CN112949216B - Online peak searching data processing method based on mixed performance function - Google Patents
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Abstract
The invention discloses an online peak searching data processing method based on a hybrid performance function. Firstly, designing an approximate function to approximate fit a related parameter function and a target performance function, and carrying out weighted combination on each related parameter function to construct a mixed performance function so as to approximate fit the target performance function; then, estimating a gradient vector and a sea plug matrix of each approximate function by adopting a time-varying Kalman filter, and determining an optimal weighting weight for constructing a hybrid performance function by adopting a least square method; and finally, quickly and approximately solving the peak coordinate of the target performance function according to the estimated gradient vector of each approximate function, the sea plug matrix and the optimal weighting weight. 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.
Description
Technical Field
The invention belongs to the field of online solving of extremum of target performance functions, and particularly relates to an online peak searching data processing method based on a hybrid performance function.
Background
In engineering practice, how to measure multiple parameters under time-varying environmental conditions and quickly determine the peak position of the target performance function in the form of an unknown function on line is always one of the challenges that the engineering practice is urgent to seek to solve, due to the unavoidable measurement noise. To address this problem, researchers and engineers have proposed many solutions, but all of the existing approaches have their inherent limitations.
The modulation-demodulation scheme employed by classical gradient methods relies on system prediction hysteresis that can deviate severely from the expected values and is not suitable for use in a multiple-input multiple-output system model. The improved parameterization method 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 hybrid performance function.
The on-line peak searching data processing method based on the mixed performance function comprises the following steps:
step S100: defining independent variable x epsilon R obtained in the measuring process, and forming a discrete set consisting of n x into
Mapping X-D (X) εR from the discrete set X to the target performance function D, and mapping X-D (X) εR from the discrete set X to the related parameter function P i Mapping X.fwdarw.P of (A) i (X) ∈R, where i is an integer from 1 to m, and m is a correlation parameter function P i Is the number of (3);
assuming the target performance function D and eachCorrelation parameter function P i Approximated by the following approximation function:
wherein A is D 、b D And A i 、b i Is an unknown approximation function parameter;
definition of the parameters by m related parameter functions P i The hybrid performance function B constructed by the weighted combination has the following form
B＝ωP (2)
Wherein ω εR m Representing the respective related parameter function P i Weighting, p= [ P ] 1 (X),P 2 (X),...,P m (X)] T Representing a set of m related parameter functions P i A discrete set of constituents;
step S200: continuously measuring, and updating to obtain a target performance function D and each related parameter function P i Is a function value of (2);
step S300: the approximation function of equation (1) is noted as a unified form f (X), and f (X) is related to X k Taylor expansion is:
wherein the subscript k represents the kth iterative update, ΔX k ＝X k-1 -X k 、Δf k ＝f(X k-1 )-f(X k ) An increment representing the independent variable and corresponding function value of step k, b k 、A k Gradient vector and sea plug matrix as function f (X); from the comparison of the formula (3) and the formula (1), b k 、A k To approximate the function parameter b (·) 、A (·) Estimating in the kth step;
expansion delta X k 、b k 、A k The method comprises the following steps:
wherein,,
(i=1, 2,) n, j=1, 2,) n, and i+.j represent gradient vectors b, respectively k And sea plug matrix A k Elements of (a) and (b); record->
And recombine the above elements into:
then equation (3) rewrites as:
Δf k ＝H k ζ k +υ k (4)
wherein v k Indicating that due to measurement DeltaX k 、Δf k The mean value introduced by the presence of noise is zero, and the variance is V k Is white gaussian noise;
due to gradient vector b k And sea plug matrix A k In iterative updating, as X changes in unknown form, the gradient vector b is therefore calculated k And sea plug matrix A k Modeling is a Brownian noise process:
ζ k+1 ＝Iζ k +θ k (5)
wherein I represents a group selected from the group consisting of k Dimension-adaptive unit array, θ k Represents zero mean and Θ variance k Is white gaussian noise;
note that equation (4) only considers for ΔX k 、Δf k In the case of one measurement, in the k-th iteration update, L delta X are obtained due to higher measurement sampling frequency k 、Δf k The situation of the measured value; thus define:
where, l=1, 2, L, then the expansion rewrite of equation (4) is:
Δf k ＝H k ζ k +υ k (6)
wherein v k ＝[υ k,1 υ k,2 …υ k,L ] T ，υ k,l Representing measurement noise during the first measurement; correspondingly, H k And V k The expansion is as follows:
wherein,,
V k,l representing the corresponding measured noise v k,l Is a variance of (2);
for a system consisting of the process equation (5) and the measurement equation (6), the following time-variant Kalman filter pair is used for the unknown gradient vector b k And sea plug matrix A k System state ζ of element constitution k And (3) estimating:
wherein,,
for the kth state covariance matrix, +.>
To predict kth step state collaborationA variance matrix; the kth step system state ζ obtained through estimation k Obtaining a gradient vector b k And sea plug matrix A k Obtaining the approximate function parameter b (·) 、A (·) ；
Step S400: in the iterative update of the kth step, an optimal weighted weight vector is determined by solving the following generalized least squares problem for equation (2)
Wherein U is a non-singular weight matrix;
step S500: approximation function parameter A according to each estimated related parameter i 、b i Peak coordinates of hybrid performance function
The following solutions are adopted:
wherein,,
for optimal weighting weight vector +.>
Is the i-th element of (a);
step S600: repeatedly iterating the steps S200 to S500 along with each related parameter function value and target performance function value obtained by time recursion measurement, and solving the obtained peak coordinates of the mixed performance function
And continuously approaching to the peak value coordinates of the target performance function until the measurement is finished.
The on-line peak-finding data processing method based on the mixed performance function firstly designs approximate functions to approximate fit related parameter functions and target performance functions, and carries out weighted combination on the related parameter functions to construct the mixed performance function so as to approximate fit the target performance functions; then, estimating a gradient vector and a sea plug matrix of each approximate function by adopting a time-varying Kalman filter, and determining an optimal weighting weight for constructing a hybrid performance function by adopting a least square method; and finally, quickly and approximately solving the peak coordinate of the target performance function according to the estimated gradient vector of each approximate function, the sea plug matrix and the optimal weighting weight.
The on-line peak searching data processing method based on the mixed performance function can realize real-time robust on-line process optimization, determine the peak position of the target performance function, and can be widely applied to industrial fields including but not limited to aerospace, automobile industry, processing and manufacturing, and the like, for example, determining the optimal formation of a flight formation to realize post-machine lift-up drag reduction, determining the maximum pressure rise of an axial-flow compressor to realize efficiency improvement, determining the optimal operation condition of a fuel cell to realize high-efficiency power output, and the like.
Drawings
FIG. 1 is a flow chart of an online peak finding data processing method based on a hybrid performance function according to the present invention;
FIG. 2 is a graph showing the post machine drag coefficient profile at various formation locations as determined by the wind tunnel test of example 1;
FIG. 3 is a graph showing the post machine roll moment coefficient at different formation positions as determined by the wind tunnel test of example 1;
FIG. 4 is a graph showing the yaw moment coefficient profile of the rear engine at different formation positions as determined by the wind tunnel test of example 1;
FIG. 5 is a graph showing the post-machine pitching moment coefficient distribution at different formation positions as determined by the wind tunnel test of example 1;
FIG. 6 is a graph showing the peak values of the target performance function, the hybrid performance function and the related parameters obtained by the online peak searching data processing method based on the hybrid performance function.
Detailed Description
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
The on-line peak-finding data processing method based on the hybrid performance function of the invention as shown in fig. 1 will be described in further detail with reference to example 1, for an example application of the invention in the field of aerospace for formation of drag reduction for flight.
Example 1
The specific steps of the online peak searching data processing method based on the hybrid performance function in this embodiment are as follows:
step S100: in engineering practice, the resistance of the formation flying rear aircraft is influenced by three independent factors, namely the flow direction relative position, the spreading direction relative position and the vertical relative position of the rear aircraft and the front aircraft. According to the analysis of the test data, the influence of the flow direction relative position of the rear engine is relatively small, so that the opposite position of the expanding direction and the opposite position of the vertical direction are selected as independent variables x in the example 1 、x 2 Both form a discrete set x= [ X ] 1 x 2 ] T . Accordingly, the coefficient of drag for the rear engine is selected as the target performance function D for drag reduction for the rear engine. Generally, the spanwise relative position x 1 Vertical relative position x 2 The rolling moment coefficient, the yaw moment coefficient and the pitching moment coefficient of the rear engine are also obviously influenced, so the rolling moment coefficient, the yaw moment coefficient and the pitching moment coefficient of the rear engine are respectively selected as three related parameter functions P 1 、P 2 、P 3 。
Assuming a target performance function D and associated parameter functions P i (i=1, 2, 3) can be approximated by the following approximation function:
wherein A is D 、b D And A i 、b i Is an unknown approximation function parameter.
The hybrid performance function B constructed from a weighted combination of 3 related parameter functions is:
B＝ωP (11)
wherein P= [ P ] 1 P 2 P 3 ] T For a discrete set of 3 related parametric functions omega i For corresponding to the relevant parameter function P i Is equal to ω= [ ω ] 1 ω 2 ω 3 ]I.e. a weighted weight vector.
Step S200: the target performance function and each related parameter function value which are measured continuously in the actual formation flight are simulated by test data obtained by the formation flight test carried out in the FL-26 wind tunnel of the China aerodynamic force research and development center. The data obtained by wind tunnel test comprises back machine resistance coefficient, rolling moment coefficient, yaw moment coefficient and pitching moment coefficient under different formations (opposite positions of different back machines and front machines in the spreading direction and vertical opposite positions). Fig. 2 to 5 show graphs of post-machine drag coefficient, roll moment coefficient, yaw moment coefficient and pitch moment coefficient at various formation positions determined experimentally.
Step S300: the approximation function for equation (10) is noted as a unified form f (X) and can be rewritten as:
wherein the subscript k represents the kth iterative update,
Δf k ＝f(X k-1 )-f(X k ) For the increment of the independent variable and the corresponding function value in the iterative update of the kth step,/for the increment of the independent variable and the corresponding function value in the iterative update of the kth step>
Gradient vector and sea plug matrix as function f (X), i.e. approximation function parameter b (·) 、A (·) Estimation at the kth step. Record->
Equation (12) can be rewritten as:
Δf k ＝H k ζ k +υ k (13)
wherein v k Indicating zero mean and V variance introduced by taking into account the presence of noise in the measurement k Is a gaussian white noise of (c).
In one iteration update, 10 ΔX's can be obtained due to the higher measurement sampling frequency k 、Δf k The measurement value, therefore, requires expansion of equation (13). And (3) recording:
wherein l=1, 2, …,10 represents the first measurement, then the expansion of equation (13) is rewritten as
Δf k ＝H k ζ k +υ k (14)
Wherein v k ＝[υ k,1 υ k,2 …υ k,10 ] T ，υ k,l Representing measurement noise during the first measurement. Correspondingly, H k And V k Expanded into
Wherein V is k,l Representing the corresponding measured noise v k,l Is a variance of (c).
Due to gradient vector b k And sea plug matrix A k Possibly varying in unknown form with X in an iterative update, thus taking the gradient vector b k And sea plug matrix A k Modeling as Brownian noise process
ζ k+1 ＝Iζ k +θ k (15)
Wherein I represents a group selected from the group consisting of k Dimension-adaptive unit array, θ k Represents zero mean and Θ variance k Is a gaussian white noise of (c).
For a system consisting of the process equation (15)) and the measurement equation (14)), the following time-variant Kalman filter pair is used to determine the unknown gradient vector b k And sea plug matrix A k System state ζ of element constitution of (2) k And (3) estimating:
wherein,,
for the kth state covariance matrix, +.>
To predict the kth state covariance matrix. The kth step system state ζ obtained through estimation k Obtaining the gradient vector b k And sea plug matrix A k I.e. obtain the approximate function parameter b (·) 、A (·) 。
Step S400: in the iterative update of the kth step, an optimal weighted weight vector is determined by solving the following generalized least squares problem for equation (11)
Wherein U is a non-singular weight matrix.
Step S500: approximation function parameter A according to each estimated related parameter i 、b i Extremum coordinates of a hybrid performance function
The method can be obtained by solving the following formula:
wherein,,
for optimal weighting weight vector +.>
Is the i-th element of (c).
Step S600: repeating the steps S200 to S500, and solving the peak coordinates of the obtained hybrid performance function
The result of this approach is shown in fig. 6, which is continuously approaching the peak coordinates of the target performance function. Compared with each related 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. The online peak searching data processing method based on the mixed performance function is characterized by comprising the following steps of:
step S100: defining independent variable x epsilon R obtained in the measuring process, and forming a discrete set consisting of n x into
Mapping X-D (X) εR from the discrete set X to the target performance function D, and mapping X-D (X) εR from the discrete set X to the related parameter function P i Mapping X.fwdarw.P of (A) i (X) ∈R, where f is an integer from 1 to m, and m is a correlation parameter function P i Is the number of (3);
the resistance of the formation flying rear aircraft is influenced by three independent factors of the flow direction relative position, the unfolding direction relative position and the vertical relative position of the rear aircraft and the front aircraft; according to the testThe analysis of test data shows that the influence of the flow direction relative position of the rear engine is small, and the relative position in the expanding direction and the vertical direction are selected as independent variables x 1 、x 2 Both form a discrete set x= [ X ] 1 x 2 ] T The method comprises the steps of carrying out a first treatment on the surface of the Correspondingly, selecting the rear engine drag coefficient as a target performance function D of the rear engine drag; spanwise relative position x 1 Vertical relative position x 2 The rolling moment coefficient, the yaw moment coefficient and the pitching moment coefficient of the rear engine are also influenced, so the rolling moment coefficient, the yaw moment coefficient and the pitching moment coefficient of the rear engine are respectively selected as three related parameter functions P 1 、P 2 、P 3 ；
Assuming a target performance function D and associated parameter functions P i I=1, 2,3, approximated by the following approximation function:
wherein A is D 、b D And A i 、b i Is an unknown approximation function parameter;
defining a hybrid performance function B constructed from a weighted combination of 3 related parameter functions as:
B＝ωP (2)
wherein P= [ P ] 1 P 2 P 3 ] T For a discrete set of 3 related parametric functions omega i For corresponding to the relevant parameter function P i Is equal to ω= [ ω ] 1 ω 2 ω 3 ]Namely, a weighted weight vector;
step S200: continuously measuring, and simulating a target performance function and each relevant parameter function value which are obtained by continuously measuring in the actual formation flight by using test data obtained by the formation flight test performed in the wind tunnel; the test data obtained by wind tunnel test comprises rear engine resistance coefficient, rolling moment coefficient, yaw moment coefficient and pitching moment coefficient of the opposite positions of the front engine and the opposite positions of the front engine in the spreading direction under different formations, and the target performance function D and each related parameter function P are updated and obtained i Is a function value of (2);
step S300: the approximation function of equation (1) is noted as a unified form f (X), and f (X) is related to X k Taylor expansion is:
wherein the subscript k represents the kth iterative update,
Δf k ＝f(X k-1 )-f(X k ) An increment representing the independent variable and the corresponding function value of the kth step,/->
Gradient vector and sea plug matrix as function f (X); from the comparison of the formula (3) and the formula (1), b k 、A k To approximate the function parameter b (.) 、A (.) Estimating in the kth step;
and (3) recording:
then equation (3) rewrites as:
Δf k ＝H k ζ k +υ k (4)
wherein v k Indicating that due to measurement DeltaX k 、Δf k The mean value introduced by the presence of noise is zero, and the variance is V k Is white gaussian noise;
due to gradient vector b k And sea plug matrix A k With X in an unknown form in iterative updatingThe equation changes, thus the gradient vector b k And sea plug matrix A k Modeling is a Brownian noise process:
ζ k+1 ＝Iζ k +θ k (5)
wherein I represents a group selected from the group consisting of k Dimension-adaptive unit array, θ k Represents zero mean and Θ variance k Is white gaussian noise;
note that equation (4) only considers for ΔX k 、Δf k In the case of one measurement, in the k-th iteration update, L delta X are obtained due to higher measurement sampling frequency k 、Δf k The situation of the measured value; thus define:
where, l=1, 2, L, then the expansion rewrite of equation (4) is:
Δf k ＝H k ζ k +υ k (6)
wherein v k ＝[υ k,1 υ k,2 …υ k,L ] T ，υ k,l Representing measurement noise during the first measurement; correspondingly, H k And V k The expansion is as follows:
for a system consisting of the process equation (5) and the measurement equation (6), the following time-variant Kalman filter pair is used for the unknown gradient vector b k And sea plug matrix A k System state ζ of element constitution k And (3) estimating:
wherein,,
for the kth state covariance matrix, +.>
A state covariance matrix is predicted in the kth step; the kth step system state ζ obtained through estimation k Obtaining a gradient vector b k And sea plug matrix A k Obtaining the approximate function parameter b (·) 、A (·) ；
Step S400: in the iterative update of the kth step, an optimal weighted weight vector is determined by solving the following generalized least squares problem for equation (2)
Wherein U is a non-singular weight matrix;
step S500: approximation function parameter A according to each estimated related parameter i 、b i Peak coordinates of hybrid performance function
The following solutions are adopted:
wherein,,
for optimal weighting weight vector +.>
Is the i-th element of (a);
step S600: repeatedly iterating the steps as each relevant parameter function value and target performance function value obtained by time recursion measurementS200 to S500, solving the obtained peak coordinates of the hybrid performance function
And continuously approaching to the peak value coordinates of the target performance function until the measurement is finished.
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