A method for aero-engine system identification and output interval estimation considering performance degradation and model mismatch

Abstract

The present invention belongs to the technical field of model parameter identification and discloses a method for identifying and estimating the output interval of an aero-engine system that comprehensively considers performance degradation and model mismatch. For an aero-engine system, a linear variable parameter modeling method is introduced to combine the state variable models of multiple operating points of the aero-engine through scheduling parameters to construct a global model with a large operating range. To address issues such as errors and model mismatch in the modeling process, a quantile regression neural network is used to perform interval estimation of the system output uncertainty, thereby improving the model's accuracy and robustness. The standard state-space equation of the aero-engine system is augmented, and the health parameters of each component of the system are treated as states for estimation. A variational Bayesian adaptive Kalman filter method is used to estimate the health parameters in real time, thereby constructing a system adaptive model. This invention provides a research foundation for fields such as fault diagnosis and nonlinear system control of aero-engine systems.

Description

Technical Field

[0001] The present invention relates to the technical field of model parameter identification, and in particular to an aero-engine system identification and output interval estimation method that comprehensively considers performance degradation and model mismatch. Background Art

[0002] As a crucial component of aircraft, aircraft engines shoulder the crucial responsibility of providing power. Aircraft performance largely depends on the quality of their engines. Therefore, developing adaptive models for aircraft engines with strong real-time performance, high accuracy, and simple expression is a key issue in the aviation industry. Due to the strong nonlinearity of aircraft engine systems, traditional linearization methods struggle to reflect system characteristics over a wide operating range. Linear variable parameter modeling improves system modeling accuracy by combining linearized state variable models at multiple stable operating points during engine operation using scheduling parameters. The adaptive Kalman filter algorithm can estimate the system model and noise characteristics online using observed data. Compared to traditional Kalman filters, it has the ability to adapt to system dynamics, making it more effective in handling nonlinear and variable parameter systems.

[0003] Aircraft engines power aircraft and operate primarily in harsh environments of high temperature and high pressure. Due to the effects of the operating environment and component wear during use, actual engine performance degrades, resulting in significant uncertainty. Currently, most linear system modeling methods for aircraft engines only provide point estimates of model parameters, which are difficult to reflect the performance degradation process and complex uncertainties. Using interval prediction, we replace point estimates with distribution estimates of output results to measure the uncertainty of aircraft engine system output estimates.

[0004] The goal of the present invention is to design an adaptive aircraft engine system model and predict system health parameters and performance degradation, which is achieved by combining a linear variable parameter model with an adaptive Kalman filter algorithm. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem of lack of a modeling method for the system's large operating range characteristics in the presence of noise and performance degradation in aircraft engine system modeling, and to propose an aircraft engine system identification and output range estimation method that comprehensively considers performance degradation and model mismatch.

[0006] The technical solution of the present invention is as follows: a method for aircraft engine system identification and output range estimation that comprehensively considers performance degradation and model mismatch, comprising the following steps:

[0007] Step 1: Based on the input, output, and state variables of the aero-engine system, a local linearized model is established at each operating point using the perturbation method. Furthermore, a global model of the aero-engine over a large operating range is established using a polynomial linear variable parameter method.

[0008] Step 2: Based on the global model of the large operating range in Step 1, the performance degradation of each aircraft engine component is estimated in the presence of external noise disturbances according to the adaptive Kalman filter theory.

[0009] Step 3: Based on the long short-term memory neural network architecture and combined with the quantile regression method, the residual error between the model prediction results obtained in step 1 and the actual aircraft engine model data is compensated:

[0010] The final model output is,

[0011] y c (n L ,u)=y c,st (n L ,u c,st )+△y c (n L ,△u c )+y pred (n L ,u c,st );

[0012] Among them, y c (n L ,u) is the final predicted value of the system output, y c,st (n L ,u c,st ) represents the estimate of the current equilibrium point output, △y c (n L ,△u c ) is the output increment estimate when the input changes, y pred (n L ,u c,st ) is the compensation value of the neural network to the global model.

[0013] The step 1 is specifically as follows:

[0014] Step 1.1: Set the nonlinear aero-thermodynamic model of the aircraft engine system as follows:

[0015]

[0016] y(t)=g(x(t),u(t))

[0017] Where x∈R n is the state quantity of the aircraft engine system, y∈R mis the output of the aircraft engine system, u∈R r is the input of the aero-engine system, while f(·) and g(·) represent the nonlinear functions in the state equation and output equation of the aero-engine model, respectively, which are used to describe the dynamic process of engine operation and the output observation results;

[0018] At a certain equilibrium point (x st ,u st ) is used to perform Taylor approximation on the above nonlinear aerodynamic thermodynamic model, and its first-order expansion is as follows:

[0019]

[0020]

[0021] Right now,

[0022]

[0023] △y=C△x+D△u

[0024] Where A, B, C, D are system matrices of corresponding dimensions, △x=xx st Indicates the increment of the true state value relative to the equilibrium state value, △u=uu st Indicates the increment of the real state input relative to the equilibrium point input, △y=yy st It represents the increment of the actual state output relative to the equilibrium point output;

[0025] The above system matrix is ​​solved based on the local perturbation method and the step signal excitation method. First, when the working state of the system is at the equilibrium point, a disturbance signal is given to a state variable of the system, and the system matrix A={a ij},C={c oj} to solve;

[0026]

[0027] Among them, △x j Represents the j-th state variable x j The disturbance is applied, and it is stipulated that the disturbance value cannot exceed one percent of the state value of the selected equilibrium point; similarly, the elements of the matrix C are also obtained by the above method, that is,

[0028]

[0029] By inputting a step signal to observe the change of a state variable to calculate the values ​​of the system matrix B and D; use the step response of the first control variable to calculate the elements of the first column of the system matrix, and keep other control variables and state variables unchanged, that is,

[0030]

[0031]

[0032] Where △u1 is the step amplitude of the first control variable, which is required not to exceed 1% of the input value of the selected equilibrium point. Similarly, the above method is used to calculate the element values ​​of each column of matrices B and D.

[0033] Step 1.2: Based on the benchmark values ​​of multiple equilibrium points and the local linear state variable model, a dynamic model of the system under large operating conditions is constructed using the linear variable parameter method;

[0034] The state variable model calculated above can only effectively approximate the characteristics of the system in a small neighborhood near the selected equilibrium operating point. When the deviation from the operating point is too large, the state variable model is difficult to apply. In order to obtain the dynamic characteristics of the aircraft engine over a large operating range, a polynomial linear variable parameter method is used to construct a variable parameter model of the system based on the state variable models corresponding to multiple equilibrium points of the system under different operating conditions.

[0035] A scheduling parameter θ is introduced to reflect the current working state of the system, and the state variable model at each equilibrium point is regarded as an affine function of the linear variable parameter model with respect to the scheduling parameter, that is,

[0036]

[0037] △y c =C c (θ)△x c +D c (θ)△u c +ν

[0038] Each element in the system matrix is ​​a variable value of the scheduling parameter, that is, A c (θ)={a c,ij (θ)}, where a c,ij Represents the matrix A c The elements in ω and ν represent the process noise and observation noise of the system respectively, both of which obey the zero-mean Gaussian distribution, with variances Q and R respectively. The low-pressure turbine speed n of the aircraft engine is selected L As the scheduling parameters of the linear variable parameter model;

[0039] In order to determine the benchmark values ​​of model input, output and state under different working conditions Where k represents the model reference value of the kth operating point, and multiple m-order polynomials are used to approximate the relationship between the scheduling parameters and each reference value, as shown below;

[0040]

[0041] During the fitting process, the value of t is continuously increased until the coefficient of determination R 2 Stop when it is greater than 90%, t=min{t:R 2 (x c,st,n (n L,c ,t))>=0.9}; calculate each state variable, output and output reference value through the above formula, and finally obtain the steady-state output of the system for the corresponding working state;

[0042] In order to express the dynamic characteristics of the system, each element in the state space system matrix of multiple operating points is fitted to obtain a power series polynomial about the scheduling parameters. The specific expression is as follows:

[0043]

[0044]

[0045]

[0046]

[0047] Among them, ta, tb, tc, and td represent the polynomial orders of different system matrices respectively. The order values ​​are continuously increased during the fitting process until the determination coefficient R of the fitting is 2 When it is greater than 90%, it stops; finally, the adaptive dynamic model of the system under large working conditions is obtained. For the working point n L,1 The state value and output value of the system are obtained through the interaction of the corresponding reference value and the variable parameter state variable model;

[0048] y c (n L,1 )=y c,st (n L,1 ,u c,st )+△y c (n L,1 ,△u c )

[0049] Among them, △u c It represents the increment of the input of the system at that moment relative to the previous sampling moment. The right side of the equal sign represents the sum of the baseline value of the observed output corresponding to the operating point and the input increment response. Similarly, the dynamic characteristics of the state variables of the system at different operating points are represented by a similar method.

[0050] The step 2 is specifically as follows: in order to estimate the system performance degradation, a health parameter is introduced to represent the efficiency and flow deviation of the engine rotating parts; the health parameter h, which reflects the performance degradation of each engine component, is augmented into the state vector of the original system, that is, Since engine performance degradation is a slow process, the partial derivative of the performance degradation factor is approximated to 0; the augmented model is

[0051]

[0052]

[0053] Right now,

[0054]

[0055] △y ext =C ext (θ)x ext +D ext (θ)△u c +ν

[0056] Among them A h (θ),B c (θ),C h (θ) is obtained by step 1, considering the change of estimated health parameters at the equilibrium point, ignoring △u c item;

[0057] Considering the state variable model at a certain operating point, the linear time-invariant model is first discretized to obtain

[0058] x k =A k x k-1 +ω k

[0059] y k =H k x k-1 +ν k

[0060] Among them, ω k ~N(0,Q k ) is the system noise that obeys Gaussian distribution, and ν k ~N(0,Σ k ) is the observation noise, the noise variance Σ k is a diagonal matrix; it is assumed that the initial state value obeys Gaussian distribution, that is, x0~N(m0,P0), and the subscript k represents the sampling time;

[0061] The working process of the adaptive Kalman filter mainly includes the following steps:

[0062] Calculate the forecast distribution parameters:

[0063]

[0064]

[0065]

[0066]

[0067] Among them, α and β are parameters in the inverse gamma distribution, which are used to describe the variance of the observation noise, and ρ∈(0,1] is an adjustable constant;

[0068] Parameter update step: First, let Then iterate and solve the following steps;

[0069]

[0070]

[0071]

[0072]

[0073] After N iterations, let Finally, the state distribution of the system at the working point is obtained, that is, the predicted value of the health parameter;

[0074] Use the current working state of the system and the scheduling parameter θ as the input x, h of the long short-term memory neural network n Represents the network output; first, the input is saved to the cell state c through the input gate t middle;

[0075]

[0076] Among them, W i is the input gate weight matrix, b i is the bias term, Indicates the output status at the previous moment; the unit state of the current input of the system is,

[0077]

[0078] After that, the forget gate decides whether to retain the cell state c at the previous moment. t-1 ;

[0079]

[0080] Determine the current state of the unit of the long short-term memory neural network;

[0081]

[0082] in Represents the Hadamard product; according to the current unit state, the final output of the long short-term memory neural network is obtained through the output gate;

[0083]

[0084]

[0085] Based on the quantile regression method, a fully connected layer is used to obtain the interval estimation of the system residual; the quantile level q∈Q={0.05,0.5,0.95} is taken to obtain the prediction results under different quantiles. At this time, the loss function of quantile regression is

[0086]

[0087] Where (y i ) + =max(y i ,0), the output when the quantile is 0.5 Represents the residual compensation term for the LPV system, that is, The prediction results when taking the other two quantiles represent interval predictions with 90% confidence.

[0088] Beneficial effects of the present invention: The present invention is aimed at aircraft engine systems. In the research field of aircraft engine system identification, the problem of poor modeling accuracy of nonlinear systems in a large working range is proposed. A method for aircraft engine system identification and output interval estimation that comprehensively considers performance degradation and model mismatch is proposed, and an adaptive model of multiple working points of the aircraft engine system is obtained. At the same time, the performance degradation and noise interference of each system component are considered to estimate the health parameters of the system. On the one hand, the present invention introduces the linear variable parameter model method into the aircraft engine system modeling process, and by constructing affine functions of multiple scheduling parameters, the state variable models of different steady-state working points of the system are combined to build a system model in a large working range; on the other hand, by augmenting the health parameters of each component of the system into the state vector and the state equation of the aircraft engine system, the health parameters of the system are estimated in real time through an adaptive Kalman filter method based on the variational Bayesian idea, and the performance degradation of the aircraft engine system is estimated according to the changes in the health parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 The schematic diagram shows a method for aircraft engine system identification and output interval estimation that comprehensively considers performance degradation and model mismatch.

[0090] Figure 2 Schematic diagram of the input disturbance signal.

[0091] Figure 3 Schematic diagram of the residual error of the neural network compensation model adaptation.

[0092] Figure 4 Output results for the low-pressure turbine speed of the system model with interval prediction.

[0093] Figure 5 Output results for the high-pressure turbine speed of the system model with interval prediction.

[0094] Figure 6 This is the turbine outlet temperature output result of the system model after model mismatch compensation.

[0095] Figure 7 is the estimation result of the health parameters of each component by the adaptive Kalman filter. DETAILED DESCRIPTION

[0096] A method for aircraft engine system identification and output interval estimation that comprehensively considers performance degradation and model mismatch is shown in the flowchart below. Figure 1 As shown, it is implemented by the following steps:

[0097] Step 1: Based on the input, output, and state variables of the aero-engine system, a local linearized model is established at each operating point using the perturbation method. A global model for the aero-engine over a wide operating range is then established using the polynomial LPV method.

[0098] Step 1.1: The nonlinear aero-thermodynamic model of the aero-engine system is as follows:

[0099]

[0100] y(t)=g(x(t),u(t))

[0101] Where x∈R n is the state quantity of the aircraft engine system, y∈R m is the observation quantity of the aircraft engine system, u∈R r is the input of the aircraft engine system, while f(·) and g(·) represent the nonlinear functions in the state equation and output equation of the aircraft engine model, respectively, which are used to describe the dynamic process and observation results of the engine operation. At a certain equilibrium operating point (x st ,u st ) is used to perform Taylor approximation on the above nonlinear model, and its first-order expansion is as follows:

[0102]

[0103]

[0104] Right now,

[0105]

[0106] △y=C△x+D△u

[0107] Where A, B, C, D are system matrices of appropriate dimensions, △x=xx st Indicates the increment of the true state value relative to the equilibrium state value, △u=uu st and △y=yy st Similarly, it represents the increment of system input and output.

[0108] The above system matrix is ​​solved based on the local perturbation method and the step signal excitation method. First, a disturbance signal is given to a state variable of the system when the working state of the system is at the equilibrium point, and the system matrix A={a ij},C={c mj} to solve.

[0109]

[0110] Among them, △x j Represents the j-th state variable x j The disturbance is applied, and the disturbance value is not allowed to exceed one percent of the state value of the selected equilibrium point. Similarly, the elements of the matrix C can also be obtained by the above method, that is,

[0111]

[0112] By inputting a step signal to observe the change of a certain state variable, the values ​​of the system matrices B and D are calculated. The elements of the first column of the system matrix are calculated using the step response of the first control variable, and the other control variables and state variables are kept unchanged, that is,

[0113]

[0114]

[0115] Where △u1 is the step amplitude of the first control variable, which is required not to exceed 1% of the input value of the selected equilibrium point. Similarly, the above method can be used to calculate the element values ​​of each column of matrices B and D.

[0116] Step 1.2: Based on the benchmark values ​​of multiple equilibrium points and the state variable model, construct a dynamic model of the system under large operating conditions using the linear variable parameter method;

[0117] The state variable model calculated above can only effectively approximate the system's characteristics within a small neighborhood near the selected equilibrium operating point. When the system deviates significantly from this operating point, the state variable model becomes difficult to apply. To determine the dynamic characteristics of aircraft engines over a wide range of operating conditions, an adaptive model of the system is constructed based on the polynomial linear variable parameter method, using state variable models corresponding to multiple equilibrium points under different operating conditions.

[0118] A scheduling parameter θ is introduced into the system model to reflect the current working state of the system. The state variable model at each equilibrium point is regarded as an affine function of the linear variable parameter model with respect to the scheduling parameter, that is,

[0119]

[0120] △y c =C c (θ)△x c +D c (θ)△u c +ν

[0121] Each element in the system matrix is ​​a variable value of the scheduling parameter, that is, A c (θ)={a c,ij (θ)}. ω and ν represent the process noise and observation noise of the system respectively, both of which obey zero-mean Gaussian distribution, with variances Q and R respectively. The low-pressure turbine speed n of the aircraft engine is selected L As the scheduling parameter of the linear variable parameter model.

[0122] In order to determine the benchmark values ​​of model input, output and state under different working conditions Where k represents the model reference value of the kth operating point, and multiple m-order polynomials are used to approximate the relationship between the scheduling parameters and each reference value, as shown below

[0123]

[0124] The fitting process is specified to continuously increase the value of t until the coefficient of determination R 2 Stop when it is greater than 90%, that is, t=min{t:R 2 (x c,st,n (n L,c ,t))>=0.9}. Similarly, the above formula can be used to calculate each state variable, output and output reference value, and finally obtain the steady-state output of the system for the corresponding working state.

[0125] In order to express the dynamic characteristics of the system, each element in the state space system matrix of multiple operating points is fitted to obtain a power series polynomial about the scheduling parameters. The specific expression is as follows:

[0126]

[0127]

[0128]

[0129]

[0130] Among them, ta, tb, tc, and td represent the polynomial orders of different system matrices respectively. The order values ​​are continuously increased during the fitting process until the determination coefficient R of the fitting is 2 When it is greater than 90%, it stops; finally, the adaptive dynamic model of the system under large working conditions is obtained. For the working point n L,1 The state value and output value of the system can be obtained by the corresponding reference value and the variable parameter state variable model.

[0131] y c (n L,1 )=y c,st (n L,1 ,u c,st )+△y c (n L,1 ,△u c )

[0132] where △u c represents the increment of the system input at that moment relative to the previous sampling moment. The right side of the equal sign represents the sum of the baseline value of the observed output corresponding to that operating point and the input increment response. Similarly, the dynamic characteristics of the system state variables at different operating points can also be expressed using a similar method.

[0133] Step 2: Based on the adaptive Kalman filter theory, the performance degradation of each aircraft engine component is estimated, while eliminating the influence of external noise on the model built in step 1.

[0134] In order to estimate the degradation of system performance, the health parameter is introduced to represent the efficiency and flow deviation of the engine rotating parts. The health parameter h is augmented to the state vector of the original system. Since engine performance degradation is a slow process, the partial derivative of the performance degradation factor can be approximated to 0. The augmented model is

[0135]

[0136]

[0137] Right now

[0138]

[0139] △yext =C ext (θ)x ext +D ext (θ)△u c +ν

[0140] Among them A h (θ),B c (θ),C h (θ),D h (θ) can be obtained by step 1, considering the changes in the estimated health parameters at the equilibrium point and ignoring △u c item.

[0141] Considering the state variable model at a certain operating point (the other operating points can be obtained by different scheduling parameters), the linear time-invariant model is first discretized to obtain

[0142] x k =A k x k-1 +ω k

[0143] y k =H k x k-1 +ν k

[0144] Among them, ω k ~N(0,Q k ) is the system noise that obeys Gaussian distribution, and ν k ~N(0,Σ k ) is the observation noise, the noise variance Σ k Assume that the initial state value follows a Gaussian distribution, that is, x0~N(m0,P0), and the subscript k represents the sampling time.

[0145] The working process of the adaptive Kalman filter mainly includes the following steps:

[0146] Calculate the forecast distribution parameters:

[0147]

[0148]

[0149]

[0150]

[0151] Among them, α and β are parameters in the inverse gamma distribution, which are used to describe the variance of the observation noise, and ρ∈(0,1] is an adjustable constant.

[0152] Parameter update step: First, let Then iterate and solve the following steps

[0153]

[0154]

[0155]

[0156]

[0157] After N iterations, let Finally, the state distribution of the system at the working point is obtained, that is, the predicted value of the health parameter.

[0158] Step 3: Based on the long short-term memory neural network architecture and combined with the quantile regression method, the residual error between the model prediction results obtained in the above steps and the actual aircraft engine model data is compensated:

[0159] Use the current working state of the system, that is, the scheduling parameter θ as the input x of the long short-term memory neural network. First, save the input to the unit state c through the input gate. t middle

[0160] i t =σ(W i ·[h t-1 ,x t ]+b i )

[0161] Among them, W i is the input gate weight matrix, b i is the bias term, h t-1 Indicates the output status at the previous moment.

[0162] The current input unit state of the system is

[0163]

[0164] After that, the forget gate decides whether to retain the cell state c at the previous moment. t-1

[0165] f t =σ(W f ·[h t-1 ,x t ]+b f )

[0166] The current unit state of the network can be determined

[0167]

[0168] in Represents the Hadamard product. According to the current unit state, the final output of the network can be obtained by passing through the output gate;

[0169] o t =σ(W o ·[h t-1 ,x t ]+b o )

[0170]

[0171] Based on the quantile regression method, a fully connected layer is used to obtain the interval estimation of the system residual. The quantile level q∈Q={0.05,0.5,0.95} is used to obtain the prediction results under different quantiles. The loss function of quantile regression is

[0172]

[0173] Where (y i ) + =max(y i ,0), that is, only positive numbers are retained, and the output when the quantile is 0.5 Represents the residual compensation term for the LPV system, that is, The prediction results for the other two quantiles represent interval predictions with a 90% confidence level. The final model output is

[0174] y c (n L ,u)=y c,st (n L ,u c,st )+△y c (n L ,△u c )+y pred (n L ,u c,st )

[0175] The following is a specific embodiment:

[0176] The Simulink simulation model of the turbofan engine JT9D developed by NASA is selected to obtain the data required for the aircraft engine system identification. The state variable x is set to the low-pressure rotor speed and high-pressure rotor speed of the aircraft engine, that is, x = [n l ,n h ] TThe output variable y is set to the high-pressure turbine outlet temperature of the aircraft engine, and the input variable u is set to the aircraft engine's input fuel-air ratio (FAR). Gaussian noise is added to the output signal as the system's observation noise. The aircraft engine is modeled based on operating data from the JT9D engine Simulink simulation model.

[0177] Near the steady-state operating point of the engine, the small perturbation method is used to excite the system, and the partial derivative method is used to obtain the approximate linearized state variable model of the system at this operating point through the input and output characteristics of the system. The disturbance input curve is as follows Figure 2 .

[0178] With the scheduling parameter θ0(n l =3500rpm) as an example, the linear model of this operating point is estimated by the small perturbation method as follows:

[0179]

[0180] △y=C△x+D△u

[0181] in:

[0182]

[0183] C=[0.4344,0.0064],D=[38092.33]

[0184] When the aircraft engine is in the range of 80% to 100% (θ 100％ =nl 100％ =4000rpm), 17 steady-state operating points (at intervals of 50rpm) were selected from the operating range and the corresponding state variable models were obtained using the perturbation method. Considering that the scheduling parameters differ from the order of magnitude of the system input and output, the scheduling parameters were normalized. Then, the model matrix elements corresponding to these operating points were fitted using the fitting method to obtain an affine function form related to the scheduling parameters. This in turn yielded a linear variable parameter model for the engine system within the operating range of 80% to 100% of the scheduling parameters:

[0185]

[0186] △y c =C c (θ)△x c +D c (θ)△u c +ν

[0187] The first element a of matrix A 11 For example, the function of scheduling parameters is:

[0188] a11 (θ) = -129.78 × θ 5 +301.98×θ 4 -250.03×θ 3 +80.77×θ 2 -7.33×θ-1.09

[0189] The index determination coefficient of fitting accuracy is R2=0.9881, and the fitting accuracy of the remaining elements of the system matrix is ​​shown in Table 1 below.

[0190] Table 1 Determination coefficient of each element in the system matrix

[0191]

[0192] From the index data in Table 1, it can be seen that the polynomial fitting accuracy of the system matrix elements with respect to the scheduling parameters meets the index requirements, and the obtained system adaptive model has high accuracy under the selected working conditions.

[0193] In order to further improve the accuracy of the model, a neural network combining long short-term memory network and quantile regression method is used to compensate for the residual of the model. The system scheduling parameters are used as the input of the network, and the residual term caused by model mismatch is used as the network output to train the network. The interval estimation result of the residual term is as follows: Figure 3 After the network training with quantile q = 0.5 is completed, it is imported into Simulink to perform online compensation on the system model. The output and state change of the system adaptive model are compared with the data of the component-level model JT9D. Figures 4 to 6 .

[0194] Compared with the traditional Kalman filter method, the adaptive Kalman filter method combined with the variational Bayesian theory has a certain degree of improvement in identification accuracy. The health parameters of each component are augmented into the state vector to obtain a new system model. The prediction of the health parameters of each component of the system based on the adaptive Kalman filter algorithm is shown in Figure 7 The comparison of the estimation accuracy using the adaptive Kalman filter algorithm and the ordinary Kalman filter algorithm is shown in Table 2.

[0195] Table 2 Method comparison diagram

[0196]

[0197] It can be seen that the accuracy of output estimation is also improved compared with the Kalman filtering method.

Claims

1. A method for aircraft engine system identification and output interval estimation that comprehensively considers performance degradation and model mismatch, characterized by: The steps are as follows: Step 1: Based on the input, output, and state variables of the aero-engine system, a local linearized model is established at each operating point using the perturbation method. Furthermore, a global model of the aero-engine over a large operating range is established using a polynomial linear variable parameter method. Step 2: Based on the global model of the large operating range in Step 1, the performance degradation of each aircraft engine component is estimated in the presence of external noise disturbances according to the adaptive Kalman filter theory. Step 3: Based on the long short-term memory neural network architecture and combined with the quantile regression method, the residual error between the model prediction results obtained in step 1 and the actual aircraft engine model data is compensated: The final model output is, ； in, is the final predicted value of the system output, represents the estimate of the output of the current equilibrium point, is the estimate of the output increment when the input changes, is the compensation value of the neural network to the global model; The step 1 is specifically as follows: Step 1.1: Set the nonlinear aero-thermodynamic model of the aircraft engine system as follows: ； in, is the state quantity of the aircraft engine system, is the output of the aircraft engine system, is the input of the aircraft engine system, and and They represent the nonlinear functions in the state equation and output equation of the aircraft engine model, respectively, and are used to describe the dynamic process of engine operation and the output observation results; At a certain balance point of the aircraft engine The Taylor approximation is performed on the above nonlinear aerodynamic thermodynamic model, and its first-order expansion is as follows: ； Right now, ； in is the system matrix of the corresponding dimension, represents the increment of the true state value relative to the equilibrium state value, It represents the increment of the real state input relative to the equilibrium point input, It represents the increment of the actual state output relative to the equilibrium point output; The above system matrix is ​​solved based on the local perturbation method and the step signal excitation method. First, when the working state of the system is at the equilibrium point, a disturbance signal is given to a state variable of the system, and the system matrix is ​​solved by the response of the system to the disturbance. Solve; ； in, Indicates the state variables The disturbance is imposed, and the disturbance value is not allowed to exceed one percent of the state value of the selected equilibrium point; similarly, the matrix The elements of are also obtained by the above method, namely ； By inputting a step signal and observing the change of a state variable, the system matrix can be calculated. and The value of; use the step response of the first control variable to calculate the elements of the first column of the system matrix, and keep other control variables and state variables unchanged, that is, ； in, is the step amplitude of the first control variable, which is required not to exceed one percent of the input value of the selected equilibrium point; similarly, the matrix is ​​calculated and The above method is used for the element values ​​of each column; Step 1.2: Based on the benchmark values ​​of multiple equilibrium points and the local linear state variable model, construct a dynamic model of the system under large working conditions using the linear variable parameter method; Based on the polynomial linear variable parameter method, a variable parameter model of the system is constructed according to the state variable models corresponding to multiple equilibrium points of the system under different working conditions; Introduce a scheduling parameter that can reflect the current working status of the system , the state variable model at each equilibrium point is regarded as an affine function of the linear variable parameter model with respect to the scheduling parameters, that is, ； Each element in the system matrix is ​​a variable value of the scheduling parameter, that is, ,in Representation matrix The elements in , They represent the process noise and observation noise of the system, both of which obey the zero-mean Gaussian distribution, and their variances are and ; Select the low-pressure turbine speed of the aircraft engine As the scheduling parameters of the linear variable parameter model; In order to determine the benchmark values ​​of model input, output and state under different working conditions ,in, Indicates the Model reference values ​​for working points, using multiple The relationship between the order polynomial approximation scheduling parameters and various benchmark values ​​is shown below; ； During the fitting process, the until the coefficient of determination of the fit is Greater than Stop when ; By calculating each state variable, output and output reference value through the above formula, we can finally get the steady-state output of the system for the corresponding working state; In order to express the dynamic characteristics of the system, each element in the state space system matrix of multiple operating points is fitted to obtain a power series polynomial about the scheduling parameters. The specific expression is as follows: ； in Represents the polynomial order of different system matrices respectively. In the fitting process, the order value is continuously increased until the determination coefficient of the fitting is Greater than Finally, the adaptive dynamic model of the system under large working conditions is obtained. The state value and output value of the system are obtained through the interaction of the corresponding reference value and the variable parameter state variable model; ； in, It represents the increment of the input of the system at that moment relative to the previous sampling moment. The right side of the equal sign represents the sum of the baseline value of the observed output corresponding to the operating point and the input increment response. Similarly, the dynamic characteristics of the state variables of the system at different operating points are represented by a similar method.

2. The method for aircraft engine system identification and output interval estimation taking into account performance degradation and model mismatch according to claim 1, characterized in that: The step 2 is specifically as follows: in order to estimate the system performance degradation, health parameters are introduced to represent the efficiency and flow deviation of the engine rotating parts; the health parameters reflecting the performance degradation of each component of the engine are Augmented to the state vector of the original system, that is ; Since engine performance degradation is a slow process, the partial derivative of the performance degradation factor is approximated to 0; the augmented model is ； Right now, ； in Obtained through step 1, consider the changes in the estimated health parameters at the equilibrium point and ignore item; Considering the state variable model at a certain operating point, the linear time-invariant model is first discretized to obtain ； in, is the system noise that obeys Gaussian distribution, and is the observation noise, the noise variance is a diagonal matrix; assuming that the initial state value obeys Gaussian distribution, that is , subscript represents the sampling time; The working process of the adaptive Kalman filter mainly includes the following steps: Calculate the forecast distribution parameters: ； in, , is the parameter in the inverse gamma distribution, which is used to describe the variance of the observation noise, and is an adjustable constant; Parameter update step: First, let , then iteratively solve the following steps; ； After N iterations, let ; Finally, the state distribution of the system at the working point is obtained, that is, the predicted value of the health parameter.

3. The method for aircraft engine system identification and output interval estimation taking into account performance degradation and model mismatch according to claim 1 or 2, characterized in that: Use the system's current working status and scheduling parameters As input to the long short-term memory neural network , Represents the network output; first, the input is saved to the unit state through the input gate middle; ； in, is the input gate weight matrix, is the bias term, Indicates the output status at the previous moment; the unit state of the current input of the system is, ； After that, the forget gate decides whether to keep the unit state of the previous moment ; ； Determine the current state of the unit of the long short-term memory neural network; ； in Represents the Hadamard product; according to the current unit state, the final output of the long short-term memory neural network is obtained through the output gate; ； ； Based on the quantile regression method, a fully connected layer is used to obtain the interval estimation of the system residual; the quantile level is taken Get the prediction results under different quantiles. At this time, the loss function of quantile regression is ； in , the output when the quantile is 0.5 Represents the residual compensation term for the LPV system, that is, , while the prediction results when taking the other two quantiles represent interval predictions with 90% confidence.

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