Aircraft engine failure state prediction method integrated with multi-task learning

Abstract

The present invention relates to a method for predicting the failure state of an aircraft engine by integrating multi-task learning, comprising: constructing a multi-task learning model based on a health index model and a failure model in advance, estimating parameters of the multi-task learning model by acquiring sensor failure signal data, acquiring sensor data to be predicted, and loading the multi-task learning model after parameter estimation, obtaining the failure state prediction result, and correspondingly predicting the remaining service life of the engine in use; the failure model uses a quadratic polynomial failure model to describe the failure state, and the health index model describes the health state by linearly superimposing each sensor signal by setting a weight coefficient; according to the relationship between the health state and the failure state, the health model and the failure model are integrated to form a multi-task learning model. Compared with the prior art, the present invention fully considers the similarities between aircraft engines under the same operating state and environment, so that the parameter estimation accuracy is higher.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft engine failure process modeling, and in particular to an aircraft engine failure state prediction method integrating multi-task learning. Background Art

[0002] In most manufacturing systems, machine failure is inevitable, such as aircraft engines, bearing systems, and lithium batteries. Therefore, machine fault prediction and health management (PHM) is crucial to ensure the stability of the entire manufacturing system. Predicting the remaining useful life (RUL) of a machine is one of the most important tasks in PHM. Based on an accurately predicted RUL, the maintenance or replacement of the machine can be arranged more reasonably.

[0003] In existing research, most methods based on data-driven prediction of RUL are based on signal data reflecting the failure status of the machine collected by a single sensor or multiple sensors. However, analysis methods based on single sensor signals, such as random process models and general path models, cannot describe the failure process of the machine in a complex system with multiple sensors containing failure status information. In the analysis methods based on multi-sensor signals, data fusion can fuse the multi-dimensional failure signals of the machine to obtain better RUL prediction results. Existing data fusion methods can be divided into decision-level fusion and data-level fusion. Decision-level fusion focuses on the fusion method of different prediction results, but because it regards each sensor signal as a single failure process, the result cannot describe the failure status well. Data-level fusion focuses on fusing the information of multiple sensor signals to obtain a more comprehensive fusion signal. The main fusion methods include constructing health index (HI), principal component analysis, hidden Markov model, neuro-fuzzy system and neural network. These methods can be summarized as single-task learning (STL), which ignores the similarity of machines due to similar production operation environments. This leads to inaccurate RUL results, especially in the presence of missing data.

[0004] In summary, with the increasing complexity of manufacturing systems, and considering the data missing problems caused by equipment downtime, remote communication failures and other factors, a method is needed that can utilize the similarities between machines through multi-task learning (MTL) to build failure models and predict RUL for high-dimensional incomplete failure signals to ensure the stability of the production system. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide an aircraft engine failure status prediction method integrating multi-task learning. By utilizing high-dimensional engine failure data, a health index model and a degradation model are established and a QOIEM algorithm is proposed for parameter solution. Even in the case of missing data, the remaining life prediction accuracy is still very high.

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

[0007] A method for predicting the failure state of an aircraft engine by integrating multi-task learning comprises: constructing a multi-task learning model based on a health index model and a failure model in advance, and estimating parameters of the multi-task learning model by acquiring sensor failure signal data; acquiring sensor data to be predicted, and loading the multi-task learning model after parameter estimation to obtain a failure state prediction result;

[0008] The failure model uses a quadratic polynomial failure model to describe the failure state, and the health index model describes the health state by linearly superimposing various sensor signals by setting weight coefficients; according to the relationship between the health state and the failure state, the health model and the failure model are fused to form the multi-task learning model.

[0009] Furthermore, the expression of the multi-task learning model is:

[0010] h l =x l w=Φ l Γ l +∈ l

[0011] In the formula, Indicates h l (t), Represents x l (t), The matrix representing φ(t), Represents ε l (t) vector;

[0012] h l (t) is the health status of aircraft engine l in time t, x l (t) = [x l1 (t), ..., x lm (t)]∈R 1×m is the sensor signal vector collected from the m sensors of the aircraft engine l in time t, w∈R m×1 is the weight coefficient; g l (t) is the failure state of aircraft engine l within time t, φ(t)=[1,t,t2 ]∈R 1×3 is the vector of quadratic basis functions at time t, is the vector of model parameters; ε l (t) represents the noise of aircraft engine l in time t.

[0013] Furthermore, the expression of the health index model is:

[0014] h l (t) = x l (t)w

[0015] In the formula, h l (t) is the health status of aircraft engine l in time t, x l (t) = [x l1 (t), ..., x lm (t)]∈R 1×m is the sensor signal vector collected from the m sensors of the aircraft engine l in time t, w∈R m×1 is the weight coefficient;

[0016] The expression of the failure model is:

[0017] g l (t) = φ(t)Γ l

[0018] In the formula, g l (t) is the failure state of aircraft engine l within time t, φ(t)=[1,t,t 2 ]∈R 1×3 is the vector of quadratic basis functions at time t, is the vector of model parameters;

[0019] The relationship between the healthy state and the failure state is expressed as:

[0020] h l (t) = z(x l (t)) = g l (t)+ε l (t)

[0021] In the formula, ε l (t) represents the noise of aircraft engine l in time t.

[0022] Furthermore, the model parameter Γ l Following the multivariate normal distribution, the model parameter Γ l The expression is:

[0023] Γ l ~N(μ Γ , CΓ )

[0024] In the formula, μ Γ and C Γ is the mean vector and covariance matrix of the multivariate normal distribution;

[0025] The noise term ∈ l Subordinate to the normal distribution N(0,σ 2 ), where σ is the variance.

[0026] Furthermore, the process of estimating parameters of the multi-task learning model specifically includes the following steps:

[0027] S1: Construct initialization parameters Θ = [μ Γ , C Γ , σ 2 ] and parameter j, and set j=0;

[0028] S2: According to the properties of the health index model, the weight coefficient w is estimated through quadratic optimization;

[0029] S3: Get the joint distribution based on the complete data The log-likelihood of l The expected logarithmic posterior Q(Θ, Θ) is calculated on the posterior distribution function of (j) );

[0030] S4: by arg max Θ Q(Θ,Θ (j) ), update Θ to Θ (j+1) ;

[0031] S5: Check Θ (j+1) and θ (j) Whether the convergence condition is met, if so, the final parameter estimation result is obtained, otherwise, return to step S2.

[0032] Furthermore, the weight coefficient w is estimated using a quadratic programming model, and the expression of the quadratic programming model of the weight coefficient w is:

[0033]

[0034] stNw=1,-Mw≤0

[0035] in,

[0036]

[0037]

[0038]

[0039]

[0040] Where l (l = 1, ..., L) is the aircraft engine serial number, L is the total number of aircraft engines, r is the adjustment coefficient determined by k-fold cross validation, N∈R 1×m , N is composed of 1 and -1, M = diag(N)∈R m×m and 0∈R m×1 All represent zero vectors, c l is the weight matrix, represents the aircraft engine l at its failure time τ l The sensor signal vector, where I∈R L×L is the identity matrix, 1∈R L×1 is a vector of all 1s.

[0041] Furthermore, we get the weight coefficient w (j) Then, the EM algorithm is used to update the parameters Θ=[μ Γ , C Γ , σ 2 ];Pick As observation data, Γ l As a latent variable; in the EM algorithm, the expected log-likelihood of the complete data is calculated by step S3, and the parameters are updated in step S4.

[0042] Further, in step S3, the expected logarithmic posterior Q(Θ, Θ (j) ) is calculated as:

[0043]

[0044] In the formula, is the logarithmic joint distribution of is the expectation of the posterior distribution of Θ, and lnP(Θ) is the logarithmic hyperprior distribution of Θ.

[0045] Further, in step S4, the parameter θ is obtained by arg max Θ Q(Θ,Θ (j) ) update, and get The specific update expression of parameter Θ is:

[0046]

[0047]

[0048]

[0049] Where l (l = 1, ..., L) is the aircraft engine serial number, L is the total number of aircraft engines, μ ΓFollow multivariate normal distribution in, and are the corresponding mean vector and covariance matrix respectively; and is Γ l |h l , Θ (j) The estimated expectation and covariance of the posterior distribution of , d is the dimension of the multivariate distribution, x l is the sensor signal vector matrix; are the mean and variance of the prior distribution, τ is the degree of freedom, and τ>2, and β represents the confidence level of the prior distribution. In the present invention, they are all hyperparameters. l is the running time of the lth training engine.

[0050] Furthermore, the method also includes predicting the remaining life of the aircraft engine in use according to the sensor data to be predicted by using the multi-task learning model after parameter estimation;

[0051] The calculation process of the remaining life of the aircraft engine in use includes:

[0052] First, the posterior distribution Γ is calculated based on the sensor data to be predicted q |h q , where h q It is through h q =x q w obtained health status;

[0053] Then, given the aircraft engine q in use at a particular time Failure state in according to and the distribution of D, in The calculation expression of the probability that the failure state exceeds the failure threshold at the next time t is:

[0054]

[0055] In the formula, T q is the remaining life of the aircraft engine q in use, CDF(·) is the cumulative distribution function of the standard normal distribution, is the sample mean, is the sample variance, and represents the last observation time of the aircraft engine q in use, n q is the number of available observations for aircraft engine q, given T q ≥0, the conditional probability of the remaining life is expressed as:

[0056]

[0057] Finally, by solving P(T q ≤t|T q ≥0)=0.5 and variable t to predict the remaining life of the aircraft engine q in use.

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] (1) The present invention proposes a multi-task learning method based on data fusion. It uses high-dimensional engine failure data to establish a health index model and a degradation model and proposes a QOIEM algorithm for parameter solution. During the iterative process of solution, the parameters of the fusion model and the failure model are updated simultaneously, making the parameter estimation more accurate.

[0060] (2) The solution of the present invention can accurately predict the remaining life of an engine in use, and still have a high degree of accuracy when data is missing. The method can be extended to other production systems, and through accurate prediction of the remaining life, efficient quality management can be achieved, reducing the hidden dangers caused by failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 1 is a sensor failure signal data, HI and corresponding failure state of a certain aircraft engine in an embodiment of the present invention, wherein the sensor failure signal data and the constructed HI are represented by points, and the corresponding failure state is represented by a solid line;

[0062] Figure 2 The figure shows the comparison of RUL prediction results of the proposed method and the comparative method under loss modes A, B and C at different data missing levels from 10% to 80%;

[0063] Figure 3 The present invention provides a flowchart of a method for predicting aircraft engine failure status by integrating multi-task learning in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0065] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0067] Example 1

[0068] like Figure 3 As shown, this embodiment provides an aircraft engine failure state prediction method integrating multi-task learning, and constructs a multi-task learning (MTL) model based on the health index (HI) model and the failure model to obtain the similarity between each engine. At the same time, the present invention proposes a quadratic programming-maximum a posteriori expectation (QOIEM) parameter algorithm to complete the solution of the above model parameters. Finally, according to the parameters obtained by the solution, the remaining service life of the engine in use can be predicted accordingly.

[0069] By adopting the technical solution provided by the present invention, it is helpful to accurately describe the health status and failure process of aircraft engines, and to accurately predict the remaining life of aircraft engines, which can effectively reduce the economic and social losses caused by damage to aircraft engines.

[0070] This embodiment uses the failure data set of an aircraft turbofan engine as an example. The failure data set of an aircraft turbofan engine used in this embodiment is generated by the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS), which is developed by NASA and is also adopted by many PHM-related studies.

[0071] Considering that the failure signal should show a consistent increasing (or decreasing) trend, 11 candidate sensor failure signals are selected from the 21 sensors in the data set, including T24, T50, P30, Nf, Ps30, Phi, NRf, BPR, htBleed, W31 and W32, to monitor the failure state of the aircraft engine under the same operating state and failure mode. The data set contains historical observation data of 100 aircraft engines (i.e., L = 100), specifically including 20,631 observation data (i.e., ); There are 100 aircraft engines in use (i.e. Q = 100) data, specifically including 13096 observation data (i.e. ). The historical observation data of 100 aircraft engines include data of the entire process from the start of operation to the occurrence of failures, and the data of 100 aircraft engines in use include data of the aircraft engines from the start of operation to a certain point in time, as well as the corresponding RUL real data. This embodiment uses the historical observation data of 100 aircraft engines to train the model, uses the data of 100 aircraft engines in use to predict RUL, and verifies the performance of the model of the present invention by comparing the predicted RUL value with the corresponding RUL real data.

[0072] The model of the present invention is used to model the health index and failure process of an aircraft engine, as well as to predict the remaining service life. The specific implementation method is as follows:

[0073] 1) Health index and failure process modeling

[0074] Failure process modeling:

[0075] The present invention considers a group of aircraft engines that are under the same operating and environmental conditions, so their failure states have similar characteristics. Without loss of generality, consider L aircraft engines with similar failure states. For each aircraft engine l (l = 1, ..., L), there are n l Based on the research experience and trend analysis of sensor signals, a quadratic polynomial failure model is used to describe the failure state:

[0076] g l (t) = φ(t)Γ l (1)

[0077] Where φ(t)=[1,t,t 2 ]∈R 1×3 is the vector of quadratic basis functions at time t, and is the vector of model parameters.

[0078] Health Index Model:

[0079] The present invention converts the failure time τ of the aircraft engine l into l Defined as failure state g l (t) Time exceeding the preset fault threshold D:

[0080]

[0081] The failure state g l (t) is a function of time t. The present invention assumes that the units are operated under the same operating and environmental conditions.

[0082] The definition of HI is given as follows. Assuming the failure state g l(t) can be obtained from the fusion function z(x) of multiple sensor signals contaminated by white noise. l (t)) is recovered, that is,

[0083] g l (t) = z(x l (t))-ε l (t) (3)

[0084] In formula (2), x l (t) = [x l1 (t), ..., x lm (t)]∈R 1×m represents the sensor signal vector collected from m sensors of aircraft engine l in time t. ε l (t) represents the noise of aircraft engine l in time t, where ε l (t)~N(0,σ 2 ). In the present invention, HI is defined as the combination of multiple sensor signals through a fusion function:

[0085] h l (t) = z(x l (t)) (4)

[0086] Among them, h l (t) represents the HI of aircraft engine l at time t. In summary, the relationship between HI and failure state can be expressed as follows:

[0087] h l (t) = z(x l (t)) = g l (t)+ε l (t) (5)

[0088] 2) Multi-task learning modeling based on data fusion

[0089] Since HI represents the health status of each aircraft engine, this study sets the weight coefficient w∈R m×1 x l (t) linear superposition to design HI, so h l (t) can be expressed as

[0090] h l (t) = z(x l (t)) = x l (t)w (6)

[0091] Consider n l observation time points, the health index expression is written in matrix form:

[0092] h l =xl w=Φ l Γ l +∈ l (7)

[0093] in, Indicates h l (t), Represents x l (t), The matrix representing φ(t), Represents ε l (t) vector.

[0094] In order to capture the similarities between aircraft engines, the present invention integrates multi-task learning into the above model structure, aiming to share the knowledge gained in a single aircraft engine. Specifically, the model parameter Γ of each aircraft engine is considered l Share common knowledge among aircraft engines and assume it follows a multivariate normal distribution:

[0095] Γ l ~N(μ Γ , C Γ ) (8)

[0096] Among them, μ Γ and C Γ is the mean vector and covariance matrix of the multivariate normal distribution. Assume μ Γ and C Γ The hyper-prior distribution of is the Normal Inverse Wishart (NIW) distribution, which is the conjugate prior distribution of the multivariate Gaussian distribution:

[0097]

[0098] Here, μ Γ Follow multivariate normal distribution in, and are the corresponding mean vector and covariance matrix, and β represents the confidence level of the prior distribution. Γ Normal inverse Wishart distribution in is the identity matrix, τ is the degree of freedom, and τ>2.

[0099] The multi-task learning model based on data fusion can be summarized as follows:

[0100] a) Construct μ based on formula (9) Γ and C Γ ;

[0101] b) From the distribution Γ l ~N(μΓ , C Γ ) is used to obtain the model parameter Γ of each aircraft engine l l , where l = 1, ..., L;

[0102] c) Given a matrix x representing the sensor signals observed by aircraft engine l l , HI can be constructed as h l =x l w, and further fitted to h using the quadratic model l =Φ l Γ l +∈ l .

[0103] Here, the estimation of model parameters will be based on all suitable aircraft engines, while the construction of health index and the parameter solution of failure process model will be completed at the same time.

[0104] 3) Parameter estimation using QOIEM algorithm

[0105] This embodiment proposes a QOIEM algorithm to estimate the parameters of a multi-task learning model based on data-level fusion. Considering the characteristics of HI structure, the weight coefficient w is estimated by quadratic programming. After obtaining the weight coefficient, the EM algorithm is used to update the parameter Θ in the failure model = [μ Γ , C Γ , σ 2 ]. After that, the corresponding HI is constructed for each aircraft engine, and multi-task learning of the failure model is realized based on the 11 selected sensor failure signal data and the constructed HI. The pseudo code of the method is as follows:

[0106] Algorithm 1 QOIEM algorithm

[0107] Input: Historical observation data of aircraft engines

[0108] Output: Estimated parameters Θ = [μ Γ , C Γ , σ 2 ] and w

[0109] step:

[0110] initialization j=0

[0111] While

[0112] Using quadratic programming to estimate the weight coefficient w in the fusion model (j)

[0113] The MAP-EM algorithm is used to estimate the parameters Θ in the failure model. Γ , C Γ , σ2 ]

[0114] Step E: Calculate the expected logarithmic posterior Q(Θ, Θ (j) )

[0115] M step: by arg max Θ Q(Θ,Θ (j) ) Update Θ and get Θ (j+1)

[0116] If the convergence condition is met, that is, RMSE j+1 %<δ

[0117] Stop loop

[0118] Else

[0119] j=j+1

[0120] Therefore, the process of the QOIEM algorithm can be summarized as follows:

[0121] 1) Initialization parameter Θ = [μ Γ , C Γ , σ 2 ], and set j = 0;

[0122] 2) By considering the properties of the HI construction, the weight coefficient w is estimated through quadratic optimization;

[0123] 3) Expectation (E) step: First obtain the joint distribution based on the complete data The log-likelihood of the latent variable Γ l The expected logarithmic posterior Q(Θ, Θ) is calculated on the posterior distribution function of (j) );

[0124] 4) Maximum (M) step: by arg max Θ Q(Θ,Θ (j) ), update Θ to Θ (j+1)

[0125] 5) Check Θ (j+1) and θ (j) Whether the convergence condition is met. Repeat 2)-5) until the condition is met.

[0126] Quadratic Programming to Estimate w

[0127] Given the jth iteration Θ (j) , the weight coefficients w in the linear fusion function are estimated by considering the following properties of the HI construction:

[0128] 1) Minimum fitting error: The fitting error between the failure model and the constructed HI should be minimal because HI, as a healthy state of an aircraft engine, should be well fitted by the failure model.

[0129] 2) Minimum variance at failure: The variance of the HI constructed for all historical aircraft engines at the time of their failure should be minimal. These aircraft engines are under the same operating conditions and failure modes, so they are assumed to have the same failure threshold.

[0130] 3) Monotonicity: The constructed HI should follow a monotonic trend at all time points so that the remaining life can be predicted by the time it reaches the threshold.

[0131] According to these attributes constructed by HI, corresponding objective functions and constraints can be created. Considering that the failure state at the time point close to the failure time has a greater impact on the RUL prediction, the present invention sets the weight matrix c for different time points. l , and according to formula (7), the weighted residual term is written as in is the failure model parameter Γ l The posterior expectation of is an expression about w.

[0132] In order to obtain Γ l The posterior expectation and variance of , firstly, are calculated based on all historical aircraft engines, with complete data (including and Γ l ) is the log-likelihood function P(h l , Γ l |Θ), it can be written as

[0133]

[0134] in,

[0135]

[0136] Z l represents the normalized coefficient of the distribution. Secondly, at the jth iteration, the latent variable Γ l The posterior expectation of can be solved by To estimate, Γ l The covariance of can be obtained through the Hessian matrix We can estimate the inverse of

[0137]

[0138] in is the result of the previous iteration, and is Γ l |hl , Θ (j) The estimated expectation and covariance of the posterior distribution of . Therefore, an unbiased estimate of the squared fitting error can be calculated as ∑ l (c l ∈ l ) T (c l ∈ l ) / (L-1).

[0139] At the same time, the unbiased estimate of the variance of the constructed HI at failure can be calculated as (x τ w) T G(x τ w). Here, and represents the aircraft engine l at its failure time τ l The sensor signal vector. represents the sensor signal matrix containing the complete failure process until the failure of the historical aircraft engine l, so its failure time τ l Equal to its last observed time point where I∈R L×L is the identity matrix, 1∈R L×1 is a vector of all 1s. Therefore, given the above expressions, the objective function of HI construction is obtained to minimize the fitting error and the variance at failure as follows:

[0140]

[0141] stNw=1,Mw≥0

[0142] where r is the adjustment factor that can be determined by k-fold cross validation. The first constraint uses Nw=1 to normalize the sensor weights, and N∈R 1×m It consists only of 1 and -1 to reflect the sensor signal corresponding to the increasing or decreasing trend of the sensor. The second constraint Mw ≥ 0 ensures the monotonicity of HI, M = diag(N) ∈ R m×m and 0∈R m×1 Represents a vector of all zeros. Through the above steps, the standard quadratic programming model for estimating the weight coefficient w in the jth iteration is obtained

[0143]

[0144] in,

[0145]

[0146]

[0147] and

[0148]

[0149]

[0150] This standard form of quadratic programming problem can be solved using existing solvers (in this case, the qpOASES module in Python). Therefore, the weight coefficient w of the jth iteration can be estimated as w (j) .

[0151] EM algorithm estimates Θ

[0152] Get the weight coefficient w (j) Then, the EM algorithm is used to update the parameters Θ=[μ Γ , C Γ , σ 2 ].Pick As observation data, Γ l As a hidden variable. In the EM algorithm, it is assumed that the expected log-likelihood of the complete data is calculated in the E step and the parameters are updated in the M step.

[0153] Step E:

[0154] According to the maximum a posteriori (MAP) estimation theory, it should be based on the joint distribution and the hyper-prior distribution (i.e., Equation (9)) function P(Θ) to calculate the expected logarithmic posterior Q(Θ, Θ) based on the latent variable distribution (j) ).

[0155] Joint Distribution and the latent variable Γ l The expectation and variance of can be obtained according to equations (10) and (11), where the variable w is solved for w (j) Therefore, the complete data in the jth iteration is Θ (j) The expected logarithm posterior on the posterior distribution of is

[0156]

[0157] in, is the logarithmic joint distribution of Θ (t) The expectation of the posterior distribution of

[0158]

[0159] and ln P(Θ) is the logarithmic hyper-prior distribution of Θ (i.e., equation (9))

[0160]

[0161] in,

[0162]

[0163] Γ d (·) represents the multivariate gamma function, d is the dimension of the multivariate distribution, which is equal to 3 in the present invention, and const has no relationship with Θ and can be ignored in the calculation.

[0164] M step: Θ can be calculated by arg max Θ Q(Θ,Θ (j) ) update, and get The update equation is derived as follows

[0165]

[0166]

[0167]

[0168] Repeat the above process to update the model parameters until convergence is achieved. Convergence condition RMSE j+1 %<δ, where RMSE j+1 is by comparing Θ (j+1) and θ (j) The calculated root mean square error, δ is a pre-specified convergence threshold.

[0169] Table 1 lists the estimated weight coefficient w of each sensor in the fusion model. The positive or negative value of the weight reflects the increase or decrease trend of each sensor. The sum of the absolute values ​​of the weight of each sensor is 1. Table 2 gives the parameter Θ = [μ Γ , C Γ , σ 2 ] is an estimated value.

[0170] Table 1 Estimated weight coefficients w in the sensor model

[0171]

[0172] Table 2 Estimated Θ in the failure model

[0173]

[0174] Figure 1 The sensor signals and constructed HI of randomly selected aircraft engines are shown. l，j The data of (t) are fitted by a quadratic polynomial failure model.

[0175]

[0176] Where l and j represent the index of the unit and sensor respectively. is the random effect parameter, ε l，j (t) is the noise term. is the model parameter vector, following the multivariate high-order distribution Γ l，j ~N(μ Γ，j， C Γ，j ).

[0177] In order to describe the failure process of each single sensor signal of the historical engine group l, we calculate the posterior distribution Γ according to (15): l，j |x l，j , and obtain the failure curve of each single sensor signal shown in the figure, Represents x l，j It can be seen that compared with any single sensor signal, HI has better monotonicity and smaller volatility, which shows that the proposed HI construction method is reasonable and effective.

[0178] 4) RUL prediction

[0179] After training the model with historical data of multi-sensor failure signals of L aircraft engines, the present invention predicts the RUL of the aircraft engines in use and compares the RUL prediction errors of the method proposed by the present invention and the benchmark method.

[0180] For the aircraft engine q in use, there is an incomplete sensor signal matrix Among them, n q is the number of available observations for aircraft engine q. For RUL prediction, we first calculate the posterior distribution Γ q |h q , where h q It is through h q =x q The HI obtained by w is as follows

[0181] Γ q |h q ~N(μ q ,∑ q ),

[0182] in,

[0183]

[0184] and represents the last observation time of the aircraft engine q in use.

[0185] Then, given the aircraft engine q in use at a particular time The failure state, that is in Can be obtained in time The failure state distribution is in, as well as In addition, consider the variation of the fault threshold D. The distribution of D is written as The mean and variance can be obtained by the sample mean and the sample variance Estimated based on historical aircraft engine failure HI. and the distribution of D, in The probability that the failure state exceeds the failure threshold at time t can be written as

[0186]

[0187] Where T q is the RUL of the aircraft engine q in use, and CDF(·) is the cumulative distribution function (CDF) of the standard normal distribution. Given T q ≥0, the conditional probability can be written as,

[0188]

[0189] Finally, by solving P(T q ≤t|T q ≥0)=0.5 and variable t to predict the RUL of the aircraft engine q in use.

[0190] The present invention converts the prediction error ∈ of the aircraft engine q being used q Defined as: Predicted RUL and the real RUL T of the aircraft engines in use q The absolute value of the difference between q Ratio of:

[0191]

[0192] The present invention calculates the ∈ of all aircraft engines in use q , q=1,...,Q, and then the corresponding means and standard errors at different true RUL levels are obtained. In order to reflect the various modes of data loss in real engineering cases, we designed three different signal loss modes to verify the performance of the proposed method, including: A) data point loss; B) time step loss; C) both data points and time steps are lost. Figure 2The figure shows the comparison of RUL prediction results of the method proposed by the present invention and the existing method under loss modes A, B and C, at different data missing rates ranging from 10% to 80%. The results show that the RUL prediction error of the method proposed by the present invention is lower than that of the existing method, because the method of the present invention can share the common information of each unit and effectively handle the problem of data missing, so it has better robustness in the case of data missing.

[0193] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for predicting aircraft engine failure status by integrating multi-task learning, characterized in that: include: A multi-task learning model is constructed in advance based on the health index model and the failure model, and parameters of the multi-task learning model are estimated by acquiring sensor failure signal data; Obtain the sensor data to be predicted and load it into the multi-task learning model after parameter estimation to obtain the failure state prediction result; The failure model uses a quadratic polynomial failure model to describe the failure state, and the health index model describes the health state by linearly superimposing various sensor signals by setting weight coefficients; according to the relationship between the health state and the failure state, the health index model and the failure model are integrated to form the multi-task learning model; The expression of the multi-task learning model is: h l =x l w=Φ l C l +∈ l In the formula, Indicates h l (t), Represents x l (t), The matrix representing φ(t), Represents ε l (t) vector; h l (t) is the health status of the aircraft engine l at time t, x1(t) = [x l1 (t), ..., x lm (t)]∈R 1×m is the sensor signal vector collected from the m sensors of the aircraft engine l in time t, w∈R mm×1 is the weight coefficient; φ(t)=[1,t,t 2 ]∈R1 ×3 is the vector of quadratic basis functions at time t, is the vector of model parameters; ε l (t) represents the noise of aircraft engine l in time t; The expression of the health index model is: h l (t)=xl(t)w In the formula, h l (t) is the health status of aircraft engine l in time t, x l (t) = [x l1 (t), ..., x lm (t)]∈R 1×m is the sensor signal vector collected from the m sensors of the aircraft engine l in time t, w∈R m×1 is the weight coefficient; The expression of the failure model is: g l (t)=φ(t)Γ l In the formula, g l (t) is the failure state of aircraft engine l within time t, φ(t)=[1,t,t 2 ]∈R 1×3 is the vector of quadratic basis functions at time t, is the vector of model parameters; The relationship between the healthy state and the failure state is expressed as: h l (t)=g l (t)+ε l (t) In the formula, ε l (t) represents the noise of aircraft engine l in time t; The model parameter Γ l Following the multivariate normal distribution, the model parameter Γ l The expression is: C l ~N(μ Γ ,C Γ ) In the formula, μ Γ and C Γ is the mean vector and covariance matrix of the multivariate normal distribution; The noise term ∈ l Subordinate to the normal distribution N(0,σ 2 ), where σ is the variance; The process of parameter estimation for a multi-task learning model specifically includes the following steps: S1: Construct initialization parameters Θ = [μ Γ , C Γ , σ 2 ] and parameter j, and set j=0; S2: According to the properties of the health index model, the weight coefficient w is estimated through quadratic optimization; S3: Get the joint distribution based on the complete data The log-likelihood of l The expected logarithmic posterior Q(Θ, Θ) is calculated on the posterior distribution function of (j) ); S4: by arg max Θ Q(Θ,Θ (j) ), update Θ to Θ (j+1) ; S5: Check Θ (j+1) and θ (j) Whether the convergence condition is met, if so, the final parameter estimation result is obtained, otherwise, return to step S2; The weight coefficient w is estimated using a quadratic programming model, and the expression of the quadratic programming model of the weight coefficient w is: st-Nw=1,-Mw≤0 in, Where l is the aircraft engine serial number, l = 1, ..., L, L is the total number of aircraft engines, r is the adjustment coefficient determined by k-fold cross validation, N∈R 1×m , N is composed of 1 and -1, M = diag(N)∈R m×m and 0∈R m×1 All represent zero vectors, c l is the weight matrix, represents the aircraft engine l at its failure time τ l The sensor signal vector, where I∈R L×L is the identity matrix, 1∈R L×1 is a vector of all 1s; Get the weight coefficient w ( j ) Then, the EM algorithm is used to update the parameters Θ=[μ Γ , C Γ , σ 2 ];Pick As observation data, Γ l As a hidden variable; in the EM algorithm, the expected log-likelihood of the complete data is calculated by step S3, and the parameters are updated in step S4; In step S3, the expected logarithmic posterior Q(Θ, Θ (j) ) is calculated as: In the formula, is the logarithmic joint distribution of Θ (t) The expectation of the posterior distribution of , lnP(Θ) is the logarithmic hyperprior distribution of Θ; In step S4, the parameter θ is calculated by arg max Θ Q(Θ,Θ (j) ) update, and get The specific update expression of parameter Θ is: Where β is the confidence level of the prior distribution, l is the aircraft engine serial number, l = 1, ..., L, L is the total number of aircraft engines, μ Γ Follow multivariate normal distribution in, and are the corresponding mean vector and covariance matrix respectively; and is Γ l |h1,Θ (j) The estimated expectation and covariance of the posterior distribution of , d is the dimension of the multivariate distribution, τ is the degrees of freedom, is the variance of the prior distribution, n l is the running time of the lth training engine, x l is the sensor signal vector matrix.

2. The method for predicting aircraft engine failure status by integrating multi-task learning according to claim 1, characterized in that: The method also includes predicting the remaining life of the aircraft engine in use according to the sensor data to be predicted by using the multi-task learning model after parameter estimation; The calculation process of the remaining life of the aircraft engine in use includes: First, the posterior distribution Γ is calculated based on the sensor data to be predicted q |h q , where h q It is through h q =x q w obtained health status; Then, given the aircraft engine q in use at a particular time Failure state in according to and the distribution of D, in The calculation expression of the probability that the failure state exceeds the failure threshold at the next time t is: In the formula, T q is the remaining life of the aircraft engine q in use, CDF(·) is the cumulative distribution function of the standard normal distribution, is the sample mean, is the sample variance, represents the last observation time of the aircraft engine q in use, n q is the number of available observations for aircraft engine q, given T q ≥0, the conditional probability of the remaining life is expressed as: Finally, by solving P(T q ≤t|T q ≥0)=0.5 and variable t to predict the remaining life of the aircraft engine q in use.

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