CN112749470A - Optimal fitting method for structural deformation sensor layout - Google Patents
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Abstract
The invention discloses a layout optimization fitting method for a structural deformation sensor, which comprises the following steps of firstly, generating a gradient map related to deformation size and position information by a structural deformation cloud map; secondly, extracting structural deformation sensors from the gradient map, and performing fitting estimation on deformation values of the extracted points by using a spatial interpolation method; then, repeatedly deleting a measuring point from the actual measuring point set, estimating the deformation estimation value of the deleted point by using the rest measuring point set, and estimating the precision of the deformation estimation value; and finally, reducing the arrangement number of the structural deformation sensors for the observation points with the estimated values meeting the precision requirement, and keeping the arrangement of the observation points of the structural deformation sensors when the estimated values do not meet the precision requirement. 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 deformation quantity 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 demand of national defense construction, the complexity, the integration and the intelligence of spacecraft products such as satellites and the like are continuously improved, and higher requirements are provided for the reliability of the spacecraft products, so that the physical quantity required to be monitored in a spacecraft prediction and health management system (PHM) is gradually increased, the monitoring difficulty is increased, and urgent needs are provided for technologies such as real-time monitoring of structural deformation, fault positioning, layout optimization of structural deformation sensors and the like.
Theoretically, the more the structural deformation sensors, the more the acquired deformation parameters are, the more the data volume obtained by corresponding detection is, the more accurate and comprehensive description on the deformation of the detected body is, however, for a large complex system such as an aerospace equipment system, it is impossible to install the structural deformation sensors on deformation quantities of all positions for measurement, otherwise, the space is difficult to support, and the installation and layout mode of the structural deformation sensors may also affect the working state of the equipment. Therefore, the number and the installation positions of the structural deformation sensors need to be optimized in layout, and the deformation condition of the star body can be comprehensively monitored under the condition that the number of the structural deformation sensors is certain.
At present, the layout optimization method of the structural deformation sensor is basically a dynamic characteristic analysis method based on an effective independence method and modal vector kinetic energy, but due to structural attributes, geometric characteristics, boundary conditions and the like of materials, excitation points or response points in a modal test cannot accurately reflect modal vectors of a structure, so that the deformation of a product cannot be accurately reflected after layout optimization.
Disclosure of Invention
The invention aims to solve the technical problem of providing a layout optimization fitting method of a structural deformation sensor capable of accurately reflecting the deformation of a product, aiming at the complex structure of a spacecraft, effectively reducing the number of the deformation sensors and optimizing the installation position of the deformation sensors while ensuring the monitoring effect of the structural deformation value of the spacecraft.
In order to solve the technical problem, the invention provides a layout optimization fitting method for a structural deformation sensor, which comprises the following steps:
and 4, reducing the arrangement number of the structural deformation sensors by the observation points with the estimated values meeting the precision requirement, and keeping the arrangement of the observation points of the structural deformation sensors when the estimated values do not meet the precision requirement.
Further, the air conditioner is provided with a fan,
the step 1 combines the deformation cloud picture and the gradient picture, the maximum value and the minimum value of the deformation quantity are reserved as the reference points extracted in the optimization fitting process, and the two points are kept unchanged in the layout optimization fitting process.
The extraction principle of the gradient map in the step 2 is as follows: and less edge points or boundary points are extracted, less points with larger change in the gradient map are extracted, and more points with smooth change are extracted.
The step 3 adopts a method of root mean square error to evaluate the precision of the deformation estimator, and the formula of the root mean square prediction error PMSPE is as follows:
in the formula,
is a position xiAn estimate of the deformation, Z (x)i) Is a position xiError in prediction of measured value of distortion quantity, root mean squareThe smaller the predicted value, the closer to the true value.
Compared with the prior art, the invention has the following beneficial effects:
according to the layout optimization fitting method of the structural deformation sensor, the deformation quantity of an unknown point of a system is estimated by utilizing a spatial interpolation method according to a set of known deformation actual measurement data of a complex system, the requirement of structural deformation monitoring precision is met, meanwhile, the arrangement quantity of the structural deformation sensor can be effectively reduced, the arrangement position of the structural deformation sensor is optimized, the structural deformation quantity of the system can be comprehensively and accurately monitored, and the health condition of the system structure is accurately evaluated.
Drawings
FIG. 1 is a cloud of the overall deformation of the star shell according to the embodiment of the present invention;
FIG. 2 is a cloud of the surface profile of the star shell according to the embodiment of the present invention;
FIG. 3 is a layout optimization fitting process of a structural deformation sensor according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a layout of a raw sensor on the upper surface of a star shell according to an embodiment of the present invention;
fig. 5 is a schematic layout diagram of a sensor after the star shell upper surface is optimized according to the embodiment of the invention.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the drawings and examples.
By taking the geometric characteristics such as the shape, the size, the spatial distribution position between the observation points and the like of the large complex system and the information such as the degree of freedom, the dynamic characteristic, the material attribute and the like into consideration through ground test and simulation data of the structural deformation of the large complex system, the structural deformation data of each observation point of the large complex system has correlation with the data of the surrounding sampling points.
Spatial interpolation is a mathematical process that derives data for unknown points or unknown regions from a set of known discrete data or partitioned data according to some mathematical relationship.
The embodiment performs data processing on a structural deformation cloud picture (distributed according to specific positions and provided with deformation magnitude values) and data obtained through actual measurement or simulation to generate a gradient picture (arranged according to the magnitude of the values, including the position and magnitude values, arranged from large to small or from small to large according to the values and basically unrelated to the specific positions) related to the deformation magnitude and position information. And (4) combining the deformation cloud picture and the gradient picture, keeping the maximum value and the minimum value of the deformation quantity as the extracted reference points in the optimization fitting process, and keeping the two points unchanged in the layout optimization fitting process.
The gradient map is subjected to structural deformation sensor extraction, and the extraction principle adopted in the embodiment is as follows: and less edge points or boundary points are extracted, less points with larger change in the gradient map are extracted, and more points with smooth change are extracted.
For the extracted points, the deformation values of the points are subjected to fitting estimation by using a spatial interpolation method.
Let x be a certain position in one-dimensional, two-dimensional or three-dimensional space in a large complex system structure, a certain structural variation value at x be z (x), and let z (x) be a second-order stationary random function, which samples at n +1 positions: z (x)0),Z(x1),Z(x2),......,Z(xn). The position of the extracted point is named x0By extracting n known quantities Z (x) in the vicinity of the pointi) ( i 1,2,3.. n) to estimate the position x0An unknown quantity of Z (x)0)。
λiIs an observation point xiOccupied weight factor, then, point x0The estimated amount of deformation at (a) is:
if it is desired to make Z*(x0) Is Z (x)0) The sum of the weight factors is required to be 1, that is:
the Lagrange multiplier method is used to construct the following function: f ═ E [ Z (x) ]0)-Z*(x0)]2-2μ(λi-1). μ is the Lagrange coefficient. The system of equations is constructed as follows:
where C is a covariance matrix, the system of equations includes n +1 equations for solving the n weighting factors.
Writing the above equation set into a matrix form for solving, then, the matrix form that can be obtained is:
[K][λ]＝[M]
wherein,
thus, the n weighting factor can be solved as:
[λ]＝[M]×[K]-1
the solved weight factor lambdaiThe deformation estimator formula is substituted with:
then the solution is obtained to point x0And (4) an estimate of the deformation of the workpiece.
And repeatedly deleting a measuring point from the actual measuring point set, estimating the attribute value of the deleted point by using the rest measuring point set to obtain the deformation estimation value on each measuring point, and then carrying out statistical analysis on the two groups of data of the deformation estimation value and the actual measuring value on the measuring point by using a statistical method to estimate the precision of the deformation estimation 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 (pmpe) is formulated as:
in the formula,
is a position xiAn estimate of the deformation, Z (x)i) Is a position xiThe smaller the root mean square prediction error is for the measured values of the deformation quantities, the closer the predicted values 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 space interpolation method. The arrangement number of the structural deformation sensors can be reduced by the observation points with the estimated values meeting the precision requirement, and the arrangement of the observation points of the structural deformation sensors is reserved under the condition that the estimated values do not meet the precision requirement.
The following is a specific embodiment of selecting a star housing surface to optimize the structural deformation sensor layout.
Firstly, the deformation of the surface of the star shell is actually measured to obtain a deformation cloud picture, and the integral deformation cloud picture of the surface of the star shell is shown in figure 1.
In order to specifically analyze the optimized fitting effect of the layout of the deformation sensor of the star shell structure, the upper surface of the star shell is selected as an analysis object in the embodiment, and a cloud image of deformation of the upper surface of the star shell is shown in fig. 2.
Firstly, constructing deformation data of the upper surface of the star shell into a gradient map.
Secondly, in the embodiment, the extraction is performed according to the rows, every other point is extracted, and the boundary points are reserved; and then extracting according to rows, similarly extracting every other point, and reserving boundary points. The extracted points are marked as x0(ii) a The remaining points, marked xi(i ═ 1,2,3 … …, n), the corresponding weighting factors are each λi(i＝1,2,3……,n)。
Thirdly, constructing a Lagrange multiplier method structure function: f ═ E [ Z (x) ]0)-Z*(x0)]2-2μ(λi-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 lambdai。
Sixthly, according to the formula of the estimated value
Solving for x0An estimated value of Z (x)0)。
And seventhly, solving the mean square error of the estimated value according to a mean square error prediction error formula to finish 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 obtained by the solution, and then the evaluation condition of the optimized fitting accuracy of the present example is shown in the following table.
And according to the result, optimizing the layout of the deformation sensor of the upper surface structure of the star shell.
Raw structure deformation sensor layout as shown in fig. 4, 1682 structure deformation sensor points are disposed on the upper surface of the star body shell. The distribution of the structural deformation sensors on the upper surface of the original star shell is uneven, the structural deformation sensors at the edges and the inner parts of the shell are supported or connected are arranged relatively densely, and other places are relatively sparse, which shows that the deformation changes relatively more complexly at the places where the structural deformation sensors at the edges and the connected parts of the shell are arranged densely, and the deformation changes relatively gently and simply at other places.
Recording the positions of the super-error points (after extraction and fitting, the root mean square error of the estimated points is greater than the points with the precision requirement, namely the points with the root mean square error of more than 1 e-05), and reserving the structural deformation sensor; the other positions are respectively extracted according to rows and columns, one is reserved at every 2 points, meanwhile, the boundary points are reserved, and then the layout of the deformation sensor of the upper surface structure of the optimized shell is shown in fig. 5. After the upper surface of the star shell is optimized, only 542 structural deformation sensor points are deployed.
Under the condition that the monitoring precision root mean square estimation error percentage of the upper surface of the star shell is less than or equal to 1e-05, the number of structural deformation sensors is reduced by 1140, and is reduced by 67.8%, and the deformation after optimization fitting through spatial interpolation is closest to the original deformation, so that the effect of optimization fitting of the layout of the structural deformation sensors is achieved.
In summary, according to the optimization fitting method for the layout of the deformation sensor of the spacecraft shell surface structure provided by the embodiment of the invention, the layout of the deformation sensor of the structure surface structure is optimized by using a spatial interpolation method, so that the number of the deformation sensors of the structure can be effectively reduced on the premise of meeting the precision requirement, and the real-time monitoring and fault location of the structural deformation of the spacecraft are realized, so that the whole structural deformation sensor system has a higher cost-to-efficiency ratio.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Claims (4)
1. A layout optimization fitting method for a structural deformation sensor is characterized by comprising the following steps:
step 1, generating a gradient map related to deformation size and position information by using a structural deformation cloud map;
step 2, extracting structural deformation sensors according to the gradient map, and performing fitting estimation on deformation values of the extracted points by using a spatial interpolation method;
step 3, deleting a measuring point from the actual measuring point set repeatedly, estimating the attribute value of the deleted point by using the rest measuring point set to obtain a deformation estimation value on each measuring point, and estimating the precision of the deformation estimation value;
and 4, reducing the arrangement number of the structural deformation sensors for the observation points with the estimated values meeting the precision requirement, and keeping the arrangement of the observation points of the structural deformation sensors when the estimated values do not meet the precision requirement.
2. The method for optimal fitting of a layout of structural deformation sensors as claimed in claim 1, wherein the step 1 combines the deformation cloud map and the gradient map, and retains the maximum and minimum values of the deformation quantity as the reference points extracted during the optimal fitting process, and the two points are retained during the optimal fitting process of the layout.
3. The method for optimally fitting the layout of the structural deformation sensor according to claim 1, wherein the extraction principle of the gradient map in the step 2 is as follows: and less edge points or boundary points are extracted, less points with larger change in the gradient map are extracted, and more points with smooth change are extracted.
4. The method of claim 1, wherein the step 3 comprises estimating the accuracy of the deformation estimator using a root mean square error (rms prediction error PMSPE) according to the following formula:
in the formula,
is a position xiAn estimate of the deformation, Z (x)i) Is a position xiThe smaller the root mean square prediction error of the measured value of the deformation quantity is, the closer the predicted value is to the real value.
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