data in the whole detection interval, and solving the problem of parameter estimation of the missing data in the detection data by using an EM algorithm;
specifically, in the present embodiment, when there are m devices for lifeDuring testing, each device corresponds to different fault occurrence time { tau } 1 ,τ 2 ,…,τ m The full data likelihood function may be expressed as:
wherein ,δk,i,j For { k.epsilon.1, 2,3} an indicator variable corresponds to the occurrence of the fault at a time τ which occurs at an increment ΔX i,j Three cases in between. Based on this, the full data likelihood log function can be expressed as:
since the purpose of the EM algorithm step E is to calculate the conditional expectation of the complete data likelihood function for missing data, its expression can be expressed as:
wherein ,
θ p ＝λ 1 ,λ 2 ,σ 2 。
the EM algorithm is only effective when the full data likelihood function is linearly separable. The conditional expectation expression can be expressed as:
wherein v consists of missing data and m consists of unknown parameter θ p and θτ Composition is prepared. Whereby the logarithmic function of the two parts is
Due to the presence of the second partial increment, +.>
Then Q 1 and Q2 Can be expressed as:
e step of EM algorithm obtains condition expectation under observation data and observation time at fault occurrence time, and condition expectation Q of first term of complete data log likelihood function 1 Can be expressed as:
due to the second term Q of the complete data log-likelihood function 2 The condition expectations related to inter-increment, the characteristics of the constant integral can be divided into three parts:
a)
b)t i,j <τ<t i,j+1
c)τ≤t i,j ＝τ<t i,1 +t i,1 ≤τ≤t i,j
wherein ,
m steps in the EM algorithm calculate partial derivatives of the complete data likelihood function on the basis of the condition expectation of obtaining the missing data, and the calculation expression is as follows:
step S5: taking the unknown parameters obtained in the step S4 as known conditions, obtaining the life distribution function determined in the step 3, and obtaining an expected value for the life distribution function, wherein the obtained expected value is a predicted residual life value, so that the life prediction of a single performance parameter of the equipment under the influence of a fault is realized, and a life prediction curve shown in the figure 3 is obtained;
step S6: and (3) describing the correlation among the plurality of parameters by using a Copula function by taking the life distribution of the single parameter under the influence of the fault obtained in the step S5 as a known condition, and obtaining the joint life distribution of the plurality of parameters under the influence of the fault, thereby completing the residual life prediction of the equipment.
In this embodiment, it is assumed that the device has n performance degradation characteristics, and the occurrence of a fault affects the change of n parameter degradation trajectories at the same time, as shown in fig. 2. Life distribution function of each performance feature under fault influence
Can be found by the steps described aboveThe remaining useful life of the target device may be expressed as:
the multiple performance parameters of the device may not affect each other during the degradation process, i.e. independent of each other, and the joint distribution function of the remaining service life of the device may be expressed as:
in the degradation process of most devices, the mutual influence of the components of the devices causes a strong correlation among a plurality of performance parameters of the devices, and the strong correlation among the parameters can be described by utilizing a Copula function, wherein the Clayton function is suitable for describing a plurality of parameters related to tail, and the expression is as follows:
wherein alpha is Copula parameter, and the corresponding calculation formula is that
tau is the correlation coefficient.
The multi-parameter life prediction model of a device under the influence of a fault can be expressed as:
wherein, the probability density function corresponding to the probability density function is:
it should be appreciated that embodiments of the invention may be implemented or realized 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 a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner, in accordance with the methods and drawings described in the specific embodiments. 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.
Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes (or variations and/or combinations thereof) described herein may be performed under 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), by hardware, or combinations thereof, collectively executing on one or more processors. 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 computing platform, including, but not limited to, a personal computer, mini-computer, mainframe, workstation, network or distributed computing environment, separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, and so forth. Aspects of the invention may be implemented 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, optical read and/or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer, which when read by a computer, is operable to configure and operate the computer to perform the processes described herein. Further, the machine readable code, or portions thereof, may be transmitted over a wired or wireless network. When such media includes instructions or programs that, in conjunction with a microprocessor or other data processor, implement the steps described above, the invention described herein includes these and other different types of non-transitory computer-readable storage media. The invention also includes the computer itself when the website intrusion detection method and technique based on big data log analysis according to the invention is programmed.
The computer program can be applied to the input data to perform the functions described herein, thereby converting the input data to generate output data that is stored to the 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 specific visual depictions of physical and tangible objects produced on a display.
In practical application, complex equipment such as turbine engines, rolling bearings, large fans and the like, which work in complex working environments, faults can occur to shorten the residual service life of the equipment, and the residual service life prediction of the equipment can be realized by executing the method.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to 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 faults is characterized by comprising the following steps of: the method comprises the following steps:
step S1: determining a degradation model of the equipment, and changing a drift coefficient by utilizing the characteristics of a Wiener process to describe a degradation track influenced by faults;
step S2: determining the relation between the front and rear of the fault occurrence and the degradation rate by taking the degradation model obtained in the step S1 as a known condition, and respectively obtaining a normal degradation state and a residual life distribution expression of the fault degradation state;
step S3: taking the residual life distribution of the two states obtained in the step S2 as a known condition, and regarding the occurrence time of the fault as a random variable, thereby obtaining a service life distribution function of the equipment under the influence of the fault;
step S4: taking the equipment life distribution function under the influence of the faults obtained in the step S3 as a known condition, regarding the occurrence time of the faults as missing data in the whole detection interval, and solving the unknown parameter estimation problem of the missing data in the detection data by using an EM algorithm;
step S5: taking the unknown parameters obtained in the step S4 as known conditions, obtaining the life distribution function determined in the step 3, namely determining the life distribution of a single parameter under the influence of a fault, and carrying out expectation on the life distribution, wherein the obtained expectation value is the predicted residual life value, so that the life prediction of the single performance parameter of the equipment under the influence of the fault is realized;
step S6: and (3) describing the correlation among the plurality of parameters by using a Copula function by taking the life distribution of the single parameter under the influence of the fault obtained in the step S5 as a known condition, and obtaining the joint life distribution of the plurality of parameters under the influence of the fault, thereby completing the residual life prediction of the equipment.
2. The method for predicting remaining life of a device under the influence of a fault as claimed in claim 1, wherein: in the step S1, the degradation model is:
wherein X (t) represents a degraded performance characteristic value of the device, lambda 1 and λ2 Is the degradation rate before and after failure occurs; b (t) is the standard Brownian motion, which obeys N (0, t), τ is the moment of failure;
considering the detection value as a discrete quantity, the corresponding degradation model is:
wherein ,ΔXi,j For increment X i,j+1 -X i,j ，Δt i,j ＝t i,j+1 -t i,j 。
3. The method for predicting remaining life of a device under the influence of a fault as claimed in claim 2, wherein: in step S2, the occurrence time of the fault is known, and the life distribution probability density function expression is
wherein ,
at t i,j A life probability density function at the moment, w is a failure threshold value set by equipment, Z i,j The performance degradation quantity at the current moment;
the corresponding cumulative distribution function of remaining life is:
where Φ (·) is the normal distribution of the standard.
4. A method of predicting the remaining useful life of a device under the influence of a fault as claimed in claim 3, wherein: in step S3, a lifetime distribution function obtained by regarding the occurrence time of the fault as a random variable is expressed as:
wherein ,fτ (τ,θ τ) and Fτ (t,θ τ ) Dividing intoProbability density function and cumulative distribution function, θ, respectively, of failure occurrence time τ τ Representing unknown parameters.
5. The method for predicting remaining life of a device under the influence of a fault as claimed in claim 4, wherein: the EM algorithm is used in step S4 to solve the parameter estimation problem under missing data, and its complete data likelihood function can be expressed as:
wherein m is the number of experimental facilities, 1 i I { · } is an indication function for the observed number of devices I under test;
Wherein { k=1, 2,3} is denoted as τ, respectively>t i,j+1 ,t i <τ<t i,j+1 and τ<ti,j 。
6. The method for predicting remaining life of a device under the influence of a fault as claimed in claim 5, wherein: the lifetime distribution of the multiple parameters under the influence of the fault in step S6 can be divided into two cases of independence and correlation between parameters, which can be expressed as:
wherein ,
remaining life for the c-th performance feature;
when there is a correlation between the performance parameters in step S6, the joint lifetime distribution function and the joint probability density function thereof can be expressed as:
wherein C (.cndot.) is the Copula function.
7. An electronic device, comprising: a processor, a memory, and a bus, wherein,
the processor and the memory complete communication 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 the computer to perform the method of any of claims 1-6.
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| CN111046564B (en) * | 2019-12-16 | 2024-04-05 | 重庆大学 | Residual life prediction method for two-stage degraded product |
| CN113378286B (en) * | 2020-03-10 | 2023-09-15 | 上海杰之能软件科技有限公司 | Fatigue life prediction method, storage medium and terminal |
| CN111460692A (en) * | 2020-04-26 | 2020-07-28 | 中国人民解放军火箭军工程大学 | Equipment residual life prediction method and system considering degradation rate mutual influence |
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