Modeling method of aero-engine fault-tolerant airborne self-adaptive model

Abstract

The invention provides an aero-engine fault-tolerant airborne adaptive model modeling method. A component-level model, an adaptive linear variable parameter model and an MIRLS-MAEKF are included. According to the method, the advantage of high precision of a component-level model and the advantage of high real-time performance of a self-adaptive LPV model are combined to establish a mixed structure model as an airborne model, and on the basis of a traditional extended Kalman filter, a covariance matrix is multiplied by a forgetting factor to compensate the adverse effect of an incomplete dynamic equation; mIRLS is improved based on IRLS, and the residual weight is determined by depending on the generalized residual; the MIRLS and the MAEKF are combined, a novel MIRLS-MAEKF is designed, and the novel MIRLS-MAEKF is applied to establishment of an aero-engine fault-tolerant airborne adaptive model. Therefore, the estimation precision and the real-time performance of the airborne model are improved, rapid fault detection and isolation can be realized when a plurality of sensors fail at the same time, the fault tolerance and the estimation precision of the airborne self-adaptive model are improved, and meanwhile, the accurate value of the parameter measured by the faulted sensor is estimated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of on-board adaptive model modeling of aero-engine, and particularly relates to a fault-tolerant on-board adaptive model modeling method of aero-engine. BACKGROUND

[0002] During the operation of an aero-engine, natural wear, corrosion, fouling and thermal creep and other factors will cause the performance degradation of the gas path components. At present, the widely used on-board models include component level model (CLM), linear parameter-varying (LPV) model and data-driven model. In fact, compared with CLM, LPV and data-driven model are more practical because they require lower computational load. However, training a data-driven model to cover the flight envelope and engine operating conditions requires a large amount of data, so it cannot ensure the model accuracy of the un-covered flight envelope. The LPV model uses a linear model established by a limited number of operating points, which is obtained by interpolation or fitting method. The performance degradation of aero-engine components and maintenance and installation will cause slight differences in individual performance between the same type of engines, so the offline LPV model cannot cover all conditions, the modeling error is inevitable, and the accuracy of the LPV model is usually lower than that of the CLM. However, the estimation accuracy is highly dependent on the update frequency of the system matrix used in the filter recursion process; the higher the frequency, the higher the estimation accuracy. Since the CLM itself has a large amount of calculation, the model needs to be linearized multiple times, which will greatly increase the total amount of calculation, making it difficult to meet the real-time requirement.

[0003] Due to the harsh working environment of aero-engine and the large number of sensors, sensor faults are prone to occur. Abnormal measurement values will lead to the decrease of the reliability of the on-board adaptive model and the large deviation of the estimated parameters. Huber first proposed the M-estimator, which can overcome the influence of abnormal measurement values by updating the measurement noise covariance matrix. However, this estimator cannot handle errors or outliers for grid topology, which will produce leverage points. To solve this problem, Maronna and Zhao designed the generalized Huber M-estimator, namely the GM-estimator. On this basis, Yacine proposed to realize the robust S-estimator on the batch mode regression representation of the extended Kalman filter (EKF), which has the advantage of high breakdown point, that is, it can still give a robust estimate when facing a large number of outliers, and will not decrease with the increase of system dimension. However, the above methods are based on the iterative reweighted least squares algorithm, which has a good isolation effect on abnormal measurement values, but such methods are only suitable for a certain type of system matrix model with special form, and in some cases there is a problem of divergence of the estimation result, which is not suitable for the estimation of gas turbine engine health parameters. In addition, the current sensor fault diagnosis method usually uses Kalman filter bank for diagnosis, which can realize the diagnosis and signal reconstruction of single sensor and double sensor faults of the engine, but this method needs a large number of filter bank calculations, which seriously affects the real-time performance of the on-board adaptive model.

[0004] In addition, the widely used filters each have problems, such as the linear Kalman filter has a large estimation error for nonlinear systems, the extended Kalman filter needs a random system with complete process and measurement noise covariance for optimal estimation, and the unscented Kalman filter has a high computational complexity due to not using the linearization prior information of different steady points of the nonlinear model. SUMMARY

[0005] To solve the problems in the prior art, the application provides a new hybrid structure fault-tolerant airborne adaptive model based on a modified iterative reweighted least squares-mixed adaptive extended Kalman filter (MIRLS-MAEKF). The model uses a component-level model to improve the model accuracy, and uses an adaptive linear parameter-varying (ALPV) model to improve the real-time performance. Meanwhile, the MAEKF introduces a covariance scaling mechanism based on an extended Kalman filter, and uses a full covariance estimation to update a system noise covariance matrix; the MIRLS is improved based on the IRLS, and determines the residual weight according to the size of the generalized residual. The MIRLS and the MAEKF are combined, the MIRLS-MAEKF is designed, and is applied to the establishment of an airborne adaptive model of an aero-engine. This not only improves the estimation accuracy and real-time performance of the airborne model, but also realizes rapid fault detection and isolation when multiple sensors fail, improves the fault tolerance and estimation accuracy of the airborne adaptive model, and estimates the accurate value of the parameter measured by the faulty sensor.

[0006] The technical scheme of the application is as follows:

[0007] The aero-engine fault-tolerant airborne adaptive model modeling method is characterized in that: the method comprises a CLM, the proposed MIRLS-MAEKF and an ALPV model for online parameter prediction, and adopts a fast-slow double-loop design. The basic working principle is that the output of the airborne engine model is used as the steady-state reference value of the MIRLS-MAEKF, the reference value is estimated in real time by extending the health parameter to the model, and the health parameter is fed back to the CLM and the ALPV model for online updating, so as to ensure the adaptive ability. The partial derivative parameters of the MIRLS-MAEKF are directly provided by the ALPV model, so as to avoid the time-consuming model linearization process, thereby improving the real-time performance. This process is updated at a high rate to realize accurate parameter estimation, and the thermal calculation of the CLM and the correction calculation of the ALPV model are performed at the same time. The adaptive CLM adopts a small deviation linearization method for linearization, so as to correct the parameters of the ALPV model, ensure the accuracy of the ALPV model at the current working point, and meet the accuracy requirements of the system matrix in the recursive process of the MIRLS-MAEKF. This process is updated at a low frequency to cope with the recalculation burden of the CLM, and serves as the slow loop of the model. Through the fast-slow double-loop design, the accuracy and real-time performance of the model are ensured, the slow loop reduces the linearization update frequency of the model, and ensures the accuracy of the model, and the fast loop improves the real-time performance of the airborne adaptive model.

[0008] The MIRLS-MAEKF is a new type of extended Kalman filter. The aero-engine has strong nonlinearity, that is, the system equation and the measurement equation of the model are nonlinear. The EKF is to perform Taylor series expansion on the original system and measurement, and to approximate the system as a first-order linear system to estimate the linear Kalman filter, and the difference from the linear KF is to use the nonlinear model to calculate the state value and the output value, so that the parameter estimation problem of the nonlinear system can be solved. However, the EKF needs a random system with complete process and measurement noise covariance to perform optimal estimation, which may be time-consuming in calculation and has low estimation accuracy. Therefore, the MAEKF algorithm is proposed on the basis of the EKF. The MIRLS is improved based on the IRLS, and the residual weight is determined according to the size of the generalized residual. The MIRLS-MAEKF is designed by combining the MIRLS with the MAEKF and applied to the establishment of the fault-tolerant airborne adaptive model of the aero-engine.

[0009] The aero-engine discrete system in the following form

[0010]

[0011] In the formula, the subscript k represents the value of the variable at the kth step.

[0012] Definition:

[0013]

[0014]

[0015] The design process of the MAEKF is as follows:

[0016] Initialization:

[0017]

[0018]

[0019] State prediction:

[0020]

[0021]

[0022] The difference from the EKF is that the covariance matrix is multiplied by a forgetting factor to compensate for the adverse effects of the incomplete dynamic equation. In this way, the weight of the old data in the filtering process is scaled.

[0023] The forgetting factor in the filter

[0024]

[0025] where λ0 is the baseline value of the forgetting factor.

[0026] N k and T k matrix is

[0027]

[0028]

[0029] where

[0030]

[0031]

[0032] The covariance estimation of the new residual can be derived by averaging the previous N-length residual sequence as follows:

[0033]

[0034] where, is the innovation residual in Kalman filter. The estimated process noise matrix can be obtained as follows:

[0035]

[0036] where, In steady state, the above equation can be obtained by the variance covariance matrix of the following equation, as follows:

[0037]

[0038] The modified step size of MAEKF can be obtained by

[0039]

[0040] The MIRLS module in MIRLS-MAEKF calculates the weight according to the weight formula. The farther the outlier is from the outlier, the smaller the weight is allocated. When the outlier exceeds a certain limit value c, its weight will become 0, which means that the faulty sensor is completely isolated. The hybrid adaptive module updates the measurement noise covariance matrix and the forgetting factor according to the historical data, thereby continuously optimizing the filter parameters. Through the use of the residual of the measurement value and the model calculation value and the parameters calculated by the filter, the state estimation is realized.

[0041] If the correction step is robust, the corresponding robust filter can be obtained. The weighted least squares (WLS) estimator is the maximum likelihood estimator under Gaussian noise, which can be regarded as the estimator that minimizes the norm of the regression residual, which means that satisfies

[0042]

[0043] in, is the standard deviation of the residuals, that is The residual vector is arg min represents the value of the variable that makes the following formula reach the minimum value.

[0044] The estimated standard deviation is affected by abnormal measurements, known as outliers. To minimize the corresponding squared residuals, the filter may even tend to lean toward outliers. The iteratively reweighted least squares (IRLS) method can overcome this problem. The IRLS method iteratively reweights all observations, assigning a weight of 1 to normal observations and a weight less than 1 to abnormal observations. The further the abnormal observation is from the normal value, the smaller the weight, until it reaches 0. When fitting using the WLS method, since the weight of abnormal observations remains 1, the fitting result will deviate significantly from the estimated circle. However, the IRLS method, because it isolates the abnormal observations, achieves a much better fitting effect than the WLS method.

[0045] If the regression minimizes the robust scale of the residual, then the estimate is robust, i.e.

[0046]

[0047] in, Is a robust scale estimator. Minimizing the robust scale estimator ensures the isolation of abnormal measurements. The estimator for estimating the residual scale is defined as follows

[0048]

[0049] Where δ∈[0,1], function ρ is a bounded ρ function satisfying ρ(0)=ρ'(0)=0 and ρ”(0)>0, ρ is an even function and ρ(r) is non-decreasing with respect to r. To ensure the consistency of the estimator under clean data, δ should be fixed to E Φ ρ(r), where Φ is the standard Gaussian distribution, scale estimator Solve by iteration

[0050]

[0051] in, is the relative standard residual, the weight function

[0052]

[0053] The ρ function is chosen to be

[0054]

[0055] The weight function is defined as

[0056]

[0057] Note that the standardized residuals correspond to an estimator with an unbounded ρ function, i.e. and δ = 1. The lack of robustness in this case can be understood as applying an equal weight to all residuals. Performing weighting to minimize the robust scale of the residuals yields a highly robust estimator.

[0058] The strategy of the traditional IRLS method to isolate abnormal observation points is to set the weight of the measurement value corresponding to the residual exceeding the threshold to 0. This method is not universally applicable and is only applicable to the measurement matrix H with a special form. k It is effective in a few cases. Because for many H k , due to H k The different weights of the measurement parameters may cause the residuals corresponding to abnormal observation points to be smaller than those corresponding to non-abnormal observation points, making the IRLS method no longer applicable. Based on IRLS, this paper improves the calculation of the weight function and proposes the MIRLS method.

[0059] First, the measurement parameters are calculated using the least squares method

[0060]

[0061] Then calculate the residual

[0062]

[0063] When all sensors are fault-free, that is, there are no abnormal measurement points, the value of the residual r is very small, and is a positive integer close to 0; when some sensors have abnormal measurement points, the value of the residual r will be relatively large.

[0064] because Is an n*n dimensional ill-conditioned matrix whose similar rows can be eliminated, that is, if Then order The i-th row element of is 0, where Representation matrix The i-th row element of the ill-conditioned matrix tolerance error τ ill is a small constant greater than 0.

[0065] Using the above method, the

[0066]

[0067] The problem of solving the problem is transformed into the problem of solving a system of non-homogeneous linear equations. Using elementary row transformation of the determinant, we can get

[0068]

[0069] wherein, is the general solution, and r g is the particular solution, k is in R, the general solution term represents a series combination of measurement parameters satisfying the residual is 0, the particular solution term represents a series combination of measurement parameters resulting in the residual is not 0, the greater the value of the particular solution term element, the more abnormal the corresponding sensor measurement parameter represents.

[0070] The new weight function is defined as

[0071]

[0072] The measurement prediction equation of MIRLS-MAEKF is

[0073]

[0074] wherein, W k is the weight matrix,

[0075] Advantages

[0076] Compared with the prior art, the aero-engine fault-tolerant on-board adaptive model modeling method of the application combines the high-precision advantage of the component-level model and the high-real-time advantage of the adaptive LPV model to establish a hybrid structure model as an on-board model, and on the basis of the traditional extended Kalman filter, the covariance matrix is multiplied by a forgetting factor to compensate for the adverse effects of incomplete dynamic equations, in this way, the weight of old data in the filtering process is scaled, and a new type of MIRLS-MAEKF is designed. MIRLS is improved based on IRLS, and the residual weight is determined according to the size of the generalized residual. MIRLS is combined with MAEKF, MIRLS-MAEKF is designed and applied to the establishment of the aero-engine fault-tolerant on-board adaptive model. This not only improves the estimation accuracy and real-time performance of the on-board model, but also realizes rapid fault detection and isolation when multiple sensors fail at the same time, improves the fault tolerance and estimation accuracy of the on-board adaptive model, and estimates the accurate value of the parameter measured by the faulty sensor.

[0077] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and / or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0078] The above and / or additional aspects and advantages of the application will become apparent and be readily appreciated from the description of the embodiments, taken in conjunction with the following drawings in which:

[0079] Figure 1 is a structural diagram of the aero-engine fault-tolerant on-board adaptive model modeling method of the application;

[0080] Figure 2 is the linearization process graph in the aero-engine fault-tolerant on-board adaptive model modeling method of the present application;

[0081] Figure 3 is the LPV model principle diagram in the aero-engine fault-tolerant on-board adaptive model modeling method of the present application;

[0082] Figure 4 is the time-varying characteristic diagram of the LPV model in the aero-engine fault-tolerant on-board adaptive model modeling method of the present application;

[0083] Figure 5 is the MAEKF flowchart in the aero-engine fault-tolerant on-board adaptive model modeling method of the present application;

[0084] Figure 6 is the MIRLS-MAEKF structure flowchart in the aero-engine fault-tolerant on-board adaptive model modeling method of the present application;

[0085] Figure 7 is the IRLS principle schematic diagram in the aero-engine fault-tolerant on-board adaptive model modeling method of the present application. DETAILED DESCRIPTION

[0086] 1. Engine hybrid structure on-board adaptive model

[0087] The MIRLS-MAEKF-based hybrid structure on-board adaptive model is shown in Figure 1 , which includes CLM, the proposed MIRLS-MAEKF and ALPV model for online parameter prediction, and adopts fast-slow double loop design. The basic working principle is to take the output of the on-board engine model as the steady-state reference value of the MIRLS-MAEKF, which is estimated in real time by extending the health parameters to the model, and the health parameters are fed back to the CLM and ALPV model for online update to ensure its adaptive ability. The partial derivative parameters of the MIRLS-MAEKF are directly provided by the ALPV model to avoid time-consuming model linearization process, thereby improving real-time performance. This process is carried out at a higher update rate to achieve accurate parameter estimation, forming Figure 1The fast loop of CLM and the correction calculation of ALPV model are shown. The adaptive CLM uses small deviation linearization method for linearization to correct the parameters of ALPV model, to ensure the accuracy of ALPV model at the current working point, and to meet the accuracy requirements of system matrix in the recursive process of MIRLS-MAEKF. This process is updated at a low frequency to cope with the recalculation burden of CLM, and is the slow loop of the model. Through the design of fast and slow double loop, the accuracy and real-time performance of the model are ensured. The slow loop reduces the linearization update frequency of the model to ensure the accuracy of the model, while the fast loop improves the real-time performance of the airborne adaptive model.

[0088] 2. Adaptive LPV model modeling

[0089] Since the performance of engine components may be deteriorated by factors such as dirt, corrosion, erosion, wear, etc., health parameters are introduced in the CLM and estimated by MAEKF. The definition of health parameters is as follows:

[0090]

[0091]

[0092] Where Wa represents the current actual flow of the engine component, Wa * represents the rated flow of the component when the engine is not degraded, η represents the current actual efficiency of the engine component, η * represents the rated efficiency of the component when the engine is not degraded.

[0093] A general adaptive nonlinear system is obtained:

[0094]

[0095] Where, is the state of the system, is the input of the system, is the health parameter, is the external input of the system, including flight condition parameters such as flight altitude, Mach number, inlet temperature, etc., is the output of the system, f represents the differential variable function, and g represents the output function of the system. It should be noted that the influence mechanism of each parameter of the engine on its output is different. The state parameter reflects the influence of the current working state of the engine on the output parameter; the input parameter reflects the influence of the internal input of the engine on the state parameter and the output parameter; the health parameter reflects the influence of the structural characteristics of the engine on the state parameter and the output parameter; the flight condition parameter reflects the influence of the external input on the state parameter and the output parameter.

[0096] After obtaining the nonlinear model of the engine, the engine is regarded as a simple static system. Then, by expanding the Taylor series of the nonlinear expression at the current operating point and taking the first order approximation, the linear model of the engine is obtained. By expanding the Taylor series of the state function at a point (x', u', h') near the current selected operating point (x0, u0, h0) to the current point (x0, u0, h0) and neglecting the high order terms other than the first order term, the following expression can be obtained:

[0097]

[0098] Further, the expansion of the state function can be obtained as follows:

[0099]

[0100] Figure 2 is a schematic diagram of the linearization process. Linearization of the operating point (x0, u0, h0) will generate an effective area. On this basis, a linear model is established, and by calculating the points (x', u', h') in the area, a more accurate output estimate can be obtained. In Figure 2 , the upper solid curve and the lower solid curve represent the nonlinear model before and after the system degradation, respectively, and the two black points represent the current operating points before and after the system degradation, respectively, and the two arrows represent the small deviation linearization model before and after the system degradation, respectively.

[0101] The Taylor series expansion of the output function in the effective area to the operating point (x0, u0, h0) can be expressed as:

[0102]

[0103] Thus, we have:

[0104] Δy = g(x', u', h') - g(x0, u0, h0)

[0105] = CΔx + DΔu + FΔh

[0106] The incremental state space equation of the nonlinear system at the current steady state point is obtained as

[0107]

[0108] Considering that the engine is also affected by various noises in the actual working process, the state variable model describing the dynamic characteristics of the real engine should be

[0109]

[0110] In the formula, ω and υ are system noise and measurement noise, respectively, which are zero-mean white noise with uncorrelated normal distribution, and the covariance matrices are Q and R, respectively.

[0111] The principle of LPV model is shown in Fig. 1. Figure 3 After obtaining the linearized model with health parameters of a single steady state point, an LTI system near the steady state point is obtained. According to this method, a series of steady state points in a certain working region of the nonlinear system are selected, and the Jacobian linearization is performed to obtain a family of LTI systems near the steady state points. Interpolation fitting is performed on these results to obtain an incremental adaptive LPV model expression of the nonlinear system in the form of the following formula.

[0112]

[0113] Δy = C(θ)Δx + D(θ)Δu + F(θ)Δh + υ

[0114] The family of LTI systems is only a set of LTI systems linearized at a series of equilibrium points of the nonlinear system, and essentially has a certain number of systems; while the LPV system is an independent time-varying system, which can approximately describe the motion trajectory of the nonlinear system. Figure 4 In Fig. 2, the dashed line is the motion trajectory of the nonlinear system, the circles represent a plurality of linearized LTI systems selected in the motion trajectory of the nonlinear system, and the solid line represents the time-varying characteristics of the LPV model.

[0115] 3. System parameter estimation method

[0116] The health parameter deviation directly reflects the performance degradation degree of the current engine component, and the health parameter of the component cannot be directly measured. However, under the condition that the working environment of the engine does not change, the change of the health parameter will cause the corresponding change of the measured parameters such as pressure, temperature and rotating speed of each section of the engine, and the two are related to each other through aerodynamic thermodynamic relationship. Therefore, two optimal estimation filters are designed to estimate the health parameters of the engine air path components by using the measured parameters of the engine.

[0117] The aero-engine has strong nonlinearity, that is, the system equation and the measurement equation of the model are nonlinear. The EKF is to perform Taylor series expansion on the original system and measurement, and then perform linear Kalman filter estimation on the first-order linear system, which is different from the linear KF in that the state value and the output value are calculated using the nonlinear model, and the parameter estimation problem of the nonlinear system can be solved. However, the EKF needs a random system with complete process and measurement noise covariance for optimal estimation, which may be time-consuming in calculation and has low estimation accuracy. Therefore, the MAEKF algorithm is proposed based on the improvement of the EKF.

[0118] Since the performance degradation of the engine occurs slowly, it can be considered that Therefore, the formula

[0119]

[0120] Δy = C(θ)Δx + D(θ)Δu + F(θ)Δh + υ

[0121] which can be rewritten as

[0122]

[0123] where

[0124]

[0125]

[0126] For the convenience of MAEKF design, the equation

[0127]

[0128] Δy = C(θ)Δx + D(θ)Δu + F(θ)Δh + υ

[0129] can be converted to discrete form

[0130]

[0131] where subscript k denotes the value of the variable at the kth step.

[0132] Define:

[0133]

[0134]

[0135] Initialize:

[0136]

[0137]

[0138] State prediction:

[0139]

[0140]

[0141] The difference from EKF is that the covariance matrix is multiplied by a forgetting factor to compensate for the adverse effects of incomplete dynamic equations. In this way, the weight of old data in the filtering process is scaled.

[0142] The forgetting factor in this filter is

[0143]

[0144] where λ0is the baseline value of the forgetting factor.

[0145] N k and T k matrix is

[0146]

[0147]

[0148] where

[0149]

[0150]

[0151] The covariance estimate of the new residual can be derived by averaging the previous length-N residual sequence as follows:

[0152]

[0153] where, is the innovation residual in the Kalman filter. The estimated process noise matrix is obtained as follows:

[0154]

[0155] where, In steady state, the above equations can be obtained by using the variance-covariance matrix of the following equations, as follows:

[0156]

[0157] Measurement prediction:

[0158]

[0159]

[0160]

[0161] Figure 5 The MAEKF flowchart is shown. MAEKF can compensate for the effects of incomplete dynamic equations and avoid reducing the estimation performance of the traditional EKF observer when the dynamic equation is incomplete. These inconsistencies can lead to divergence, resulting in unstable control of the controlled object. At the same time, the observer uses a covariance scaling mechanism to improve estimation performance under dynamic changes in the estimated object state, without the need for a time-consuming tuning phase.

[0162] The error introduced when the nonlinear term h(x k ) is linearized is compared with the noise v k . The noise in the vicinity can be neglected. The first order Taylor expansion can be obtained k

[0163]

[0164] The batch regression formula of MAEKF can be obtained

[0165]

[0166] where, The estimation problem in the above formula can be rewritten as

[0167]

[0168]

[0169]

[0170] The updated state of MAEKF calculated in the correction step is It can also be obtained by performing weighted least squares, linear regression

[0171]

[0172] It can be converted to

[0173]

[0174] The correction step of MAEKF can be obtained by the following formula

[0175]

[0176] The structure flow chart of the improved iterative reweighted least squares-mixed adaptive extended Kalman filter (MIRLS-MAEKF) is shown in Figure 6 The MIRLS module in the structure flow chart of MIRLS-MAEKF calculates the weight according to the weight formula. The farther the outlier is from the group, the smaller the weight allocated is. When the outlier exceeds a certain limit value c, its weight will become 0, which means that the faulty sensor is completely isolated. The mixed adaptive module updates the measurement noise covariance matrix and the forgetting factor according to the historical data, thereby constantly optimizing the filter parameters. By using the residual of the measurement value and the model calculation value and the parameters calculated by the filter to perform iterative operation, the estimation of the state quantity is realized.

[0177] ​The flight envelope of an aero-engine is large, the working mode is more, and the working environment is harsh, so it is easy to be disturbed in complex environment. In addition, the number of sensors is large and prone to failure, which is easy to produce large measurement outliers. This means that the classic weighted least squares method, that is, the maximum likelihood estimator under Gaussian noise, will be affected by the decrease in accuracy, which is manifested as the increase in the variance of the estimated value and the increase in the bias, thereby affecting its reliability and estimation accuracy, and has poor robustness.

[0178] The Huber M estimator is a method of studying filter outliers. By introducing weights to reconstruct the measurement noise covariance matrix, the influence of outliers on the system is reduced, and the robustness of the filter is improved. The Huber cost function is the most commonly used cost function in M estimation, and its expression is shown in the following formula.

[0179]

[0180] In the formula, γ is the adjustment factor, i is 1, 2, … m, m is the dimension of the observation, and is the observation residual.

[0181] The modified measurement noise covariance matrix is

[0182]

[0183] In the formula, is the weight function, ψ(τ i )=ρ′(τ i ).

[0184] By replacing the measurement noise covariance matrix in the EKF with the above formula, the robust EKF algorithm based on Huber (HREKF) is obtained. The essence is to reweight the measurement noise covariance matrix, construct different weights for different sizes of observation residuals, and reconstruct the measurement noise covariance matrix to overcome the influence of outliers on the estimation accuracy, and achieve the purpose of improving the robustness of the estimator.

[0185] However, according to the formula

[0186]

[0187] It can be seen that since the innovation outliers appear in the predicted state , their influence will pass through the matrix M kThe error propagates to the observation vector on the left side of the above formula, resulting in a large estimation error. This method has a certain effect on isolating small outliers caused by disturbances such as noise, which can improve the robustness of the filter and the estimation accuracy to a certain extent. However, when the sensor fails and the measured value deviates significantly from the actual value, this method cannot overcome the influence of the outlier measurement value.

[0188] If the correction step is robust, the corresponding robust filter can be obtained. The weighted least squares (WLS) estimator is a maximum likelihood estimator under Gaussian noise, which can be regarded as an estimator that minimizes the norm of the regression residual, which means that satisfy

[0189]

[0190] in, is the standard deviation of the residuals, that is The residual vector is arg min represents the value of the variable that makes the following formula reach the minimum value.

[0191] The size of the standard deviation estimate is affected by abnormal measurements, i.e., outliers. In order to minimize the corresponding residual squares, the filter even tends to lean towards the outliers. Iterative Reweighted Least Squares (IRLS) can overcome this problem. Its principle diagram is shown in the figure below. Figure 7 As shown in the figure, the solid circle in the lower left corner represents the circle to be estimated, the dots in the lower left corner represent normal observations, and the dotted dots in the upper right corner represent abnormal observations. The solid circle in the upper right corner represents the WLS fitting result, and the dashed circle represents the IRLS fitting result. The IRLS method iteratively reweights all observations, assigning a weight of 1 to normal observations and a weight less than 1 to abnormal observations. The farther the abnormal observation is from the normal value, the smaller the weight, until it reaches 0. When the WLS method is used for fitting, because the weight of the abnormal observation is still 1, the fitting result will deviate significantly from the estimated circle. However, the IRLS method, because it isolates the abnormal observations, achieves a much better fitting effect than the WLS method.

[0192] If the regression minimizes the robust scale of the residual, then the estimate is robust, i.e.

[0193]

[0194] in, Is a robust scale estimator. Minimizing the robust scale estimator ensures the isolation of abnormal measurements. The estimator for estimating the residual scale is defined as follows

[0195]

[0196] Where δ∈[0,1], function ρ is a bounded ρ function satisfying ρ(0)=ρ'(0)=0 and ρ”(0)>0, ρ is an even function and ρ(r) is non-decreasing with respect to r. To ensure the consistency of the estimator under clean data, δ should be fixed to E Φ ρ(r), where Φ is the standard Gaussian distribution, scale estimator Solve by iteration

[0197]

[0198] in, is the relative standard residual, the weight function

[0199]

[0200] The ρ function is chosen to be

[0201]

[0202] The weight function is defined as

[0203]

[0204] Note that the standardized residuals correspond to an estimator with an unbounded ρ function, i.e. and δ = 1. The lack of robustness in this case can be understood as applying an equal weight to all residuals. Performing weighting to minimize the robust scale of the residuals yields a highly robust estimator.

[0205] The strategy of the traditional IRLS method to isolate abnormal observation points is to set the weight of the measurement value corresponding to the residual exceeding the threshold to 0. This method is not universally applicable and is only applicable to the measurement matrix H with a special form. k It is effective in a few cases. Because for many H k , due to H k The different weights applied to the measurement parameters can cause the residuals corresponding to anomalous observation points to be smaller than those corresponding to non-abnormal observation points, making the IRLS method no longer applicable. Therefore, the present invention improves the calculation of the weight function based on IRLS and proposes the MIRLS method.

[0206] First, the measurement parameters are calculated using the least squares method

[0207]

[0208] Then calculate the residual

[0209]

[0210] When all sensors are fault-free, i.e. no abnormal measurement points, the value of residual r is very small, a positive integer close to 0; when some sensors have abnormal measurement points, the value of residual r will be larger.

[0211] Since is a n*n dimensional ill-conditioned matrix, its similar rows can be eliminated, i.e. if then let be the i-th row element of matrix , the i-th row element of matrix , the ill-conditioned matrix tolerance error τ ill is a very small constant greater than 0.

[0212] Using the above method, the problem of solving equation

[0213]

[0214] is converted into the problem of solving a non-homogeneous linear equation group. Using elementary row transformation of determinant, can be solved

[0215]

[0216] where, is the general solution, the generalized residual r g is the particular solution, k∈R, the general solution term represents a series of combinations of measurement parameters that satisfy the residual of 0, the particular solution term represents a series of combinations of measurement parameters that cause the residual not to be 0, the greater the value of the particular solution element, the more abnormal the corresponding sensor measurement parameter.

[0217] The new weight function is defined as

[0218]

[0219] The measurement prediction equation of MIRLS-MAEKF is

[0220]

[0221]

[0222]

[0223] where, W k is the weight matrix,

[0224] Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments without departing from the principles and purposes of the present application within the scope of the present application.

Claims

1. An aeroengine fault-tolerant on-board adaptive model building method, characterized in that: The MIRLS-MAEKF is a new type of extended Kalman filter; the MIRLS is improved based on the IRLS, and relies on the size of the generalized residual to determine the residual weight; the MIRLS is combined with the MAEKF to design the MIRLS-MAEKF and apply it to the establishment of the fault-tolerant airborne adaptive model of the aero-engine; the aero-engine discrete system is as follows The subscript k represents the value of the variable at the kth step; The hybrid structure on-board model generates estimated output parameters under the action of a control input vector u And the difference with the real aero-engine sensor measurement parameters y is passed to the hybrid adaptive extended Kalman filter; The component-level model continuously corrects the parameters of the adaptive LPV model to ensure the accuracy of the adaptive LPV model; The adaptive LPV model continuously corrects parameters F and H of the hybrid adaptive extended Kalman filter to ensure estimation accuracy of the hybrid adaptive extended Kalman filter; and the hybrid adaptive extended Kalman filter estimates the performance degradation degree of the real engine according to the difference 2. The fault-tolerant on-board adaptive modeling method for an aeroengine according to claim 1, characterized in that: The definition is as follows The design process of the MAEKF is as follows Initialization 3. The fault-tolerant on-board adaptive modeling method for an aeroengine according to claim 1, characterized in that: State prediction The difference from the EKF is that the covariance matrix is multiplied by a forgetting factor to compensate for the adverse effects of the incomplete dynamic equation; in this way, the weight of the old data in the filtering process is scaled; The forgetting factor in the filter is Where λ0 is the reference value of the forgetting factor; Where The covariance estimation of the new residual can be derived by averaging the residual sequence of the previous length N The correction step of the MAEKF can be obtained by the following formula ​ ​ N k and T k matrix is ​ ​ wherein is the innovation residual in the Kalman filter; the estimated process noise matrix is obtained as follows: wherein, In steady state, the above equations can be obtained in terms of the variance-covariance matrix of the following equations, as follows: ​ The MIRLS module in MIRLS-MAEKF calculates the weight according to the weight formula. The farther the abnormal value is from the group, the smaller the weight is. When the abnormal value exceeds a certain limit value c, the weight will become 0, which means that the faulty sensor is completely isolated. The mixed adaptive module updates the measurement noise covariance matrix and the forgetting factor according to the historical data, thereby continuously optimizing the filter parameters. Through the iterative operation of the residual between the measurement value and the model calculation value and the parameters calculated by the filter, the estimation of the state quantity is realized. ​ If the correction step is robust, the corresponding robust filter can be obtained; the weighted least squares (WLS) estimator is the maximum likelihood estimator under Gaussian noise, which can be regarded as the estimator that minimizes the norm of the regression residual, which means satisfies wherein, is the standard deviation of the residuals, i.e. is the residual vector, argmin denotes the value of the variable for which the following expression is minimized. The size of the standard deviation estimate is affected by abnormal measurement values, i.e. outliers, and in order to minimize the corresponding residual squares, the filter even tends to tilt towards outliers; the iteratively reweighted least squares (IRLS) can overcome this problem, the IRLS method iteratively reweights all observations, giving normal observations a weight of 1 and abnormal observations a weight less than 1, the farther the abnormal observation is from the normal value, the smaller the weight, until 0; when the WLS method is used for fitting, because the weight of the abnormal observation is still 1, the fitting result will have a large deviation from the circle to be estimated, and because the IRLS method isolates abnormal observations, the fitting effect is much better than the WLS method fitting result; If the robust scale of the regression minimizes the residual, the estimation is robust, i.e. wherein is a robust scale estimator, the minimization of the robust scale estimator can ensure isolation of outliers, and the estimator of the scale of the residuals is defined as where δ ∈ [0, 1], the function p is a bounded p-function satisfying p(0) = p'(0) = 0 and p"(0) > 0, p is an even function and p(r) is not decreasing in r; to ensure the consistency of the estimator under clean data, δ should be fixed as E Φ p(r), where Φ is the standard Gaussian distribution, the scale estimator by iterating the solution wherein is the relative standard residual, the weight function The selected ρ function is The weight function is defined as Note that the standard residual corresponds to an estimator with an unbounded ρ function, i.e. and δ = 1; the lack of robustness in this case can be understood as the use of an equal weight for all residuals Weighting, minimizing a robust scale of the residuals, can lead to highly robust estimators; The strategy of the traditional IRLS method to isolate abnormal observation points is to set the weight of the measurement value corresponding to the residual exceeding the threshold value to 0, which is not universally applicable and is only effective in a few cases with a special form of the measurement matrix H k ; because for many H k , due to the different weights of H k on the measurement parameters, the residual corresponding to the abnormal observation point may be smaller than that corresponding to the non-abnormal observation point, so that the IRLS method is no longer applicable; the present application improves the calculation of the weight function on the basis of IRLS and proposes the MIRLS method; First, the measurement parameters are calculated by using the least squares method Then the residual is calculated When all sensors are fault-free, i.e. there are no abnormal measurement points, the value of the residual r is very small, which is a positive integer close to 0; when part of the sensors have abnormal measurement points, the value of the residual r will be larger; because Is an n*n dimensional ill-conditioned matrix whose similar rows can be eliminated, that is, if Then order The i-th row element of is 0, where Representation matrix The i-th row element of the ill-conditioned matrix tolerance error τ ill is a very small constant greater than 0; The above method is used to solve the problem of solving equation (1); by using the elementary row transformation of the determinant, can be solved The new weight function is defined as wherein, is a general solution, r g is a particular solution, k ∈ R, the general solution term represents a series of combinations of measurement parameters that satisfy the residual being 0, the particular solution term represents a series of combinations of measurement parameters that cause the residual not to be 0, the greater the value of the particular solution term element, the more abnormal the corresponding sensor measurement parameter represents; The measurement prediction equation of the MIRLS-MAEKF is The measurement parameters include the temperature and pressure at the inlet of the air duct, the outlet of the fan, the outlet of the compressor, the rear of the high-pressure turbine and the rear of the low-pressure turbine, the fan speed and the compressor speed. wherein W k is a weight matrix, 4. The fault-tolerant on-board adaptive modeling method for an aeroengine according to claim 1, characterized in that: ​

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