CN116124455A

CN116124455A - Aircraft engine multi-failure mode prediction method based on sensor data degradation modeling

Info

Publication number: CN116124455A
Application number: CN202310086813.6A
Authority: CN
Inventors: 王昱晖; 王迪
Original assignee: Shanghai Jiaotong University
Current assignee: Shanghai Jiaotong University
Priority date: 2023-02-01
Filing date: 2023-02-01
Publication date: 2023-05-16

Abstract

The invention relates to an aircraft engine multi-failure mode prediction method based on sensing data degradation modeling, which comprises the following steps: s1, fusing multi-element sensor signals for monitoring an aircraft engine to obtain a health index, and capturing a degradation state of the engine based on a degradation model in a multi-failure mode; s2, taking the derivative of the degradation state as a failure characteristic, and carrying out parameter estimation of the degradation model by adopting a multi-element expectation maximization algorithm based on a fusion coefficient; and S3, identifying an aircraft engine failure mode, and predicting the residual service life RUL of the aircraft engine by adopting conditional probability distribution. Compared with the prior art, the method has the advantage of high prediction accuracy.

Description

Aircraft engine multi-failure mode prediction method based on sensor data degradation modeling

Technical Field

The invention relates to the technical field of engine failure prediction, in particular to an aircraft engine multi-failure mode prediction method based on sensor data degradation modeling.

Background

Life Prediction and Health Management (PHM) is a hotspot problem in quality management that analyzes the current states of machines and predicts their likely future states. To implement PHM, researchers typically build models to accommodate degradation paths of the machine and predict their Remaining Useful Life (RUL) in a single failure mode. In addition, for failure processes containing multiple sensors, methods such as Health Index (HI) and principal component analysis are used for fusion. However, during most complex operations, multiple failure modes may exist because the failure of different components on the machine exhibits different patterns. Thus, the degradation paths exhibit different trends in various failure modes, and the diversity of the degradation paths may significantly affect the corresponding RUL predictions. Machine failure caused by different failure modes requires different repair, replacement and maintenance plans. Thus, considering failure mode identification and RUL prediction issues in multiple failure modes is critical to achieving an efficient PHM for a machine.

In most studies on prediction of residual useful life RUL in multiple failure modes, researchers first identify the failure mode of each aircraft engine and then build a corresponding degradation model for the failure mode. In the case of a pre-known failure mode modeling an aircraft engine, the failure mode recognition model may be established by supervised learning, which may be achieved by many conventional machine learning and deep learning methods. Such as naive bayes classification models, logistic regression, decision trees, and support vector machines. In actual engineering practice, the actual failure mode of each machine is typically unknown/unlabeled, and therefore such failure mode classification should be assumed using an unsupervised learning approach. Such as entropy-based K-means algorithms, hierarchical clustering, EM algorithms, etc. Although there have been many studies to combine unsupervised learning of pattern recognition with RUL prediction, the related studies are still not in depth. In particular, more efficient feature extraction methods may be implemented to obtain features that are more interpreted on the sensor signal and have higher accuracy in the classification model. Furthermore, since the classification and modeling methods are separate in the study, inaccurate classification can lead to modeling bias, and combining the two methods can optimally improve the problem.

In summary, failure mode identification and residual life RUL prediction in multiple failure modes currently mainly have the following challenges: 1) How to realize failure mode identification and RUL prediction through degradation modeling combination so as to reduce modeling errors caused by classification errors; 2) How to identify failure modes in data limited cases, especially in cases where the failure modes are not known in advance; 3) How to use the comprehensive information of a plurality of sensors to weaken the influence of noise.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a high-accuracy multi-failure mode prediction method for an aircraft engine based on sensor data degradation modeling.

The aim of the invention can be achieved by the following technical scheme:

the invention provides an aircraft engine multi-failure mode prediction method based on sensor data degradation modeling, which comprises the following steps:

s1, fusing multi-element sensor signals for monitoring an aircraft engine to obtain a health index, and capturing a degradation state of the engine based on a degradation model in a multi-failure mode;

s2, taking the derivative of the degradation state as a failure characteristic, and carrying out parameter estimation of the degradation model by adopting a multi-element expectation maximization algorithm based on a fusion coefficient;

and S3, identifying an aircraft engine failure mode, and predicting the residual service life of the aircraft engine by adopting conditional probability distribution.

Preferably, the step S1 comprises the following sub-steps:

step S11, modeling failure mode distribution by using polynomial distribution;

z _l ～Multinomial(π ₁ ,…,π _k ,…,π _K ),(1)

wherein z is _l Indicating the failure mode variable, pi, of the engine l _k The prior probability of the engine in failure mode K is represented, K is the class number of the failure mode, and Multinomial represents polynomial distribution;

step S12, constructing a degradation model of the sensor signal, and capturing the degradation state of the engine:

x _lm (t)＝g _lm (t)+∈ _lm (t)＝Φ(t)Γ _lm +∈ _lm (t),(2)

wherein, the subscript m is the number of the sensor, and the subscript l is the aircraft engineIs the number of (2); x is x _lm (t) is the measurement value of sensor m at time t, g _lm (t) is the degradation state of the sensor m signal at time t, ε _km (t) is a noise term corresponding to the m signal of the sensor, and represents z _l Variance at =k

White noise of (a); m=1, …, M being the number of sensors; phi (t) is a basis function; Γ -shaped structure _lm The degradation model parameter of the sensor signal m accords with the multi-element normal distribution, and the expression is;

wherein mu is _mk Sum sigma _mk Representing a mean and covariance matrix in failure mode k based on the sensor m signal;

s13, fusing signals of the multiple sensors, and constructing a health index, wherein the expression is as follows:

y _l (t)＝x _l (t)w＝Φ(t)Γ _ly +∈ _ly (t),(4)

wherein x is _l (t) is a sensor signal matrix of the engine l, and w is a fusion weight coefficient; Γ -shaped structure _ly Is the degradation model parameter in step S12, E _ly And (t) is a corresponding noise term.

Preferably, said step S2 comprises the following sub-steps:

step S21, taking the derivative of the degradation state of the engine captured in step S1 as a failure characteristic, wherein the expression is as follows:

in phi, phi ⁽¹⁾ (t) is the first derivative basis of the degradation model,

is a matrix form of a first derivative basis Γ _ly Is the degradation of the engine lModel coefficients; />

N is the health index of engine l _l The number of observation time steps of the engine l;

and S22, performing parameter estimation by adopting a multi-element expectation maximization algorithm based on the fusion coefficient.

Preferably, the step S22 specifically includes: estimating unknown parameters by adopting a multi-element expectation maximization algorithm based on a fusion coefficient based on historical signal data of the engine; the unknown parameters comprise a parameter set theta of failure modes and corresponding weight coefficients w, wherein the parameter set theta of the failure modes comprises prior probabilities of the engine in different failure modes, a mean value and covariance matrix of a degradation model and variances of noise items.

Preferably, in the step S22, the estimating the unknown parameter using a multivariate expectation maximization algorithm based on the fusion coefficient includes the following steps:

step S221, calculating posterior log expectation of likelihood functions of the complete data;

step S222, maximizing the parameter set Θ expected to update each failure mode k;

step S223, estimating a weight coefficient w of each failure mode k.

Preferably, the step S221 specifically includes:

the complete data includes:

failure feature based on sensor m signal extraction

Failure feature extracted based on health index ∈ ->

Wherein (1)>

Number n of observation time steps for engine l _l Next corresponding time, l=1, …, L;

the likelihood function expression of the complete data is:

in the formula g ⁽¹⁾ Referring to failure characteristics of all sensors of the engine, Γ is a degradation model parameter, and z is a failure mode variable; the subscript L is the number of the engines, and L is the number of the engines;

wherein:

in the method, in the process of the invention,

failure feature of sensor m, Γ, of engine l, respectively _lm 、Γ _ly Respectively corresponding degradation model parameters; pi represents likelihood cumulative product, +.>

Mean and variance are shown as mu _mk ,∑ _mk Is a normal distribution probability density function of (2), later->

The meaning of the symbols is the same; when the engine is in failure mode k, ρ _lk =1, otherwise ρ _lk ＝0。

Preferably, the step S222 specifically includes:

1) Desired E step: using the parameter theta of the previous iteration j ^9j) And a fusion weight coefficient w ^9j) Calculating an expected logarithm posterior of the complete data likelihood function; according to the theory of EM algorithm, the likelihood function for bringing the posterior expectation of the hidden variable into the complete data is specifically:

11 For hidden variable z) _l According to the Bayesian formula, the parameter ρ _lk Posterior expectation of (2)

The calculated expression of (2) is:

wherein:

P(z _l ＝k)＝π _k

in the method, in the process of the invention,

respectively refer to failure characteristics extracted based on sensor m signals and failure characteristics extracted based on health indexes of the engine l, and Γ _lm 、Γ _ly Respectively corresponding degradation model parameters; y is _l (t) is the health index value of the engine l at time t,>

is a first derivative group, phi _l Is a functional basis for a degradation model; mu (mu) _yk ,∑ _yk Respectively degrading model coefficient Γ _ly Mean and covariance matrix of normal distribution, +.>

Is noise epsilon _ly (t) variance of distribution;

12 Calculating hidden variable Γ _l Posterior distribution of (c):

wherein:

in the method, in the process of the invention,

respectively, sensor and HI failure feature of engine l Γ _lm ，Γ _ly Respectively corresponding degradation model parameters; mu (mu) _yk ,∑ _yk Respectively degrading model coefficient Γ _ly Mean and covariance matrix of normal distribution, +.>

Is noise epsilon _ly (t) variance of distribution, z _l Is a failure mode variable for engine l;

13 Based on the expectation and covariance of the hidden variables), calculating an expected log likelihood for the complete data:

in the method, in the process of the invention,

representing the logarithm expected based on the hidden variable posterior; q (Q) _lmk Representing a parameter mu related to the sensor m _mk ,∑ _mk ,/>

Calculation and mu _yk ,∑ _lyk ,/>

The calculation process of (2) is the same;

2) Maximizing the M step:

expected log likelihood E (Θ, Θ) of complete data ^(j) ) Setting the partial derivative for each degradation model parameter to zero to update the degradation model parameter;

for the j+1th iteration, pi _k ,μ _yk ,∑ _lyk ,

The update expression is:

/>

similarly, the parameter mu related to the sensor m _mk ,∑ _mk ,

And updating.

Preferably, the step S223 is specifically:

for the j+1th iteration, based on updated Θ ^(j+1) Updating the fusion weight coefficient under each failure mode and obtaining an updated estimated value w ^(j+1) ；

HI degradation model parameter Γ of aircraft engine _ly Posterior distribution of (c):

wherein:

wherein x is _l Is a sensor degradation signal matrix of the engine l, w is a sensor fusion coefficient, and Γ _lm 、Γ _ly Respectively corresponding degradation model parameters phi _l Is a functional basis for the degradation model; mu (mu) _yk 、∑ _yk Separate HI degradation model parameters Γ _ly The mean and covariance matrices of the normal distribution,

for a given failure mode k, the conditional distribution of the health index at the time of failure is calculated as:

in the method, in the process of the invention,

is a function base at the time of failure; threshold of failure mode K, k=1, …, K, defined as D _k Is a degradation state value of the engine at the time of failure;

the log-likelihood expression of the degradation state of the health index HI at failure in failure mode k is:

wherein:

in the method, in the process of the invention,

representing a likelihood product of the engine belonging to failure mode k;

by solving for

To estimate w, thus obtaining updated fusion coefficients w in failure mode k at iteration j+1 times ^(j+1) |z _l =k, the expression is:

wherein:

。

preferably, the identifying an aircraft engine failure mode in step S3 is specifically:

wherein:

P(z _q ＝k)＝π _k

wherein z is _q As a failure mode of the engine q,

sensor m and failure feature representing engine q, respectively,/->

And are both sets.

Preferably, in the step S3, a conditional probability distribution is used to predict the remaining service life RUL of the aircraft engine, specifically:

1) Obtaining a degradation model parameter Γ of an engine q based on a health index _qy Posterior distribution of (c):

wherein z is _q =k denotes the failure mode k, y of the identified engine q _q As an index of the health of the engine q,

respectively mean and covariance matrixes of posterior distribution of failure model parameters; g _qy (t) is the state of degradation of engine q based on the health index;

2) Calculation of

Failure state distribution of engine q at time:

wherein:

in the method, in the process of the invention,

is at->

A function base of time t after the moment; />

3) Health index y for a given engine q _q The remaining service life RUL distribution is equal to the degradation state

At last observation time +.>

The time t thereafter exceeds the failure threshold D _k Probability of (2):

in the formula, RUL _q To be able to use the remaining service life RUL of the aircraft engine q,

a RUL cumulative distribution function representing the engine q; ψ (·) represents the cumulative distribution function CDF of normal distribution, ++>

Given RUL _q 0 or more, conditional probability P (RUL) _q ≤t|RUL _q The calculation expression of ≡0) is:

by P (RUL) _q ≤t|T _q Gtoreq 0) =0.5 solves for the residual life RUL prediction value of the engine q.

Compared with the prior art, the invention has the following advantages:

1) The invention considers classification and regression problems under multiple failure modes to predict the residual service life RUL under multiple failure modes, and identifies the specific failure mode of the machine through degradation modeling based on sensor signals;

2) The invention designs an FCIMEM algorithm which is used for estimating model parameters under the condition that model training does not provide failure mode data, and unsupervised classification is realized by setting the failure mode as a hidden variable;

3) The more efficient identification of failure modes based on features extracted from the degraded state rather than the raw sensor data eliminates noise present in the raw sensor data, which is more efficient and interpretable for failure mode identification and RUL prediction.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a failure mode estimation result in an embodiment; the abscissa axis of the picture has the following meanings: for each RUL status, "25, 50, 75, 100, 125" means failure mode identification and results for all in-use aircraft engines in the RUL real data less than or equal to 20, 40, 60, 80 and 120 status, "+ -infinity" indicates the classification result for all aircraft engines in use, the vertical axis represents prediction accuracy;

FIG. 3 is a residual life estimation result in the embodiment; the horizontal axis represents the RUL level, and the vertical axis represents the prediction error, and the error bar represents the standard deviation of the prediction error in the RUL level.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.

Examples

The embodiment provides the multi-failure mode prediction method for the aircraft engine based on the sensing data degradation modeling, which is beneficial to accurately describing the health state and failure process of the multi-failure mode aircraft engine, realizes accurate prediction of the residual life of the aircraft engine, and can effectively reduce economic and social losses caused by damage of the aircraft engine; the method comprises the following steps:

The present embodiment contemplates a data set for a commercial modular aviation propulsion system simulation (C-MAPSS). This dataset provides a plurality of sensor signals for the aircraft 2 engine, developed by NASA, has been widely used for PHM research. Sub-data set FD-003 contained 21 aircraft engine sensor signals, containing 100 historical aircraft engines with complete degradation data and 100 in-use aircraft engines with incomplete degradation data. There are two failure modes due to the High Pressure Compressor (HPC) or the engine fan. The main task of the present invention is to train the proposed model with historical aircraft engines and to make accurate failure mode identification and RUL predictions for the aircraft engines being used, the actual RUL of which is used for verification. In combination with the knowledge of data filtering and the knowledge of experience, six sensor signals, namely T24, T30, T50, P30, ps30 and Phi, are selected for experiments. The present invention performs the preprocessing procedure by z-score normalization and logarithmic transformation.

The invention provides an aircraft engine multi-failure mode prediction method based on sensing data fusion and feature extraction. In particular, since the failure mode of the machine is not known in advance, it is assumed that the failure mode of the machine follows a plurality of distributions. Given the failure mode distribution of the machine, the present invention characterizes the health state of the machine by fusing information from multiple sensor signals to establish a Health Index (HI), and further captures the degradation state of the machine by a degradation model based on the health index HI and each sensor. By taking into account the dependencies and heterogeneities between machines, the degradation model consists of basis functions in terms of time and model coefficients that obey a conditional multivariate normal distribution for a given failure mode. In order to comprehensively utilize information from multiple sensors, the present invention extracts derivatives of the degradation state as features and implements feature enhancement when the sensor data is insufficient, which is more efficient and interpretable for failure mode identification and RUL prediction, and develops an FCIMEM algorithm for parameter estimation. Finally, a failure mode is identified according to the extracted features, and RUL is predicted through conditional probability distribution.

The specific implementation mode is as follows:

1. degradation modeling and sensor fusion in multiple failure modes

In a data-driven predictive problem, the degradation state of an aircraft engine is monitored by placing a plurality of sensors. From these sensors, the present invention can obtain the entire degradation signal of the historical aircraft engine from start to failure. Similarly, only sensor signals at a point in time prior to its failure can be acquired for an aircraft engine in operation. The present invention is concerned with the fact that there are multiple failure modes within a group of aircraft engines, but the specific failure mode of each engine is unknown. The object of the present invention is to propose a method to 1) identify failure modes of different engines 2) predict the RUL of the engine being used.

The present invention assumes K failure modes and each engine degrades in one particular failure mode.

In view of the unknown failure modes of the engine, the failure mode distribution is first modeled by a polynomial distribution:

z _l ～Multinomial(π ₁ ,…,π _k ,…,π _K ),(1)

wherein z is _l Indicating the failure mode variable, pi, of the engine l _K Representing the prior probability of the engine in failure mode k, multinomial represents a polynomial distribution.

For engine l, M sensor signals are observed to reflect the state of the engine, and each engine l degradation state is captured from each sensor signal M, where m=1, …, M, as follows:

x _lm (t)＝g _lm (t)+∈ _lm (t)＝Φ(t)Γ _lm +∈ _lm (t),(2)

wherein x is _lm 9 t) represents the measured value of the sensor signal m at time t, g _km (t) represents the degradation state of the sensor signal m at time t, ε _lm And (t) represents a corresponding noise term. From empirical degradation modeling, by combining a time-dependent basis function Φ (t) with a degradation model parameter Γ of the sensor signal m _lm The degradation state is modeled.

Will fail the mode variable z _l Setting k, carrying out parameter modeling on a degradation model through multivariate normal distribution, and further capturing similarity and heterogeneity of the degradation state of the engine:

wherein mu is _mk Sum sigma _mk Representing the mean and covariance matrix in failure mode k based on sensor signal m. Suppose E _lm (t) is z _l Variance at =k

White noise of (c):

since each sensor contains only a portion of machine degradation information, the present invention provides for obtaining the internal health of each engineConstruction of a health index HI, y, containing more information using sensor fusion method _l (t)＝x _l (t) w, wherein y _l (t) is the health index, x of the engine/constructed _l The sensor signal matrix of the engine l is fused weight coefficient, and w is the fused weight coefficient, wherein the weight coefficient values of the failure modes are different.

Considering the health index HI as a new sensor signal, it can also be modeled by the degradation model described above, which can be written in the form of a matrix as follows:

y _l (t)＝x _l (t)w＝Φ(t)Γ _ly +∈ _ly (t),(5)

wherein, Γ _ly Is a model parameter of HI degradation model, E _ly And (t) is its noise term. At the same time Γ _ly |z _l ＝k～

μ _yk ,∑ _yk Respectively is gamma _ly The mean and covariance matrices of the normal distribution of the conditions obeyed,

is noise epsilon _ly (t) variance of distribution.

2. Feature extraction

Will g ⁽¹⁾ The first derivative of the degradation state, denoted as sensor signal/HI, acts as its extracted failure feature.

To more clearly explain g ⁽¹⁾ Taking the health index HI as an example, the first derivative obtained from the health index HI

Expressed as:

wherein phi is ⁽¹⁾ (t) is the first derivative of the degradation model, Γ _ly Is the HI degradation model coefficient of engine l, and when HI is assumed to be known, Γ can be estimated from equation (5) by least squares _ly 。

Thus, based on the health index HI calculation

/>

Wherein, the liquid crystal display device comprises a liquid crystal display device,

is a matrix form of the first derivative basis.

Is a constructed health index. n is n _l Is the number of observation time steps for engine l.

3. Fusion coefficient-based multivariate expectation maximization FCIMEM algorithm

The unknown parameters of the model proposed in this embodiment can be summarized as follows:

(1) Failure mode index z _l And the polynomial distribution coefficients of the corresponding engine;

(2) Mean mu of multiple normal distribution degradation model parameters _mk ,μ _yk Sum covariance matrix sigma _mk ,Σ _yk ；

(3) Variance of noise term

(4) The weight coefficient w of each failure mode in the sensor fusion method.

For convenience of description, the model unknown parameters in (1) to (3) are expressed as:

the invention is thatAnd (3) completing the estimation of unknown parameters by using the signal data of the L historical engines, wherein the unknown parameters comprise Θ and a fusion weight coefficient w.

The method of the invention comprises the following steps: 1) Calculating posterior log expectation of the complete likelihood function; 2) Maximizing the parameter set Θ expected to update each failure mode k; 3) The weight coefficient w of each failure mode k is estimated.

The general framework of the FCIMEM algorithm is shown in table 1 below:

TABLE 1

And (3) completing the estimation of unknown parameters by using the signal data of the L historical engines, wherein the estimation comprises a parameter set theta and fusion weights w. Wherein Θ ^(j) And w ^(j) Referring to the result of the jth iteration, the following is an introduction to the calculation of a specific formula.

3.1 updating failure model parameters

The likelihood function of the complete data for parameter estimation is obtained taking the extracted features into account.

The complete data includes features extracted based on the sensor signals m and HI

And->

l=1, …, L. For convenience, it is expressed as g ⁽¹⁾ The method comprises the steps of carrying out a first treatment on the surface of the Failure mode variable z _l L=1, …, L, for convenience denoted as z; degradation model coefficient Γ _lm ,Γ _ly L=1, …, L, and Γ is noted for convenience.

The likelihood function of the complete data can be written as:

in the method, in the process of the invention,

referring to failure characteristics of all sensors/HI of engine l Γ _l Representing corresponding failure model parameters. If the engine l is in failure mode k, ρ is defined _lk =1 (i.e. z _l =k), otherwise 0; />

Can be decomposed into:

in the method, in the process of the invention,

failure characteristics of the sensors m/HI, Γ, respectively, of the engine l _lm ，Γ _ly Respectively corresponding degradation model parameters.

For the purpose of detailed calculation of

By way of example, by means of the equation (5), an estimated failure model parameter distribution +.>

And according to formula (6),>

by passing through

Can be calculated, therefore:

J(Φ _l )＝diag[G(t ₁ ),…G(t _nl )]

in the method, in the process of the invention,

probability Density Functions (PDFs) representing normal distributions with known mean and variance.

Is a first derivative group, phi _l Is a functional group of the degradation model, +.>

Is the variance of the error term modeling HI degradation in failure mode k. While the other part P (Γ) of formula (8) _l |z _l ),P(z _l ) The respective can be written as:

in the formula, pi _k Is the prior probability of the engine in failure mode k.

Calculation of the desired (E) step:

and by using the EM algorithm thought, the unknown parameters of the model are estimated and updated by using an iterative algorithm.

In step E, the parameter Θ of the previous iteration j is used ^(j) And a fusion weight coefficient w ^(j) To calculate the expected log posterior of the complete data likelihood function. According to the theory of EM algorithm, the posterior expectation of the hidden variables is brought into the likelihood function of the complete data, and the result obtained in the expected step can be calculated.

For hidden variable z _l According to Bayes formula ρ _lk Posterior expectation of (2)

It can be calculated as:

in the method, in the process of the invention,

respectively, sensor and HI failure feature of engine l Γ _lm ，Γ _ly Respectively corresponding degradation model parameters, and P (z _l ＝k)＝π _k 。/>

Similar to the calculation method of (a)

As an example. According to formula (5), y _l (t) at z _l The conditional distribution is +.>

And then y is _l (t)|z _l =k is brought into (6), so:

and is also provided with

Wherein y is _l (t) is the value of the HI time t,

is a first derivative group, phi _l Is a functional basis for the degradation model. Mu (mu) _yk ,∑ _yk Respectively degrading model coefficient Γ _ly Mean and covariance matrix of normal distribution, +.>

Is noise epsilon _ly (t) variance of distribution.

Next, another hidden variable Γ needs to be calculated _l The posterior distribution of (c) is, as above,

all sensor failure characteristics, μ of engine l _l Representing corresponding failure model parameters. Posterior distribution->

For example, the formula is calculated according to posterior distribution>

The posterior can be obtained as follows:

and is also provided with

In the method, in the process of the invention,

sensor and HI failure feature, μ for engine l, respectively _lm ，μ _ly Respectively corresponding degradation model parameters. Mu (mu) _yk ,∑ _yk Respectively degrading model coefficient Γ _ly Mean and co-formulation of normal distributionDifference matrix, < >>

Is noise epsilon _ly (t) variance of distribution, z _l Is a failure mode variable for engine l. Finally, the expected log likelihood of the hidden variables and covariance are brought in, and the expected log likelihood of the complete data is obtained as follows:

in the method, in the process of the invention,

the remaining symbols represent the logarithm expected based on the hidden variable posterior and are identical to the above. Q (Q) _lmk Representing a parameter mu related to the sensor m _mk ,∑ _mk ,/>

Calculation of the correlation with μ _yk ,∑ _lyk ,/>

Similarly, they are not described in detail herein. />

Calculation of the maximization (M) step:

the maximization step is performed by multiplying E (Sigma ) ^(j) ) The partial derivative for each degradation model parameter is set to zero to update the degradation model parameter. For the j+1th iteration, pi _k ,μ _yk ,∑ _lyk ,

The updates are as follows:

sensor m related parameter mu _mk ,∑ _mk ,

Is similar to the above formula and is not described in detail herein.

3.2 estimating the sensor fusion coefficient w

In the previous step, updated Θ is obtained ^(j+1) . For the j+1st iteration, updating the fusion weight coefficient under each failure mode and obtaining an updated estimated value w ^(j+1) 。

HI degradation model parameter Γ of aircraft engine _ky The posterior distribution of (2) can be calculated as follows:

and is also provided with

is noise epsilon _ly (t) variance of distribution, z _l Is a failure mode variable for engine l.

Thus, given failure mode k, the conditional distribution calculation expression of health index HI at the time of failure is:

in the method, in the process of the invention,

is a function base at the time of failure; threshold of failure mode K, k=1, …, K, defined as D _k The degradation state value of the engine at the time of failure may be specified as an arbitrary real value.

Therefore, the calculation expression of the log likelihood of the degradation state of HI at the time of failure in the pattern k is:

/>

in the method, in the process of the invention,

representing the likelihood product of engines belonging to failure mode k, while

Then, can be solved by

To estimate w, so that updated fusion coefficients in failure mode k can be obtained at iteration j+1, i.e., w ^(j+1) |z _l =k, as follows:

wherein:

4. failure mode identification and RUL prediction

After parameter estimation, it is necessary to identify failure modes and predict the RUL of the engine being used.

The present embodiment represents the sensor signal being represented using engine q as x _q Which has been observed prior to failure

Number of time steps.

For failure mode identification, calculate by equation (12)

Failure mode z of engine q _q Identified as:

in the method, in the process of the invention,

sensor m and HI failure feature, representing engine q, respectively, < >>

Then it is a set of both. At the same time P (z) _q ＝k)＝π _k 。

And->

Calculation is similar>

In (13), there is given, wherein l is replaced with q.

Then, for the RUL prediction in the identified failure mode k, the failure model parameters Γ of the HI-based engine q are obtained according to equation (17) _qy Posterior distribution of (i), i.e

Wherein y is _q HI, & I constructed for Engine q>

The mean and covariance matrices of the posterior distribution of the failure model parameters, respectively. And according to (5) failure model q _qy (t)＝Φ(t)Γ _qy ，g _qy (t) is the degradation state of the engine q based on HI, the time available +.>

The distribution of failure states is: />

And is also provided with

and

Is at->

A function basis of the time t thereafter. Given HIy _q RUL distribution is equal to the degenerated state +.>

At last observation time +.>

After thatTime t of (2) exceeds failure threshold D _k Is shown below:

in the formula, RUL _q For RUL in which the aircraft engine q is being used,

an RUL cumulative distribution function representing the engine q, wherein ψ (·) represents a Cumulative Distribution Function (CDF) of normal distribution, +.>

finally, by P (RUL _q ≤t|T _q Gtoreq 0) =0.5 to obtain the RUL predicted value of the engine q.

5. Parameter estimation results and predictive analysis

Table 2 below shows the estimation results of the key parameters.

TABLE 2

Meanwhile, the method utilizes the prediction accuracy to measure the recognition result of the failure mode of the aircraft engine, specifically, the number of correctly recognized aircraft engines is divided by the total number of aircraft engines, and meanwhile, the prediction error is adopted to measure the prediction result of the residual life of the aircraft engine, and a specific calculation formula is as follows:

wherein ε _q Is an index of the evaluation and is used for evaluating,

RUL, which is the prediction of engine q _q Is a true RUL, T _q Is the total lifetime.

Fig. 2 is a failure mode estimation result according to an embodiment of the present invention. The abscissa axis of the picture has the following meanings: for each RUL status, "25, 50, 75, 100, 125" means failure mode identification and results for all in-use aircraft engines in the RUL real data less than or equal to 20, 40, 60, 80 and 120 status, "+ -infinity" means all in use is a result of classification of aircraft engines. The vertical axis means the prediction accuracy of the present method. It can be seen that the classification accuracy of the invention is still as high as 96% when the RUL grade is greater than 125.

Fig. 3 is a residual life estimation result according to an embodiment of the present invention. The horizontal axis of the picture is the RUL level, which is identical to the meaning of fig. 1, the vertical axis represents the prediction error, while the error bars represent the standard deviation of the prediction error at this RUL level. When the RUL grade is smaller, the result of the invention has quite small prediction error and prediction standard deviation, and when the RUL grade is larger than 125, the error rate of the invention is 7.866 percent and the standard deviation is smaller.

Therefore, the method can realize more accurate classification and prediction effects under different RUL grades, and has important guiding significance for classification and prediction of the faults of the aircraft engine.

While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the invention. Therefore, the protection scope of the invention is subject to the protection scope of the claims.

Claims

1. An aircraft engine multi-failure mode prediction method based on sensor data degradation modeling is characterized by comprising the following steps:

2. An aircraft engine multi-failure mode prediction method based on sensor data degradation modeling according to claim 1, wherein the step S1 comprises the following sub-steps:

step S11, modeling failure mode distribution by using polynomial distribution;

z _l ～Multinomial(π ₁ ，...，π _k ，...，π _K )， (1)

x _lm (t)＝g _lm (t)+∈ _lm (t)＝Φ(t)Γ _lm +∈ _lm (t)， (2)

wherein, the subscript m is the number of the sensor, and the subscript l is the number of the aircraft engine; x is x _lm (t) is the measurement value of sensor m at time t, g _lm (t) is the degradation state of the sensor m signal at time t, ε _lm (t) is a noise term corresponding to the m signal of the sensor, and represents z _l Variance at =k

White noise of (a); m=1,., M is the number of sensors; phi (t) is a basis function; Γ -shaped structure _lm The degradation model parameter of the sensor signal m accords with the multi-element normal distribution, and the expression is;

y _l (t)＝x _l (t)w＝Φ(t)Γ _ly +∈ _ly (t)， (4)

3. An aircraft engine multi-failure mode prediction method based on sensor data degradation modeling according to claim 1, wherein the step S2 comprises the following sub-steps:

is a matrix form of a first derivative basis Γ _ly Is the degradation model coefficient of engine l; />

4. The method for predicting multiple failure modes of an aircraft engine based on sensor data degradation modeling of claim 3, wherein the step S22 specifically comprises: estimating unknown parameters by adopting a multi-element expectation maximization algorithm based on a fusion coefficient based on historical signal data of the engine; the unknown parameters comprise a parameter set theta of failure modes and corresponding weight coefficients w, wherein the parameter set theta of the failure modes comprises prior probabilities of the engine in different failure modes, a mean value and covariance matrix of a degradation model and variances of noise items.

5. The method for predicting multiple failure modes of an aircraft engine based on sensor data degradation modeling according to claim 4, wherein estimating the unknown parameters in step S22 by using a fusion coefficient-based multivariate expectation maximization algorithm comprises the following steps:

step S223, estimating a weight coefficient w of each failure mode k.

6. The method for predicting multiple failure modes of an aircraft engine based on sensor data degradation modeling of claim 5, wherein the step S221 specifically comprises:

the complete data includes:

failure feature based on sensor m signal extraction

Failure feature extracted based on health index ∈ ->

Wherein (1)>

Number n of observation time steps for engine l _l The corresponding time period is set in the next, l=1.. L is;

the likelihood function expression of the complete data is:

wherein:

in the method, in the process of the invention,

Mean and variance are shown as mu _mk ，∑ _mk Is a normal distribution probability density function; when the engine is in failure mode k, ρ _lk =1, otherwise ρ _lk ＝0。

7. The method for predicting multiple failure modes of an aircraft engine based on sensor data degradation modeling of claim 6, wherein the step S222 specifically comprises:

1) Desired E step: using the parameter theta of the previous iteration j ^(j) And a fusion weight coefficient w ^(j) Calculating an expected logarithm posterior of the complete data likelihood function; according to the theory of EM algorithm, the likelihood function for bringing the posterior expectation of the hidden variable into the complete data is specifically:

The calculated expression of (2) is:

wherein:

P(z _l ＝k)＝π _k

in the method, in the process of the invention,

respectively refer to failure characteristics extracted based on sensor m signals and failure characteristics extracted based on health indexes of the engine l, and Γ _lm 、Γ _ly Respectively corresponding degradation model parameters; y is _l (t) is the health index value of the engine l at time t,

is a first derivative group, phi _l Is a functional basis for a degradation model; mu (mu) _yk ，∑ _yk Respectively degrading model coefficient Γ _ly Mean and covariance matrix of normal distribution, +.>

Is noise epsilon _ly (t) variance of distribution;

12 Calculating hidden variable Γ _l Posterior distribution of (c):

wherein:

in the method, in the process of the invention,

respectively, sensor and HI failure feature of engine l Γ _lm ，Γ _ly Respectively corresponding degradation model parameters; mu (mu) _yk ，∑ _yk Respectively degrading model coefficient Γ _ly Mean and covariance matrix of normal distribution, +.>

in the method, in the process of the invention,

representing the logarithm expected based on the hidden variable posterior; q (Q) _lmk Representing a parameter mu related to the sensor m _mk ，∑ _mk ，/>

Calculation and mu _yk ，∑ _lyk ，/>

The calculation process of (2) is the same;

2) Maximizing the M step:

for the j+1th iteration, pi _k ，μ _yk ，∑ _lyk ，

The update expression is: />

Similarly, the parameter mu related to the sensor m _mk ，∑ _mk ，

And updating.

8. The method for predicting multiple failure modes of an aircraft engine based on sensor data degradation modeling of claim 5, wherein the step S223 specifically comprises:

wherein:

in the method, in the process of the invention,

is a function base at the time of failure; threshold of failure mode K, k=1,..k, defined as D _k Is a degradation state value of the engine at the time of failure;

wherein:

/>

in the method, in the process of the invention,

representing a likelihood product of the engine belonging to failure mode k;

by solving for

To estimate w, thus obtaining updated fusion coefficients w in failure mode k at iteration j+1 times ^(j ⁺¹⁾ |z _l =k, the expression is:

wherein:

9. the method for predicting multiple failure modes of an aircraft engine based on sensor data degradation modeling according to claim 2, wherein the identifying the failure modes of the aircraft engine in step S3 specifically comprises:

wherein:

P(z _q ＝k)＝π _k

wherein z is _q As a failure mode of the engine q,

sensor m and failure feature representing engine q respectively,

and are both sets.

10. The method for predicting multiple failure modes of an aircraft engine based on sensor data degradation modeling according to claim 9, wherein the step S3 is to predict the remaining service life RUL of the aircraft engine by using a conditional probability distribution, specifically: