Aircraft Engine Multi-Failure Mode Prediction Method Based on Degradation Modeling of Sensing Data

Abstract

The present invention relates to a method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data. The method comprises the following steps: Step S1, fusing multi-source sensor signals for monitoring the aircraft engine to obtain a health index, and capturing the degradation state of the engine based on a degradation model under multiple failure modes; Step S2, using the derivative of the degradation state as a failure feature, and adopting a multi-source expectation maximization algorithm based on a fusion coefficient to estimate the parameters of the degradation model; Step S3, identifying the failure mode of the aircraft engine, and predicting the remaining useful life (RUL) of the aircraft engine by using a conditional probability distribution. Compared with the prior art, the present invention has the advantage of high prediction accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of engine failure prediction, and more particularly to a method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data. Background Art

[0002] Remaining useful life (RUL) prediction and health management (PHM) is a hot topic in quality management, which analyzes the current state of machines and predicts their possible future states. To implement PHM, researchers usually build models to fit the degradation paths of machines and predict their remaining useful life (RUL) under a single failure mode. In addition, for failure processes with multiple sensors, methods such as health index (HI) and principal component analysis are used for fusion. However, in most complex operating processes, since the failures of different components on a machine exhibit different patterns, there may be multiple failure modes. Therefore, the degradation paths show different trends under multiple failure modes, and the diversity of degradation paths may significantly affect the corresponding RUL prediction. Machine failures caused by different failure modes require different repair, replacement, and maintenance plans. Therefore, considering the failure mode identification and RUL prediction problems under multiple failure modes is crucial for achieving effective PHM of machines.

[0003] In most studies on predicting the remaining useful life (RUL) under multiple failure modes, researchers first identify the failure modes of each aircraft engine, and then establish corresponding degradation models for the failure modes. When the failure modes of the modeled aircraft engines are known in advance, a failure mode identification model can be established through supervised learning, and many traditional machine learning and deep learning methods can achieve this. For example, the naive Bayes classification model, logistic regression, decision tree, and support vector machine. In actual engineering practice, the actual failure modes of each machine are usually unknown / unlabeled, so this failure mode classification should be envisioned using unsupervised learning methods. For example, the entropy-based K-means algorithm, hierarchical clustering, EM algorithm, etc. Although many studies have combined unsupervised learning of pattern recognition with RUL prediction, the related research is still not in-depth. Specifically, more effective feature extraction methods can be implemented to obtain features that are more interpretable for sensor signals and have higher accuracy in classification models. In addition, since the classification and modeling methods in the research are separate, inaccurate classification will lead to modeling bias, and combining these two methods can optimize and improve this problem.

[0004] In summary, the main challenges in failure mode recognition and remaining useful life (RUL) prediction under multiple current failure modes are as follows: 1) How to jointly achieve failure mode recognition and RUL prediction through degradation modeling to reduce the modeling error caused by classification errors; 2) How to identify failure modes in the case of limited data, especially when the failure modes are unknown in advance; 3) How to utilize the comprehensive information of multiple sensors to weaken the influence of noise. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data with high accuracy, which overcomes the defects of the existing technologies described above.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] The present invention provides a method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data, and the method includes the following steps:

[0008] Step S1: Fuse the multi-sensor signals for monitoring the aircraft engine to obtain a health index, and capture the degradation state of the engine based on the degradation model under multiple failure modes;

[0009] Step S2: Use the derivative of the degradation state as a failure feature, and adopt a multivariate expectation-maximization algorithm based on a fusion coefficient to estimate the parameters of the degradation model;

[0010] Step S3: Identify the failure modes of the aircraft engine, and predict the remaining useful life of the aircraft engine using the conditional probability distribution.

[0011] Preferably, the step S1 includes the following sub-steps:

[0012] Step S11: Model the failure mode distribution using the multinomial distribution;

[0013] z l ~Multinomial(π1,…,π k ,…,π K ),(1)

[0014] where z l represents the failure mode variable of engine l, π k represents the prior probability of the engine in failure mode k, K is the number of failure mode categories, and Multinomial represents the multinomial distribution;

[0015] Step S12: Construct a degradation model of the sensor signal to capture the degradation state of the engine:

[0016] x lm (t)=glm (t)+∈ lm (t) = Φ(t)Γ lm +∈ lm (t),(2)

[0017] Where the subscript m is the number of the sensor, and the subscript l is the number of the aircraft engine; x lm (t) is the measured value of sensor m at time t, g lm (t) is the degradation state of the signal of sensor m at time t, ∈ km (t) is the noise term corresponding to the signal of sensor m, representing z l When = k, the variance is of white noise; m = 1, …, M, where M is the number of sensors; Φ(t) is the basis function; Γ lm is the degradation model parameter of sensor signal m, which conforms to the multivariate normal distribution, and the expression is;

[0018]

[0019] Where μ mk and ∑ mk represent the mean and covariance matrix based on the signal of sensor m in failure mode k;

[0020] Step S13, fuse the multi-sensor signals to construct a health index, and the expression is:

[0021] y l (t) = x l (t)w = Φ(t)Γ ly +∈ ly (t),(4)

[0022] Where x l (t) is the sensor signal matrix of engine l, w is the fusion weight coefficient; Γ ly is the degradation model parameter in step S12, ∈ ly (t) is the corresponding noise term.

[0023] Preferably, step S2 includes the following sub-steps:

[0024] Step S21, take the derivative of the degradation state of the engine captured in step S1 as the failure feature, and the expression is:

[0025]

[0026] Where Φ (1) (t) is the first derivative basis of the degradation model, is the matrix form of the first derivative basis, Γ ly is the degradation model coefficient of engine l; is the health index of engine l, n l is the number of observed time steps of engine l;

[0027] Step S22: Use the multi - expectation maximization algorithm based on the fusion coefficient for parameter estimation.

[0028] Preferably, the specific content of step S22 is as follows: Based on the historical signal data of the engine, use the multi - expectation maximization algorithm based on the fusion coefficient to estimate the unknown parameters; where the unknown parameters include the parameter set Θ of the failure mode and the corresponding weight coefficient w, and the parameter set Θ of the failure mode includes the prior probability of the engine under different failure modes, the mean and covariance matrix of the degradation model, and the variance of the noise term.

[0029] Preferably, using the multi - expectation maximization algorithm based on the fusion coefficient to estimate the unknown parameters in step S22 includes iterations:

[0030] Step S221: Calculate the posterior logarithmic expectation of the likelihood function of the complete data;

[0031] Step S222: Maximize the expectation to update the parameter set Θ of each failure mode k;

[0032] Step S223: Estimate the weight coefficient w of each failure mode k.

[0033] Preferably, the specific content of step S221 is as follows:

[0034] The complete data includes:

[0035] Failure features extracted based on the signal of sensor m and failure features extracted based on the health index where, is the time corresponding to the number of observed time steps n of engine l, l = 1, …, L; l l = 1, …, L;

[0036] The expression of the likelihood function of the complete data is:

[0037]

[0038] In the formula, g (1) refers to the failure features of all sensors of the engine, Γ is the degradation model parameter, z is the failure mode variable; the subscript l is the engine number, and L is the number of engines;

[0039] where:

[0040]

[0041]

[0042]

[0043] In the formula, are the failure characteristics of the sensor m of the engine l, respectively, Γ lm , Γ ly are the corresponding degradation model parameters respectively; Π represents the likelihood cumulative product, represents the normal distribution probability density function with the mean and variance being μ mk , ∑ mk respectively, and the meaning of the following symbol is the same; when the engine is in the failure mode k, ρ lk = 1, otherwise ρ lk = 0.

[0044] Preferably, the step S222 is specifically:

[0045] 1) Expectation E step: Use the parameters Θ 9j) of the previous iteration j and the fusion weight coefficient w 9j) to calculate the expected log posterior of the complete data likelihood function; According to the theory of the EM algorithm, substitute the posterior expectation of the latent variable into the likelihood function of the complete data, specifically:

[0046] 11) For the latent variable z l , according to Bayes' formula, the calculation expression of the posterior expectation lk of the parameter ρ is:

[0047]

[0048] Where:

[0049]

[0050]

[0051]

[0052] P(z l = k) = π k

[0053] In the formula, refer to the failure characteristics extracted from the signal of the sensor m of the engine l and the failure characteristics extracted from the health index respectively, Γ lm , Γ ly are the corresponding degradation model parameters respectively; y l (t) is the health index value of the engine l at time t, is the first derivative basis, Φ l is the function basis of the degradation model; μ yk, ∑ yk Degenerate the model coefficients Γ separately ly The mean and covariance matrix of the normal distribution is the noise ∈ ly (t) The variance of the distribution

[0054] 12) Calculate the posterior distribution of the latent variable Γ l :

[0055]

[0056] Where:

[0057]

[0058]

[0059] In the formula, respectively refer to the sensor and HI failure characteristics of engine l, Γ lm , Γ ly are the corresponding degenerate model parameters respectively; μ yk , ∑ yk Degenerate the model coefficients Γ separately ly The mean and covariance matrix of the normal distribution is the noise ∈ ly (t) The variance of the distribution, z l is the failure mode variable of engine l;

[0060] 13) Calculate the expected log-likelihood of the complete data based on the expectation and covariance of the latent variable:

[0061]

[0062] In the formula, represents the logarithm based on the posterior expectation of the latent variable; Q lmk represents the parameter μ related to sensor m mk , ∑ mk , Calculate, the same as the calculation process of μ yk , ∑ lyk , ;

[0063] 2) Maximize the M step:

[0064] Set the partial derivative of the expected log-likelihood E(Θ, Θ (j) ) of the complete data with respect to each degenerate model parameter to zero to update the degenerate model parameters;

[0065] For the (j + 1)-th iteration, π k , μ yk , ∑ lyk, The update expression is:

[0066]

[0067] Similarly, for the relevant parameter μ of sensor m mk , ∑ mk , is updated.

[0068] Preferably, the step S223 is specifically:

[0069] For the (j + 1)-th iteration, based on the updated Θ (j+1) , update the fusion weight coefficient under each failure mode and obtain the updated estimated value w (j+1) ;

[0070] The posterior distribution of the HI degradation model parameter Γ of aircraft engine l ly is:

[0071]

[0072] Where:

[0073]

[0074]

[0075] In the formula, x l is the sensor degradation signal matrix of engine l, w is the sensor fusion coefficient, Γ lm , Γ ly are the corresponding degradation model parameters respectively, Φ l is the function basis of the degradation model; μ yk , ∑ yk are the mean and covariance matrix of the normal distribution of the HI degradation model parameter Γ ly respectively, is the variance of the noise ∈ ly (t) distribution, z l is the failure mode variable of engine l;

[0076] For a given failure mode k, the calculation expression of the conditional distribution of the health index at the fault time is:

[0077]

[0078] In the formula, is the function basis at the fault; the threshold of failure mode k, k = 1, …, K, is defined as D k , which is the degradation state value of the engine at the fault;

[0079] The logarithmic likelihood expression of the degradation state of the health index HI when failing in failure mode k is as follows:

[0080]

[0081] Where:

[0082]

[0083] In the formula, represents the likelihood product of the engine belonging to failure mode k;

[0084] By solving to estimate w, so the updated fusion coefficient w under failure mode k is obtained at the (j + 1)-th iteration (j+1) |z l = k, the expression is:

[0085]

[0086] Where:

[0087]

[0088]

[0089] Preferably, in step S3, identifying the failure mode of the aircraft engine specifically is:

[0090]

[0091] Where:

[0092]

[0093] P(z q = k)= π k

[0094] In the formula, z q is the failure mode of engine q, respectively represent the sensor m and failure characteristics of engine q, is the set of the two.

[0095] Preferably, in step S3, predicting the remaining useful life RUL of the aircraft engine by using the conditional probability distribution specifically is:

[0096] 1) Obtain the posterior distribution of the degradation model parameter Γ qy of engine q based on the health index:

[0097]

[0098] In the formula, z q= k represents the identified fault mode k of the engine q, and y q is the health index of the engine q, are the mean and covariance matrix of the posterior distribution of the failure model parameters respectively; g qy (t) is the degradation state of the engine q based on the health index;

[0099] 2) Calculate the failure state distribution of the engine q at time

[0100]

[0101] where:

[0102]

[0103]

[0104] In the formula, is the function basis of time t after time;

[0105] 3) Given the health index y of the engine q q , the remaining useful life RUL distribution is equal to the probability that the degradation state exceeds the failure threshold D at time t after the last observation time : k In the formula, RUL

[0106]

[0107] In the formula, RUL q is the remaining useful life RUL of the aircraft engine q in use, represents the cumulative distribution function of the RUL of the engine q; Ψ(·) represents the cumulative distribution function CDF of the normal distribution,

[0108] Given RUL q ≥0, the calculation expression of the conditional probability P(RUL q ≤t|RUL q ≥0) is:

[0109]

[0110] By solving P(RUL q ≤t|T q ≥0) = 0.5, the predicted value of the remaining useful life RUL of the engine q is obtained.

[0111] Compared with the prior art, the present invention has the following advantages:

[0112] 1) The present invention considers the classification and regression problems under multiple failure modes to predict the remaining useful life (RUL) under multiple failure modes, and identifies specific failure modes of the machine through degradation modeling based on sensor signals;

[0113] 2) The present invention designs an FCIMEM algorithm for estimating model parameters when failure mode data is not provided in model training, and realizes unsupervised classification by setting the failure mode as a latent variable;

[0114] 3) Identifying failure modes more effectively based on features extracted from the degradation state rather than the original sensor data, eliminating the noise existing in the original sensor data, which is more effective and interpretable for failure mode identification and RUL prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Figure 1 is the flowchart of the method of the present invention;

[0116] Figure 2 is the failure mode estimation result in the embodiment; wherein, the meaning of the horizontal axis of the picture is: for each RUL state, "25, 50, 75, 100, 125" represents the failure mode identification and results of all in-service aircraft engines in the state where the true RUL data is less than or equal to 20, 40, 60, 80, and 120, and "+∞" represents the classification results of all in-service aircraft engines, and the vertical axis represents the prediction accuracy;

[0117] Figure 3 is the remaining life estimation result in the embodiment; wherein, the abscissa is the same as the meaning of the RUL level and Figure 1 the vertical axis represents the prediction error, and the error bar represents the standard deviation of the prediction error at this RUL level. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0118] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0119] Embodiment

[0120] This embodiment provides a method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data. This method helps to accurately describe the health state and failure process of an aircraft engine with multiple failure modes, and realizes accurate prediction of the remaining life of the aircraft engine, which can effectively reduce economic and social losses caused by the damage of the aircraft engine; this method includes:

[0121] Step S1: Fuse the multi-sensor signals for monitoring the aircraft engine to obtain a health index, and capture the degradation state of the engine based on the degradation models under multiple failure modes;

[0122] Step S2: Use the derivative of the degradation state as a failure feature, and adopt a multi-expectation maximization algorithm based on the fusion coefficient to estimate the parameters of the degradation model;

[0123] Step S3: Identify the failure modes of the aircraft engine, and predict the remaining useful life of the aircraft engine using the conditional probability distribution.

[0124] This embodiment considers the dataset of the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS). This dataset provides multiple sensor signals of the aircraft 2 engine, developed by NASA, and has been widely used in PHM research. The sub-dataset FD-003 contains 21 aircraft engine sensor signals, including 100 historical aircraft engines with fully degraded data and 100 in-service aircraft engines with incomplete degraded 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 using the historical aircraft engines, and perform accurate failure mode identification and RUL prediction on the in-service aircraft engines, and its actual RUL is used for verification. Combining the data filtering knowledge and empirical knowledge, the present invention selects six sensor signals for experiments, namely T24, T30, T50, P30, Ps30, and Phi. The present invention performs a preprocessing procedure through z-score normalization and logarithmic transformation.

[0125] Next, use the method of the present invention to perform unknown failure mode identification and remaining life prediction on this dataset. The present invention proposes a multi-failure mode prediction method for aircraft engines based on sensing data fusion and feature extraction. Specifically, since the failure mode of the machine is not known in advance, it is assumed that the failure mode of the machine follows a multinomial distribution. Given the failure mode distribution of the machine, the present invention establishes a health index (HI) by fusing the information from multiple sensor signals to characterize the health state of the machine, and further captures the degradation state of the machine through the degradation models based on the health index HI and each sensor. By considering the dependencies and heterogeneities between machines, the degradation models consist of basis functions in terms of time and model coefficients, and these model coefficients follow a conditional multivariate normal distribution given the failure mode. In order to comprehensively utilize the information from multiple sensors, the present invention extracts the derivative of the degradation state as a feature, and implements feature enhancement when the sensor data is insufficient, which is more effective and interpretable for failure mode identification and RUL prediction, and develops an FCIMEM algorithm for parameter estimation. Finally, identify the failure mode according to the extracted features, and predict the RUL through the conditional probability distribution.

[0126] The specific implementation is as follows:

[0127] 1. Degradation Modeling and Sensor Fusion under Multiple Failure Modes

[0128] In data-driven prediction problems, multiple sensors are placed to monitor the degradation state of aircraft engines. From these sensors, the present invention can obtain the entire degradation signal of a historical aircraft engine from start to failure. Similarly, for an operating aircraft engine, only the sensor signals at a certain time point before failure can be obtained. The situation that the present invention focuses on is that there are multiple failure modes in a group of aircraft engines, but the specific failure mode of each engine is unknown. The objective of the present invention is to propose a method to 1) identify the failure modes of different engines 2) predict the RUL of the engines in use.

[0129] The present invention assumes that there are K failure modes, and each engine degrades under a specific failure mode.

[0130] Given that the failure mode of the engine is unknown, first, the failure mode distribution is modeled by a multinomial distribution:

[0131] z l ~Multinomial(π1,…,π k ,…,π K ),(1)

[0132] In the formula, z l represents the failure mode variable of engine l, π K represents the prior probability of the engine in failure mode k, and Multinomial represents the multinomial distribution.

[0133] For engine l, M sensor signals are observed to reflect the state of the engine. According to each sensor signal m, the degradation state of each engine l is captured, where m = 1,…,M, as follows:

[0134] x lm (t) = g lm (t)+∈ lm (t) = Φ(t)Γ lm +∈ lm (t),(2)

[0135] In the formula, x lm 9t) represents the measured value of sensor signal m at time t, g km (t) represents the degradation state of sensor signal m at time t, ∈ lm (t) represents the corresponding noise term. According to empirical degradation modeling, by combining the time-varying basis function Φ(t) with the degradation model parameters Γ of sensor signal mlm Model the degradation state.

[0136] Set the failure mode variable z l to k, and parametrically model the degradation model through a multivariate normal distribution to further capture the similarities and heterogeneities of the engine degradation state:

[0137]

[0138] where μ mk and ∑ mk represent the mean and covariance matrix under failure mode k based on the sensor signal m. Assume ∈ lm (t) is white noise with variance l when z = k:

[0139]

[0140] Since each sensor only contains part of the machine degradation information, in order to obtain the internal health status of each engine, the present invention uses a sensor fusion method to construct a health index HI containing more information, that is, y l (t) = x l (t)w, where y l (t) is the health index of engine l constructed, x l is the sensor signal matrix of engine l, and w is the fusion weight coefficient, where the weight coefficient values of each failure mode are different.

[0141] Regarding the health index HI as a new sensor signal, it can also be modeled by the above degradation model and can be written in the following matrix form:

[0142] y l (t) = x l (t)w = Φ(t)Γ ly + ∈ ly (t),(5)

[0143] where Γ ly is the model parameter of the HI degradation model, ∈ ly (t) is its noise term. At the same time, Γ ly |z l = k ~ μ yk ,∑ yk are respectively the mean and covariance matrix of the conditional normal distribution that Γ ly follows, is the variance of the noise ∈ ly (t) distribution.

[0144] 2. Feature Extraction

[0145] Express g (1) as the first derivative of the degradation state of the sensor signal / HI as the extracted failure feature.

[0146] To explain g more clearly (1) Taking the health index HI as an example, its first derivative obtained from the health index HI is expressed as:

[0147]

[0148] where Φ (1) (t) is the first derivative basis of the degradation model, and Γ ly is the HI degradation model coefficient of engine l. When assuming that HI is known, Γ can be estimated from Equation (5) by the least squares method ly .

[0149] Therefore, calculate according to the health index HI

[0150]

[0151] where is the matrix form of the first derivative basis. is the constructed health index. n l is the number of observed time steps of engine l.

[0152] 3. Multivariate Expectation-Maximization FCIMEM Algorithm Based on Fusion Coefficient

[0153] The unknown parameters of the model proposed in this embodiment can be summarized as follows:

[0154] (1) Failure mode index z l and the polynomial distribution coefficients of the corresponding engine;

[0155] (2) Mean μ of the degradation model parameters of the multivariate normal distribution mk , μ yk and covariance matrix ∑ mk , Σ yk ;

[0156] (3) Variance of the noise term

[0157] (4) Weight coefficient w of each failure mode in the sensor fusion method.

[0158] For convenience of description, the model unknown parameters in (1) to (3) are expressed as: The present invention uses the signal data of L historical engines to complete the estimation of unknown parameters, including Θ and the fusion weight coefficient w.

[0159] The method of the present invention includes iterations: 1) calculating the posterior logarithmic expectation of the complete likelihood function; 2) maximizing the expectation to update the parameter set Θ for each failure mode k; 3) estimating the weight coefficient w for each failure mode k.

[0160] The overall framework of the FCIMEM algorithm is shown in Table 1 below:

[0161] Table 1

[0162]

[0163] Use the signal data of L historical engines to complete the estimation of unknown parameters, including the parameter set Θ and the fusion weight w. Among them, Θ (j) and w (j) refer to the results of the j-th iteration. The following is an introduction to the specific formula calculation.

[0164] 3.1 Update failure model parameters

[0165] Considering the extracted features, obtain the likelihood function of the complete data for parameter estimation.

[0166] The complete data includes the features extracted based on the sensor signal m and HI and l = 1,..., L. For convenience, it is denoted as g (1) ; the failure mode variable z l , l = 1,..., L, is denoted as z for convenience; the degradation model coefficient Γ lm , Γ ly , l = 1,..., L, is denoted as Γ for convenience.

[0167] The likelihood function of the complete data can be written as:

[0168]

[0169] In the formula, refers to the failure characteristics of all sensors / HI of engine l, and Γ l represents the corresponding failure model parameters. If engine l is in failure mode k, define ρ lk = 1 (i.e., z l = k), otherwise it is 0; can be decomposed into:

[0170]

[0171] In the formula, Refer to the failure characteristics of the sensor m / HI of the engine l respectively, Γ lm , Γ ly are the corresponding degradation model parameters respectively.

[0172] For detailed calculation, take as an example. Through Equation (5), the estimated failure model parameter distribution can be obtained And according to Equation (6), Through the calculation can be obtained, so:

[0173]

[0174] J(Φ l ) = diag[G(t1),…G(t nl )]

[0175]

[0176] In the formula, represents the probability density function (PDF) of a normal distribution with known mean and variance. is the first derivative basis, Φ l is the function basis of the degradation model, is the variance of the error term for HI degradation modeling under failure mode k. At the same time, the other parts of Equation (8), P(Γ l |z l ), P(z l ) can be written as:

[0177]

[0178]

[0179] In the formula, π k is the prior probability of the engine under failure mode k.

[0180] Calculation of the expectation (E) step:

[0181] Drawing on the idea of the EM algorithm, an iterative algorithm is used to estimate and update the unknown parameters of the model.

[0182] In the E step, the parameters Θ (j) of the previous iteration j and the fusion weight coefficient w (j) are used to calculate the expected log posterior of the complete data likelihood function. According to the theory of the EM algorithm, substituting the posterior expectation of the latent variable into the likelihood function of the complete data can calculate the result obtained in the expectation step.

[0183] For the latent variable z l , according to Bayes' formula, ρlk The posterior expectation can be calculated as follows:

[0184]

[0185] wherein, respectively refer to the sensor and HI failure characteristics of engine l, Γ lm , Γ ly are the corresponding degradation model parameters respectively, and P(z l = k) = π k . The calculation method of is similar. Taking l l = k, the conditional distribution of y l Substituting y l (t)|z l = k into (6), thus:

[0186]

[0187] And

[0188] wherein, y l (t) is the value of HI at time t, is the first derivative basis, Φ l is the function basis of the degradation model. μ yk , ∑ yk are the mean and covariance matrix of the degradation model coefficients Γ ly respectively, and is the variance of the noise ∈ ly (t) distribution.

[0189] Next, it is necessary to calculate the posterior distribution of another latent variable Γ l . Similarly, refers to all sensor failure characteristics of engine l, and μ l represents the corresponding failure model parameter. Taking the posterior distribution as an example, according to the posterior distribution calculation formula the posterior can be obtained as follows:

[0190]

[0191] And

[0192]

[0193]

[0194] In the formula, respectively refer to the sensor and HI failure characteristics of engine l, μ lm , μ ly are the corresponding degradation model parameters respectively. μ yk , ∑ yk are the degradation model coefficients Γ ly the mean and covariance matrix of the normal distribution, is the noise ∈ ly (t) the variance of the distribution, z l is the failure mode variable of engine l. Finally, substituting the expectations and covariances of the above latent variables, the expected log-likelihood of the complete data is obtained as follows:

[0195]

[0196] In the formula, represents the logarithm based on the posterior expectation of the latent variable, and the meanings of the remaining symbols are the same as above. Q lmk represents the calculation related to the parameters μ mk , ∑ mk , related to sensor m, similar to μ yk , ∑ lyk , so it will not be elaborated in detail here.

[0197] Calculation of the maximization (M) step:

[0198] The maximization step updates the degradation model parameters by setting the partial derivatives of E(∑, ∑ (j) ) with respect to each degradation model parameter to zero. For the (j + 1)-th iteration, π k , μ yk , ∑ lyk , are updated as follows:

[0199]

[0200] The update of the parameters μ mk , ∑ mk , related to sensor m is similar to the above formula, so it will not be elaborated in detail here.

[0201] 3.2 Estimating the sensor fusion coefficient w

[0202] In the previous step, the updated Θ (j+1) was obtained. For the (j + 1)-th iteration, update the fusion weight coefficient under each failure mode and obtain the updated estimated value w (j+1) .

[0203] HI degradation model parameters Γ of aircraft engine l ky The posterior distribution can be calculated as follows:

[0204]

[0205] And

[0206]

[0207]

[0208] Where x l is the sensor degradation signal matrix of engine l, w is the sensor fusion coefficient, Γ lm , Γ ly are the corresponding degradation model parameters respectively, Φ l is the function basis of the degradation model; μ yk , ∑ yk are the mean and covariance matrix of the normal distribution of the HI degradation model parameters Γ ly respectively, is the variance of the noise ∈ ly (t) distribution, z l is the failure mode variable of engine l.

[0209] Therefore, given the failure mode k, the conditional distribution calculation expression of the health index HI at the failure moment is:

[0210]

[0211] Where is the function basis at the time of failure; the threshold of failure mode k, k = 1,…,K, is defined as D k , which is the degradation state value of the engine at the time of failure and can also be specified as any real value.

[0212] Therefore, the calculation expression of the log-likelihood of the degradation state of HI when failing in mode k is:

[0213]

[0214] Where represents the likelihood product of the engines belonging to failure mode k, and at the same time

[0215]

[0216] Then, w can be estimated by solving Therefore, the updated fusion coefficient in failure mode k can be obtained at the (j + 1)-th iteration, that is, w (j+1) |z l = k, as follows:

[0217]

[0218] Wherein:

[0219]

[0220]

[0221] 4. Failure mode identification and RUL prediction

[0222] After parameter estimation, it is necessary to identify the failure mode and predict the RUL of the engine in use.

[0223] In this embodiment, the sensor signal represented by the engine q is denoted as x q , which has been observed before failure Number of time steps.

[0224] For failure mode identification, it is calculated by Equation (12) The failure mode z of the engine q q is identified as:

[0225]

[0226] In the formula, respectively represent the failure characteristics of the sensor m and HI of the engine q, then it is the set of the two. At the same time, P(z q =k)=π k . and The calculation is similar, which is given in (13), where l is replaced by q.

[0227] Then, for the RUL prediction under the identified failure mode k, the posterior distribution of the failure model parameters Γ of the engine q based on HI is obtained according to Equation (17) qy , that is where y q is the HI constructed for the engine q, are the mean and covariance matrix of the posterior distribution of the failure model parameters respectively. And according to the failure model q of (5) qy (t)=Φ(t)Γ qy , g qy (t) is the degradation state of the engine q based on HI, and the distribution of the time to the failure state can be obtained as:

[0228]

[0229] And and is a function basis at time t after Given HIy q , the RUL distribution is equal to the degradation state at the probability that the time t after the last observation time exceeds the failure threshold D k is as follows:

[0230]

[0231] where RUL q is the RUL of the in-use aircraft engine q, represents the cumulative distribution function of the RUL of engine q, where Ψ(·) represents the cumulative distribution function (CDF) of the normal distribution, Given RUL q ≥0, the calculation expression for the conditional probability P(RUL q ≤t|RUL q ≥0) is:

[0232]

[0233] Finally, the RUL prediction value of engine q is obtained by solving P(RUL q ≤t|T q ≥0) = 0.5.

[0234] 5. Parameter Estimation Results and Prediction Analysis

[0235] Table 2 below shows the estimation results of the key parameters.

[0236] Table 2

[0237]

[0238] Meanwhile, this method uses the prediction accuracy to measure the recognition result of the failure mode of the aircraft engine, specifically the number of correctly recognized engines divided by the total number of engines. At the same time, the prediction error is used to measure the prediction result of the remaining life of the aircraft engine. The specific calculation formula is as follows:

[0239]

[0240] where ε q is the evaluation index, is the predicted RUL of engine q, RUL q is the true RUL, and T q is the total life.

[0241] Figure 2This is the failure mode estimation result of the embodiment of the present invention. Among them, the meaning of the horizontal axis of the picture is: for each RUL state, "25, 50, 75, 100, 125" represents the failure mode recognition and results of all in-use aircraft engines in the state where the RUL true data is less than or equal to 20, 40, 60, 80, and 120, and "+∞" represents the classification results of all in-use aircraft engines. The meaning of the vertical axis is the prediction accuracy of this method. It can be seen that when the RUL level is greater than 125, the classification accuracy of the present invention is still as high as 96%.

[0242] Figure 3 This is the remaining useful life estimation result of the embodiment of the present invention. The abscissa of the picture is the RUL level and Figure 1 has the same meaning. The vertical axis represents the prediction error, and at the same time, the error bar represents the standard deviation of the prediction error at this RUL level. When the RUL level is small, the result of the present invention has a relatively small prediction error and prediction standard deviation. When the RUL level is greater than 125, the error rate of the present invention is 7.866% and the standard deviation is also small.

[0243] Thus, it can be seen that the present invention can achieve relatively accurate classification and prediction effects at different RUL levels, and has important guiding significance for the classification and prediction of aircraft engine failures.

[0244] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data, characterized in that, The method includes the following steps: Step S1: Fuse the multi-sensor signals for monitoring the aircraft engine to obtain a health index, and capture the degradation state of the engine based on the degradation models under multiple failure modes, including: Step S11: Model the failure mode distribution using a polynomial distribution; z l ~Multinomial(π1,…,π k ,…,π K ),(1) where z l represents the failure mode variable of engine l, and π k represents the prior probability of the engine in failure mode k, K is the number of categories of failure modes, and Multinomial represents the multinomial distribution; Step S12: Construct a degradation model of the sensor signals to capture the degradation state of the engine: x lm x(t) = g lm x(t) + ∈ lm y(t) = Φ(t)Γ lm + ∈ lm y(t), (2) It should be noted that the original text seems to have some unclear or incomplete expressions, and the translation is based on the best understanding of the given content. where the subscript m is the number of the sensor, and the subscript l is the number of the aircraft engine; x lm (t) is the measured value of sensor m at time t, g lm (t) is the degradation state of the signal of sensor m at time t, ∈ lm (t) is the noise term corresponding to the signal of sensor m, representing z l When = k, the variance is white noise; m = 1, …, M, where M is the number of sensors; Φ(t) is the basis function; Γ lm is the degradation model parameter of sensor signal m, which follows a multivariate normal distribution, and the expression is; where μ mk and ∑ mk represent the mean and covariance matrix based on the signal of sensor m under failure mode k; Step S13: Fuse the multi-sensor signals to construct a health index, and the expression is: where x l (t) is the sensor signal matrix of engine l, w is the fusion weight coefficient; Γ ly are the degradation model parameters in step S12, ∈ ly (t) is the corresponding noise term; Step S2: Use the derivative of the degradation state as a failure feature, and adopt a multi-expectation maximization algorithm based on the fusion coefficient to estimate the parameters of the degradation model, including: Step S21: Use the derivative of the degradation state of the engine captured in Step S1 as a failure feature, and the expression is: where, Φ (1) (t) is the first derivative basis of the degradation model, is the matrix form of the first derivative basis, Γ ly is the degradation model coefficient of engine l; y l = [y l (t1), …, y l (t nl )] T is the health index of engine l, n l is the number of observation time steps of engine l; Step S22: Based on the historical signal data of the engine, adopt a multi-expectation maximization algorithm based on the fusion coefficient to estimate the unknown parameters. Among them, the unknown parameters include the parameter set Θ of the failure mode and the corresponding weight coefficient w. The parameter set Θ of the failure mode includes the prior probability of the engine under different failure modes, the mean and covariance matrix of the degradation model, and the variance of the noise term. The unknown parameter estimation process includes iteration: Step S221: Calculate the posterior logarithmic expectation of the likelihood function of the complete data; Step S222: Maximize the expectation to update the parameter set Θ of each failure mode k; Step S223: Estimate the weight coefficient w of each failure mode k; Step S3: Identify the failure mode of the aircraft engine, and adopt a conditional probability distribution to predict the remaining useful life of the aircraft engine.

2. The method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data according to claim 1, characterized in that, The specific content of Step S221 is: The complete data includes: Failure features extracted based on sensor m signals and failure features extracted based on health indices where is the time corresponding to the observation time step n of the engine l, l = 1, …, L; l at The expression of the likelihood function of the complete data is: where g (1) denotes the failure characteristics of all sensors of the engine, Γ is the degradation model parameter, and z is the failure mode variable; the subscript l is the engine number, and L is the number of engines; Where: P(z l ) = ∏ j (π k ) ρlk , (9) In the formula, are the failure characteristics of the sensor m of the engine l, Γ lm , Γ ly are the corresponding degradation model parameters respectively; Π represents the likelihood cumulative product, represents the normal distribution probability density function with mean μ mk , ∑ mk ; when the engine is in the failure mode k, ρ lk = 1, otherwise ρ lk = 0.

3. The method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data according to claim 2, characterized in that, The specific content of Step S222 is: 1) Expectation E step: Use the parameters Θ of the previous iteration j (j) and the fusion weight coefficient w (j) Calculate the expected log posterior of the complete data likelihood function; According to the theory of the EM algorithm, substitute the posterior expectation of the latent variable into the likelihood function of the complete data, specifically: 11) For the latent variable z l , according to Bayes' formula, the posterior expectation lk of the parameter ρ has the following calculation expression: Where: P(z l = k) = π k In the formula, respectively refer to the failure features extracted from the signals of sensor m by engine l and the failure features extracted based on the health index, Γ lm , Γ ly are the corresponding degradation model parameters; y l (t) is the health index value of engine l at time t, is the first derivative basis, Φ l is the function basis of the degradation model; μ yk , ∑ yk are the mean and covariance matrix of the normal distribution of the degradation model coefficients Γ ly respectively, is the noise ∈ ly (t) the variance of the distribution; 12) Calculate the posterior distribution of the latent variable Γ l : Where: In the formula, respectively refer to the sensor and HI failure characteristics of the engine l, Γ lm , Γ ly are the corresponding degradation model parameters; μ yk , ∑ yk are the degradation model coefficients Γ ly the mean and covariance matrix of the normal distribution, is the noise ∈ ly (t) the variance of the distribution, z l is the failure mode variable of the engine l; 13) Calculate the expected logarithmic likelihood of the complete data based on the expectation and covariance of the latent variable; In the formula, represents the logarithm based on the posterior expectation of the latent variable; Q lmk represents the parameter related to sensor m is calculated, which is the same as the calculation process of ; 2) Maximize the M step: Set the partial derivative of the expected log-likelihood E(Θ, Θ (j) ) with respect to each degradation model parameter to zero to update the degradation model parameters; For the (j + 1)-th iteration, The update expression is: Similarly, relevant parameters of the sensor m are updated.

4. A method for predicting multiple failure modes of an aircraft engine based on sensing data degradation modeling, characterized in that, The specific content of Step S223 is: For the (j + 1)-th iteration, based on the updated Θ (j+1) , update the fusion weight coefficients under each failure mode and obtain the updated estimated value w (j+1) ; Posterior distribution of HI degradation model parameter Γ of aircraft engine l ly : Where: where x l is the sensor degradation signal matrix of engine l, w is the sensor fusion coefficient, Γ lm , Γ ly are the corresponding degradation model parameters respectively, Φ l is the function basis of the degradation model; μ yk , ∑ yk are the mean and covariance matrix of the normal distribution of the HI degradation model parameter Γ ly respectively, is the variance of the noise ∈ ly (t) distribution, z l is the failure mode variable of engine l; For a given failure mode k, the calculation expression of the conditional distribution of the health index at the failure moment is: where Φ(t nl ) is the function basis at the time of failure; the threshold value of failure mode k, k = 1, …, K, is defined as D k , which is the degradation state value of the engine at the time of failure; The logarithmic likelihood expression of the degradation state of the health index HI at the time of failure under the failure mode k is: Where: wherein, represents the likelihood product of the engine belonging to failure mode k; By solving to estimate w, so that the updated fusion coefficient w under failure mode k is obtained at the (j + 1)-th iteration (j +1) ∣z l = k, the expression is: Where:

5. A method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data according to claim 1, characterized in that, In Step S3, the identification of the failure mode of the aircraft engine is specifically: Where: P(z q = k) = π k where z q is the failure mode of engine q, respectively represent the sensor m and failure characteristics of engine q, is the set of the two.

6. A method for predicting multiple failure modes of an aircraft engine based on degradation modeling of sensing data according to claim 5, characterized in that, In Step S3, the prediction of the remaining useful life RUL of the aircraft engine using the conditional probability distribution is specifically: 1) Obtain the posterior distribution of the degradation model parameter Γ of the engine q based on the health index qy : where z q = k represents the fault mode k of the identified engine q, and y q is the health index of the engine q, are the mean and covariance matrix of the posterior distribution of the failure model parameters, respectively; g qy (t) is the degradation state of the engine q based on the health index; 2) Calculation Failure state distribution of engine q at a moment: Where: In the formula, is a function basis of time t after the moment; 3) Given the health index y of the engine q q , the remaining useful life RUL distribution is equal to the degradation state at the last observation time and the probability that the time t after that exceeds the failure threshold D k is: where, RUL q is the remaining useful life RUL of the aircraft engine q in use, represents the RUL cumulative distribution function of the engine q; Ψ(·) represents the cumulative distribution function CDF of the normal distribution, Given RUL q ≥ 0, the calculation expression of the conditional probability P(RUL q ≤ t|RUL q ≥ 0) is as follows: Solve for the predicted remaining useful life (RUL) value of engine q by P(RUL q ≤t∣T q ≥0) = 0.5

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