TBCC engine fault-tolerant airborne adaptive model modeling method

Abstract

The invention provides a TBCC 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; mIRLS and MAEKF are combined, a novel MIRLS-MAEKF is designed, and the novel MIRLS-MAEKF is applied to establishment of a TBCC 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 invention relates to the technical field of TBCC engine airborne adaptive model modeling, and in particular to a TBCC engine fault-tolerant airborne adaptive model modeling method. Background Art

[0002] With the development of supersonic aircraft, horizontal take-off and landing aircraft that can integrate air and space have been proposed. Due to the increase in altitude and Mach number, traditional turbofan engines cannot meet the demand for thrust. Turbine-based combined cycle power has become one of the ideal power sources for reusable air-breathing hypersonic aircraft due to its wide working envelope and the ability to autonomously accelerate the aircraft from a stationary state to a hypersonic state. As an innovative aviation gas turbine technology, the turbine-based combined cycle (TBCC) engine is considered to be a potential power solution for future military fighters.

[0003] During the operation of TBCC engines, factors such as natural wear, corrosion, fouling and thermal creep will cause the performance degradation of gas path components. Currently, widely used airborne models include component level models (CLM), linear parameter-varying (LPV) models and data-driven models. In fact, compared with CLM, LPV and data-driven models are more practical because they require lower computational load. However, training data-driven models to cover the flight envelope and engine operating conditions requires a large amount of data, so the accuracy of the model that does not cover the flight envelope cannot be ensured. The LPV model uses a linear model established with limited operating points and is obtained by interpolation or fitting methods. The performance degradation of TBCC engine components and maintenance and installation will cause slight differences in individual performance between engines of the same type. Therefore, the offline LPV model cannot cover all conditions, modeling errors are 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 recursive process; the higher the frequency, the higher the estimation accuracy. Since the CLM itself has a large amount of computation, the model needs to be linearized multiple times, which will greatly increase the total amount of computation and make it difficult to meet real-time requirements.

[0004] Due to the harsh working environment of TBCC engines and the large number of sensors, sensor failures are prone to occur. Abnormal measurements can reduce the reliability of the onboard adaptive model and produce large deviations in the estimated parameters. Huber first proposed the M estimator, which updates the measurement noise covariance matrix to overcome the influence of abnormal measurements. However, this estimator cannot handle errors or outliers for grid topologies, which produce leverage points. To address this problem, Maronna and Zhao designed the generalized Huber M estimator, namely the GM estimator. On this basis, Yacine proposed a robust S estimator implemented on the batch mode regression representation of the extended Kalman filter (EKF). The S estimator has the advantage of a high breakdown point, that is, it can still give a robust estimate when facing a large number of outliers, and it will not decrease with the increase of system dimension. However, the above methods are all based on the iterative reweighted least squares algorithm. Although they have a good isolation effect on abnormal measurements, such methods are only applicable to the estimation of a very limited class of system matrix models with special forms. In some cases, there is a problem of divergence in the estimation results, which is not suitable for the estimation of gas turbine engine health parameters. In addition, the current sensor fault diagnosis method usually uses a Kalman filter group for diagnosis to realize the diagnosis and signal reconstruction of single and dual sensor faults of the engine. However, this method requires a large number of filter group calculations, which seriously affects the real-time performance of the airborne adaptive model.

[0005] In addition, the filters that are widely used currently have their own problems. For example, the linearized Kalman filter has large estimation errors for nonlinear systems, the extended Kalman filter requires a random system with a complete process and measurement noise covariance for optimal estimation, and the unscented Kalman filter does not use the linearization prior information of different steady-state points of the nonlinear model, resulting in excessive computational complexity. Summary of the invention

[0006] In order to solve the problems existing in the prior art, the present invention proposes a new hybrid structural fault-tolerant airborne adaptive model based on 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 adopts an adaptive linear parameter-varying (ALPV) model to improve real-time performance. At the same time, MAEKF introduces a covariance scaling mechanism based on the extended Kalman filter, and uses the full covariance estimation to update the system noise covariance matrix; MIRLS is improved based on IRLS, and the residual weight is determined by the size of the generalized residual. MIRLS is combined with MAEKF to design MIRLS-MAEKF and apply it to the establishment of a fault-tolerant airborne adaptive model for TBCC engines. This not only improves the estimation accuracy and real-time performance of the onboard model, but also enables rapid fault detection and isolation when multiple sensors fail at the same time, thereby improving the fault tolerance and estimation accuracy of the onboard adaptive model, while estimating the accurate values ​​of the parameters measured by the faulty sensors.

[0007] The technical solution of the present invention is:

[0008] The method for modeling a fault-tolerant airborne adaptive model of a TBCC engine is characterized by comprising a CLM, a proposed MIRLS-MAEKF and an ALPV model for online parameter prediction, and adopting a fast and slow dual-loop design. The basic working principle is to use the output of the airborne 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 models for online updating to ensure their adaptive capabilities. The partial derivative parameters of the MIRLS-MAEKF are directly provided by the ALPV model to avoid the time-consuming model linearization process, thereby improving the real-time performance. This process is carried out at a high update rate to achieve accurate parameter estimation, and the thermal calculation of the CLM and the correction calculation of the ALPV model are carried out simultaneously. The adaptive CLM adopts a small deviation linearization method for linearization 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 lower frequency to cope with the heavy calculation burden of the CLM, which is the slow loop of the model. Through the fast and slow dual-loop design, the accuracy and real-time performance of the model are guaranteed at the same time. The slow loop reduces the frequency of model linearization updates and ensures the accuracy of the model, while the fast loop improves the real-time performance of the onboard adaptive model.

[0009] The MIRLS-MAEKF is a new type of extended Kalman filter. The TBCC engine has strong nonlinearity, that is, the system equations and measurement equations of the model are nonlinear. EKF first performs Taylor series expansion on the original system and measurement, approximates the system as a first-order linear system, and then estimates the linear Kalman filter. The difference from the linear KF is that the state value and output value are calculated using a nonlinear model, which can solve the parameter estimation problem of the nonlinear system. However, EKF requires a random system with a complete process and measurement noise covariance for optimal estimation, which may be time-consuming in calculation and has low estimation accuracy. Therefore, the present invention improves on the basis of EKF and proposes a MAEKF algorithm. MIRLS is based on the improvement of IRLS, and the residual weight is determined by the size of the generalized residual. MIRLS is combined with MAEKF to design MIRLS-MAEKF and apply it to the establishment of a fault-tolerant airborne adaptive model of the TBCC engine.

[0010] For the following TBCC engine discrete system

[0011]

[0012] The subscript k here represents the value of the variable at the kth step.

[0013] definition:

[0014]

[0015] The design process of MAEKF is:

[0016] initialization:

[0017]

[0018] Status prediction:

[0019]

[0020] The difference here with the EKF is that the covariance matrix is ​​multiplied by a forgetting factor to compensate for the adverse effects of the incomplete dynamic equations. In this way, the weight of old data in the filtering process is scaled.

[0021] The forgetting factor in this filter

[0022]

[0023] Among them, λ0 is the reference value of the forgetting factor.

[0024] N k and T k The matrix is

[0025]

[0026] in

[0027]

[0028] By averaging the previous residual sequence of length N, the covariance estimate of the new residual can be derived as:

[0029]

[0030] in, is the innovation residual in Kalman filtering. The estimated process noise matrix is ​​as follows:

[0031]

[0032] in, In steady state, the above equation can be obtained using the variance-covariance matrix of the following equation, as follows:

[0033]

[0034] The modified step size of MAEKF can be obtained by the following formula:

[0035]

[0036] The MIRLS module in MIRLS-MAEKF calculates the weight according to the weight formula. The farther the outlier is from the group, the smaller the weight assigned. 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 based on historical data to continuously optimize the filter parameters. The state quantity is realized by iteratively calculating the residual of the measured value and the model calculated value and the parameters calculated by the filter. Estimates.

[0037] 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. It can be regarded as an estimator that minimizes the norm of the regression residual, which means that satisfy

[0038]

[0039] in, is the standard deviation of the residual, that is The residual vector is arg min represents the value of the variable when the following formula reaches the minimum value.

[0040] 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 toward outliers. Iterative reweighted least squares (IRLS) can overcome this problem. The IRLS method performs iterative reweighting operations on all observations, assigning a weight of 1 to normal observations and a weight less than 1 to abnormal observations. The farther the abnormal observations are from the normal values, the smaller the weight, until it is 0. When the WLS method is used for fitting, since the weight of the abnormal observations is still 1, the fitting result will have a large deviation from the estimated circle. However, since the IRLS method isolates the abnormal observations, the fitting effect is much better than the WLS method fitting result.

[0041] If the regression minimizes the robust scale of the residual, then the estimate is robust, that is,

[0042]

[0043] 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

[0044]

[0045] 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 for 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, the scale estimator Solving by iteration

[0046]

[0047] in, is the relative standard residual, the weight function

[0048]

[0049] The ρ function chosen is

[0050]

[0051] The weight function is defined as

[0052]

[0053] Note that the standardized residuals correspond to an estimator with an unbounded ρ function, namely and δ = 1. The lack of robustness in this case can be understood as applying an equal weight to all residuals Weighting to minimize the robust scale of the residuals leads to a highly robust estimator.

[0054] 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 generally applicable and is only applicable to the measurement matrix H with a special form. k is valid 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, which makes the IRLS method no longer applicable. The present invention improves the calculation of the weight function based on IRLS and proposes the MIRLS method.

[0055] First, the measurement parameters are calculated using the least squares method

[0056]

[0057] Then calculate the residual

[0058]

[0059] 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.

[0060] because is an n*n dimensional ill-conditioned matrix whose similar rows can be eliminated, that is, if Then The i-th row element of is 0, where Representation moment The i-th row element of the ill-conditioned matrix tolerance error τ ill is a small constant greater than 0.

[0061] Using the above method,

[0062]

[0063] The problem of solving is transformed into the problem of solving a system of non-homogeneous linear equations. Using elementary row transformation of the determinant, we can get

[0064]

[0065] in, is the general solution, the generalized residual r g is a special solution, k∈R, the general solution term represents a series combination of measurement parameters that satisfies the residual of 0, and the special solution term represents a series combination of measurement parameters that causes the residual to be non-zero. The larger the value of the element of the special solution term, the more abnormal the corresponding sensor measurement parameter is.

[0066] The new weight function is defined as

[0067]

[0068] The measurement prediction equation of MIRLS-MAEKF is:

[0069]

[0070] Among them, W k is the weight matrix,

[0071] Beneficial Effects

[0072] Compared with the prior art, the fault-tolerant airborne adaptive model modeling method of the TBCC engine of the present invention combines the advantages of high precision of the component-level model and high real-time performance of the adaptive LPV model to establish a hybrid structure model as an airborne 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 the incomplete dynamic equation. In this way, the weight of the old data in the filtering process is scaled, and a new type of MIRLS-MAEKF is designed. MIRLS is based on the improvement of IRLS, and the residual weight is determined by the size of the generalized residual. MIRLS is combined with MAEKF to design MIRLS-MAEKF and apply it to the establishment of the fault-tolerant airborne adaptive model of the TBCC engine. This not only improves the estimation accuracy and real-time performance of the airborne model, but also can realize rapid fault detection and isolation when multiple sensors fail at the same time, improve the fault tolerance and estimation accuracy of the airborne adaptive model, and at the same time estimate the accurate value of the parameter measured by the faulty sensor.

[0073] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0075] Figure 1 It is a structural diagram of the method for modeling a fault-tolerant airborne adaptive model of a TBCC engine according to the present invention;

[0076] Figure 2 It is a simplified structural diagram of a TBCC engine in the fault-tolerant airborne adaptive modeling method of a TBCC engine of the present invention;

[0077] Figure 3 It is a linearization process diagram in the fault-tolerant airborne adaptive model modeling method of the TBCC engine of the present invention;

[0078] Figure 4 It is a schematic diagram of the LPV model in the fault-tolerant airborne adaptive model modeling method of the TBCC engine of the present invention;

[0079] Figure 5 It is a time-varying characteristic diagram of the LPV model in the fault-tolerant airborne adaptive model modeling method of the TBCC engine of the present invention;

[0080] Figure 6 It is a MAEKF flow chart in the fault-tolerant airborne adaptive model modeling method of the TBCC engine of the present invention;

[0081] Figure 7 It is a MIRLS-MAEKF structure flow chart in the fault-tolerant airborne adaptive model modeling method of the TBCC engine of the present invention;

[0082] Figure 8 It is a schematic diagram of the IRLS principle in the TBCC engine fault-tolerant airborne adaptive model modeling method of the present invention. DETAILED DESCRIPTION

[0083] 1. Engine hybrid structure airborne adaptive model

[0084] The hybrid structure airborne adaptive model based on MIRLS-MAEKF is as follows Figure 1 As shown in the figure, its structure includes CLM, the proposed MIRLS-MAEKF and the ALPV model for online parameter prediction, and adopts a fast-slow dual-loop design. The basic working principle is to use the output of the onboard engine model as the steady-state reference value of 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 models for online updating to ensure their adaptability. The partial derivative parameters of MIRLS-MAEKF are directly provided by the ALPV model to avoid the time-consuming model linearization process, thereby improving the real-time performance. This process is carried out at a high update rate to achieve accurate parameter estimation, forming Figure 1 In the fast loop shown, the thermal calculation of CLM and the correction calculation of the ALPV model are performed simultaneously. The adaptive CLM uses a small deviation linearization method for linearization 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 MIRLS-MAEKF recursive process. This process is updated at a lower frequency to cope with the heavy computational burden of CLM, which is the slow loop of the model. Through the fast and slow dual-loop design, the accuracy and real-time performance of the model are guaranteed at the same time. The slow loop reduces the frequency of model linearization updates and ensures the accuracy of the model, while the fast loop improves the real-time performance of the airborne adaptive model.

[0085] 2. Working principle of TBCC engine

[0086] The TBCC studied in the present invention is an internal parallel type, and its structure is as follows Figure 2 As shown. The airflow enters the supersonic inlet after being compressed by the forebody, becomes subsonic after being compressed by the shock wave in the inlet, and enters the ramjet engine and turbine engine respectively through the splitter plate; after passing through the ramjet base and turbine base components in turn, it is discharged through the exhaust tail nozzles.

[0087] In order to ensure the gas compression capacity in a larger Mach number range, the inlet adopts a mixed pressure type. Among them, the external pressure part of the inlet is in the form of a three-wedge angle. The ramjet engine is designed to have a Mach number of 4, and adopts a sub-combustion ramjet combustion chamber and a divergent tail nozzle. 5% of the gas at the inlet of the combustion chamber is used for cooling, and pressure dynamics are considered when modeling. The turbine engine is a small bypass ratio dual-shaft mixed exhaust turbofan engine. The influence of rotor dynamics, jet precooling and bleed air is considered when modeling. In addition, it is assumed here that the two tail nozzles exhaust separately and do not affect each other.

[0088] It should be noted that the current inlet model is quasi-one-dimensional. The model input is the inlet pressure, temperature, aircraft angle of attack, and inlet positive shock wave position; the output is the inlet outlet temperature, pressure, and flow rate. This method of modeling can reflect the inlet positive shock wave position, thereby determining the inlet start-up state; it can also be quickly calculated to meet the control system design requirements.

[0089] In the TBCC engine model, there is a strong correlation between the working state of the inlet and the working state of the engine, which is specifically described and restricted by the flow balance equation. Therefore, on the basis of obtaining the characteristics of the three, it is necessary to select appropriate iterative variables and perform comprehensive iterative calculations on the inlet, turbine engine, and ramjet models to ensure the correct matching of the three. Compared with the traditional engine model, the positive shock wave position needs to be input in the inlet internal pressure section. In actual work, the position of the inlet positive shock wave is mainly determined by the inlet inlet and outlet pressures.

[0090] 3. Modeling of Adaptive LPV Model

[0091] Since the performance of engine components may be deteriorated by factors such as dirt, corrosion, erosion, and wear, health parameters are introduced in CLM and estimated by MAEKF. The definition of health parameters is as follows:

[0092]

[0093] Among them, Wa represents the current actual flow of engine components, Wa * represents the rated flow of the components when the engine is not degraded, η represents the current actual efficiency of the engine components, η * Indicates the rated efficiency of a component when the engine is not degraded.

[0094] We obtain a general adaptive nonlinear system:

[0095]

[0096] in, is the state of the system, is the input of the system, is a health parameter, It 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 engine parameter 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 output parameter; the health parameter reflects the influence of the engine structural characteristics on the state parameter and output parameter; the flight condition parameter reflects the influence of the external input on the state parameter and output parameter.

[0097] After obtaining the nonlinear model of the engine, the engine is regarded as a simple static system. Then, the linear model of the engine is obtained by expanding the nonlinear expression at the current operating point using the Taylor series and taking the first-order approximation. The state function is expanded from a point (x',u',h') near the currently selected operating point to the current point (x0,u0,h0) using the Taylor series and ignoring the higher-order terms other than the first order, and the following expression can be obtained:

[0098]

[0099] Then, the expansion of the state function can be obtained:

[0100]

[0101] Figure 3 is a schematic diagram of the linearization process. The linearization of the working point (x0, u0, h0) will produce an effective region. On this basis, a linear model is established, and by calculating the points (x', u', h') in the region, a more accurate output estimate can be obtained. Figure 3 In the figure, the upper solid curve and the lower solid curve represent the nonlinear models before and after the system is degraded, respectively. The two black dots represent the current working points before and after the system is degraded, respectively. The two arrows represent the small deviation linearization models before and after the system is degraded, respectively.

[0102] The Taylor series expansion of the output function for the working point (x0, u0, h0) in the effective region can be expressed as:

[0103]

[0104] Thus we get:

[0105] Δy=g(x',u',h')-g(x0,u0,h0)

[0106] =CΔx+DΔu+FΔh

[0107] Get the incremental state space equation of the nonlinear system at the current steady-state point

[0108]

[0109] Considering that the engine is also affected by various noises during actual operation, the state variable model describing the dynamic characteristics of the real engine should be

[0110]

[0111] Where ω and υ are system noise and measurement noise, respectively, both of which are uncorrelated normally distributed zero-mean white noise, and their covariance matrices are Q and R, respectively.

[0112] The principle of LPV model is as follows Figure 4 As shown. After obtaining the linearized model with health parameters of a single steady-state point, an LTI system near a steady-state point is obtained. According to this method, by selecting several steady-state points in a certain working area of ​​the nonlinear system and performing Jacobian linearization, a family of LTI systems near a series of steady-state points can be obtained. By interpolating and fitting these results, the incremental adaptive LPV model expression of the nonlinear system in the form of the following formula can be obtained.

[0113]

[0114] Δy=C(θ)Δx+D(θ)Δu+(θ)Δh+υ

[0115] The LTI system family is just a collection of LTI systems after the nonlinear system is linearized at a series of equilibrium points. In essence, it is a number of systems with a certain number; while the LPV system is an independent time-varying system that can approximately describe the motion trajectory of the nonlinear system. Figure 5 In the figure, the dotted line is the motion trajectory of the nonlinear system, the circles represent several linearized LTI systems selected from the motion trajectory of the nonlinear system, and the solid line represents the time-varying characteristics of the system reflected by the LPV model.

[0116] 4. Research on system parameter estimation methods

[0117] The health parameter deviation directly reflects the performance degradation of the current engine components, while the health parameters of the components cannot be directly measured. However, when the engine working environment does not change, the change of health parameters will cause corresponding changes in the measured parameters such as pressure, temperature, and speed of each section of the engine, and the two are interconnected through the aerodynamic thermodynamic relationship. Therefore, the present invention designs two optimal estimation filters to estimate the health parameters of the engine gas path components using the measured parameters of the engine.

[0118] The TBCC engine has strong nonlinearity, that is, the system equations and measurement equations of the model are nonlinear. EKF first performs Taylor series expansion on the original system and measurement, approximates the system as a first-order linear system, and then performs linear Kalman filter estimation. The difference from linear KF is that it uses a nonlinear model to calculate state values ​​and output values, which can solve the parameter estimation problem of nonlinear systems. However, EKF requires a random system with a complete process and measurement noise covariance to perform optimal estimation, which may be time-consuming in calculation and has low estimation accuracy. Therefore, the present invention improves on the basis of EKF and proposes a MAEKF algorithm.

[0119] Since the engine performance degradation occurs slowly, it can be considered that Therefore, the formula

[0120]

[0121] Δy=C(θ)Δx+D(θ)Δu+(θ)Δh+υ

[0122] can be rewritten as:

[0123]

[0124] In the formula

[0125]

[0126] In order to facilitate the design of MAEKF, Eq.

[0127]

[0128] Δy=C(θ)Δx+D(θ)Δu+(θ)Δh+υ

[0129] Can be converted to discrete form:

[0130]

[0131] The subscript k here represents the value of the variable at the kth step.

[0132] definition:

[0133]

[0134] initialization:

[0135]

[0136] Status prediction:

[0137]

[0138] The difference here with the EKF is that the covariance matrix is ​​multiplied by a forgetting factor to compensate for the adverse effects of the incomplete dynamic equations. In this way, the weight of old data in the filtering process is scaled.

[0139] The forgetting factor in this filter

[0140]

[0141] Among them, λ0 is the reference value of the forgetting factor.

[0142] N k and T k The matrix is

[0143]

[0144] in

[0145]

[0146] By averaging the previous residual sequence of length N, the covariance estimate of the new residual can be derived as:

[0147]

[0148] in, is the innovation residual in Kalman filtering. The estimated process noise matrix is ​​as follows:

[0149]

[0150] in, In steady state, the above equation can be obtained using the variance-covariance matrix of the following equation, as follows:

[0151]

[0152] Measurement prediction:

[0153]

[0154] Figure 6The MAEKF flow chart is shown. MAEKF is able to compensate for the effects of incomplete dynamic equations, avoiding degradation of the estimation performance of the traditional EKF observer when the dynamic equations are incomplete. These inconsistencies may lead to divergence, which may cause control instability of the controlled object. At the same time, the observer uses a covariance scaling mechanism to improve the estimation performance under dynamic changes in the state of the estimated object, without the need for a time-consuming tuning phase.

[0155] The nonlinear term h(x k ) Error and noise introduced during linearization v k compared to, The noise nearby can be ignored. k Performing a first-order Taylor expansion yields

[0156]

[0157] Then we can get the batch regression formula of MAEKF

[0158]

[0159] in, The estimation problem in the above formula can be rewritten as

[0160]

[0161] The observation vector is The regression matrix is The noise is error The covariance matrix of

[0162]

[0163] The MAEKF update state calculated in the correction step It can also be obtained by performing weighted least squares, linear regression

[0164]

[0165] Can be converted into

[0166]

[0167] The modified step size of MAEKF can be obtained by the following formula:

[0168]

[0169] The structure flow chart of the improved iterative reweighted least squares-hybrid adaptive extended Kalman filter (MIRLS-MAEKF) is as follows: Figure 7As shown in the figure, the MIRLS module in the MIRLS-MAEKF structure flow chart calculates the weight according to the weight formula. The farther the outlier is from the group, the smaller the weight assigned. 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 based on historical data, thereby continuously optimizing the filter parameters. The state quantity is realized by iteratively calculating the residual of the measured value and the model calculated value and the parameters calculated by the filter. Estimates.

[0170] The TBCC engine has a large flight envelope, many operating modes, and a harsh operating environment, so it is easily disturbed in a complex environment. In addition, there are many sensors and they are prone to failure, which easily produces 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 an increase in the variance and bias of the estimated value, thus affecting its reliability and estimation accuracy, and having poor robustness.

[0171] The Huber M estimator is a method for studying abnormal observations of filters. It reconstructs the measurement noise covariance matrix by introducing weights, thereby reducing the impact of abnormal observations on the system and improving the robustness of the filter. The Huber cost function is the most commonly used cost function in M ​​estimation, and its expression is shown in the following formula.

[0172]

[0173] In the formula, γ is the adjustment factor, i is 1, 2, ... m, and m is the dimension of the observation. is the observed residual.

[0174] The corrected measurement noise covariance matrix is:

[0175]

[0176] In the formula, is the weight function, ψ(τ i )=ρ′(τ i ).

[0177] By replacing the measurement noise covariance matrix in EKF with the above formula, the Huber-based robust EKF algorithm (HREKF) is obtained. Its essence is to reweight the measurement noise covariance matrix and construct different weights for observation residuals of different sizes, thereby reconstructing the measurement noise covariance matrix to overcome the influence of abnormal observations on the estimation accuracy and achieve the purpose of improving the robustness of the estimator.

[0178] However, according to the formula

[0179]

[0180] It can be seen that due to the abnormal value of the new information appearing in the forecast state In the matrix M, their influence will be k The 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 isolation effect on small deviation outliers caused by disturbances such as noise, and can improve the robustness and estimation accuracy of the filter to a certain extent. However, when the sensor fails and the measured value deviates greatly from the actual value, this method cannot overcome the influence of abnormal measured values.

[0181] 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. It can be regarded as an estimator that minimizes the norm of the regression residual, which means that satisfy

[0182]

[0183] in, is the standard deviation of the residual, that is The residual vector is arg min represents the value of the variable when the following formula reaches the minimum value.

[0184] The size of the standard deviation estimate is affected by abnormal measurements, i.e., outliers. In order to minimize the corresponding residual square, the filter even tends to lean towards the outliers. Iterative reweighted least squares (IRLS) can overcome this problem. Its principle diagram is shown in Figure 8 As shown in the figure, the solid circle on the lower left represents the circle to be estimated, the dots on the lower left represent normal observations, the prominent dots on the upper right represent abnormal observations, the solid circle on the upper right represents the WLS fitting result, and the dotted circle represents the IRLS fitting result. The IRLS method performs iterative reweighting operations on all observations, assigning a weight of 1 to normal observations and a weight less than 1 to abnormal observations. The farther the abnormal observations are from the normal values, the smaller the weight is, until it is 0. When the WLS method is used for fitting, since the weight of the abnormal observations is still 1, the fitting result will have a large deviation from the estimated circle. However, since the IRLS method isolates the abnormal observations, the fitting effect is much better than the WLS method fitting result.

[0185] If the regression minimizes the robust scale of the residual, then the estimate is robust, that is,

[0186]

[0187] 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

[0188]

[0189] 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 for 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, the scale estimator Solving by iteration

[0190]

[0191] in, is the relative standard residual, the weight function

[0192]

[0193] The ρ function chosen is

[0194]

[0195] The weight function is defined as

[0196]

[0197] Note that the standardized residuals correspond to an estimator with an unbounded ρ function, namely and δ = 1. The lack of robustness in this case can be understood as applying an equal weight to all residuals Weighting to minimize the robust scale of the residuals leads to a highly robust estimator.

[0198] 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 generally applicable and is only applicable to the measurement matrix H with a special form. k is valid 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 the residuals corresponding to non-abnormal observation points, which makes 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.

[0199] First, the measurement parameters are calculated using the least squares method

[0200]

[0201] Then calculate the residual

[0202]

[0203] 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.

[0204] because is an n*n dimensional ill-conditioned matrix whose similar rows can be eliminated, that is, if Then 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.

[0205] Using the above method,

[0206]

[0207] The problem of solving is transformed into the problem of solving a system of non-homogeneous linear equations. Using elementary row transformation of the determinant, we can get

[0208]

[0209] in, is the general solution, the generalized residual r g is a special solution, k∈R, the general solution term represents a series combination of measurement parameters that satisfies the residual of 0, and the special solution term represents a series combination of measurement parameters that causes the residual to be non-zero. The larger the value of the element of the special solution term, the more abnormal the corresponding sensor measurement parameter is.

[0210] The new weight function is defined as

[0211]

[0212] The measurement prediction equation of MIRLS-MAEKF is:

[0213]

[0214] Among them, W k is the weight matrix,

[0215] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A method for modeling a fault-tolerant airborne adaptive model of a TBCC engine, characterized by: Including component-level models, adaptive linear variable parameter models and MIRLS-MAEKF; The component-level model and the adaptive linear variable parameter model constitute a hybrid structural airborne model; The hybrid structure airborne model generates estimated output parameters under the control input vector u The difference between the measured parameters y of the sensor of the real TBCC engine is transmitted 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 modifies the parameters F and H of the hybrid adaptive extended Kalman filter to ensure the estimation accuracy of the hybrid adaptive extended Kalman filter; the hybrid adaptive extended Kalman filter estimates the performance degradation of the real engine based on the difference 2. The method for modeling a fault-tolerant airborne adaptive model of a TBCC engine according to claim 1, characterized in that: The airborne adaptive model includes a hybrid structure airborne model and MIRLS-MAEKF; the hybrid structure airborne model includes an ALPV model for online parameter prediction, which adopts a fast and slow dual-loop design; The basic working principle is to use the output of the onboard engine model as the steady-state reference value of 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 component-level model and the ALPV model for online update to ensure its adaptive capability; The partial derivative parameters of MIRLS-MAEKF are directly provided by the ALPV model to avoid the time-consuming model linearization process, thereby improving the real-time performance; this process is carried out at a high update rate to achieve accurate parameter estimation, and the thermal calculation of the component-level model and the correction calculation of the ALPV model are carried out simultaneously; the adaptive component-level model is linearized using a small deviation linearization method 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 MIRLS-MAEKF recursive process; this process is updated at a lower frequency to cope with the heavy computational burden of the component-level model, which is the slow loop of the model; through the fast and slow dual-loop design, the accuracy and real-time performance of the model are guaranteed at the same time, the slow loop reduces the model linearization update frequency and ensures the accuracy of the model, while the fast loop improves the real-time performance of the airborne adaptive model.

3. The method for modeling a fault-tolerant airborne adaptive model of a TBCC engine according to claim 1, characterized in that: The MIRLS-MAEKF is a new extended Kalman filter; MIRLS is improved based on IRLS and determines the residual weight by the size of the generalized residual; MIRLS is combined with MAEKF to design MIRLS-MAEKF and apply it to the establishment of a fault-tolerant airborne adaptive model for TBCC engines; for the following TBCC engine discrete system The subscript k in the formula represents the value of the variable at the kth step; definition: The design process of MAEKF is: initialization: Status prediction: The difference here with 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 this filter Among them, λ0 is the reference value of the forgetting factor; N k and T k The matrix is in By averaging the previous residual sequence of length N, the covariance estimate of the new residual can be derived as: in, is the innovation residual in Kalman filtering; the estimated process noise matrix is ​​as follows: in, In steady state, the above equation can be obtained using the variance-covariance matrix of the following equation, as follows: The modified step size of MAEKF can be obtained by the following formula: The MIRLS module in MIRLS-MAEKF calculates the weight according to the weight formula. The farther the outlier is from the group, the smaller the weight assigned. 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 historical data, thereby continuously optimizing the filter parameters. The state quantity is realized by iteratively calculating the residual of the measured value and the model calculated value and the parameters calculated by the filter. estimates; 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 satisfy in, is the standard deviation of the residual, that is The residual vector is argmin represents the value of the variable that makes the following formula reach the minimum value; The size of the standard deviation estimate is affected by abnormal measurements, i.e., outliers. In order to minimize the corresponding residual square, the filter even tends to lean toward outliers. Iterative reweighted least squares (IRLS) can overcome this problem. The IRLS method performs iterative reweighting operations on 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 is, until it is 0. When the WLS method is used for fitting, since the weight of the abnormal observation is still 1, the fitting result will have a large deviation from the estimated circle. However, since the IRLS method isolates the abnormal observations, the fitting effect is much better than the WLS method fitting result. If the regression minimizes the robust scale of the residual, then the estimate is robust, that is, 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 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 for 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, the scale estimator Solving by iteration in, is the relative standard residual, the weight function The ρ function chosen is The weight function is defined as Note that the standardized residuals correspond to an estimator with an unbounded ρ function, namely and δ = 1; the lack of robustness in this case can be understood as applying an equal weight to all residuals Weighting to minimize the robust scale of the residuals can yield a highly robust estimator; 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 generally applicable and is only applicable to the measurement matrix H with a special form. k is valid in a few cases; because for many H k , due to H k The influence of different weights on the measurement parameters may cause the residual corresponding to the abnormal observation point to be smaller than the residual corresponding to the non-abnormal observation point, resulting in the IRLS method being no longer applicable. The present invention improves the calculation of the weight function on the basis of IRLS and proposes the MIRLS method. First, the measurement parameters are calculated using the least squares method Then calculate the residual 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; because is an n*n dimensional ill-conditioned matrix whose similar rows can be eliminated, that is, if Then 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; Using the above method, The problem to be solved is transformed into the problem of solving a system of non-homogeneous linear equations; using elementary row transformation of the determinant, we can get in, is the general solution, the generalized residual r g is a special solution, k∈R, the general solution term represents the series combination of measurement parameters that satisfy the residual of 0, and the special solution term represents the series combination of measurement parameters that cause the residual to be non-zero. The larger the value of the element of the special solution term, the more abnormal the corresponding sensor measurement parameter is; The new weight function is defined as The measurement prediction equation of MIRLS-MAEKF is: Among them, W k is the weight matrix, 4. The method for modeling a fault-tolerant airborne adaptive model of a TBCC engine according to claim 1, characterized in that: The measurement parameters include the temperature and pressure at the inlet outlet, the fan outlet, the compressor outlet, after the high-pressure turbine, after the low-pressure turbine, the fan speed and the compressor speed.

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