CN112949216A - Online peak-finding data processing method based on mixed performance function - Google Patents

Abstract

The invention discloses an online peak-searching data processing method based on a mixed performance function. Firstly, designing an approximate function to approximately fit a related parameter function and a target performance function, and carrying out weighted combination on the related parameter functions to construct a mixed performance function so as to approximately fit the target performance function; then, a time-varying Kalman filter is adopted to estimate the gradient vector and the sea plug matrix of each approximate function, and the optimal weighting weight for constructing the mixed performance function is determined by adopting a least square method; and finally, according to the gradient vector of each approximate function, the sea plug matrix and the optimal weighting weight obtained by estimation, quickly and approximately solving the peak value coordinate of the target performance function. The data processing method can realize real-time robust online process optimization, determine the peak position of the target performance function, and can be widely applied to the industrial fields including but not limited to aerospace, automobile industry, processing and manufacturing and the like.

Description

Online peak-finding data processing method based on mixed performance function

Technical Field

The invention belongs to the research field of on-line solving of an extreme value of a target performance function, and particularly relates to an on-line peak-searching data processing method based on a mixed performance function.

Background

In engineering practice, due to the influence of inevitable measurement noise, how to measure a plurality of parameters under time-varying environmental conditions and quickly determine the peak position of a target performance function in an unknown function form on line is one of the problems that are urgently sought to be solved in engineering practice. To address this problem, researchers and engineers have proposed many solutions, but existing methods have inherent limitations.

The modulation-demodulation scheme employed by the classical gradient method relies on system prediction lag which can deviate significantly from expected values and is not suitable for multiple-input multiple-output system models. The improved parameterization method mostly adopts a frequency division continuous excitation method, and how to select compatible frequencies is a difficult problem.

Currently, there is a need to develop an online peak-finding data processing method based on a hybrid performance function.

Disclosure of Invention

The invention aims to provide an online peak-searching data processing method based on a mixed performance function.

The online peak-searching data processing method based on the mixed performance function comprises the following steps:

step S100: defining independent variable x ∈ R obtained in the measuring process, and forming a discrete set by n x into

Mapping X → D (X) e R from the discrete set X to the target performance function D, and from the discrete set X to the associated parametric function P_iMapping X → P_i(X) e R, where i is an integer from 1 to m, m being a function P of the relevant parameter_iThe number of (2);

assuming a target performance function D and related parameter functions P_iApproximated by the approximation function:

wherein A is_D、b_DAnd A_i、b_iIs an unknown approximation function parameter;

defining a function P consisting of m related parameters_iThe mixed performance function B constructed by weighted combination has the following form

B＝ωP (2)

Wherein ω ∈ R^mRepresenting each relevant parametric function P_iWeighted weight, P ═ P₁(X),P₂(X),...,P_m(X)]^TRepresenting a function P consisting of m related parameters_iA discrete set of constructs;

step S200: continuously measuring, updating to obtain target performance function D and each related parameter function P_iThe function value of (a);

step S300: the approximation function of equation (1) is denoted as unity form f (X), and f (X) is related to X_kThe taylor expansion is:

where the subscript k denotes the kth iterative update, Δ X_k＝X_k-1-X_k、Δf_k＝f(X_k-1)-f(X_k) Increment representing independent variable and corresponding function value of step k, b^k、A^kA gradient vector and sea plug matrix that is a function f (X); from the comparison between formula (3) and formula (1), b^k、A^kTo approximate function parameter b_(·)、A_(·)Estimation in the k step;

spread DeltaX_k、b^k、A^kComprises the following steps:

wherein the content of the first and second substances,

(i ═ 1, 2., n, j ≦ 1, 2., n, and i ≦ j) respectively represent gradient vectors b^kAnd sea plug matrix A^kThe elements of (1); note the book

And recombining the above elements as follows:

equation (3) is rewritten as:

Δf_k＝H_kζ_k+υ_k (4)

wherein upsilon is_kIs due to measurement of Δ X_k、Δf_kThe mean value introduced in the presence of noise is zero and the variance is V_kWhite gaussian noise of (1);

due to the gradient vector b^kAnd sea plug matrix A^kAs X varies in an unknown form in the iterative update, the gradient vector b is therefore modified^kAnd sea plug matrix A^kModeling as brownian noise process:

ζ_k+1＝Iζ_k+θ_k (5)

wherein I represents and ζ_kDimensional adaptive unit array, theta_kDenotes mean zero and variance theta_kWhite gaussian noise of (1);

note that equation (4) only considers for Δ X_k、Δf_kIn the case of one measurement, in the k-th iteration update, L Δ X values are obtained due to the higher measurement sampling frequency_k、Δf_kThe situation of the measured value; thus define:

where, L1, 2, r, L, the formula (4) is expanded and rewritten as:

Δf_k＝H_kζ_k+υ_k (6)

wherein upsilon is_k＝[υ_k,1 υ_k,2…υ_k,L]^T，υ_k,lRepresenting the measurement noise during the first measurement; corresponding to (H)_kAnd V_kThe expansion is as follows:

wherein the content of the first and second substances,

V_k,lrepresenting the corresponding measurement noise v_k,lThe variance of (a);

for a system consisting of process equation (5) and measurement equation (6), the following time-varying kalman filter pair is used to model the unknown gradient vector b^kAnd sea plug matrix A^kSystem state ζ of element composition_kAnd (3) estimating:

wherein the content of the first and second substances,

for the state covariance matrix at the k-th step,

predicting a state covariance matrix of the k step; the state zeta of the system in the k step obtained by estimation_kObtaining the gradient vector b^kAnd sea plug matrix A^kObtaining the approximate function parameter b_(·)、A_(·)；

Step S400: in the k-th iterative update, the optimal weighting vector is determined by solving the following generalized least squares problem for equation (2)

Wherein U is a nonsingular weight matrix;

step S500: obtaining approximate function parameter A of each related parameter according to estimation_i、b_iPeak coordinate of the mixing performance function

The following solution is used:

wherein the content of the first and second substances,

for optimal weighting of weight vectors

The ith element of (1);

step S600: repeating the steps S200 to S500 by iterating the relevant parameter function values and the target performance function values obtained by time recursion measurement, and solving the obtained mixed performance function peak value coordinate

And continuously approaching to the target performance function peak value coordinate until the measurement is finished.

The online peak-searching data processing method based on the mixed performance function firstly designs an approximate function approximate fitting related parameter function and a target performance function, and carries out weighted combination on all related parameter functions to construct the mixed performance function so as to approximately fit the target performance function; then, a time-varying Kalman filter is adopted to estimate the gradient vector and the sea plug matrix of each approximate function, and the optimal weighting weight for constructing the mixed performance function is determined by adopting a least square method; and finally, according to the gradient vector of each approximate function, the sea plug matrix and the optimal weighting weight obtained by estimation, quickly and approximately solving the peak value coordinate of the target performance function.

The online peak-searching data processing method based on the mixed performance function can realize the online process optimization of real-time robustness, determine the peak value position of the target performance function, and can be widely applied to the industrial fields including but not limited to aerospace, automobile industry, processing and manufacturing and the like, such as determining the optimal formation of a flying formation to realize the post-aircraft lift-increasing and drag-reducing, determining the maximum pressure rise of an axial flow compressor to realize the efficiency improvement, determining the optimal operation condition of a fuel cell to realize the efficient power output and the like.

Drawings

FIG. 1 is a flow chart of an on-line peak-finding data processing method based on a hybrid performance function according to the present invention;

FIG. 2 is a plot of the post-aircraft drag coefficient at various formation positions as determined by the wind tunnel test of example 1;

FIG. 3 is a plot of the aft-engine roll moment coefficient at different formation positions as determined by the wind tunnel test of example 1;

FIG. 4 is a plot of the rear-machine yaw moment coefficient at different formation positions as determined by the wind tunnel test of example 1;

FIG. 5 is a plot of the rear-machine pitch moment coefficients at different formation positions as determined by the wind tunnel test of example 1;

FIG. 6 is a comparison graph of the peak values of the target performance function, the mixing performance function and the related parameter functions obtained by the online peak-searching data processing method based on the mixing performance function.

Detailed Description

The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention.

The following describes in detail the online peak-finding data processing method based on the hybrid performance function shown in fig. 1 with reference to example 1, with respect to the example application of the formation flight drag reduction in the aerospace field.

Example 1

The method for processing the on-line peak-searching data based on the mixed performance function comprises the following specific steps:

step S100: in engineering practice, the resistance of the formation flying rear machine is influenced by three independent factors, namely the relative position of the rear machine and the front machine in the flow direction, the relative position of the spreading direction and the vertical relative position. According to the analysis of test data, the influence of the relative position of the rear machine by the flow direction is relatively small, so that the relative position of the extension direction and the relative position of the vertical direction are selected as independent variables x in the example₁、x₂The two form a discrete set X ═ X₁ x₂]^T. Correspondingly, the rear machine resistance coefficient is selected as a target performance function D of rear machine resistance reduction. Generally, the spanwise relative position x₁And the vertical relative position x₂The roll moment coefficient, the yaw moment coefficient and the pitch moment coefficient of the rear machine are also obviously influenced, so that the roll moment coefficient, the yaw moment coefficient and the pitch moment coefficient of the rear machine are respectively selected as three related parameter functions P₁、P₂、P₃。

Assuming a target performance function D and related parameter functions P_i(i ═ 1,2,3) can be approximated by the following approximation function:

wherein A is_D、b_DAnd A_i、b_iAre unknown parameters of the approximation function.

The mixed performance function B constructed by the weighted combination of the 3 relevant parameter functions is as follows:

B＝ωP (11)

wherein, P ═ P₁ P₂ P₃]^TFor a discrete set of 3 related parameter functions, ω_iFor corresponding related parameter function P_iIs weighted, ω ═ ω [ ω ]₁ ω₂ ω₃]I.e. a weighted weight vector.

Step S200: the target performance function and each relevant parameter function value obtained by continuously measuring in actual formation flight are simulated by test data obtained by formation flight test in FL-26 wind tunnel of China aerodynamic research and development center. The data acquired by the wind tunnel test comprise rear aircraft resistance coefficients, rolling moment coefficients, yawing moment coefficients and pitching moment coefficients under different formation conditions (different rear aircraft and front aircraft spanwise relative positions and vertical relative positions). Fig. 2 to 5 show distribution diagrams of rear machine resistance coefficient, roll moment coefficient, yaw moment coefficient and pitch moment coefficient at different formation positions determined by experiments.

Step S300: the approximation function described in equation (10) is written as uniform form f (x) and can be rewritten as:

wherein the subscript k denotes the kth iterative update,

Δf_k＝f(X_k-1)-f(X_k) For the increments of the independent variables and corresponding function values in the iterative update of step k,

for gradient vectors and sea-plug matrices of function f (X), i.e. approximation function parameters b_(·)、A_(·)Estimation at step k. Note the book

Equation (12) can be rewritten as:

Δf_k＝H_kζ_k+υ_k (13)

wherein upsilon is_kMeaning that the mean value introduced taking into account the presence of noise in the measurement is zero and the variance is V_kWhite gaussian noise.

In one iteration update, 10 Δ xs can be obtained due to the high measurement sampling frequency_k、Δf_kThe measured value, therefore, requires the expansion equation (13). Recording:

where l 1,2, …,10 indicates the l-th measurement, the formula (13) is expanded and rewritten as

Δf_k＝H_kζ_k+υ_k (14)

Wherein upsilon is_k＝[υ_k,1 υ_k,2…υ_k,10]^T，υ_k,lRepresenting the measurement noise during the l-th measurement. Corresponding to (H)_kAnd V_kExpand into

Wherein, V_k,lRepresenting the corresponding measurement noise v_k,lThe variance of (c).

Due to the gradient vector b^kAnd sea plug matrix A^kIt is possible in an iterative update to vary with X in an unknown form, thus the gradient vector b will be^kAnd sea plug matrix A^kModeling as Brown noise Process

ζ_k+1＝Iζ_k+θ_k (15)

Wherein I represents and ζ_kDimensional adaptive unit array, theta_kDenotes mean zero and variance theta_kWhite gaussian noise.

For a system consisting of the process equation (15)) and the measurement equation (14)), the following time-varying kalman filter pair is used to model the unknown gradient vector b^kAnd sea plug matrix A^kZeta system state of the element composition_kAnd (3) estimating:

wherein the content of the first and second substances,

for the state covariance matrix at the k-th step,

to predict the state covariance matrix at step k. The state zeta of the system in the k step obtained by estimation_kObtaining the gradient vector b^kAnd sea plug matrix A^kI.e. obtaining the parameter b of the approximation function_(·)、A_(·)。

Step S400: in the k-th iterative update, the optimal weighting vector is determined by solving the following generalized least squares problem for equation (11)

Wherein U is a non-singular weight matrix.

Step S500: obtaining approximate function parameter A of each related parameter according to estimation_i、b_iExtreme coordinates of the mixing performance function

The following formula can be used to obtain a simple solution:

wherein the content of the first and second substances,

for optimal weighting of weight vectors

The ith element of (1).

Step S600: repeating the steps S200 to S500, and solving the peak value coordinate of the obtained mixing performance function

The peak coordinate of the target performance function is continuously approached, and the result is shown in fig. 6. Compared with each relevant parameter function, the peak coordinate of the mixed performance function is closer to the peak coordinate of the target performance function, so that the effectiveness of the online peak searching data processing method based on the mixed performance function is verified.

Claims (1)

1. An online peak-searching data processing method based on a mixed performance function is characterized by comprising the following steps:

step S100: defining independent variable x ∈ R obtained in the measuring process, and forming a discrete set by n x into

Mapping X → D (X) e R from the discrete set X to the target performance function D, and from the discrete set X to the associated parametric function P_iMapping X → P_i(X) e R, where i is an integer from 1 to m, m being a function P of the relevant parameter_iThe number of (2);

assuming a target performance function D and related parameter functions P_iApproximated by the approximation function:

wherein A is_D、b_DAnd A_i、b_iIs an unknown approximation function parameter;

defining a function P consisting of m related parameters_iThe mixed performance function B constructed by weighted combination has the following form

B＝ωP (2)

Wherein ω ∈ R^mRepresenting each relevant parametric function P_iWeighted weight, P ═ P₁(X),P₂(X),...,P_m(X)]^TRepresenting a function P consisting of m related parameters_iA discrete set of constructs;

step S200: continuously measuring, updating to obtain target performance function D and each related parameter function P_iThe function value of (a);

step S300: the approximation function of equation (1) is denoted as unity form f (X), and f (X) is related to X_kThe taylor expansion is:

where the subscript k denotes the kth iterative update, Δ X_k＝X_k-1-X_k、Δf_k＝f(X_k-1)-f(X_k) Increment representing independent variable and corresponding function value of step k, b^k、A^kA gradient vector and sea plug matrix that is a function f (X); from the comparison between formula (3) and formula (1), b^k、A^kTo approximate function parameter b_(·)、A_(·)Estimation in the k step;

spread DeltaX_k、b^k、A^kComprises the following steps:

wherein the content of the first and second substances,

respectively representing gradient vectors b^kAnd sea plug matrix A^kThe elements of (1); note the book

And recombining the above elements as follows:

equation (3) is rewritten as:

Δf_k＝H_kζ_k+υ_k (4)

wherein upsilon is_kIs due to measurement of Δ X_k、Δf_kThe mean value introduced in the presence of noise is zero and the variance is V_kWhite gaussian noise of (1);

due to the gradient vector b^kAnd sea plug matrix A^kAs X varies in an unknown form in the iterative update, the gradient vector b is therefore modified^kAnd sea plug matrix A^kModeling as brownian noise process:

ζ_k+1＝Iζ_k+θ_k (5)

wherein I represents and ζ_kDimensional adaptive unit array, theta_kDenotes mean zero and variance theta_kWhite gaussian noise of (1);

note that equation (4) only considers for Δ X_k、Δf_kIn the case of one measurement, in the k-th iteration update, L Δ X values are obtained due to the higher measurement sampling frequency_k、Δf_kThe situation of the measured value; thus define:

where, L1, 2, r, L, the formula (4) is expanded and rewritten as:

Δf_k＝H_kζ_k+υ_k (6)

wherein upsilon is_k＝[υ_k,1 υ_k,2 … υ_k,L]^T，υ_k,lRepresenting the measurement noise during the first measurement; corresponding to (H)_kAnd V_kThe expansion is as follows:

wherein the content of the first and second substances,

V_k,lrepresenting the corresponding measurement noise v_k,lThe variance of (a);

for a system consisting of process equation (5) and measurement equation (6), the following time-varying kalman filter pair is used to model the unknown gradient vector b^kAnd sea plug matrix A^kSystem state ζ of element composition_kAnd (3) estimating:

wherein the content of the first and second substances,

for the state covariance matrix at the k-th step,

predicting a state covariance matrix of the k step; the state zeta of the system in the k step obtained by estimation_kObtaining the gradient vector b^kAnd sea plug matrix A^kObtaining the approximate function parameter b_(·)、A_(·)；

Step S400: in the k-th iterative update, the optimal weighting vector is determined by solving the following generalized least squares problem for equation (2)

Wherein U is a nonsingular weight matrix;

step S500: obtaining approximate function parameter A of each related parameter according to estimation_i、b_iPeak coordinate of the mixing performance function

The following solution is used:

wherein the content of the first and second substances,

for optimal weighting of weight vectors

The ith element of (1);

step S600: repeating the steps S200 to S500 by iterating the relevant parameter function values and the target performance function values obtained by time recursion measurement, and solving the obtained mixed performance function peak value coordinate

And continuously approaching to the target performance function peak value coordinate until the measurement is finished.

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