CN112749470B - Layout optimization fitting method for structural deformation sensor - Google Patents
Layout optimization fitting method for structural deformation sensor Download PDFInfo
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Abstract
The invention discloses a layout optimization fitting method of a structural deformation sensor, which comprises the steps of firstly, generating a gradient map related to deformation size and position information from a structural deformation cloud map; secondly, extracting a structural deformation sensor from the gradient map, and carrying out fitting estimation on deformation values of extracted points by using a spatial interpolation method; then repeatedly deleting one measuring point from the real measuring point set, estimating the deformation estimated value of the deleted point by using the residual measuring point set, and estimating the accuracy of the deformation estimated value; and finally, reducing the arrangement quantity of the structural deformation sensors for the observation points of which the estimated values meet the precision requirements, and reserving the arrangement of the observation points of the structural deformation sensors when the estimated values do not meet the precision requirements. The invention can effectively reduce the arrangement quantity of the deformation sensors, optimize the arrangement positions of the deformation sensors, and comprehensively and accurately monitor the structural variables of the system.
Description
Technical Field
The invention relates to the technical field of aerospace, in particular to a spacecraft structure deformation sensor layout optimization fitting method.
Background
With the rapid development of national economy and the requirement of national defense construction, the complexity, the synthesis and the intelligent degree of spacecraft products such as satellites are continuously improved, and higher requirements are also put forward on the reliability of the spacecraft products, so that the monitoring physical quantity required in a spacecraft prediction and health management system (PHM) is gradually increased, the monitoring difficulty is also increased, and urgent requirements are put forward for the technologies such as real-time monitoring and fault positioning of structural deformation, layout optimization of structural deformation sensors and the like.
In theory, the more the number of the structural deformation sensors is, the more the obtained deformation parameters are, the more the corresponding detected data volume is, the more accurate and comprehensive the deformation of the measured body is described, however, for a large-scale complex system such as an aerospace equipment system, the structural deformation sensors cannot be installed for measuring the deformation of all positions, otherwise, the structural deformation sensors are difficult to support in space, and the installation and layout modes of the structural deformation sensors can also influence the working state of the equipment. Therefore, the number and the installation position of the structural deformation sensors need to be subjected to layout optimization, and the deformation condition of the star can be comprehensively monitored under the condition that the number of the structural deformation sensors is fixed.
At present, the layout optimization method of the structural deformation sensor is basically a dynamic characteristic analysis method based on an effective independent method and modal vector kinetic energy, but excitation points or response points in a modal test cannot accurately reflect the modal vector of a structure due to structural properties, geometric features, boundary conditions and the like of materials, so that the deformation of a product cannot be accurately reflected after the layout optimization.
Disclosure of Invention
The invention aims to solve the technical problem of providing a structural deformation sensor layout optimization fitting method capable of accurately reflecting the deformation of a product, and aims to ensure the monitoring effect of the structural deformation value of a spacecraft aiming at the complex structure of the spacecraft, effectively reduce the number of deformation sensors and optimize the installation position of the deformation sensors.
In order to solve the technical problems, the invention provides a structural deformation sensor layout optimization fitting method, which comprises the following steps:
and 4, the number of the structural deformation sensors arranged at the observation points with the estimated values meeting the precision requirement can be reduced, and the arrangement of the structural deformation sensors is reserved when the estimated values do not meet the precision requirement.
Further, the method comprises the steps of,
and step 1, combining the deformation cloud image and the gradient image, and reserving the maximum value and the minimum value of the deformation quantity as reference points extracted in the optimization fitting process, wherein the two points are reserved unchanged in the layout optimization fitting process.
The extraction principle of the step 2 on the gradient map is as follows: edge points or boundary points are extracted less, points with larger changes in the gradient map are extracted less, and points with gentle changes are extracted more.
The evaluation method in the step 3 adopts a root mean square error method to evaluate the precision of the deformation estimator, and the formula of the root mean square prediction error PMSPE is as follows:
in the method, in the process of the invention,
for position x i An estimate of the deformation at Z (x i ) For position x i The smaller the root mean square prediction error is, the closer the predicted value is to the true value.
Compared with the prior art, the invention has the following beneficial effects:
according to the structural deformation sensor layout optimization fitting method provided by the invention, the deformation quantity of the unknown points of the system is estimated by utilizing a spatial interpolation method according to the deformation actual measurement data of a group of known complex systems, so that the structural deformation sensor layout optimization fitting method can effectively reduce the number of structural deformation sensors while meeting the structural deformation monitoring precision requirement, optimize the layout positions of the structural deformation sensors, comprehensively and accurately monitor structural variables of the system, and accurately evaluate the health condition of the system structure.
Drawings
FIG. 1 is a diagram of an overall deformation cloud of a star housing according to an embodiment of the present invention;
FIG. 2 is a cloud image of deformation of the upper surface of a star housing according to an embodiment of the present invention;
FIG. 3 is a flow chart of a layout optimization fit of a structural deformation sensor according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an original sensor layout of the upper surface of a star housing according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a sensor layout after optimization of the upper surface of the star housing according to an embodiment of the present invention.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings and examples.
By means of ground test and simulation data of structural deformation of the large-scale complex system, geometrical characteristics such as the shape, the size and the spatial distribution position among the observation points of the large-scale complex system, and information such as degrees of freedom, dynamic characteristics and material properties are considered, and structural deformation data of the observation points of the large-scale complex system and data of surrounding sampling points have correlation.
Spatial interpolation is a mathematical process that derives data for unknown points or unknown regions according to some mathematical relationship from a set of known discrete or partitioned data.
The embodiment carries out data processing on the structure deformation cloud image (with deformation magnitude values according to the specific position distribution) obtained by actual measurement or simulation and the data to generate a gradient image (which is arranged according to the magnitude of the values and comprises the position and magnitude values and is arranged from large to small or from small to large according to the value, and the specific position is basically irrelevant). And combining the deformation cloud image and the gradient image, and reserving the maximum value and the minimum value of the deformation quantity as reference points extracted in the optimization fitting process, wherein the two points are reserved unchanged in the layout optimization fitting process.
The following structure deformation sensor extraction is performed on the gradient map, and the extraction principle adopted in the embodiment is as follows: edge points or boundary points are extracted less, points with larger changes in the gradient map are extracted less, and points with gentle changes are extracted more.
For the extracted points, a spatial interpolation method is utilized to carry out fitting estimation on deformation values of the points.
Let x be a position in one-dimensional, two-dimensional or three-dimensional space in a large complex system structure, a certain structural deformation value at x be Z (x), and let Z (x) Is a second order stationary random function that samples at n+1 positions: z (x) 0 ),Z(x 1 ),Z(x 2 ),......,Z(x n ). The position of the extracted point is named x 0 By extracting n known quantities Z (x i ) (i=1, 2, 3.) linear combination to estimate position x 0 Unknown Z (x) 0 )。
λ i For the observation point x i The occupied weight factor, then, point x 0 The deformation estimator at this point is:
if it is to make Z * (x 0 ) Is Z (x) 0 ) For unbiased estimation of (2), then the sum of the required weighting factors is 1, namely:
the Lagrange multiplier method is used to construct the following functions: f=e [ Z (x) 0 )-Z * (x 0 )] 2 -2μ(λ i -1). μ is Lagrange coefficient. The set of equations is constructed as follows:
wherein C is a covariance matrix, and the equation set comprises n+1 equations for solving n weight factors.
Writing the above equation set as a matrix form for solving, then the matrix form that can be obtained is:
[K][λ]＝[M]
wherein, the liquid crystal display device comprises a liquid crystal display device,
from this, the n weight factor can be solved as:
[λ]＝[M]×[K] -1
the weight factor lambda to be solved i The method is brought into a deformation estimation formula, namely:
solving to obtain the point x 0 Deformation estimators at the location.
Repeating deleting one measuring point from the actual measuring point set, estimating the attribute value of the deleted point by using the residual measuring point set to obtain a deformation estimated value on each measuring point, and then carrying out statistical analysis on two groups of data of the deformation estimated value and the actual measured value on the measuring points by using a statistical method to evaluate the accuracy of the deformation estimated value.
Further, the evaluation method in the embodiment adopts a root mean square error method to evaluate the accuracy of the deformation estimator. The root mean square prediction error (PMSPE) is given by:
in the method, in the process of the invention,
for position x i An estimate of the deformation at Z (x i ) For position x i The smaller the root mean square prediction error, the closer the predictions are to their true values.
Through the steps, the error between the estimated value and the measured value of the extraction point is obtained by solving through a spatial interpolation method. The number of the structural deformation sensors arranged at the observation points with the estimated values meeting the precision requirement can be reduced, and the arrangement of the structural deformation sensors arranged at the observation points is reserved when the estimated values do not meet the precision requirement.
The following is a specific example of selecting a star housing surface for structural transformation sensor layout optimization.
Firstly, the deformation of the surface of the star shell is actually measured to obtain a deformation cloud picture, and the whole deformation cloud picture of the surface of the star shell is shown in figure 1.
In order to specifically analyze the layout optimization fitting effect of the deformation sensor of the star housing structure, in this embodiment, the upper surface of the star housing is selected as the analysis object, and the deformation cloud chart of the upper surface of the star housing is shown in fig. 2.
Firstly, constructing deformation data of the upper surface of a star shell into a gradient map.
Secondly, in the embodiment, firstly, extracting every other point according to the columns, and reserving boundary points; and extracting according to the row, namely extracting every other point, and keeping the boundary points. The extracted points are marked as x 0 The method comprises the steps of carrying out a first treatment on the surface of the The remaining points, marked x i (i=1, 2,3 … …, n) and the corresponding weight factors are λ respectively i (i＝1,2,3……,n)。
Thirdly, constructing Lagrange multiplier method constructors: f=e [ Z (x) 0 )-Z * (x 0 )] 2 -2μ(λ i -1)。
And fourthly, constructing a weight factor equation set.
Fifthly, transforming the weight factor equation set into a matrix form, and solving the weight factor lambda i 。
Sixth, according to the estimated value formula
Solving for x 0 Estimated value Z (x 0 )。
And seventhly, solving the mean square error of the estimated value according to a mean square error prediction error formula, and finishing precision evaluation.
According to the flow shown in fig. 3, the root mean square error of the estimated value of the observation point is finally solved, and then the evaluation condition of the optimization fitting accuracy of this example is shown in the following table.
And according to the result, optimizing layout of the deformation sensor of the upper surface structure of the star shell.
The original structure deformation sensor layout is shown in fig. 4, and 1682 structure deformation sensor points are deployed on the upper surface of the star shell. The deformation sensors are distributed unevenly on the upper surface of the original star body shell, the structural deformation sensors are supported or connected in the edge and the interior of the shell, the structural deformation sensors are deployed relatively densely, and other places are relatively sparse, so that the deformation changes in the places where the structural deformation sensors are deployed densely, such as the edge and the connection place of the shell, are relatively complex, and the deformation changes in other places are relatively gentle and simple.
Recording the position of the out-of-tolerance point (after the fitting is extracted, the root mean square error of the estimated point is greater than the point with the precision requirement, namely the point with the root mean square error of more than 1 e-05), and reserving the structural deformation sensor; the rest positions are extracted according to rows and columns respectively, one point is reserved for every 2 points, meanwhile, boundary points are reserved, and the layout of the optimized deformation sensor of the upper surface structure of the shell is shown in fig. 5. After the upper surface of the star shell is optimized, only 542 structural deformation sensor points are required to be deployed.
Under the condition that the percentage of the root mean square estimation error of the monitoring precision of the upper surface of the star shell is less than or equal to 1e-05, the number of the structural deformation sensors is reduced by 1140, 67.8% is reduced, the deformation after optimization fitting through spatial interpolation is closest to the original deformation, and the effect of optimization fitting of the structural deformation sensors is achieved.
In summary, according to the optimization fitting method for the structural deformation sensor layout of the spacecraft shell surface structure provided by the embodiment of the invention, the structural surface deformation sensor layout is optimized by utilizing a spatial interpolation method, so that the number of structural deformation sensors can be effectively reduced on the premise of meeting the precision requirement, the real-time monitoring and fault positioning of the structural deformation of the spacecraft are realized, and the whole structural deformation sensor system has a higher cost-effective ratio.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (3)
1. The structural deformation sensor layout optimization fitting method is characterized by comprising the following steps of:
step 1, generating a gradient map related to deformation size and position information from a structure deformation cloud picture obtained through actual measurement, arranging according to the size of a numerical value, including positions and size numerical values, arranging according to the size of the numerical value from large to small or from small to large, and combining the deformation cloud picture and the gradient map, and keeping the maximum value and the minimum value of deformation as reference points extracted in the optimization fitting process, wherein the two points are kept unchanged in the layout optimization fitting process;
step 2, extracting a structural deformation sensor according to the gradient map, and carrying out fitting estimation on deformation values of extracted points by using a spatial interpolation method;
step 3, repeatedly extracting one measuring point from the actual measuring point set, estimating attribute values of the extracted points by using the residual measuring point set to obtain deformation estimated values of each extracting point, and estimating the accuracy of the deformation estimated values;
and 4, reducing the number of the structural deformation sensors for the observation points of which the deformation estimated values meet the precision requirements, and reserving the arrangement of the observation points of the structural deformation sensors when the deformation estimated values do not meet the precision requirements.
2. The method for optimizing and fitting a structural deformation sensor layout according to claim 1, wherein the extraction principle of the gradient map in the step 2 is as follows: edge points or boundary points are extracted less, points with larger changes in the gradient map are extracted less, and points with gentle changes are extracted more.
3. The method for optimizing and fitting a layout of a structural deformation sensor according to claim 1, wherein the estimating method in step 3 adopts a root mean square error method to estimate the accuracy of the deformation estimator, and the root mean square prediction error PMSPE has the formula:
in the method, in the process of the invention,
for position x i An estimate of the deformation at Z (x i ) For position x i The smaller the root mean square prediction error, the closer the prediction value is to the true value, n represents the known quantity Z (x i ) Quantity, i=1, 2,3.
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