A method for maximum likelihood parameter estimation of a wind tunnel system main control valve

Abstract

The application discloses a maximum likelihood recursive data modeling method of a Hammerstein output error autoregressive model of a main exhaust valve of a wind tunnel system. The main exhaust valve is an important actuator of the total pressure and the Mach number of the system. After changing the model attack angle fixed in the central flow field area, the blockage of the wind tunnel airflow changes, the total pressure and the Mach number deviate from the set value, and the Mach number can reach the required precision value by adjusting the opening degree of the main exhaust valve. Data modeling can abstract and organize the input and output sampling data of the main exhaust valve after the accuracy requirement is clear, define the relationship and structure between the data, and improve the performance as much as possible. In the process of continuously adjusting the parameters and optimizing the model, the interpretation ability and practicability of the model are continuously improved. Therefore, the maximum likelihood weighted recursive least square algorithm is used for data modeling of the Hammerstein output error autoregressive model of the main exhaust valve of the wind tunnel system. The application comprises the steps of constructing an identification model based on the Hammerstein output error autoregressive model of the main exhaust valve of the wind tunnel system, constructing a maximum likelihood weighted recursive least square algorithm process, and constructing a maximum likelihood weighted recursive least square algorithm. The application is simple and efficient, and can be applied to data modeling of a main exhaust valve control system of a wind tunnel system.

Description

Technical Field

[0001] This invention relates to a maximum likelihood recursive parameter estimation method for the Hammerstein output error autoregressive model of the main control valve of a wind tunnel system. Background Technology

[0002] The main exhaust valve is a crucial actuator for controlling the total pressure and Mach number of a wind tunnel system. Changing the angle of attack of the model, which is pre-fixed in the central flow field region, alters the obstruction of the airflow in the wind tunnel, causing the total pressure and Mach number to deviate from the set values. Adjusting the opening of the main exhaust valve allows the Mach number to quickly reach the required accuracy. Data modeling, after clarifying the accuracy requirements, involves abstracting and organizing the input and output sampling data of the main exhaust valve, defining the relationships and structures between the data, and maximizing performance. Through continuous parameter adjustments and model optimization, the model's interpretability and practicality will continuously improve.

[0003] The maximum likelihood weighted recursive least squares algorithm can be used to construct models of Hammerstein systems affected by colored noise. It can also effectively estimate the parameters of piecewise nonlinear systems with dead zones. Therefore, this invention employs the maximum likelihood weighted recursive least squares algorithm to model the Hammerstein output error autoregressive model of the main exhaust valve of a wind tunnel system.

[0004] The purpose of this invention is to identify the parameters of the Hammerstein output error autoregressive model of the main control valve of a wind tunnel system using the maximum likelihood weighted recursive least squares method.

[0005] The solution of this invention is:

[0006] (1) Construct an overparameterized identification model for the Hammerstein output error autoregressive model based on the main control valve. The specific steps are as follows:

[0007] Step 1: Construct the Hammerstein-based autoregressive model for output error (see attached structure). Figure 2 :

[0008] Step 2: Based on this model, the expression for the piecewise nonlinear subsystem with dead zone is as follows:

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[0010] Step 3: Construct the expressions for the piecewise nonlinear functions f1(t), f2(t), f3(t), and f4(t), and the intermediate variables x(t) and w(t) of the linear subsystem of the Hammerstein output error autoregressive model:

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[0015] Step 4: Based on this model, construct the Hammerstein output error autoregressive model expression as follows:

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[0017] The symbols in the above formulas have the following meanings: u(t) and y(t) are the system's input and output, The output of the nonlinear subsystem is υ(t), which is white noise with zero mean, variance σ², and follows a Gaussian distribution. A(z), B(z), and C(z) are the functions of the unit shift operator z. -1 polynomial (z) -1 u(t) = u(t-1), k1 and k2 are the slopes of the piecewise function, d1 and d2 are the intercepts of the piecewise function, f1(t), f2(t), f3(t), and f4(t) are linear functions, and n is assumed to be a linear function. a n b and n c Given that when t≤0, u(t), y(t), and υ(t)=0.

[0018] Step 5: Construct the Hammerstein output error autoregressive model and identify the model as follows:

[0019] y(t)=Φ T Θ+υ(t). (3)

[0020] Step 6: Construct the filter vector x f (t), w f (t) and f jf (t).

[0021] (2) The algorithm flow for maximum likelihood weighted recursive least squares parameter identification is constructed as follows:

[0022] Step 1: Start the recognition algorithm;

[0023] Step 2: Set the initial value by setting t = 1;

[0024] Step 3: Obtain input and output data;

[0025] Step 4: Calculate functions f1(t), f2(t), f3(t), and f4(t);

[0026] Step 5: Calculation and

[0027] Step 6: Calculate the filter variable x f (t), f 1f (t), f 2f (t), f 3f (t), f 4f (t) and w f (t). Constructs the information vector Φ(t) and the filtered information vector.

[0028] Step 7: Calculate the gain vector L(t) and covariance matrix P(t);

[0029] Step 8: Update the parameter vector

[0030] Step 9: Calculate the parameter estimates and

[0031] Step 10: Generate the parameter vector

[0032] Step 11: If t ≤ L, let t := t+1 and jump to step 2; otherwise, obtain the parameter estimate. Terminate the calculation process.

[0033] The definitions of each variable are as follows:

[0034] Define the input as u(t) and the output as y(t);

[0035] Define υ(t) as a function with zero mean and variance σ. 2 And it is white noise that satisfies a Gaussian distribution;

[0036] definition and For the relevant parameter vector;

[0037] Define x f (t), f 1f (t), f 2f (t), f 3f (t), f 4f (t) and w f (t) is the filter variable;

[0038] definition and The intermediate vector;

[0039] Define Φ(t) and For information vectors;

[0040] definition and Let Θ(t) and Ξ(t) be the estimated values ​​at time t; and Let υ(t), x(t), and w(t) be the estimates of time t. and Let k1, k2, d1, d2, and b be the values ​​at time t. i And the estimated value of m, Φ at time t f The estimated value of (t).

[0041] (3) Based on the maximum likelihood weighted recursive least squares estimation algorithm, the maximum likelihood weighted recursive least squares estimation algorithm is constructed.

[0042] 2. The maximum likelihood weighted recursive least squares estimation algorithm described in step (3) is as follows:

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[0067] The specific steps of the above algorithm are as follows:

[0068] (1) Start the identification algorithm, let t=1, and set the initial value. and p0 = 10 6 ;

[0069] (2) Acquire input data and output data;

[0070] (3) Calculate f1(t), f2(t), f3(t) and f4(t) using equations (12)-(15);

[0071] (4) Obtain the results through equations (16) and (17) respectively. and

[0072] (5) Calculate the filter variable x using equations (18)-(23) respectively. f (t), f 1f (t), f 2f (t), f 3f (t), f 4f (t) and w f (t). The information vector Φ(t) and the filtered information vector are formed by equations (8)-(11).

[0073] (6) Calculate the gain vector L(t) and covariance matrix P(t) using equations (5) and (6);

[0074] (7) Update the parameter vector using equation (4)

[0075] (8) Calculate parameter estimates using equations (24) and (27). and

[0076] (9) Generate the parameter vector using equation (7).

[0077] (10) If t≤L, let t:=t+1 and jump to step 2; otherwise, obtain the parameter estimate. Terminate the calculation process.

[0078] Define the input as u(t) and the output as y(t);

[0079] Define υ(t) as a function with zero mean and variance σ. 2 And it is white noise that satisfies a Gaussian distribution;

[0080] definition and For the relevant parameter vector;

[0081] Define x f (t), f 1f (t), f 2f (t), f 3f (t), f 4f (t) and w f (t) is the filter variable;

[0082] definition and The intermediate vector;

[0083] Define Φ(t) and For information vectors;

[0084] definition and Let Θ(t) and Ξ(t) be the estimated values ​​at time t; and Let υ(t), x(t), and w(t) be the estimates of time t. and Let k1, k2, d1, d2, and b be the values ​​at time t. i And the estimated value of m, Φ at time t f The estimated value of (t). Attached Figure Description

[0085] The present invention will be further described below with reference to the accompanying drawings and examples.

[0086] Figure 1 This is a flowchart of the maximum likelihood recursive parameter identification algorithm for this model.

[0087] Figure 2 It is based on the Hammerstein output error autoregressive model structure.

[0088] Figures 3 to 5 This is a schematic diagram illustrating a specific example of the method of the present invention. Figure 3 The waveforms show the parameter estimation errors under different noise variances. Figure 4 The graph shows the parameter estimation error curves under different weights. Figure 5 This is a structural diagram of a wind tunnel system.

Claims

1. A method for estimating the maximum likelihood parameters of the main control valve in a wind tunnel system, characterized by: Includes the following steps: (1) Construct an overparameterized identification model for the Hammerstein output error autoregressive model based on the main control valve. The specific steps are as follows: Step 1: Construct the structure of the Hammerstein output error autoregressive model: Step 2: Based on this model, the expression for the piecewise nonlinear subsystem with dead zone is as follows: Step 3: Construct the Hammerstein output error autoregressive model. The piecewise nonlinear functions f1(t), f2(t), f3(t), and f4(t) of the linear subsystem, and the intermediate variables x(t) and w(t) are expressed as follows: Step 4: Based on this model, construct the Hammerstein output error autoregressive model expression as follows: The symbols in the above formulas have the following meanings: u(t) and y(t) are the system's input and output, It is the output of the nonlinear subsystem, where υ(t) is a function with zero mean and variance σ. 2 Furthermore, the noise follows a Gaussian distribution and is white noise. A(z), B(z), and C(z) are expressions with respect to the unit shift operator z. -1 polynomial (z) -1 u(t) = u(t-1), k1 and k2 are the slopes of the piecewise function, d1 and d2 are the intercepts of the piecewise function, f1(t), f2(t), f3(t), and f4(t) are linear functions, and n is assumed to be a linear function. a n b and n c It is known that when t≤0, u(t), y(t), and υ(t)=0; Step 5: Construct the Hammerstein output error autoregressive model and identify the model as follows: y(t)=Φ T Θ+υ(t) (2) Step 6: Construct the filter variable x f (t), w f (t) and f jf (t); (2) The algorithm flow for maximum likelihood weighted recursive least squares parameter identification is constructed as follows: Step 1: Start the recognition algorithm; Step 2: Set the initial value by setting t = 1; Step 3: Obtain input and output data; Step 4: Calculate functions f1(t), f2(t), f3(t), and f4(t); Step 5: Calculation and Step 6: Calculate the filter variable x f (t), f 1f (t), f 2f (t), f 3f (t), f 4f (t) and w f (t) constitutes the information vector Φ(t) and the filtered information vector. Step 7: Calculate the gain vector L(t) and covariance matrix P(t); Step 8: Update the parameter vector Step 9: Calculate the parameter estimates and Step 10: Generate the parameter vector Step 11: If t ≤ L, let t := t+1 and jump to step 2; otherwise, obtain the parameter estimate. Terminate the calculation process; The definitions of each variable are as follows: Define the input as u(t) and the output as y(t); Define υ(t) as a function with zero mean and variance σ. 2 And it is white noise that satisfies a Gaussian distribution; definition and For the relevant parameter vector; Define x f (t), f 1f (t), f 2f (t), f 3f (t), f 4f (t) and w f (t) is the filter variable; definition and The intermediate vector; Define Φ(t) and For information vectors; definition and Let Θ(t) and Ξ(t) be the estimated values ​​at time t; and Let υ(t), x(t), and w(t) be the estimates of time t. and Let k1, k2, d1, d2, and b be the values ​​at time t. i And the estimated value of m, Φ at time t f The estimated value of (t); (3) Based on the maximum likelihood weighted recursive least squares estimation algorithm, the maximum likelihood weighted recursive least squares estimation algorithm is constructed.

2. The maximum likelihood recursive parameter estimation method based on the Hammerstein output error autoregressive model according to claim 1, characterized in that: The maximum likelihood weighted recursive least squares estimation algorithm described in step (3) is as follows: The specific steps of the above algorithm are as follows: (1) Start the identification algorithm, let t=1, and set the initial value. and p0 = 10 6 ; (2) Acquire input data and output data; (3) Calculate f1(t), f2(t), f3(t) and f4(t) using equations (11)-(14); (4) Obtained through equations (15) and (16) respectively. and (5) Calculate the filter variable x using equations (17)-(22) respectively. f (t), f 1f (t), f 2f (t), f 3f (t), f 4f (t) and w f (t). The information vector Φ(t) and the filtered information vector are formed by equations (7)-(10). (6) Calculate the gain vector L(t) and covariance matrix P(t) using equations (4)-(5); (7) Update the parameter vector using equation (3). (8) Calculate parameter estimates using equations (23)-(26). and (9) Generate the parameter vector using equation (6). (10) If t≤L, let t:=t+1 and jump to step 2; otherwise, obtain the parameter estimate. Terminate the calculation process; Define the input as u(t) and the output as y(t); Define υ(t) as a function with zero mean and variance σ. 2 And it is white noise that satisfies a Gaussian distribution; definition and For the relevant parameter vector; Define x f (t), f 1f (t), f 2f (t), f 3f (t), f 4f (t) and w f (t) is the filter variable; definition and The intermediate vector; Define Φ(t) and For information vectors; definition and Let Θ(t) and Ξ(t) be the estimated values ​​at time t; and Let υ(t), x(t), and w(t) be the estimates of time t. and Let k1, k2, d1, d2, and b be the values ​​at time t. i And the estimated value of m, Φ at time t f The estimated value of (t).

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