CN114894110A - Method for calibrating deformation of intelligent skin antenna structure - Google Patents
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Abstract
A method for calibrating deformation of an intelligent skin antenna structure comprises the steps that a plurality of strain sensors and position sensors are installed on a skin antenna, different types of forces are applied to the skin antenna, static loading is carried out, and strain data and deformation data under different working conditions are obtained; establishing a relation between the strain coefficient and the surface deformation of the skin antenna, and solving a strain coefficient calibration value of each strain sensor; distributing the displacement deformation error of the measurable point on the skin antenna to the degree of freedom of the neutral axis to obtain error distribution data; fitting error distribution data under different working conditions to realize data dimension expansion; and training a self-framework fuzzy network by using the data after the dimension expansion to obtain a self-calibration system, establishing a relation between strain and the degree of freedom of the neutral axis, and obtaining a deformation displacement value of any point on the antenna through the degree of freedom of the neutral axis and the shape function. According to the method, the final deformation displacement value is obtained through the estimation of the deformation coefficient and the calibration of the degree of freedom of the neutral axis, so that the reconstruction precision is improved.
Description
Technical Field
The invention belongs to the technical field of antenna structures, and particularly relates to a method for calibrating deformation of an intelligent skin antenna structure.
Background
The intelligent skin antenna can be applied to the outer surfaces of airplanes, ships, submarines, even space shuttles and the like, generally comprises a detection device, a driving device, a microprocessing control system and the like, and aims to realize the tasks of monitoring, early warning, stealth, communication and the like. However, when the antenna works, the antenna structure is inevitably affected by wind, high temperature, low temperature, vibration and other environments, so that the antenna structure is deformed or the position of an antenna array element is deviated, and therefore the problems of beam pointing deviation, poor directivity, gain reduction and the like are caused, and the performance of the antenna is reduced. Under the condition, the deformation displacement of the antenna of the machine needs to be reconstructed in real time through the acquired strain data, so that data support is provided for the follow-up active measures to compensate the electrical property of the antenna. Therefore, the method has important significance in calibrating the deformation of the intelligent skin antenna.
At present, methods for measuring the deformation field of the antenna structure mainly include two types, namely an optical imaging method and a measurement method based on strain information. In recent years, measurement methods based on strain information have been paid attention by many scholars because of the advantages of relatively easy data acquisition, no limitation on the size of components in the measurement process, good real-time performance and the like. Among these, the advantages of the Inverse Finite Element Method (iFEM) are numerous. When the arrangement scheme of the measuring point positions is determined, the deformation field solving time is the time for carrying out one-time matrix multiplication calculation, so that the real-time performance is good. However, for complex deformation fields, large errors sometimes occur, so that calibration is required.
Therefore, the deformation of the skin antenna can be calibrated in real time by using a fiber bragg grating strain sensor (FBG). However, when the structure of the anisotropic material is deformed and reconstructed, the network formed by a plurality of FBG strain sensors shows a phenomenon that the strain coefficients of the sensors are different, and the coefficients are generally regarded as the same value in the reconstruction process, which results in the reduction of reconstruction accuracy.
Disclosure of Invention
Aiming at the problem that the accuracy of skin antenna deformation measurement is influenced by factors such as sensor assembly errors and strain measurement errors, the invention aims to provide a method for calibrating the deformation of an intelligent skin antenna structure.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for calibrating deformation of an intelligent skin antenna structure comprises the following steps:
and 5, training a self-framework fuzzy network by using the data after the dimension expansion to obtain a self-calibration system, establishing a relation between the strain and the degree of freedom of the neutral axis by using the generalization capability of the fuzzy network, and then obtaining a deformation displacement value of any point on the antenna through the degree of freedom of the neutral axis and the shape function.
Compared with the prior art, the invention has the beneficial effects that:
1) the method for estimating the strain coefficient based on the Bayesian is provided for the first time aiming at the difference of the anisotropic strain coefficients of the fiber grating sensor, and the strain coefficient value of the fiber grating sensor can be finally estimated by well combining the prior information obtained by expert knowledge and the sample information.
2) Aiming at the phenomenon that the deformation value estimated by the inverse finite element model is inaccurate due to sensor installation errors and other external factors, sample information of a single working condition is obtained by using error distribution for the first time, data expansion is carried out through NURBS fitting, and finally the expanded data is used for training the fuzzy self-framework fuzzy network to finally obtain a calibration network model.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a diagram of an experimental system for sensor installation.
FIG. 3 is a comparison of x-direction deformation errors.
FIG. 4 is a y-direction deformation error comparison.
FIG. 5 is a z-direction deformation error comparison.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the drawings and examples.
In the deformation measurement of the skin antenna structure, the existing strain sensor such as an FBG strain sensor has mounting errors and measurement errors which cannot be avoided. Meanwhile, the strain deformation of the skin antenna is measured in real time, and a two-step compensation method is provided in consideration of the influence of the installation of a sensor, the external environment and the like on the deformation measurement result. Firstly, aiming at the problem that the strain coefficients of the strain sensor at different positions on the surface of the anisotropic material are different, a strain coefficient calibration algorithm based on the Bayesian theory is provided. And secondly, establishing a fuzzy self-calibration network according to the error between the reconstruction deformation and the actual deformation, thereby compensating the error in real time. And aiming at the problem of small working condition number, the dimension expansion of the data sample is realized through a non-uniform rational B-spline algorithm, and then the dimension expansion data is used for training and generating a fuzzy network to complete the construction of the calibration system.
Specifically, as shown in fig. 1, the method for calibrating deformation of an intelligent skin antenna structure of the present invention includes the following steps:
In one embodiment of the invention, the strain sensor adopts an FBG sensor, the strain data is collected in real time through an optical fiber demodulator, the optimal position of the strain sensor can be obtained through position optimization, and the strain sensor is adhered to the position. The position sensor adopts a displacement coordinate sensor, the coordinate change is acquired in real time through a three-dimensional dynamic displacement measuring instrument (NDI) to obtain deformation data, and the position sensor can be installed on any position on the surface of the antenna.
In the invention, in order to simulate the external force on the skin antenna in flight, different types of forces generally comprise two types, namely concentrated force and uniform force, wherein the concentrated force is applied by hanging a heavy object at the tail end of the skin antenna, and the uniform force is applied by hydraulic loading.
In the invention, static loading refers to applying different forces on the skin antenna in stages.
And 2, establishing a relation between the strain coefficient and the surface deformation of the skin antenna, and further obtaining the strain coefficient calibration value of each strain sensor.
In the step, strain values of all points are calculated to surface deformation displacement based on an Inverse Finite Element (iFEM) principle, matrix representation forms of all the points are deduced one by one, finally, a relation between a strain coefficient and the surface deformation of the skin antenna is established, and the strain coefficient calibration value of each strain sensor is obtained according to a Bayes algorithm.
In the calibration of the strain coefficient of the network sensor, the problems of simultaneous calibration of multiple parameters and less data of samples under the condition that the collected data is less exist, and the Bayesian theory can effectively integrate the prior information before the experiment and the sample information during the experiment to obtain the estimation result of the strain parameter which is more in line with the reality.
Specifically, the relationship between the strain coefficient and the surface deformation of the skin antenna is constructed in the step as follows:
Y＝N·U
wherein Y is the surface deformation, N is the shape function, A is the quasi-stiffness matrix, λ 1 …λ n For measured strain data, U is the neutral axis node, k 1 …k n For the strain coefficient to be estimated, the k is estimated in a Bayesian estimation mode by using Bayesian theory due to the limited number of samples 1 …k n As a random variable, and the variable follows a known distribution, which can be determined by known data or human experience, and finally serves as a prior distribution of bayesian estimation; then Bayesian reasoning is carried out by combining the information observed in the process, posterior distribution of the estimated parameters is solved so as to predict the parameter values, the expectation value of the posterior distribution of the strain coefficient to be estimated is usually taken as the final estimation value, and the final estimation value can be obtained by Bayesian theorem:
p(k|Y)∝p(k)·p(Y|k)
p (k | Y) represents a posterior distribution of k, p (k) represents a prior distribution of k, p (Y | k) represents a probability density function of Y, oc represents a proportional ratio, and k ═ k (k ═ Y) 1 k 2 …k n ) And representing the strain coefficient to be estimated, wherein n is the number of the strain coefficients to be estimated.
Obtaining the strain coefficient k to be estimated by the formula 1 …k n The sequence obtained by the jeep sampling of the markov chain monte carlo method is a markov chain which is in accordance with pi (k) stable distribution; in the actual parameter calibration, after enough iterations of the Gilles sampling, the strain coefficient to be estimated is converged to a steady distribution, the distribution is completely unrelated to the initial value, and the final distribution value is the strainAnd calibrating the value of the coefficient.
And 3, obtaining the deformation displacement value of any point on the skin antenna through the degree of freedom of the neutral axis and the shape function. And mismatching the displacement deformation difference of the measurable points on the skin antenna to the degree of freedom of the neutral axis under the working conditions of different static loading forces to obtain the data of the error distribution under different working conditions.
The measurable points are all position sensors installed on the surface, for example, displacement deformation errors of the measurable points can be respectively distributed to the degree of freedom of the neutral axis for the end points and the middle points, and based on the distributed degree of freedom, the deformation displacement of any point on the skin antenna can be interpolated by using a shape function, so that preliminary calibration is realized.
In this step, the actual deformation of the skin antenna is expressed as follows:
Y e ＝Y s +ΔY
wherein Y is e Expressed as the actual deformation, Y, of the skin antenna s Represents the amount of deformation after reconstruction obtained by the inverse finite element principle, Δ Y represents the reconstruction error, Δ Y-N (N.Δ U, σ) 2 ) Denotes that Δ Y obeys a positive Tailored distribution N (N · Δ U, σ) 2 )，σ 2 And expressing a variance, wherein delta U refers to the error amount of the neutral axis degree of freedom when the reconstruction error is delta Y, distributing the displacement deformation error of the tail end and the middle point of the reconstruction error to the neutral axis degree of freedom U, and obtaining the reconstruction error of any point on the skin antenna through a shape function N so as to obtain the reconstruction error, wherein the formula is as follows:
ΔY＝N·ΔU
because sample point data has errors in actual conditions, in order to obtain an accurate estimation coefficient, an accurate Δ U value can be obtained through bayesian ridge estimation, and it is assumed that the estimation coefficient obeys a variance of τ 2 Gaussian prior distribution, Δ U-N (0, τ) 2 ) Equivalent to applying one
Then the deltau is estimated according to the bayes estimation method described in step 2.
And 4, fitting the error distribution data under different working conditions by using a non-uniform rational B spline (NURBS) function to realize data dimension expansion.
The data of the error distribution is one sample data composed of strain data and an error amount delta U of the degree of freedom of the neutral axis, and the data of the error distribution under different working conditions is a plurality of sample data.
Aiming at the problem that an error distribution algorithm can only calibrate specific working conditions and does not have generalization capability, a self-calibration network algorithm based on small samples is provided. And carrying out sample dimension expansion and generalization characteristics of a self-calibration network by using a non-uniform rational B spline function, and realizing real-time calibration on reconfiguration variable displacement errors. The equation of the B-order non-uniform rational B-spline curve is as follows:
wherein u is an independent variable, r is more than or equal to 0 and less than or equal to 1, and omega i Is the ith weight factor, i is 0,1, …, t, t is the number of weight factors, c i Is the ith control point, N i,b (u) is a B-spline basis function defined by a node vector R ═ u 0 ,u i ,…,u t+b+1 ]The B-spline basis function is obtained in the form:
u i a subvector that is the node vector R;
since each sample data is equally important and when different weights are set, the complexity of the algorithm increases and the actual effect is small, let ω be i When performing NURBS fitting approximation, node vectors as well as control points need to be obtained. The data needs to be parameterized before the node vectors are obtained. Using a centripetal parameterisation method, order
And
others
The following formula:
Then, a node vector is obtained according to a non-uniform vector construction method as follows:
The sample data obtained in the step 2 is Q i (i-0, 1, …, n), it is necessary to obtain a control point C from the sample data to obtain a NURBS curve, and to obtain a large number of data points Q 'by substituting r into equation (1) from 0 to 1 in a fixed step size from r' i 。
In particular, to approximate the sample data point Q i (i-0, 1, …, n), it is desirable to minimize the following:
the above formula is expressed in a matrix form as follows:
the above formula can be written as a · C ═ Q, resulting in the best resultsSolution of small two times to C ═ A T ·A) -1 ·A T P, resulting in a control point C and thus a NURBS curve approximating the data points, from which more data is obtained.
And 5, training a self-framework fuzzy network by using the data after the dimension expansion to obtain a self-calibration system, establishing a relation between the strain and the degree of freedom of the neutral axis by using the generalization capability of the fuzzy network, and then obtaining a deformation displacement value of any point on the antenna through the degree of freedom of the neutral axis and the shape function.
Specifically, the data after the dimension expansion is substituted into the self-frame fuzzy network, and the self-calibration network can be obtained through training data, and the process is as follows:
1) initializing the self-frame fuzzy network, enabling one input of the self-frame fuzzy network to be a strain value, outputting the strain value as a fuzzy rule of the central axis freedom degree, and substituting training sample data to obtain an output error of the self-frame fuzzy network;
2) Judging whether the output error meets the expected error or not, and if not, entering the step 3); if yes, continuously judging whether the membership function meets the completeness, and if yes, entering the step 5); if not, go to step 3).
Illustratively, the membership function is a triangular membership function, as follows:
wherein, a, b and c are respectively a left end point, a middle point and a right end point, and x is an independent variable.
3) Increasing a membership function, increasing fuzzy rules, finding the fuzzy rule with the maximum matching degree, increasing the membership function for the input with the maximum membership degree, and then increasing the rules according to the increased membership function;
4) the self-adaptive rule back-part corrects the back-part of the fuzzy rule according to the deviation value between the self-framework fuzzy network output value and the given training data output value, and then the step 2) is carried out;
5) and storing the self-constructed fuzzy network.
The self-calibration network can increase the rules and adjust the distribution thereof by automatically increasing Membership Functions (MF), so that the network obtained by training can more accurately approximate the relationship between the degree of freedom of the misdifferential matching and the measured strain.
In a specific embodiment of the invention, in order to evaluate the effectiveness of a strain coefficient estimation algorithm on improving the deformation reconstruction precision and check the effect of the proposed deformation perception calibration method with small sample characteristics, a loading deformation reconstruction experiment is carried out by taking a skin-like antenna wing structure as an experimental object, an experimental model can be divided into three parts, wherein the part close to a fixed position is a first section, the middle section is a second section, and the tail end is a third section. Length L 1 ＝660mm,L 2 ＝660mm,L 3 660 mm. In the manner shown in FIG. 2, 18 FBG sensors are mounted on the inner surface of the wing at the positions shown in Table 1 below, where x k Representing relative positions within the segment; (θ, β) means that the sensors are placed at a circumferential angle θ, and are angled from the x-axis of the frame by an angle β, θ and β being in degrees. And the strain value of the FBG sensor is acquired in real time through a fiber bragg grating demodulator. In order to observe the real-time deformation of the wing, 16 position sensors are installed on the outer upper surface of the wing to sense the spatial position change of the point, and the installation positions are shown in the following table 2. The infrared light emitted by the position sensor after being electrified is detected by the three-dimensional dynamic displacement measuring instrument positioned on the ground, a coordinate system is established at the root of the wing, the coordinate of the position sensor is stored in real time, and the deformation of the wing can be obtained by observing the coordinate change of each sensor. After the preparation work is finished, applying the combination of different forms of forces to deform the wing, and collecting the deformation conditions of the wing under different working conditions
The main deformation direction of the wing in the deformation experiment is the y direction. The deformation reconstruction calibration experiment is used for carrying out real-time calibration on deformation displacement of the wings in the x direction, the y direction and the z direction. The experiment adopts the steps that the weight is added from 1kg, the weight is added every 1kg and the weight is added till 27kg, the coefficient calibration and the fuzzy self-frame fuzzy network training are carried out on the measured displacement and strain data of 14 working conditions in total, and the data of 10 working conditions are added from 8kg and the load is added every 1kg and the weight is added till 26kg for verifying the calibration effect.
The calculation results are shown in the table. After the second step, the 18 calibrated values of the strain coefficient are
k＝(2.58,1.39,4.00,6.13,-0.67,1.74,2.88,0.90,-0.40,
1.56,-1.03,-0.16,5.04,27.01,-10.73,-26.58,-9.25,19.35)
10 checking working conditions are set in the experiment, and the RMSE value index is used for evaluating factors. The superscript "IFEM" represents the error between the inverse finite element method reconstructed displacement and the NDI captured displacement, i.e. the error when no calibration is performed; "modify" represents the error between the scaled reconstructed displacement and the NDI captured displacement. As can be seen from the analysis of fig. 3, fig. 4 and fig. 5, and tables 3 to 5, the error values in the x, y, and z directions after calibration, which are measured by NDI as the standard values, are significantly reduced in error RMS value compared to the error values directly subjected to the inverse finite element reconstruction, and the data demonstrates the correctness and effectiveness of the present invention.
TABLE 1 Strain sensor position
| Axial position x k | 0.3L 1 | 0.7L 1 | 0.3L 2 | 0.7L 2 | 0.3L 3 | 0.7L 3 |
| (θ 1 ,β 1 ) | (0,0) | (0,45) | (0,0) | (120,0) | (0,0) | (0,45) |
| (θ 2 ,β 2 ) | (120,0) | (-120,0) | (-120,0) | (-120,0) | (-120,0) | (-120,0) |
| (θ 3 ,β 3 ) | (-120,0) | (120,0) | (120,0) | (120,0) | (120,0) | (120,0) |
Table 2: position sensor no-load coordinate
Table 3: x-direction check point deformation error RMSE
Table 4: y-direction check point deformation error RMSE
Table 5: z-direction check point deformation error RMSE
Claims (10)
1. A method for calibrating the deformation of an intelligent skin antenna structure is characterized by comprising the following steps:
step 1, mounting a plurality of strain sensors and position sensors on a skin antenna, applying different types of forces to the skin antenna, and carrying out static loading to obtain strain data and deformation data under different working conditions;
Step 2, establishing a relation between the strain coefficient and the surface deformation of the skin antenna, and further obtaining the strain coefficient calibration value of each strain sensor;
step 3, distributing the displacement deformation error of the measurable point on the skin antenna to the degree of freedom of a neutral axis under different working conditions of static loading to obtain error distribution data under different working conditions;
step 4, fitting error distribution data under different working conditions by using a non-uniform rational B spline (NURBS) function to realize data dimension expansion;
and 5, training a self-framework fuzzy network by using the data after the dimension expansion to obtain a self-calibration system, establishing a relation between the strain and the neutral axis degree of freedom by using the generalization capability of the fuzzy network, and then obtaining the deformation displacement value of any point on the antenna through the neutral axis degree of freedom and the shape function.
2. The method for calibrating the deformation of the smart skin antenna structure according to claim 1, wherein in the step 1, the strain sensor adopts an FBG sensor, and strain data are collected in real time through a fiber-optic demodulator; the position sensor adopts a displacement coordinate sensor, and the coordinate change is collected in real time through a three-dimensional dynamic displacement measuring instrument (NDI) to obtain deformation data.
3. The method for calibrating the deformation of the smart skin antenna structure according to claim 1 or 2, wherein in the step 1, the different types of forces include a concentrated force and a uniform force, wherein the concentrated force is applied by hanging a weight at the tail end of the smart skin antenna, and the uniform force is applied by hydraulic loading; the static loading refers to applying different forces on the skin antenna according to stages.
4. The method for calibrating the deformation of the intelligent skin antenna structure according to claim 1, wherein in the step 2, strain values of all points are calculated to surface deformation displacement based on an Inverse Finite Element (iFEM) principle, matrix representation forms of all the points are deduced one by one, finally, a relation between a strain coefficient and the surface deformation of the skin antenna is established, and the strain coefficient calibration value of each strain sensor is obtained according to a Bayesian algorithm.
5. The method for calibrating deformation of the smart skin antenna structure according to claim 4, wherein the relationship between the constructed strain coefficient and the deformation of the skin antenna surface is as follows:
Y＝N·U
wherein Y is the surface deformation, N is the shape function, A is the quasi-stiffness matrix, λ 1 …λ n For measured strain data, U is the neutral axis node, k 1 …k n For the strain coefficient to be estimated, by Bayes Theory k 1 …k n Taking the variable as a random variable and the variable obeys the known distribution, then carrying out Bayesian inference, taking the expected value of the posterior distribution of the strain coefficient to be estimated as the final estimated value, and obtaining the strain coefficient k to be estimated through the following formula 1 …k n Posterior distribution of (a):
p(k|Y)∝p(k)·p(Y|k)
then, a sequence obtained by the Gempse sampling of the Markov chain Monte Carlo method is a Markov chain which is in accordance with pi (k) stable distribution; after enough iterations of the Gilles sampling, the strain coefficient to be estimated is converged to a steady distribution, the distribution is completely unrelated to the initial value, and the final distribution value is the strain coefficient calibration value.
p (k | Y) represents posterior distribution of k, p (k) represents prior distribution of k, p (Y | k) represents probability density function of Y, oc represents proportional, and k ═ k (k ═ k) 1 k 2 … k n ) And representing the strain coefficient to be estimated, wherein n is the number of the strain coefficients to be estimated.
6. The method for calibrating the deformation of the intelligent skin antenna structure according to claim 1, wherein in the step 3, the measurable points are all position sensors arranged on the surface, displacement deformation errors of the measurable points are respectively distributed to the freedom degrees of the neutral axis, and the deformation displacement of any point on the skin antenna is interpolated based on the distributed freedom degrees to realize initial calibration;
The skin antenna actual deformation is expressed as follows:
Y e ＝Y s +ΔY
wherein Y is e Expressed as the actual deflection, Y, of the skin antenna s Represents the amount of deformation after reconstruction obtained by the inverse finite element principle, Δ Y represents the reconstruction error, Δ Y-N (N.Δ U, σ) 2 ) Denotes that Δ Y obeys the positive-Tailored distribution N (N · Δ U, σ) 2 )，σ 2 Expressing variance, wherein delta U refers to the error of the degree of freedom of the neutral axis when the reconstruction error is delta Y, distributing the reconstruction displacement deformation error to the degree of freedom U of the neutral axis, and obtaining the skin antenna through a shape function NThe reconstruction error at any point is obtained, and the reconstruction error is obtained as follows:
ΔY＝N·ΔU
obtaining accurate delta U through Bayesian ridge estimation, and assuming that the estimation coefficient obeys variance tau 2 Gaussian prior distribution, Δ U-N (0, τ) 2 ) Equivalent to applying one
Then the delta U is estimated according to the bayesian estimation method described in step 2.
7. The method for calibrating deformation of the smart skin antenna structure according to claim 1, wherein in the step 4, the data of the error distribution is one sample data composed of strain data and an error amount Δ U of the degree of freedom of the neutral axis, and the data of the error distribution under different working conditions is a plurality of sample data.
8. The method for calibrating deformation of an intelligent skin antenna structure according to claim 1, wherein in the step 5, the data after dimensional expansion is substituted into a self-constructed fuzzy network, and the self-calibrated network can be obtained by training data, and the self-calibrated network can more accurately approximate the relationship between the degree of freedom of error distribution and the measured strain by automatically adding a Membership Function (MF) and a fuzzy rule and adjusting the distribution of the MF and the fuzzy rule.
9. The method for deformation calibration of a smart skin antenna structure of claim 8, wherein the membership function is a triangular membership function as follows:
wherein, a, b and c are respectively a left end point, a middle point and a right end point, and x is an independent variable.
10. The method for calibrating deformation of a smart skin antenna structure according to claim 8, wherein the training process of the self-calibration network is as follows:
1) initializing the self-frame fuzzy network, enabling one input of the self-frame fuzzy network to be a strain value, outputting the strain value as a fuzzy rule of the central axis freedom degree, and substituting training sample data to obtain an output error of the self-frame fuzzy network;
2) judging whether the output error meets the expected error or not, and if not, entering the step 3); if yes, continuously judging whether the membership function meets the completeness, and if yes, entering the step 5); if not, entering step 3);
3) increasing a membership function, increasing fuzzy rules, finding the fuzzy rule with the maximum matching degree, increasing the membership function for the input with the maximum membership degree, and then increasing the number of rules according to the increased membership function;
4) the self-adaptive rule back-part corrects the back-part of the fuzzy rule according to the deviation value between the self-framework fuzzy network output value and the given training data output value, and then the step 2) is carried out;
5) And saving the self-constructed fuzzy network.
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