Turbofan engine-based square root volume Kalman filter design method

Abstract

The invention provides a square root volume Kalman filter design method based on a turbofan engine, and belongs to the technical field of aerospace propulsion system control and simulation. The square root cubature Kalman filter method SRCKF is applied to the problem of turbofan engine gas path health parameter estimation, so as to solve the problems that a traditional Kalman filter method is slow in convergence speed and low in estimation precision in state estimation of complex nonlinear systems such as aero-engines, multiple parameters decline to different degrees at the same time, and the estimation precision is low. The problems of inaccurate positioning of recession parts, incapability of judging recession types, inaccurate recession degree estimation and the like are solved.

Description

Technical Field

[0001] The invention provides a square root volume Kalman filter design method based on a turbofan engine, belonging to the technical field of aerospace propulsion system control and simulation. Background Art

[0002] As the most dazzling pearl in the industrial field, aircraft engines bring together knowledge and technology from multiple disciplines such as material science, structural strength, manufacturing process, aerodynamics, automatic control, and combustion. In addition, aircraft engine systems are classified as complex engineering systems that are knowledge-intensive, high-quality, technology-intensive, high-R&D costs, and long scientific research cycles. Model-based direct performance control methods are the development direction of aircraft engine control system design, and the key problem to be solved is the quantification of engine health parameters and the acquisition of performance parameters such as thrust and surge margin that cannot be directly measured by sensors. Therefore, conducting research on the estimation method of unmeasurable parameters of aircraft engines is of great significance to the development of advanced model-based control methods for aircraft engines.

[0003] In 1960, Kalman proposed the Kalman filter (KF) in the time domain in the article "A New Approach to Linear Filtering and Prediction Problems". The Kalman filter combines the state space method with the filtering idea, uses the current estimated value and the most recent observed value to estimate the current value of the signal, and estimates it through the recursive method, which greatly reduces the storage and calculation amount, and is suitable for the optimal estimation of multi-dimensional non-stationary random signals. In practical applications, the system model often has certain nonlinear characteristics, and it is impossible to achieve accurate state estimation through linear filtering methods. In 2009, Arasaratnam introduced the volume integration rule in the article "A Numerical-Integration Perspective on Gaussian Filters" and proposed the Cubature Kalman Filter (CKF). The volume integration method decomposes the Gaussian integral into the form of spherical integral and radial integral, and uses 2n points for weighted approximation. Since the weight coefficient is positive, the positive definiteness of the covariance matrix in the weighted calculation step is guaranteed. Compared with the traditional KF, CKF has higher accuracy in estimating the state of nonlinear systems and significantly improves the convergence speed, but it still has problems such as large amount of calculation and numerical instability in the recursive process.

[0004] The present invention designs a square root volumetric Kalman filter for the problem of estimating the health parameters of a turbofan engine. The square root volumetric filter algorithm directly calculates the mean and variance of a nonlinear random function based on the numerical integration method of the volume principle. The algorithm only needs to calculate the function value, avoiding the derivative operation and reducing the computational complexity. In addition, the algorithm propagates the square root of the state covariance, ensuring the symmetry and semi-positive definiteness of the covariance matrix, which greatly improves the numerical accuracy and stability. Summary of the invention

[0005] In view of the problems of slow convergence speed and low estimation accuracy of the Kalman filter method when estimating the state of complex nonlinear systems such as aircraft engines, the present invention proposes a design method to apply the square root volumetric filter method to the estimation of aircraft engine health parameters.

[0006] The technical solution of the present invention:

[0007] A method for designing a square root volumetric Kalman filter based on a turbofan engine. The system consists of a normal turbofan engine dynamic model, a recession-injected turbofan engine dynamic model, and a square root volumetric Kalman filter. The normal turbofan engine model outputs temperature and pressure data of each section of the engine for establishing a corresponding state variable model. The recession-injected turbofan engine dynamic model is used to artificially adjust recession components, recession types, and recession amounts. The estimated results of the Kalman filter are compared with the actual recession to determine the estimated effect of the Kalman filter. The Kalman filter receives recession data from the engine based on the state variable model, and obtains an estimated value of the recession amount through iterative calculation. The specific steps are as follows:

[0008] S1: Establishing the Augmented State Variable Model of Turbofan Engine

[0009] S1.1: The state space equations are established by the following nonlinear equations:

[0010]

[0011] y=f 2 (x,u)+v=Cx+Du+ν

[0012] In the formula, x is the state variable, is the first-order derivative of x, y is the system output, and u is the control variable. 1 (·) and f 2 (·) are the system dynamic equations and measurement equations. ω and ν are zero-mean Gaussian white noise with R and Q covariance matrices. A is the state matrix; B is the input matrix; C is the output matrix; and D is the direct transfer matrix.

[0013] Turbofan engine state variables include: low pressure shaft speed n 1, high pressure shaft speed n 2 ; Output variables include: low pressure shaft speed n 1 , high pressure shaft speed n 2 , low pressure compressor outlet temperature T 25 , low pressure compressor outlet pressure P 25 , high pressure compressor outlet temperature T 3 , low pressure turbine outlet temperature T 5 The control variables include: main fuel flow W f . Component health parameters h include: turbofan engine fan efficiency η Fan , Fan flow W Fan , low pressure compressor flow W LPC , high pressure compressor flow W HPC , high pressure turbine flow W HPT , low pressure turbine flow W LPT .

[0014] S1.2: The augmented state space equation is obtained through the state space equation, and then the augmented state variable model of the turbofan engine is established:

[0015] Since the engine will cause its output parameters relative to the rated working state to change in any non-rated working state, the non-rated working characteristics of the turbofan engine can be obtained by the change of the turbofan engine output parameters. The present invention mainly selects the turbofan engine fan efficiency η Fan , Fan flow W Fan , low pressure compressor flow W LPC , high pressure compressor flow W HPC , high pressure turbine flow W HPT , low pressure turbine flow W LPT These six health parameters are used to characterize the non-rated working characteristics of the turbofan engine. In order to obtain the relationship between the health parameters and the output variables of the turbofan engine, it is necessary to augment the health parameters as "control quantities" into the state variable equation. The augmented state space equation describing the real turbofan engine system is as follows:

[0016]

[0017] Δy=CΔx+DΔu+MΔh+ν

[0018] The control input W f When a certain steady-state point remains unchanged, the steady-state model corresponding to the turbofan engine can be obtained. The control input quantity W near this steady-state point is f By making a step input within ±10%, the dynamic model corresponding to the turbofan engine can be obtained. The output of the dynamic model is subtracted from the output of the steady-state model to obtain the deviation signal of the dynamic response of the nonlinear model of the turbofan engine. Among them, Δx is the deviation signal of the state variable, is the first-order derivative of the state variable deviation signal, Δy is the deviation signal of the system output, and Δh is the deviation signal of the health parameter of the turbofan engine under non-rated working conditions. Δu represents the deviation signal of the control variable; the A, B, C, and D matrices can be calculated by the least squares method. The solution of matrices L and M can be obtained by the following formula:

[0019]

[0020] in, Where a ij 、c ij , l ij and m ij are the elements in matrices A, C, L, and M respectively; Δn 1 and Δn 2 are the speed differences of the high and low pressure rotors respectively; Δη Fan is the decay of fan efficiency; ΔT 25 , ΔP 25 , ΔT 3 and ΔT 5 They are the difference between the low-pressure compressor outlet temperature, the low-pressure compressor outlet pressure, the high-pressure compressor outlet temperature and the low-pressure turbine outlet temperature.

[0021] The above formula can be used to find the first column elements of the L and M matrices. The same method can be used to find other elements in the L and M matrices.

[0022] S2: Square root volumetric Kalman filter approach to turbofan engine design

[0023] S2.1: For the nonlinear dynamic system of the turbofan engine, the basic volume points and corresponding weights of the square root volume Kalman filter method are first calculated using the third-order volume principle.

[0024] Furthermore, the general calculation formulas of volume point ξ and weight ω are:

[0025]

[0026] Where m represents the total number of volume points. Using the third-order volume principle, the total number of volume points is twice the state dimension, that is, m = 2n x The basic volume point is generated in the following way: x The unit vector is e = [1,0,…0] T , we use the symbol [1] to represent the point set generated by fully permuting the elements of e and changing the signs of the elements, which is called the complete and fully symmetric point set. [1] j represents the jth point in the point set [1]. If the posterior probability at time k-1 is Among them, z1:k-1 represents the observation sequence from the 1st to the k-1th time, that is, the set of all observation data of the system between time points 1 to k-1, x k-1 represents the actual state vector of the system at time k-1, represents the posterior mean of the state at time k-1, that is, x estimated based on the previous observation data and the system model k-1 ; Get the variance P k-1 The Cholesky factorization S k-1 , that is: S k-1 =chol{P k-1 When updating time or measurement, the volume points are still constructed according to this formula, but the mean and covariance matrix they rely on will be different.

[0027] S2.2: Implement the time update of the square root volume Kalman filter method. The time update first calculates the volume point based on the current state estimate and the square root matrix of the covariance. The generated volume point will be propagated through the state equation of the system. For each volume point X j,k-1 , predict the state at the next moment through the state equation. Next, calculate the state prediction and variance prediction, and finally get the Cholesky decomposition factor by calculating the variance of the propagated volume point and the predicted state.

[0028] Furthermore, the volume points are calculated:

[0029]

[0030] Among them, X j,k-1 Represents the volume point generated in the time update phase, which is used to predict the state at the next moment through the state equation. k-1 represents the square root matrix of the posterior covariance at the previous moment, ξ j represents a set of standard volume points, Represents the posterior mean estimate of the state at the previous moment.

[0031] Furthermore, the volume points propagated through the state equation are calculated:

[0032]

[0033] Furthermore, the Cholesky decomposition factors for state prediction and variance prediction are calculated:

[0034]

[0035] in, represents the predicted mean of the state at time k, represents the Cholesky decomposition factor of the state prediction at time k, ω j represents the weight associated with the volume point, represents the volume point after the state equation propagates, S Q,k-1 Represents the Cholesky decomposition factor of the system process noise variance prediction; Tria() represents triangulating the matrix to obtain a square matrix. Matrix Defined as:

[0036]

[0037] S2.3: Implement the measurement update of the square root volumetric Kalman filter method. Similar to the time update, the measurement update also first calculates the volume point, and calculates the predicted measurement value of the volume point at the next moment through the measurement equation. Next, the measurement prediction, the Cholesky decomposition factor and covariance of the new information variance are calculated, and the Kalman gain is calculated through the Cholesky decomposition factor of the current state and variance. Finally, the Kalman gain is used to update the state estimation and covariance prediction, completing the design of the square root volumetric Kalman filter method in the turbofan engine health parameter estimation model.

[0038] Furthermore, the state volume point is calculated

[0039]

[0040] in, represents the Cholesky decomposition factor of the state prediction at time k; Represents the predicted mean of the state at time k.

[0041] Further, the measurement volume points propagated through the measurement equation are calculated

[0042] Z j,k =h(X j,k )

[0043] Among them, Z j,k represents the predicted measurement value of the volume point propagated through the measurement equation, and h() is the nonlinear measurement equation used to map points in the state space to the measurement space.

[0044] Furthermore, the Cholesky decomposition factors of the measurement prediction, innovation variance and covariance are calculated

[0045]

[0046] S zz,k = Tria([Y k S R,k ])

[0047]

[0048] in, represents the mean of the predicted measured values; S zz,kCholesky factor representing the covariance of the predicted measurements; S R,k represents the square root matrix of the current measurement noise covariance; P xz,k|k-1 represents the cross covariance between the predicted state and the predicted measurement before the prediction update, which describes the linear relationship between the state distribution and the measurement distribution; Y k is a matrix whose column vectors are the scaled values ​​of the difference between each measured volume point and the predicted measurement mean, which is used to calculate the measurement variance square root matrix and the state-measurement cross covariance; k It is also a matrix whose column vector is the scaled value of the difference between each state volume point and the predicted state mean, which is used to calculate the cross covariance and the updated covariance square root matrix; the matrix Y k and χ k Defined as:

[0049]

[0050]

[0051] Furthermore, the Cholesky decomposition factor of the calculated gain, state and variance at time k is estimated as:

[0052]

[0053] Among them, P xz,k Represents the cross covariance between the predicted state and the predicted measurement after the measurement update.

[0054] Furthermore, the Kalman gain is used to update the state estimate and covariance prediction:

[0055]

[0056] S k = Tria([χ k -W k Y k W k S R,k ])

[0057] Among them, z k Represents the actual measurement value at time k, which is used to update the observation information of the state estimation.

[0058] Beneficial effects of the present invention:

[0059] The present invention applies the square root volumetric Kalman filter method SRCKF to the problem of estimating the healthy parameters of the gas path of a turbofan engine, so as to solve the problems of the traditional Kalman filter method in the state estimation of complex nonlinear systems such as aircraft engines, such as slow convergence speed, low estimation accuracy, inaccurate positioning of decaying components, inability to judge the decay type, and inaccurate estimation of the decay degree when multiple parameters decay to different degrees at the same time. Through simulation comparison and verification with various Kalman filter methods, the following conclusions are obtained:

[0060] (1) The square root volumetric filtering method only needs to calculate the function value, avoiding the derivative operation and reducing the computational complexity. Compared with the ensemble Kalman filtering method, which must ensure that the ensemble is large enough to meet the filtering accuracy, the square root volumetric filtering method can take into account both filtering accuracy and calculation speed.

[0061] (2) The square root cubature filtering method adopts the calculation method of the square root of the state covariance, which solves the problems of large computational complexity and numerical instability in the recursive process of the cubature Kalman filtering method, ensures the symmetry and semi-positive definiteness of the covariance matrix, and greatly improves the stability.

[0062] (3) The square root volumetric Kalman filter designed based on the turbofan engine performs better than the ensemble Kalman filter and the volumetric Kalman filter in the cases of single parameter degradation and multiple parameters simultaneously decaying to varying degrees. It can achieve accurate estimation of aircraft engine health parameters and is of great significance to the research on aircraft engine gas path fault diagnosis and degradation prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a schematic diagram of the JT9D turbofan engine structure.

[0064] FIG2( a ) is an estimation diagram of the degradation effect of a single health parameter of a turbofan engine by an ensemble Kalman filter;

[0065] Figure 2(b) is a graph showing the estimation of the decay effect of a single health parameter of a turbofan engine by the volumetric Kalman filter;

[0066] Figure 2(c) is an estimation diagram of the square root volumetric Kalman filter on the degradation effect of a single health parameter of a turbofan engine.

[0067] FIG3( a ) is an estimation diagram of the degradation effect of three health parameters of a turbofan engine by an ensemble Kalman filter;

[0068] FIG3( b ) is an estimation diagram of the decay effect of three health parameters of a turbofan engine by a volumetric Kalman filter;

[0069] Figure 3(c) is an estimation diagram of the square root volumetric Kalman filter on the degradation effect of three health parameters of a turbofan engine.

[0070] FIG4( a ) is an estimation diagram of the degradation effect of six health parameters of a turbofan engine by an ensemble Kalman filter;

[0071] Figure 4(b) is a graph showing the estimation of the decay effects of six health parameters of a turbofan engine by the volumetric Kalman filter;

[0072] Figure 4(c) is an estimation diagram of the square root volumetric Kalman filter on the degradation effect of six health parameters of a turbofan engine. DETAILED DESCRIPTION

[0073] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0074] A method for designing a square root volume Kalman filter based on a turbofan engine comprises the following steps:

[0075] Step 1: Establish the augmented state variable model of the turbofan engine

[0076] The present invention takes the JT9D high bypass ratio turbofan engine as the object to carry out the study of the health parameter estimation method. This type of turbofan engine mainly includes 12 components as shown in the figure below: air inlet, fan, low-pressure compressor, high-pressure compressor, combustion chamber, low-pressure turbine, high-pressure turbine, inner duct tail nozzle, outer duct tail nozzle, duct, low-pressure shaft and high-pressure shaft. The internal operation mechanism of this type of engine is as follows: the gas flows into the fan from the air inlet and is discharged, and then sent to the compressor for isentropic compression, during which the gas flow rate slows down and the pressure increases. After entering the combustion chamber, the gas is mixed with aviation fuel and ignited, and the gas flows into the turbine for isentropic expansion, converting its own heat energy into mechanical energy, thereby driving the turbine to rotate, and the front compressor and other components also follow, and then continue to work and bleed air. Finally, the gas is ejected through the tail nozzle to generate the forward propulsion of the aircraft. The operation steps are consistent with the technical solution and will not be repeated.

[0077] Step 2: Design a square root volumetric Kalman filter method suitable for the JT9D turbofan engine

[0078] Step 2.1: For the nonlinear dynamic system of the turbofan engine, first use the third-order volume principle to calculate the basic volume points and corresponding weights of the square root volume Kalman filter method.

[0079] For the nonlinear dynamic system of turbofan engine, to realize the square root volume Kalman filter method, we must first calculate the basic volume points and corresponding weights. The basic volume points and weights obtained using the third-order volume principle are:

[0080]

[0081] Where m represents the total number of volume points. Using the third-order volume principle, the total number of volume points is twice the state dimension, that is, m = 2n x The basic volume point is generated in the following way: x The unit vector is e = [1,0,…0] T , we use the symbol [1] to represent the point set generated by fully permuting the elements of e and changing the signs of the elements, which is called the complete and fully symmetric point set. [1] j represents the jth point in the point set [1]. If the posterior probability at time k-1 is Among them, z 1:k-1 represents the observation sequence from the 1st to the k-1th time, that is, the set of all observation data of the system between time points 1 to k-1, x k-1 represents the actual state vector of the system at time k-1, represents the posterior mean of the state at time k-1, that is, x estimated based on the previous observation data and the system model k-1 ; Get the variance P k-1 The Cholesky factorization S k-1 , that is: S k-1 =chol{P k-1 When updating time or measurement, the volume points are still constructed according to this formula, but the mean and covariance matrix they rely on will be different.

[0082] Step 2.2: Implement the time update of the square root cubature Kalman filter method.

[0083] ① Calculate volume points

[0084]

[0085] Among them, X j,k-1 Represents the volume point generated in the time update phase, which is used to predict the state at the next moment through the state equation. k-1 represents the square root matrix of the posterior covariance at the previous moment, ξ j represents a set of standard volume points, Represents the posterior mean estimate of the state at the previous moment.

[0086] ② Calculate the volume points propagated through the state equation

[0087]

[0088] ③ Calculate the Cholesky decomposition factors for state prediction and variance prediction

[0089]

[0090] in, represents the predicted mean of the state at time k, represents the Cholesky decomposition factor of the state prediction at time k, ω j represents the weight associated with the volume point, represents the volume point after the state equation propagates, S Q,k-1 Represents the Cholesky decomposition factor of the system process noise variance prediction; Tria() represents triangulating the matrix to obtain a square matrix. Matrix Defined as:

[0091]

[0092] Step 2.3: Implement the measurement update of the square root cubature Kalman filter method.

[0093] ① Calculate volume points

[0094]

[0095] in, represents the Cholesky decomposition factor of the state prediction at time k; Represents the predicted mean of the state at time k.

[0096] ② Calculate the volume points propagated through the measurement equation

[0097] Z j,k =h(X j,k )

[0098] Among them, Z j,k represents the predicted measurement value of the volume point propagated through the measurement equation, and h() is the nonlinear measurement equation used to map points in the state space to the measurement space.

[0099] ③ Calculate the Cholesky decomposition factors and covariance of measurement prediction and innovation variance

[0100]

[0101] S zz,k = Tria([Y k S R,k ])

[0102]

[0103] in, represents the mean of the predicted measured values; S zz,k Cholesky factor representing the covariance of the predicted measurements; S R,k represents the square root matrix of the current measurement noise covariance; P xz,k|k-1 represents the cross covariance between the predicted state and the predicted measurement before the prediction update, which describes the linear relationship between the state distribution and the measurement distribution; Yk is a matrix whose column vectors are the scaled values ​​of the difference between each measured volume point and the predicted measurement mean, which is used to calculate the measurement variance square root matrix and the state-measurement cross covariance; k It is also a matrix whose column vector is the scaled value of the difference between each state volume point and the predicted state mean, which is used to calculate the cross covariance and the updated covariance square root matrix; the matrix Y k and χ k Defined as:

[0104]

[0105] ④ Calculate the gain, the state at time k and the Cholesky decomposition factor of the variance is estimated as:

[0106]

[0107] ⑤Use Kalman gain to update state estimation and covariance prediction:

[0108]

[0109] S k = Tria([χ k -W k Y k W k S R,k ])

[0110] Step 3: Method simulation verification

[0111] By selecting a certain working point of the turbofan engine and injecting component recession at any time, the output parameters of the turbofan engine recession model can be obtained. The output parameters are calculated by various methods such as the square root volume Kalman filter method to obtain the estimated value of the recession.

[0112] Step 3.1: Single parameter decay analysis

[0113] According to the established augmented state space model, the working point is selected as H=0, Ma=0, W f =1.9028kg / s, 50s, the efficiency or flow of each component decays by 2%, the simulation step is 0.04s, and the estimation of the decay effect by the ensemble Kalman filter (EnKF), the cubature Kalman filter (CKF) and the square root cubature Kalman filter (SRCKF) is compared.

[0114] Figure 2(a) to Figure 2(c) The estimation of single component degradation using three filtering methods, namely, ensemble Kalman filter, cubature Kalman filter and square root cubature Kalman filter, is given.

[0115] Step 3.2: Multi-parameter decay analysis.

[0116] Under the condition of the same working point of the turbofan engine, at 50s, different types and degrees of decay of different components are injected into the turbofan engine decay model at the same time, and the simultaneous decay of multiple components of the nonlinear model of the turbofan engine is analyzed. The fan efficiency η is selected Fan , high pressure compressor flow W HPC and low pressure turbine flow W LPT The decays of 2%, 1% and 3% are given respectively, and the decay of the remaining components is set to 0. Figure 3(a) to Figure 3(c) The prediction results of three different filtering methods are given.

[0117] Given the fan efficiency η of the turbofan engine Fan Decline 1%, fan flow W Fan Decline 4%, low pressure compressor flow W LPC Decline 2%, high pressure compressor flow W HPC Decline 4%, high pressure turbine flow W HPT Decline 3% and low pressure turbine flow W LPT The three filtering methods are used to estimate the decline of each parameter under the extreme condition that the six parameters decline to different degrees at the same time. Figure 4(a) to Figure 4(c) Three filtering methods are given to estimate the six parameters when all of them are degraded to different degrees.

[0118] Step 4: Evaluate the advantages and disadvantages of various filtering methods

[0119] In order to evaluate the advantages and disadvantages of various filtering methods, the estimation effect diagrams of different filtering methods are analyzed and compared, and the accuracy of the estimation of various Kalman filtering methods is judged by the standard relative error between the true value of parameter decay.

[0120] Table 1 shows the actual degradation of each component under the condition of single parameter degradation, and Table 2 shows the estimation error of single parameter degradation by three different filtering methods.

[0121] Table 1 Actual degradation of each component

[0122]

[0123] Table 2 Comparison of single parameter recession prediction errors

[0124]

[0125]

[0126] By comparing the three methods in the prediction of single parameter degradation of each component, it can be seen that the maximum prediction error of the square root volumetric Kalman filter method is about 1%, and the average prediction error is 0.27%. The estimation accuracy of each parameter is better than that of the ensemble Kalman filter method and the volumetric Kalman filter method. Compared with the ensemble Kalman filter method, the average accuracy is improved by 0.94%, and compared with the volumetric Kalman filter method, the average accuracy is improved by 0.57%. Compared with the ensemble Kalman filter and the volumetric Kalman filter, this method has a smaller parameter fluctuation range and the best prediction effect of single parameter degradation.

[0127] The prediction error results of the three filtering methods for the simultaneous decay of fan efficiency, high-pressure compressor flow and high-pressure turbine flow are shown in the figure. Figure 3(a) to Figure 3(c) As shown, it can be seen that the parameter fluctuation range of the ensemble Kalman filter method is larger and is more seriously affected by noise. The comparison results of different filtering methods on the three-parameter decay prediction error are shown in Table 3.

[0128] Table 3 Comparison of three-parameter recession prediction errors

[0129]

[0130] It can be seen from Table 3 that the three filtering methods can accurately estimate the different degrees of decay of the three parameters. When the three parameters decay, the average standard error of the square root volumetric Kalman filter method is 1.27, which is not much different from the estimation accuracy of the volumetric Kalman filter method and is better than the ensemble Kalman filter method.

[0131] Figure 4(a) to Figure 4(c) The estimation of the three filtering methods for all six parameters with different degrees of degradation is given. Table 4 shows the true degradation of each parameter and the estimation of the Kalman filtering method, and Table 5 shows the standard estimation errors of the three different filtering methods.

[0132] Table 4 Actual degradation and estimated values ​​of all parameters

[0133]

[0134] Table 5 Comparison of all parameter recession prediction errors

[0135]

[0136] Comparing the prediction results of the three methods under full parameter degradation, it can be seen that the square root volumetric Kalman filter method has the smallest average prediction error, which is only 8.72%. The estimation accuracy is improved by 35.54% compared with the ensemble Kalman filter method and by 6.22% compared with the volumetric Kalman filter method.

[0137] The present invention proposes a square root volumetric filtering method to solve the problems of slow convergence speed and low estimation accuracy of the Kalman filtering method when estimating the state of complex nonlinear systems such as aircraft engines. Compared with the large amount of calculation and numerical instability in the recursive process of the volumetric Kalman filtering method, the square root volumetric filtering method can ensure the positive definiteness of the state covariance matrix and enhance numerical robustness. Through simulation comparison of various filtering methods, the results show that: under the condition of single parameter degradation, the average estimation error of the health parameters of this method is less than 0.5%; under the condition of multi-parameter degradation, the logarithmic average estimation error of the health parameters is less than 9%; the filtering accuracy of this method is better than that of the volumetric Kalman filtering method and the ensemble Kalman filtering method.

Claims

1. A square root volume Kalman filter design method based on a turbofan engine, characterized in that: The specific steps are as follows: S1: Establish the augmented state variable model of turbofan engine; S2: Square root volumetric Kalman filter method for designing turbofan engines; S2.1: For the nonlinear dynamic system of the turbofan engine, the basic volume points and corresponding weights of the square root volume Kalman filter method are first calculated using the third-order volume principle; S2.2: Implement the time update of the square root volumetric Kalman filter method; the time update first calculates the volume point based on the current state estimate and the square root matrix of the covariance, and the generated volume point will be propagated through the state equation of the system; for each volume point, the state at the next moment is predicted through the state equation; then the state prediction and variance prediction are calculated, and finally the Cholesky decomposition factor is obtained by calculating the variance of the propagated volume point and the predicted state; S2.3: Implement measurement update of the square root volumetric Kalman filter method; Similar to time update, measurement update also first calculates the volume point, and calculates the predicted measurement value of the volume point at the next moment through the measurement equation; next, calculate the measurement prediction, the Cholesky decomposition factor and covariance of the new information variance, and calculate the Kalman gain through the Cholesky decomposition factor of the state and variance at the current moment; finally, use the Kalman gain to update the state estimate and covariance prediction, and complete the design of the square root volumetric Kalman filter method in the turbofan engine health parameter estimation model.

2. A method for designing a square root volumetric Kalman filter based on a turbofan engine according to claim 1, characterized in that: The S1 is specifically as follows: S1.1: The state space equations are established by the following nonlinear equations: y=f2(x,u)+ν=Cx+Du+ν In the formula, x is the state variable, is the first-order derivative of x, y is the system output, and u is the control variable; f1(·) and f2(·) are the system dynamic equation and measurement equation; ω and ν are zero-mean Gaussian white noise with R and Q covariance matrices; A is the state matrix; B is the input matrix; C is the output matrix; D is the direct transfer matrix; The state variables of the turbofan engine include: low-pressure shaft speed n1, high-pressure shaft speed n2; the output variables include: low-pressure shaft speed n1, high-pressure shaft speed n2, low-pressure compressor outlet temperature T 25 , low pressure compressor outlet pressure P 25 , high pressure compressor outlet temperature T3, low pressure turbine outlet temperature T5; the controlled variables include: main fuel flow W f ; Component health parameters h include: turbofan engine fan efficiency η Fan , Fan flow W Fan , low pressure compressor flow W LPC , high pressure compressor flow W HPC , high pressure turbine flow W HPT , low pressure turbine flow W LPT ; S1.2: The augmented state space equation is obtained through the state space equation, and then the augmented state variable model of the turbofan engine is established: The non-rated working characteristics of the turbofan engine are obtained by changing the output parameters of the turbofan engine; the fan efficiency η of the turbofan engine is selected Fan , Fan flow W Fan , low pressure compressor flow W LPC , high pressure compressor flow W HPC , high pressure turbine flow W HPT , low pressure turbine flow W LPT These six health parameters are used to characterize the non-rated working characteristics of the turbofan engine. In order to obtain the relationship between the health parameters and the output variables of the turbofan engine, it is necessary to augment the health parameters as "control quantities" into the state variable equation. The augmented state space equation describing the real turbofan engine system is as follows: Δy=CΔx+DΔu+MΔh+ν The control input W f When a certain steady-state point remains unchanged, the steady-state model corresponding to the turbofan engine can be obtained. The control input quantity W near this steady-state point is f By making a step input within ±10%, the dynamic model corresponding to the turbofan engine can be obtained; the output of the dynamic model is subtracted from the output of the steady-state model to obtain the deviation signal of the dynamic response of the nonlinear model of the turbofan engine; where Δx is the deviation signal of the state variable, is the first-order derivative of the state variable deviation signal, Δy is the deviation signal of the system output, Δh is the deviation signal of the health parameter of the turbofan engine under non-rated working conditions; Δu represents the deviation signal of the control variable; the A, B, C, and D matrices can be calculated by the least squares method; the solution of the matrices L and M can be obtained by the following formula: in, Where a ij 、c ij , l ij and m ij are the elements in matrices A, C, L, and M respectively; Δn1 and Δn2 are the speed differences of the high-pressure and low-pressure rotors respectively; Δη Fan is the decay of fan efficiency; ΔT 25 , ΔP 25 , ΔT3 and ΔT5 are the differences of low-pressure compressor outlet temperature, low-pressure compressor outlet pressure, high-pressure compressor outlet temperature and low-pressure turbine outlet temperature respectively; The above formula can be used to find the first column elements of the L and M matrices. The same method can be used to find other elements in the L and M matrices.

3. A method for designing a square root volumetric Kalman filter based on a turbofan engine according to claim 1, characterized in that: Step 2.1 is as follows: The general calculation formulas for volume point ξ and weight ω are: Where m represents the total number of volume points. Using the third-order volume principle, the total number of volume points is twice the state dimension, that is, m = 2n x ; The basic volume point is generated in the following way: x The unit vector is e = [1,0,…0] T , we use the symbol [1] to represent the point set generated by fully permuting the elements of e and changing the signs of the elements, which is called the complete and fully symmetric point set. [1] j represents the jth point in the point set [1]; if the posterior probability at time k-1 is Among them, z 1:k-1 represents the observation sequence from the 1st to the k-1th time, that is, the set of all observation data of the system between time points 1 to k-1, x k-1 represents the actual state vector of the system at time k-1, Represents the posterior mean of the state at time k-1, which is estimated based on the previous observation data and system model. Get the variance P k-1 The Cholesky factorization S k-1 , that is: S k-1 =chol{P k-1 }; When the time is updated or the measurement is updated, the volume points are still constructed according to this formula, but the mean and covariance matrix they rely on will be different.

4. The square root volume Kalman filter design method based on a turbofan engine according to claim 1, characterized in that: Step 2.2 is as follows: Calculate volume points: Among them, X j,k-1 Represents the volume point generated in the time update phase, which is used to predict the state at the next moment through the state equation. k-1 represents the square root matrix of the posterior covariance at the previous moment, ξ j represents a set of standard volume points, Represents the posterior mean estimate of the state at the previous moment; Compute volume points propagating through the equation of state: Compute the Cholesky decomposition factors for the state forecast and variance forecast: in, represents the predicted mean of the state at time k, represents the Cholesky decomposition factor of the state prediction at time k, ω j represents the weight associated with the volume point, represents the volume point after the state equation propagates, S Q,k-1 Represents the Cholesky decomposition factor of the system process noise variance prediction; Tria() represents triangulating the matrix to obtain a square matrix; the matrix Defined as:

5. The square root volume Kalman filter design method based on a turbofan engine according to claim 1, characterized in that: Step 2.3 is as follows: Calculate state volume point in, represents the Cholesky decomposition factor of the state prediction at time k; Represents the predicted mean of the state at time k; Calculates the measurement volume points propagated through the measurement equation Z j,k =h(X j,k ) Among them, Z j,k represents the predicted measurement value of the volume point propagated through the measurement equation, h() is the nonlinear measurement equation used to map points in the state space to the measurement space; Computes the Cholesky factorization of measurement forecasts, innovation variances, and covariances S zz,k =Tria([And k S R,k ]) in, represents the mean of the predicted measured values; S zz,k Cholesky factor representing the covariance of the predicted measurements; S R,k represents the square root matrix of the current measurement noise covariance; P xz,k|k-1 represents the cross covariance between the predicted state and the predicted measurement before the prediction update, which describes the linear relationship between the state distribution and the measurement distribution; Y k is a matrix whose column vectors are the scaled values ​​of the difference between each measured volume point and the predicted measurement mean, which is used to calculate the measurement variance square root matrix and the state-measurement cross covariance; k It is also a matrix whose column vector is the scaled value of the difference between each state volume point and the predicted state mean, which is used to calculate the cross covariance and the updated covariance square root matrix; the matrix Y k and χ k Defined as: The Cholesky factorization of the gain, state and variance at time k is estimated as: Among them, P xz,k represents the cross covariance between the predicted state and the predicted measurement after the measurement update; Use the Kalman gain to update the state estimate and covariance prediction: S k =Tria([χ k -IN k Y k IN k S R,k ]) Among them, z k Represents the actual measurement value at time k, which is used to update the observation information of the state estimation.

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