Engine online adaptive model predictive method based on reduced dimension kalman filter

Abstract

The application provides an online adaptive model prediction method for an engine based on dimension reduction Kalman filtering, which comprises the following steps: S1, obtaining a state space equation of the engine; S2, performing dimension reduction on a health parameter by using a dimension reduction matrix V to obtain a state space equation after dimension reduction of the parameter; S3, performing offline optimization on the dimension reduction matrix V by using a nonlinear least square optimization algorithm to obtain an optimal dimension reduction matrix V; and S4, estimating and predicting the health parameter of the engine and an output vector of the engine by using a dimension reduction Kalman filtering algorithm to obtain a real-time updated and optimized health parameter, and substituting the real-time updated and optimized health parameter and the optimal dimension reduction matrix V into the state space equation of the engine to obtain a state space equation with minimum dimension reduction error and adaptive adjustment of the health parameter, namely, an adaptive estimation model of the engine. The application can give the best health parameter of the variable cycle engine according to the current working state of the engine by using the dimension reduction Kalman filtering algorithm.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine control technology and relates to an online adaptive model prediction method for engines based on dimension-reduced Kalman filtering. Background Technology

[0002] Currently, commonly used aero-engine component-level models are built based on the engine's nominal characteristics, ignoring the performance differences between different aero-engines. Furthermore, an engine is a complex system composed of multiple components, which are interconnected and highly coupled. Combined with external factors during operation, even if the component model characteristics are highly accurate, the nominal nonlinear component-level model will still deviate, making it difficult to meet application requirements. Initially, engines are typically built using nominal conditions without considering performance variations. During engine operation, the actual engine performance degrades due to the operating environment and component wear. This is accompanied by sudden performance changes due to component failures or overhauls. These performance changes are ultimately reflected in sensor readings. If the model lacks adaptive capabilities, the residuals between the model and the engine will inevitably change. Therefore, aero-engines designed for control system applications need excellent output adaptive capabilities to adapt to uncertainties such as engine performance degradation and sudden changes, further improving the matching degree between the aero-engine and the actual engine during service.

[0003] In the field of aero-engine control and health management, the mainstream approach is to estimate engine performance degradation during flight by establishing a real-time airborne adaptive model of the engine based on Kalman filters and their variants (such as extended Kalman filters and unscented Kalman filters). By establishing an airborne adaptive model of the aero-engine, it is possible to estimate unmeasurable engine performance parameters, such as surge margin and thrust. These parameters can be directly used in control, prediction, and health management programs. Furthermore, it can estimate the degree of engine degradation, thereby eliminating modeling errors at the component level. The degree of degradation is usually described by unmeasurable health parameters, such as the efficiency of the fan and compressor. However, traditional Kalman filtering methods have low accuracy. While extended Kalman filters and unscented Kalman filters offer better estimation performance, their computational complexity is high, making it difficult to meet the real-time performance requirements of aero-engines. To maximize the engine's operational potential and ensure reliable and efficient operation of the aircraft throughout its large flight envelope, it is essential to optimize traditional Kalman filtering methods to achieve an aero-engine adaptive model with high real-time performance and accuracy. Summary of the Invention

[0004] The purpose of this invention is to at least solve one of the problems existing in the prior art.

[0005] Therefore, in order to overcome the problem that the traditional Kalman filter (KF) algorithm cannot simultaneously achieve both real-time performance and accuracy, this invention provides an online adaptive model prediction method for engines based on dimension-reduced Kalman filtering. This method is applicable to a certain type of turbofan variable cycle engine and can use the dimension-reduced Kalman filter algorithm to provide the optimal health parameters of the variable cycle engine based on the current engine operating state.

[0006] The technical solution of the present invention is as follows:

[0007] An online adaptive model prediction method for engines based on dimension-reduced Kalman filtering is proposed, and the steps of the method are as follows:

[0008] Step S1: Linearize the variable cycle engine model to obtain the engine's state space equations. The input vector of the state space equations includes: engine fuel quantity, exhaust nozzle area, and health parameters. The state vector of the state space equations includes the engine's high and low pressure shaft speeds. The output vector of the state space equations includes thrust and surge margin.

[0009] Step S2: Design the dimension reduction matrix V of the health parameters, use the dimension reduction matrix V to reduce the dimension of the health parameters, and convert the state space equation obtained in step S1 into the state space equation after parameter dimension transformation.

[0010] Step S3: Use a nonlinear least squares optimization algorithm to perform offline optimization on the dimension reduction matrix V to obtain the optimal dimension reduction matrix V;

[0011] Step S4: Construct a dimension-reduced Kalman filter algorithm. Use the dimension-reduced Kalman filter algorithm to estimate and predict the engine's health parameters and output vector to obtain real-time updated and optimized health parameters. Substitute the real-time updated and optimized health parameters into the engine's state-space equation to obtain the state-space equation for adaptive adjustment of health parameters. Substitute the optimal dimension-reduction matrix V from step S3 into this state-space equation for adaptive adjustment of health parameters to obtain the state-space equation with the minimum dimension reduction error and adaptive adjustment of health parameters. This state-space equation with the minimum dimension reduction error and adaptive adjustment of health parameters is the adaptive estimation model of the engine.

[0012] Furthermore, in step S4, the posterior estimate of the state vector is obtained by iterating the Kalman gain and covariance matrix in the Kalman filter algorithm. The posterior estimate of the state vector is then substituted into the state space equation after parameter dimension transformation to achieve estimation and prediction of the engine's health parameters and output vector. The estimated and predicted health parameters are then updated and optimized in real time to the engine's state space equation, resulting in the state space equation for adaptive adjustment of health parameters.

[0013] Furthermore, the specific steps of step S1 are as follows:

[0014] S1.1: When the health parameter h remains at the nominal operating state, the state-space equation for the nonlinear model of the variable cycle engine at any nominal operating point is:

[0015] Dx k+1 =ADx k +BDu k

[0016] Dy k =CDx k +DDu k (2)

[0017] In the formula, x is the state vector, y is the output vector, u is the input vector, including the engine fuel quantity, exhaust nozzle area, and health parameter h; k is the time stamp, indicating that the current time step is k, i.e., time k; D represents the changes in each variable before and after a small disturbance in the nonlinear model of the variable cycle engine; A and C are the matrices corresponding to the state vector, and B and D are the matrices corresponding to the input vector; x k+1 Let x represent the state vector at time k+1. k Let u represent the state vector at time k. k Let y represent the input vector at time k. k This represents the output vector at time k;

[0018] S1.2: Input a disturbance Du to the variable cycle engine. After the variable cycle engine reaches steady state again, calculate the difference between the output and state variables before and after the disturbance, and solve A, B, C, and D by the least squares method.

[0019] S1.3: A, B, C, and D are optimized using a normalization method. The optimized A, B, C, and D are then substituted into formula (2) to obtain the optimized state-space equation.

[0020] Furthermore, in step 1.2, the formulas for solving A, B, C, and D using the least squares method are as follows:

[0021]

[0022] Among them, y k This represents the output vector at time k.

[0023] Furthermore, after obtaining the optimized state-space equation at any nominal operating state point in S1.3, the state-space equations of all nominal operating state points are combined into an LPV model.

[0024] Furthermore, the specific steps of step S2 are as follows:

[0025] S2.1: Construct a state-space equation considering health parameters and noise using a small perturbation method:

[0026] Dx k+1 =ADx k +BDu k +LDh k +w

[0027] Dy k =CDx k +DDu k +MDh k +v (6)

[0028] Where L and M are matrices corresponding to health parameters; vector h k The engine's health parameters at time k; vectors w and v are uncorrelated zero-mean white noise;

[0029] S2.2: Assuming the health parameter h is slowly time-varying, the augmented state-space equation can be obtained:

[0030]

[0031] Wherein, vector Dh k+1 For the engine's health parameters at time k+1, send to w k sum vector v k These are zero-mean white noise at time k, and vector w. h,k The zero-mean white noise at time k corresponds to the health parameter h; vector w xh For the augmented vector [DxDh] T Zero-mean white noise; vector v xh =vector v k ;x xh A is the augmented state vector; xh C xh These are the matrices corresponding to the augmented state vectors; B xh D xh These are the matrices corresponding to the augmented input vectors; D xh =D;

[0032] S2.3: Use the dimension-reduced matrix V to perform a linear combination transformation on the health parameter h in the following form:

[0033] Dq=V*Dh (8)

[0034] In the formula, q is the parameter vector obtained after the dimensionality reduction transformation;

[0035] Based on formula (8), we obtain Dh:

[0036] Dh = V * *Dq (9)

[0037] In the formula, V * It is the pseudo-inverse of the dimension-reduced matrix V;

[0038] S2.4: Set Dh = V * Substituting Dq into formula (7), we obtain the state-space equation after dimensionality reduction transformation:

[0039]

[0040] In the formula, q k+1 Let q be the parameter vector obtained after the dimensionality reduction transformation at time k+1. k The parameter vector obtained after the dimensionality reduction transformation at time k; w q,k The zero-mean white noise at time k corresponding to the parameter vector q obtained after dimensionality reduction transformation; vector w xq The augmented vector [Dx Dq] is the result of the dimensionality reduction transformation. T Zero-mean white noise; vector v xq =vector v k ;x xq It is the augmented state vector after dimensionality reduction transformation; A xq C xq These are the matrices corresponding to the augmented state vectors after the dimensionality reduction transformation; B xq D xq These are the matrices corresponding to the augmented input vectors after the dimensionality reduction transformation; D xq =D.

[0041] Furthermore, the w xq and w xq The covariance matrix Q xq It can be calculated using the following formula:

[0042]

[0043] In the formula, Q xh For vector w xh The covariance matrix.

[0044] Furthermore, the specific steps of step S3 are as follows:

[0045] S3.1: Design the sum of squared estimation errors as the objective function SSEE. The objective function SSEE consists of two parts: the mean and the deviation of the estimation errors. and the estimated error variance P xh,k The mathematical expression is as follows:

[0046]

[0047] Where, x xh,k Let be the true value of the augmented state vector at time k. tr{*} represents the posterior estimate of the augmented state vector at time k; tr{*} denotes the trace function;

[0048] S3.2: When the Kalman filter algorithm converges, estimate the mean deviation of the error. and the estimated error variance P xh,k It can be expressed by the following formula:

[0049]

[0050] in, P h The expected covariance matrix of the health parameters;

[0051] S3.3: Before the calculation, set the covariance matrix R and w of v. xq The covariance matrix Q xq Health parameter expected covariance matrix P h Find an initial value for the dimension-reduced matrix V, and ensure that the Frobenius norm of the initial value of V is 1, i.e., ||V||. F =1; Calculate the current optimization objective function SSEE based on S3.1 and S3.2;

[0052] S3.4: Repeat step S3.3 for iteration. In each iteration, evaluate the change of SSEE relative to the previous iteration to determine whether convergence has been achieved within the specified tolerance.

[0053] If convergence is achieved, proceed to step S3.6.

[0054] If convergence is not achieved, proceed to step S3.5.

[0055] S3.5: Update V using a nonlinear least squares optimization algorithm, and return the updated and optimized V to S4.3 for SSEE calculation;

[0056] S3.6: The V value in the current iteration is the optimal V value.

[0057] Furthermore, the specific steps of step S4 are as follows:

[0058] S4.1: Perform prior estimation on the state space equation after dimensionality reduction transformation, i.e., formula (10), to obtain the prior estimate of the augmented state vector after dimensionality reduction transformation.

[0059]

[0060] in, x is the prior estimate of the augmented state vector after the dimension reduction transformation at time k; xq,k-1 It is the augmented state vector after the dimension reduction transformation at time k-1;

[0061] S4.2: Perform prior estimation of error covariance:

[0062]

[0063] in, Let P be the prior estimate of the error covariance at time k. k-1 This is the posterior estimate of the error covariance at time k-1;

[0064] S4.3: Calculate the Kalman filter gain K based on the prior estimate of the error covariance. k Calculation:

[0065]

[0066] S4.4: Based on the Kalman filter gain K k Update the state vector to obtain the posterior estimate of the state vector:

[0067]

[0068] in, Let z be the posterior estimate of the state vector at time k. k These are actual engine output measurements;

[0069] S4.5: Calculate the updated error covariance:

[0070]

[0071] S4.6: Repeat steps S4.2-S4.5 iteratively: obtain the posterior estimate of the error covariance P at time k. k Substituting this into formula (14) of S4.2, that is, P of formula (14) of S4.2 k-1 Replace with P k The prior estimate of the error covariance at time k+1 is obtained, and then sequentially passed through S4.3 until the Kalman filter gain K is reached. k After convergence, output S4.4 to obtain the posterior estimate of the iterated state vector, which contains the estimated prediction of the engine's health parameters; and input the posterior estimate of the iterated state vector into formula (10) to output Δy. At this time, the estimated prediction of the engine's output vector is obtained. By comparing the estimated prediction of the engine's output vector with the measured value of the sensor output of the real engine, the accuracy of the estimated prediction can be judged; at the same time, the estimated prediction of the engine's health parameters is optimized and updated in real time into formula (10) to obtain the state space equation for adaptive adjustment of health parameters.

[0072] Substituting the optimal V value of S3.6 into the state-space equation for adaptive adjustment of the health parameter yields the state-space equation with the minimum dimension reduction error and adaptive adjustment of the health parameter. This state-space equation with the minimum dimension reduction error and adaptive adjustment of the health parameter is the adaptive estimation model of the engine.

[0073] Furthermore, in S4.2, the posterior estimate of the error covariance at the initial time is the initial covariance matrix P. ￥ :

[0074]

[0075] In the formula, R is the covariance matrix of zero-mean white noise v.

[0076] By applying the above technical solution, the present invention has the following beneficial effects:

[0077] (1) To address the issue that variable cycle engines cannot fully realize their performance advantages within the flight envelope, this invention utilizes an improved low-dimensional Kalman filter (LDKF) algorithm to update and optimize the engine's health parameters in real time. Combined with a nonlinear least squares optimization algorithm to update the optimized low-dimensional matrix, this improves the accuracy of real-time prediction by the traditional Kalman filter algorithm and greatly develops the performance advantages of variable cycle engines in supersonic cruise. This enables variable cycle engines to maximize their performance advantages within the flight envelope. By using the optimal low-dimensional Kalman filter to predict degradation factors and key engine output parameters, the accuracy, efficiency, and stability of combined engine control can be improved.

[0078] (2) This invention applies a small perturbation to the input of the variable cycle engine, solves the state space equation of the nonlinear model of the variable cycle engine offline, performs matrix transformation on the state space equation, and unifies the parameters to be predicted under the state and output prediction model framework based on Kalman filter. This can reduce the computational load of Kalman filter and improve the real-time performance of the operation.

[0079] (3) To address the problem that traditional Kalman filtering algorithms have limited available sensor parameters and low prediction accuracy, this invention first proposes a dimension reduction matrix based on singular value decomposition. After adjusting the dimension of the state space equation of the variable cycle engine, it serves as the state space equation of the Kalman filtering algorithm. Then, considering the estimation error caused by parameter dimension reduction due to the underdeterminacy of the estimation problem, the optimal dimension reduction matrix is ​​determined based on the least squares optimization algorithm. Ultimately, this can improve the accuracy and real-time performance of predicting unmeasurable parameters of the variable cycle engine, thereby bringing more technological advancements to the aviation industry and air transport. Attached Figure Description

[0080] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0081] Figure 1 This is a schematic diagram of the online adaptive model prediction method for variable cycle engines based on dimension-reduced Kalman filtering.

[0082] Figure 2 This is a schematic diagram of a small-perturbation linearization model based on the least squares method and optimization algorithm.

[0083] Figure 3 Optimize the flowchart for estimating the sum of squared errors;

[0084] Figure 4 The diagram shows the predicted surge margin of a certain type of variable cycle engine under a certain operating condition.

[0085] Figure 5 This is a prediction diagram of the degradation of a certain type of variable cycle engine under a certain operating condition. Detailed Implementation

[0086] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0088] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0089] Example 1:

[0090] This embodiment provides an online adaptive model prediction method for engines based on dimension-reduced Kalman filtering. See Appendix. Figure 1 The steps of this method are as follows:

[0091] Step S1: Linearize the variable cycle engine model to obtain the engine's state-space equations. To ensure that the state-space equations can predict the engine's health parameters in real time, the input vectors selected for the state-space equations include: engine fuel quantity, exhaust nozzle area, and health parameters. The state vectors of the state-space equations are selected as the engine's high and low pressure shaft speeds (i.e., n). H n L The output vector of the state-space equation is selected as a key parameter that has a significant impact on engine performance, such as thrust and surge margin.

[0092] Step S2: Design the dimension reduction matrix V for the health parameters. Use the dimension reduction matrix V to reduce the dimension of the health parameters and convert the state space equation obtained in step S1 into the state space equation after parameter dimension transformation. The dimension reduction matrix is ​​used to reduce the dimension of the health parameters, thrust, and surge margin to be estimated to be less than or equal to the dimension of the measured values ​​of the sensor output of the real engine, so as to facilitate finding the global optimal solution when using the Kalman filter algorithm for estimation.

[0093] Step S3: To address the estimation error caused by the dimensionality reduction operation, an offline optimization algorithm is used to optimize the dimensionality reduction matrix V. That is, the nonlinear least squares optimization algorithm is added to the original dimensionality reduction Kalman filter algorithm to update the optimized dimensionality reduction matrix V, thus obtaining the optimal dimensionality reduction matrix V.

[0094] Step S4: Construct a dimension-reduced Kalman filter algorithm. Use this algorithm to estimate and predict the engine's health parameters and key parameters (i.e., output vectors, including thrust and surge margin) to obtain real-time updated and optimized health parameters. Substitute these parameters into the engine's state-space equations to obtain the state-space equations for adaptive adjustment of the health parameters, specifically:

[0095] By iterating through the Kalman filter algorithm and using the Kalman gain and covariance matrix, a posterior estimate of the state vector is obtained. This posterior estimate is then substituted into the state-space equation after parameter dimension transformation to estimate and predict the engine's health parameters and output vector. The estimated and predicted health parameters are then updated and optimized in real time to the engine's state-space equation, resulting in an adaptive state-space equation for health parameter adjustment. The Kalman gain and covariance matrix in the iterative Kalman filter algorithm further optimize the estimated and predicted values ​​of the engine's health parameters and output vector.

[0096] Substituting the optimal dimension reduction matrix V obtained in step S3 into the state space equation for adaptive adjustment of the health parameter, we can obtain the state space equation with the minimum dimension reduction error and adaptive adjustment of the health parameter. This state space equation with the minimum dimension reduction error and adaptive adjustment of the health parameter is the adaptive estimation model of the engine. Using this adaptive estimation model of the engine, we can realize online adaptive prediction and estimation of the engine output.

[0097] Step S5: Verify the reliability and superiority of the dimension-reduced Kalman filter algorithm by building a hardware-in-the-loop simulation environment suitable for the dimension-reduced Kalman filter algorithm for simulation verification.

[0098] Example 2:

[0099] This embodiment, based on Embodiment 1, provides an online adaptive model prediction method for engines based on dimension-reduced Kalman filtering:

[0100] In step S1, based on the operating conditions of the variable cycle engine at a certain operating point, the engine parameter difference is obtained using the small perturbation method, and an initial guess value is obtained using the least squares method. This initial value is used for optimization to obtain the state-space equation at that point. (See Appendix) Figure 2 The specific steps are as follows:

[0101] S1.1: Characteristic analysis of the variable cycle engine is conducted using the controlled variable method. Through digital simulation, the influence of various components on key parameters (such as surge margin and thrust) of the variable cycle engine in the intermediate state and afterburner state is explored. The adjustable control variable sensitive parameters of the variable cycle engine are identified, and the sensitive parameters are used as the input vectors of the engine's state-space equations. The selected sensitive parameters include: engine fuel quantity, exhaust nozzle area, and health parameters.

[0102] S1.2: For the operating states of the variable cycle engine at different altitudes and Mach numbers, the variable cycle engine model is linearized by using a method of small perturbation of the input vector. Assuming that the aerodynamic and thermodynamic characteristics of the variable cycle engine components have been obtained, its nonlinear model can be expressed as:

[0103]

[0104] In the formula, x is the state vector, including the high and low pressure speeds of the variable cycle engine [n]. L n H ] T y is the output vector, including surge margin and thrust, where surge margin includes front fan surge margin, rear fan surge margin, front turbine surge margin, and rear turbine surge margin; u is the input vector, including engine fuel quantity Wf, exhaust nozzle area A8, and health parameter h, i.e., u = [Wf A8 h] T The health parameter h includes the flow factor and efficiency factor of the variable cycle engine fan and compressor; Let x be the first derivative. Let f(*) be the first derivative of y, and let f(*) and g(*) both represent functions;

[0105] With the health parameter h maintained at the nominal operating state, a first-order Taylor expansion of the nonlinear model of the variable cycle engine at any nominal operating point yields the state-space equations of the nonlinear model of the variable cycle engine:

[0106] Dx k+1 =ADx k +BDu k

[0107] Dy k =CDx k +DDu k (2)

[0108] In the formula, k is a time marker, indicating that the current time step is k, i.e., time k; D represents the changes in each variable before and after a small disturbance in the nonlinear model of the variable cycle engine (applicable to the entire text); A and C are the matrices corresponding to the state vector, and B and D are the matrices corresponding to the input vector; x k+1Let x represent the state vector at time k+1. k Let u represent the state vector at time k. k Let y represent the input vector at time k. k This represents the output vector at time k;

[0109] S1.3: To obtain the values ​​of A, B, C, and D in the state-space equations, a small disturbance Du is input to the variable cycle engine. After the variable cycle engine reaches steady state again, the differences in output and state variables before and after the disturbance are calculated. A, B, C, and D are then solved using the least squares method, as shown in the following formula:

[0110]

[0111] Among them, y k This represents the output vector at time k;

[0112] S1.4: Substitute A, B, C, and D obtained in step S1.3 into formula (2). At this point, formula (2) has a certain error compared with the actual variable cycle engine. Therefore, formula (2) needs to be further optimized to obtain higher prediction accuracy. The optimization process is as follows:

[0113] Normalize the matrices A, B, C, and D of the state-space equations, that is, let Among them, S -1 For a normalized diagonal matrix, The diagonal elements are the steady-state baseline values ​​of the state vector. The diagonal elements are the steady-state baseline values ​​of the output vector. The diagonal elements are the steady-state baseline values ​​of the input vector; It is a normalized state vector. It is the normalized output vector. It is a normalized input vector;

[0114] Therefore, by using A, B, C, and D obtained from S1.3 as initial values ​​to solve the objective function as shown in formula (4), we can obtain the normalized and optimized A, B, C, and D.

[0115]

[0116] In the formula, K is the current simulation time, k is the time stamp, indicating that the current time step is the kth time step, k = 1, 2, ..., K; m is the array dimension of the output vector y, and i represents the i-th element in the output vector y, i = 1, 2, ..., m; This is the actual output of the engine. This is the output of the state-space equations;

[0117] Substituting the optimized A, B, C, and D into formula (2) yields the optimized state-space equation.

[0118] S1.5: Based on the optimized state-space equations at a predetermined nominal operating point under different altitudes and Mach numbers of the variable cycle engine, the state-space equations of all nominal operating points are combined into a linear parameter-varying (LPV) model; and the scheduling variables of the LPV model are defined as altitude, Mach number, and engine speed (the engine speed is taken as the high and low pressure speed [n]). L n H ] T (any one of them) to ensure the linearization accuracy of the LPV model within the full flight envelope, while ensuring that the optimized state-space equations achieve better performance within engine safety limits.

[0119] In this embodiment, in step S1.3, a small perturbation Δu = [0.01, 0.01929, 0.01, 0.01, 0.01, 0.01, -0.01, 0.01, 0.01] is taken, where the first two terms are the changes in the fuel quantity and tailpipe area of ​​the engine, and the last seven terms are the changes in health parameters. After solving by the linear least squares method, the optimized state space equation under a certain working condition is obtained, which initially meets the target of no more than 5% error, and the effectiveness is verified by numerical simulation.

[0120] The specific steps of step S2 are as follows:

[0121] S2.1: Using a small perturbation method, adjust the engine's height H, Mach number Ma, and low-pressure speed n. L Inputting the data into the LPV model yields the height H, Mach number Ma, and low-pressure rotational speed n. L State-space equations considering health parameters and noise under operating conditions:

[0122] Dx k+1 =ADx k +BDu k =ADx k +[BL][Du k Dh k ] T +w

[0123] Dy k =CDx k +DDu k =CDx k +[DM][Du k Dh k ] T +v (5)

[0124] where \(L\) and \(M\) are matrices corresponding to the health parameters in the state vector; the vector \(h\) k is the health parameter of the engine at time \(k\), which is the unknown input of the system; the vectors \(w\) and \(v\) are uncorrelated zero-mean white noises;

[0125] Expanding formula (5) gives:

[0126] \(Dx\) k+1 \(= ADx\) k \(+ BDu\) k \(+ LDh\) k \(+ w\)

[0127] \(Dy\) k \(= CDx\) k \(+ DDu\) k \(+ MDh\) k \(+ v\ (6)\)

[0128] S2.2: When the health parameter \(h\) deviates from the nominal value corresponding to the nominal operating state, it will cause changes in other variables; assuming that the health parameter \(h\) is slowly time-varying, the following augmented state space equation can be obtained:

[0129]

[0130] where the vector \(Dh\) k+1 is the health parameter of the engine at time \(k + 1\), the vector \(w\) k and the vector \(v\) k are zero-mean white noises at time \(k\) respectively, the vector \(w\) h,k is the zero-mean white noise at time \(k\) corresponding to the health parameter \(h\) (with the same dimension); the vector \(w\) xh is the zero-mean white noise of the augmented vector \([Dx\ Dh]\) T , that is, the combined vector of the white noise \(w\) of the initial state vector \(x\) and the noise \(w\) of the health parameter \(h\) h ; the vector \(v\) xh = vector \(v\) k ; \(x\) xh is the augmented state vector; \(A\) xh , \(C\) xh are matrices corresponding to the augmented state vector respectively; \(B\) xh , \(D\) xh are matrices corresponding to the augmented input vector respectively; \(D\) xh = \(D\);

[0131] S2.3: Since \(\dim(y)<\dim(h)\), that is, the dimension of the output vector < the dimension of the health parameter to be estimated, so the Kalman filter estimation equation, that is, the Kalman filtering algorithm, cannot be directly constructed according to formula (7) to estimate the change of the health parameter; therefore, a dimensionality reduction matrix \(V\) is used to perform the following linear combination transformation on the health parameter \(h\):

[0132] Dq=V*Dh (8)

[0133] In the formula, q is the parameter vector obtained after the dimension reduction transformation, and V is a row full-rank dimension reduction matrix of dimension dim(y)*dim(h). The optimal V is obtained through offline optimization in the subsequent step S3, so that the estimation error generated by using the optimal V for parameter dimension transformation is minimized.

[0134] Based on formula (8), we obtain Dh:

[0135] Dh = V * *Dq (9)

[0136] In the formula, V * It is the pseudo-inverse of the dimension-reduced matrix V;

[0137] S2.4: Set Dh = V * Substituting Dq into formula (7), we obtain the state-space equation after dimensionality reduction transformation:

[0138]

[0139] In the formula, q k+1 Let q be the parameter vector obtained after the dimensionality reduction transformation at time k+1. k The parameter vector obtained after the dimensionality reduction transformation at time k; w q,k The zero-mean white noise at time k corresponding to the parameter vector q (of the same dimension) obtained after dimensionality reduction transformation; vector w xq The augmented vector [Dx Dq] is the result of the dimensionality reduction transformation. T Zero-mean white noise, i.e., state-process noise; vector v xq =vector v k ;x xq It is the augmented state vector after dimensionality reduction transformation; A xq C xq These are the matrices corresponding to the augmented state vectors after the dimensionality reduction transformation; B xq D xq These are the matrices corresponding to the input vectors after the dimensionality reduction transformation; D xq =D;

[0140] Among them, the state process noise w xq and w xq The covariance matrix Q xq It can be calculated using the following formula:

[0141]

[0142] In the formula, Q xh For vector w xh The covariance matrix.

[0143] In step S3, an optimization method for the parameter dimensionality reduction matrix is ​​designed. For the sum of squared estimation errors of the dimensionality reduction Kalman filter, an optimal dimensionality reduction matrix solution method based on nonlinear least squares is proposed to minimize the estimation error. Specifically, an initial guess value for the dimensionality reduction matrix V is set, and the sum of squared estimation errors is solved. The initial parameter dimensionality reduction matrix V is then optimized offline using a nonlinear least squares optimization algorithm. (See Appendix) Figure 3 The specific steps are as follows:

[0144] S3.1: Design the sum of squared estimation errors as the objective function SSEE. The objective function SSEE consists of two parts: the mean and the deviation of the estimation errors. and the estimated error variance P xh,k The mathematical expression is as follows:

[0145]

[0146] Where, x xh,k Let be the true value of the augmented state vector at time k. tr{*} represents the posterior estimate of the augmented state vector at time k; tr{*} denotes the trace function;

[0147] S3.2: When the Kalman filter algorithm converges, estimate the mean deviation of the error. and the estimated error variance P xh,k It can be expressed by the following formula:

[0148]

[0149] in, P h The expected covariance matrix of the health parameters;

[0150] S3.3: Before the calculation, set the covariance matrix R and w of v. xq The covariance matrix Q xq Health parameter expected covariance matrix P h The initial guess of the dimensionality reduction matrix V; to prevent poor convergence of the optimization calculation, it is necessary to ensure that the Frobenius norm of the initial guess of V is 1, that is, ||V|| F =1; Calculate the current optimization objective function SSEE based on S3.1 and S3.2;

[0151] In this embodiment, R is set as a diagonal matrix with elements of 0.1 and dimensions of 5*5, and Q... xq =blkdiag(eye(2),V1)*Q xh *(blkdiag(eye(2),V1)),Q xhP is a 9x9 diagonal matrix with elements of 0.64. h Given a 7x7 diagonal matrix with elements of 0.01, the initial guess for the dimension reduction matrix V is randn(5, 7).

[0152] S3.4: Repeat step S3.3 for iteration. In each iteration, evaluate the change of SSEE relative to the previous iteration to determine whether convergence has been achieved within the specified tolerance.

[0153] If convergence is achieved, proceed to step S3.6.

[0154] If convergence is not achieved, proceed to step S3.5.

[0155] S3.5: Update V using a nonlinear least squares optimization algorithm, specifically using the Matlab Lsqnonlin function, while ensuring that ||V|| F =1, return the updated and optimized V to S3.3 for SSEE calculation;

[0156] S3.6: The V value in the current iteration is the optimal V value.

[0157] In step S4, a dimension-reduced Kalman filter algorithm is constructed to predict and estimate the engine's health parameters and output vector, and the prediction results are fed back to the state-space equations of the variable cycle engine. The specific steps are as follows:

[0158] S4.1: Since the initial covariance matrix of the Kalman filter algorithm determines the derived value of the steady-state Kalman filter, when the engine's slow time-varying degradation accumulates to a certain value, leading to significant performance differences, a larger initial covariance will generate a larger Kalman gain, thus accelerating the convergence speed. Therefore, the initial covariance matrix P of the Kalman filter algorithm... ￥ for:

[0159]

[0160] In the formula, R is the covariance matrix of zero-mean white noise v;

[0161] S4.2: The workflow of the dimension-reduced Kalman filter algorithm is as follows: the state-space equation after dimension reduction transformation, i.e., formula (10), is estimated a priori, i.e., the system state and covariance at the next time step are calculated based on the current system state and covariance:

[0162]

[0163] in, x is the prior estimate of the augmented state vector after the dimension reduction transformation at time k; xq,k-1 It is the augmented state vector after the dimension reduction transformation at time k-1;

[0164] S4.3: Perform prior estimation of error covariance:

[0165]

[0166] in, Let P be the prior estimate of the error covariance at time k. k-1 Let P be the posterior estimate of the error covariance at time k-1; where the posterior estimate of the error covariance at the initial time is the initial covariance matrix P. ￥ ;

[0167] S4.4: Calculate the Kalman filter gain K based on the prior estimate of the error covariance. k Calculation:

[0168]

[0169] S4.5: Based on the Kalman filter gain K k Update the state vector to obtain the posterior estimate of the state vector:

[0170]

[0171] in, Let z be the posterior estimate of the state vector at time k. k These are actual engine output measurements;

[0172] S4.6: Calculate the updated error covariance:

[0173]

[0174] S4.7: Repeat steps S4.3-S4.6 iteratively: obtain the posterior estimate of the error covariance P at time k. k Substituting this into formula (14) of S4.3, that is, P of formula (14) of S4.3 k-1 Replace with P k The prior estimate of the error covariance at time k+1 is obtained, and then sequentially passed through S4.4 until the Kalman filter gain K is reached. kAfter convergence, output S4.5 to obtain the posterior estimate of the iterated state vector, which contains the estimated prediction of the engine's health parameters; and input the posterior estimate of the iterated state vector into formula (10) in S2.4 to output Δy. At this time, the estimated prediction of the engine's output vector is obtained. By comparing the estimated prediction of the engine's output vector with the measured value of the sensor output of the real engine, the accuracy of the estimated prediction can be judged; at the same time, the estimated prediction of the engine's health parameters is optimized and updated in real time into formula (10) to obtain the state space equation for adaptive adjustment of health parameters.

[0175] Substituting the optimal V value of S3.6 into the state-space equation for adaptive adjustment of the health parameter yields the state-space equation with the minimum dimension reduction error and adaptive adjustment of the health parameter. This state-space equation with the minimum dimension reduction error and adaptive adjustment of the health parameter is the adaptive estimation model of the engine.

[0176] During verification in step S5, such as Figure 4 As shown in Figure A, at a certain operating point during supersonic cruise, the fan surge margin predicted by the state-space equations of this type of variable cycle engine using an optimal model linearization method is shown by the blue line. Compared with the fan surge margin output of the engine's nonlinear model (red line), it can well simulate the change process of the engine's fan surge margin under small disturbances. Figure 4 As shown in B, the prediction accuracy is no less than 99%, achieving the target indicator.

[0177] like Figure 5 As shown, this type of variable cycle engine experiences performance degradation at a certain operating point during supersonic cruise. Degradation simulation was performed using optimal reduced-dimensional Kalman filtering (red line). After a short iteration, the degradation factor rapidly approximates the actual degradation level (blue line), achieving the target performance.

[0178] In summary, the online adaptive model prediction method for variable cycle engines based on dimension-reduced Kalman filtering enables the variable cycle engine to maximize its performance advantages within the flight envelope. By utilizing the optimal dimension-reduced Kalman filter to predict degradation factors and key engine output parameters, the accuracy, efficiency, and stability of combined engine control can be improved.

[0179] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0180] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0181] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for online adaptive model prediction of engines based on dimensionality-reduced Kalman filtering, characterized in that, The steps of this method are as follows: Step S1: Linearize the variable cycle engine model to obtain the engine's state space equations. The input vector of the state space equations includes: engine fuel quantity, exhaust nozzle area, and health parameters. The state vector of the state space equations includes the engine's high and low pressure shaft speeds. The output vector of the state space equations includes thrust and surge margin. Step S2: Design the dimension reduction matrix V of the health parameters, use the dimension reduction matrix V to reduce the dimension of the health parameters, and convert the state space equation obtained in step S1 into the state space equation after parameter dimension transformation. Step S3: Use a nonlinear least squares optimization algorithm to perform offline optimization on the dimension reduction matrix V to obtain the optimal dimension reduction matrix V; Step S4: Construct a dimension-reduced Kalman filter algorithm. Use the dimension-reduced Kalman filter algorithm to estimate and predict the engine's health parameters and output vector to obtain real-time updated and optimized health parameters. Substitute the real-time updated and optimized health parameters into the engine's state-space equation to obtain the state-space equation for adaptive adjustment of health parameters. Substitute the optimal dimension-reduction matrix V from step S3 into this state-space equation for adaptive adjustment of health parameters to obtain the state-space equation with the minimum dimension reduction error and adaptive adjustment of health parameters. This state-space equation with the minimum dimension reduction error and adaptive adjustment of health parameters is the adaptive estimation model of the engine.

2. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 1, characterized in that, In step S4, the posterior estimate of the state vector is obtained by iterating the Kalman gain and covariance matrix in the Kalman filter algorithm. The posterior estimate of the state vector is then substituted into the state space equation after parameter dimension transformation to achieve estimation and prediction of the engine's health parameters and output vector. The estimated and predicted health parameters are then updated and optimized in real time to the engine's state space equation, resulting in the state space equation for adaptive adjustment of health parameters.

3. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 1, characterized in that, The specific steps of step S1 are as follows: S1.1: When the health parameter h remains at the nominal operating state, the state-space equation for the nonlinear model of the variable cycle engine at any nominal operating point is: Δx k+1 =AΔx k +BΔu k Δy k =CΔx k +DΔu k (2) In the formula, x is the state vector, y is the output vector, u is the input vector, including the engine fuel quantity, exhaust nozzle area, and health parameter h; k is the time stamp, indicating that the current time step is k, i.e., time k; Δ represents the change values ​​of each variable before and after a small disturbance in the nonlinear model of the variable cycle engine; A and C are the matrices corresponding to the state vector, and B and D are the matrices corresponding to the input vector; x k+1 Let x represent the state vector at time k+1. k Let u represent the state vector at time k. k Let y represent the input vector at time k. k This represents the output vector at time k; S1.2: Input a disturbance Δu to the variable cycle engine. After the variable cycle engine reaches steady state again, calculate the difference between the output and state variables before and after the disturbance, and solve A, B, C, and D by the least squares method. S1.3: A, B, C, and D are optimized using a normalization method. The optimized A, B, C, and D are then substituted into formula (2) to obtain the optimized state-space equation.

4. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 3, characterized in that, In step 1.2, the formulas for solving A, B, C, and D using the least squares method are as follows: Among them, y k This represents the output vector at time k.

5. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 3, characterized in that, After obtaining the optimized state-space equation at any nominal operating state point in S1.3, the state-space equations of all nominal operating state points are combined to form an LPV model.

6. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 3, characterized in that, The specific steps of step S2 are as follows: S2.1: Construct a state-space equation considering health parameters and noise using a small perturbation method: Δx k+1 =AΔx k +BΔu k +LΔh k +w Δy k =CΔx k +DΔu k +MΔh k +v (6) Where L and M are matrices corresponding to health parameters; vector h k The engine's health parameters at time k; vectors w and v are uncorrelated zero-mean white noise; S2.2: Assuming the health parameter h is slowly time-varying, the augmented state-space equation can be obtained: Wherein, vector Δh k+1 For the engine's health parameters at time k+1, send to w k sum vector v k These are zero-mean white noise at time k, and vector w. h,k The zero-mean white noise at time k corresponds to the health parameter h; vector w xh For the augmented vector [Δx Δh] T Zero-mean white noise; vector v xh =vector v k ;x xh A is the augmented state vector; xh C xh These are the matrices corresponding to the augmented state vectors; B xh D xh These are the matrices corresponding to the augmented input vectors; D xh =D; S2.3: Use the dimension-reduced matrix V to perform a linear combination transformation on the health parameter h in the following form: Δq=V*Δh (8) In the formula, q is the parameter vector obtained after the dimensionality reduction transformation; Based on formula (8), we can obtain Δh: Δh=V * *Δq (9) In the formula, V * It is the pseudo-inverse of the dimension-reduced matrix V; S2.4: Δh = V * Substituting Δq into formula (7), we obtain the state-space equation after dimensionality reduction transformation: In the formula, q k+1 Let q be the parameter vector obtained after the dimensionality reduction transformation at time k+1. k The parameter vector obtained after the dimensionality reduction transformation at time k; w q,k The zero-mean white noise at time k corresponding to the parameter vector q obtained after dimensionality reduction transformation; vector w xq The augmented vector [Δx Δq] is the result of the dimensionality reduction transformation. T Zero-mean white noise; vector v xq =vector v k ;x xq It is the augmented state vector after dimensionality reduction transformation; A xq C xq These are the matrices corresponding to the augmented state vectors after the dimensionality reduction transformation; B xq D xq These are the matrices corresponding to the augmented input vectors after the dimensionality reduction transformation; D xq =D.

7. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 6, characterized in that, The w xq and w xq The covariance matrix Q xq It can be calculated using the following formula: In the formula, Q xh For vector w xh The covariance matrix.

8. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 6, characterized in that, The specific steps of step S3 are as follows: S3.1: Design the sum of squared estimation errors as the objective function SSEE. The objective function SSEE consists of two parts: the mean and the deviation of the estimation errors. and the estimated error variance P xh,k The mathematical expression is as follows: Where, x xh,k Let be the true value of the augmented state vector at time k. tr{*} represents the posterior estimate of the augmented state vector at time k; tr{*} denotes the trace function; S3.2: When the Kalman filter algorithm converges, estimate the mean deviation of the error. and the estimated error variance P xh,k It can be expressed by the following formula: in, P h The expected covariance matrix of the health parameters; S3.3: Before the calculation, set the covariance matrix R and w of v. xq The covariance matrix Q xq Health parameter expected covariance matrix P h Find an initial value for the dimension-reduced matrix V, and ensure that the Frobenius norm of the initial value of V is 1, i.e., ||V||. F =1; Calculate the current optimization objective function SSEE based on S3.1 and S3.2; S3.4: Repeat step S3.3 for iteration. In each iteration, evaluate the change of SSEE relative to the previous iteration to determine whether convergence has been achieved within the specified tolerance. If convergence is achieved, proceed to step S3.

6. If convergence is not achieved, proceed to step S3.

5. S3.5: Update V using a nonlinear least squares optimization algorithm, and return the updated and optimized V to S4.3 for SSEE calculation; S3.6: The V value in the current iteration is the optimal V value.

9. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 8, characterized in that, The specific steps of step S4 are as follows: S4.1: Perform prior estimation on the state space equation after dimensionality reduction transformation, i.e., formula (10), to obtain the prior estimate of the augmented state vector after dimensionality reduction transformation. in, x is the prior estimate of the augmented state vector after the dimension reduction transformation at time k; xq,k-1 It is the augmented state vector after the dimension reduction transformation at time k-1; S4.2: Perform prior estimation of error covariance: in, Let P be the prior estimate of the error covariance at time k. k-1 This is the posterior estimate of the error covariance at time k-1; S4.3: Calculate the Kalman filter gain K based on the prior estimate of the error covariance. k Calculation: S4.4: Based on the Kalman filter gain K k Update the state vector to obtain the posterior estimate of the state vector: in, Let z be the posterior estimate of the state vector at time k. k These are actual engine output measurements; S4.5: Calculate the updated error covariance: S4.6: Repeat steps S4.2-S4.5 iteratively: obtain the posterior estimate of the error covariance P at time k. k Substituting this into formula (14) of S4.2, that is, P of formula (14) of S4.2 k-1 Replace with P k The prior estimate of the error covariance at time k+1 is obtained, and then sequentially passed through S4.3 until the Kalman filter gain K is reached. k After convergence, output S4.4 to obtain the posterior estimate of the iterated state vector, which contains the estimated prediction of the engine's health parameters; and input the posterior estimate of the iterated state vector into formula (10) to output Δy. At this time, the estimated prediction of the engine's output vector is obtained. By comparing the estimated prediction of the engine's output vector with the measured value of the sensor output of the real engine, the accuracy of the estimated prediction can be judged; at the same time, the estimated prediction of the engine's health parameters is optimized and updated in real time into formula (10) to obtain the state space equation for adaptive adjustment of health parameters. Substituting the optimal V value of S3.6 into the state-space equation for adaptive adjustment of the health parameter yields the state-space equation with the minimum dimension reduction error and adaptive adjustment of the health parameter. This state-space equation with the minimum dimension reduction error and adaptive adjustment of the health parameter is the adaptive estimation model of the engine.

10. The online adaptive model prediction method for engines based on dimensionality-reduced Kalman filtering as described in claim 9, characterized in that, In S4.2, the posterior estimate of the error covariance at the initial time is the initial covariance matrix P. ∞ : In the formula, R is the covariance matrix of zero-mean white noise v.

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