CN110197288B - Method for predicting residual service life of equipment under influence of faults - Google Patents

Abstract

The invention discloses a method for predicting the remaining service life of equipment under the influence of a fault, which specifically includes: 1) determining the degradation model of the fault in the equipment; 2) determining the remaining life distribution function of the equipment under the influence of the fault; 3) determining the unknown parameters of the model ; 4) Determine a multi-parameter equipment life prediction model. The present invention uses the Wiener process to establish the degradation model of the equipment, calculates the life distribution function based on the first arrival time, estimates the unknown parameters of the degradation model and the unknown parameters of the time distribution of the fault through the EM algorithm, and finally completes the remaining life prediction of the equipment under the influence of the fault , the invention can effectively predict the remaining life of the equipment in a complex environment, which is beneficial to the maintenance and maintenance of the equipment, and ensures that the equipment can work safely and reliably.

Description

Prediction method of remaining useful life of equipment under the influence of faults

Technical Field

The invention relates to the field of remaining service life prediction of equipment, and in particular to a method for predicting the remaining service life of equipment under the influence of a fault.

Background Art

As an important part of prediction and health management technology (PHM), remaining life has been widely used in aerospace, military and large complex equipment fields. Remaining life prediction technology is the key to ensuring equipment reliability and safety, and is also an important means to reduce equipment maintenance costs. Therefore, studying the remaining life prediction method of equipment is of great practical significance.

Since the performance degradation data of the equipment is directly related to the health status of the equipment, the equipment life prediction method based on degradation data has become the mainstream. However, since the working environment of most equipment is very complex, such as aircraft engines, rotating bearings and large fans, they will be subject to wear and tear between equipment, overload operation, high temperature, high pressure and other environments. The equipment will cause some kind of fault during its performance degradation process. The occurrence of this fault does not affect the continued operation of the equipment, but it will change the original degradation trend, accelerate the failure of the equipment, and ultimately shorten the remaining life of the equipment. Figure 1 shows the equipment degradation curve where the fault occurs during the degradation process. For example, a blade of the fan has a defect, and this defect does not affect the continued operation of the fan, but the occurrence of this fault will affect the life of the entire system.

Most of the existing methods for predicting equipment life consider that the equipment is in a normal degradation state throughout its life cycle, without considering that faults may occur during the degradation process, thus reducing the accuracy of life prediction. In recent years, many studies have also shown that the degradation trajectory of equipment will change at a certain moment or even multiple moments (operating condition switching). However, this moment is often regarded as certain, and the number of conversions is known. According to the uncertainty of the fault, the time of occurrence of the fault is unobservable and unknown. The fault may occur at any time, and its probability of occurrence increases with the increase of equipment working time. This results in a large difference between the life prediction results obtained by general methods and the actual life, and the reference value is relatively limited. Considering the impact of faults on the degradation process of equipment is a difficulty in equipment life prediction research.

Summary of the invention

In view of this, the purpose of the present invention is to provide a method for predicting the remaining service life of equipment under the influence of faults. In view of this, the purpose of the present invention is to provide a method for predicting the remaining service life of equipment under the influence of faults. The degradation model under the influence of faults is established by using the Wiener process, and its drift coefficient is used to describe the change of the degradation trajectory, and the diffusion coefficient is used to describe the stability of the degradation process; then, by assuming that the time of fault occurrence is a random variable and obeys a certain distribution, the remaining life distribution based on the first arrival time is obtained; due to the uncertainty of the fault, the time of occurrence cannot be observed, so that there are missing values in the observation interval, and the EM algorithm is used to solve the parameter estimation problem under the existence of missing data; the occurrence of the fault will affect the change of multiple performance parameters at the same time, and there is a strong correlation between the parameters in the degradation process. The multi-parameter equipment life prediction under the influence of the fault is obtained through the Copula function, thereby realizing the remaining life prediction of the equipment under the influence of the fault, which can effectively improve the accuracy of the life prediction, is conducive to the maintenance and maintenance of the equipment, and ensures that it can work safely and reliably.

The objective of the present invention is achieved through the following technical solutions:

In a first aspect, a method for predicting the remaining useful life of equipment under the influence of a fault of the present invention comprises the following steps:

Step S1: Determine the equipment degradation model, use the characteristics of the Wiener process, and change the drift coefficient to describe the degradation trajectory of the fault impact;

Step S2: Taking the degradation model obtained in step S1 as a known condition, determine the relationship between the degradation rate before and after the fault occurs, and obtain the remaining life distribution expressions of the normal degradation state and the fault degradation state respectively;

Step S3: Taking the life distribution of the two states obtained in step S2 as known conditions, the time of the fault occurrence is regarded as a random variable, thereby obtaining the life distribution function under the uncertainty of the fault;

Step S4: Taking the equipment life distribution function under the influence of the fault obtained in step S3 as a known condition, the fault occurrence time is regarded as missing data in the entire detection interval, and the EM algorithm is used to solve the parameter estimation problem of the detection data with missing data;

Step S5: Taking the unknown parameters obtained in step S4 as known conditions, the life distribution function determined in step 3 is obtained, and the expectation thereof is calculated. The expected value obtained is the predicted remaining life value, thereby realizing the life prediction of a single performance parameter of the equipment under the influence of the fault;

Step S6: Taking the life distribution of a single parameter under the influence of the fault obtained in step S5 as a known condition, the Copula function is used to describe the correlation between multiple parameters, and the joint life distribution of multiple parameters under the influence of the fault is obtained, thereby completing the remaining life prediction of the equipment.

In particular, in step S1, the degradation model is:

Where X(t) represents the characteristic value of the equipment's degradation performance, _λ1 and _λ2 are the degradation rates before and after the fault occurs; B(t) is the standard Brownian motion, which obeys N(0,t), and τ is the time when the fault occurs;

Considering the detection value is a discrete quantity, the corresponding degradation model is:

Wherein, ΔX _i,j is the increment Xi _,j+1 -X _i,j , and Δt _i,j =ti _,j+1 -t _i,j .

In particular, in step S2, the time of fault occurrence is known, and its life distribution function expression is:

为在t_i,j时刻的寿命概率密度函数，w为设备设定的失效阈值，Z_i,j为当前时刻的性能退化量；in,

is the life probability density function at time t _i,j , w is the failure threshold set for the equipment, and Zi _,j is the performance degradation at the current moment;

The corresponding remaining life cumulative distribution function is:

where Φ(·) is the standard normal distribution.

In particular, in step S3, the life distribution function obtained by considering the fault occurrence time as a random variable is expressed as:

Among them, f _τ (τ,θ _τ ) and F _τ (t,θ _τ ) are the probability density function and cumulative distribution function of the fault occurrence time τ, respectively, and θ _τ represents the unknown parameter.

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:

Where m is the number of experimental devices, _ni is the number of observations of the tested device i, and I{·} is the indicator function;

为故障发生时刻发生在增量三个不同位置的增量概率密度函数，其表达式为：

is the incremental probability density function of the fault occurring at three different increment positions, and its expression is:

Among them, {k＝1,2,3} respectively represents τ> _ti,j+1 , _ti <τ< _ti,j+1 and τ< _ti,j .

In particular, the life distribution of multiple parameters under the influence of the fault in step S6 can be divided into two cases: the parameters are independent and related. In the case of parameter independence, it can be expressed as:

为第c个性能特征的剩余寿命；in,

is the remaining life of the cth performance characteristic;

When multiple performance parameters are correlated in step S6, their joint life distribution function and 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 communicate with each other via the bus;

The memory stores program instructions that can be executed by the processor, and the processor can execute the aforementioned method by calling the program instructions.

In a third aspect, the present invention provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the method as described above.

The beneficial effects of the present invention are:

1. A life prediction method is provided, which introduces the impact of failure into the life prediction method for the first time, improving the reliability and accuracy of life prediction.

2. Treat the time of failure occurrence as a random variable and obtain the life distribution function based on the first arrival time.

3. Use the EM algorithm to simultaneously estimate the unknown parameters of the degradation model and the distribution function of the fault occurrence time.

4. Consider multiple performance parameters simultaneously in the life prediction under the influence of failure.

5. When there is a strong correlation between multiple degradation parameters, the Copula function is used to describe the correlation between the parameters, and a multi-parameter life prediction model for the equipment under the influence of faults is obtained.

Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

FIG1 is a schematic diagram of degradation curves of a normal state and a fault state of the present invention;

FIG2 is a schematic diagram of degradation trajectories of multiple performance parameters under the influence of a fault;

FIG3 is a schematic diagram of the prediction results of the remaining useful life of the equipment;

FIG4 is a flow chart of the present invention.

DETAILED DESCRIPTION

The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the preferred embodiments are only for illustrating the present invention, rather than for limiting the protection scope of the present invention.

The implementation process of the present invention includes: 1) determining the degradation model under the influence of the fault; 2) determining various performance parameters that can characterize the equipment; 3) determining the life distribution under the influence of the fault; 4) determining the unknown parameters; 5) determining the life prediction model of multiple parameters under the influence of the fault. The whole process of the invention is shown in FIG4. Specifically, it includes the following steps:

Step S1: Determine the equipment degradation model, use the characteristics of the Wiener process, and change the drift coefficient to describe the degradation trajectory under the influence of the fault as shown in Figure 1;

The degradation model expression of the equipment under normal conditions is:

6.X(t)＝X(0)+λt+σB(t)

Then under the influence of the fault, the degradation model of the equipment is:

Where X(t) represents the characteristic value of the equipment's degradation performance, _λ1 and _λ2 are the degradation rates before and after the fault occurs; B(t) is the standard Brownian motion, which obeys N(0,t), and τ is the time when the fault occurs;

Considering the detection value is a discrete quantity, the corresponding degradation model is:

Wherein, ΔX _i,j is the increment Xi _,j+1 -X _i,j , and Δt _i,j =ti _,j+1 -t _i,j .

Step S2: Taking the degradation model obtained in step S1 as a known condition, determine the relationship between the degradation rate before and after the fault occurs, and obtain the remaining life distribution expressions of the normal degradation state and the fault degradation state respectively;

Specifically, the remaining useful life of the equipment based on the first arrival time can be expressed as:

T＝inf{t:X(t)≥w|X(0)<w}

Furthermore, the remaining service life of the equipment at the current moment can be expressed as:

L _i,j =inf{l:X(t _i,j +l)≥w|X _i,j <w}

Where l is the remaining useful life.

Since the remaining life distribution under normal circumstances obeys Gaussian distribution, the expressions of its probability density function and cumulative distribution function are:

Considering that the fault occurrence time is known, the degradation rate before and after the fault occurs changes, so the probability density function and cumulative distribution function of the remaining service life distribution corresponding to the fixed fault occurrence time can be expressed as:

where Φ(·) is the standard normal distribution.

Since the moment of failure is undetectable, it is considered as a random variable and the distribution of the remaining life of the equipment can be expressed as:

Among them, f _τ (τ,θ _τ ) and F _τ (t,θ _τ ) are the probability density function and cumulative probability density function of the fault occurrence time as a random variable obeying a certain distribution.

Step S3: Taking the life distribution of the two states obtained in step S2 as known conditions, the time of the fault occurrence is regarded as a random variable, thereby obtaining the life distribution function under the uncertainty of the fault;

Specifically, the time when the fault occurs is taken as missing data, and the joint probability density function is:

Among them, A(ΔX _i ), B(ΔX _i,j ) and C(ΔX _i ) are the incremental joint probability density functions of the fault occurring before the entire detection interval, within the detection interval and after the entire detection interval respectively. They can be expressed as:

Step S4: Taking the equipment life distribution function under the influence of the fault obtained in step S3 as a known condition, the fault occurrence time is regarded as missing data in the entire detection interval, and the EM algorithm is used to solve the parameter estimation problem of the detection data with missing data;

Specifically, in this embodiment, when there are m devices for life testing, each device corresponds to a different fault occurrence time {τ ₁ ,τ ₂ ,…,τ _m }, and the complete data likelihood function can be expressed as:

Among them, δ _k,i,j is an indicator variable {k∈1,2,3} corresponding to the three situations where the fault occurrence time τ occurs between the increments ΔX _i,j . Based on this, the complete data likelihood logarithm function can be expressed as:

Since the purpose of the E step of the EM algorithm is to calculate the conditional expectation of the complete data likelihood function under missing data, its expression can be expressed as:

θ_p＝λ₁,λ₂,σ²。in,

θ _p =λ ₁ ,λ ₂ ,σ ² .

The EM algorithm is effective only when the complete data likelihood function is linearly separable. So the conditional expectation expression can be expressed as:

由于第二部分增量的存在，

则Q₁和Q₂可以表示为：Here, v consists of missing data and m consists of unknown parameters θ _p and θ _τ . The logarithmic function of the two parts is thus

Due to the existence of the second part of the increment,

Then _Q1 and _Q2 can be expressed as:

The E step of the EM algorithm obtains the conditional expectation of the fault occurrence time under the observed data and observation time, and the conditional expectation _Q1 of the first term of the complete data log-likelihood function can be expressed as:

Since the second term _Q2 of the complete data log-likelihood function involves the conditional expectation between increments, it can be divided into three parts according to the characteristics of the definite integral:

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

in,

The M step in the EM algorithm obtains the partial derivative of the complete data likelihood function based on the conditional expectation of the missing data. The calculation expression is:

Step S5: Taking the unknown parameters obtained in step S4 as known conditions, the life distribution function determined in step 3 is obtained, and the expectation thereof is calculated. The expected value obtained is the predicted remaining life value, thereby realizing the life prediction of a single performance parameter of the equipment under the influence of the fault, and obtaining the life prediction curve shown in FIG3;

Step S6: Taking the life distribution of a single parameter under the influence of the fault obtained in step S5 as a known condition, the Copula function is used to describe the correlation between multiple parameters, and the joint life distribution of multiple parameters under the influence of the fault is obtained, thereby completing the remaining life prediction of the equipment.

可以由前面所述步骤求出，目标设备的剩余使用寿命可以表示为：In this embodiment, it is assumed that the device has n performance degradation characteristics, and the occurrence of a fault will simultaneously affect the change of n parameter degradation trajectories, as shown in Figure 2. The life distribution function of each performance characteristic under the influence of a fault

It can be obtained from the above steps that the remaining service life of the target equipment can be expressed as:

The multiple performance parameters of the equipment may not affect each other during the degradation process, that is, they are independent of each other. Then the joint distribution function of the remaining service life of the equipment can be expressed as:

In the degradation process of most devices, the mutual influence of their components makes multiple performance parameters of the devices strongly correlated. The Copula function can be used to describe the strong correlation between parameters. The Clayton function is suitable for describing multiple parameters with tail correlation, and its expression is:

tau为相关系数。Among them, α is the Copula parameter, and its corresponding calculation formula is:

tau is the correlation coefficient.

The multi-parameter life prediction model of equipment under the influence of failure can be expressed as:

Among them, the corresponding probability density function is:

It should be appreciated that embodiments of the present invention may be implemented or enforced by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable memory. The method may be implemented in a computer program using standard programming techniques - including a non-transitory computer-readable storage medium configured with a computer program, wherein the storage medium so configured causes the computer to operate in a specific and predefined manner - according to 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, if desired, the program may be implemented in an assembly or machine language. In any case, the language may be a compiled or interpreted language. In addition, the program may be run on a programmed ASIC 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 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) that is executed collectively on one or more processors, by hardware, or a combination thereof. The computer program includes a plurality of instructions that may be executed by one or more processors.

Further, the method can be implemented in any type of computing platform that is operably connected to a suitable computer, including but not limited to a personal computer, a minicomputer, a mainframe, a workstation, a network or distributed computing environment, a separate or integrated computer platform, or communicates with a charged particle tool or other imaging device, etc. Aspects of the present invention can be implemented as 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, an optical read and/or write storage medium, a RAM, a ROM, etc., so that it can be read by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the process described herein. In addition, the machine-readable code, or part thereof, can be transmitted via a wired or wireless network. When such media includes instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor, the invention described herein includes these and other different types of non-transitory computer-readable storage media. When programming according to the website intrusion detection method and technology based on big data log analysis described in the present invention, the present invention also includes the computer itself.

The computer program can be applied to input data to perform the functions described herein, thereby converting the input data to generate output data stored in a non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the present invention, the converted data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on the display.

In practical applications, complex equipment such as turbine engines, rolling bearings and large fans may experience failures when working in complex working environments, which may shorten the remaining service life of the equipment. The method of the present invention can be used to predict the remaining service life of such equipment.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of 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 ,ΔX_i,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 ,f_τ (τ,θ _τ) and F_τ (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;

the expression of the incremental probability density function which occurs at three different positions of the increment for the fault occurrence time is as follows: />

Wherein { k=1, 2,3} is denoted as τ, respectively>t _i,j+1 ,t _i <τ<t _i,j+1 and τ<t_i,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.

Images