CN114707116B - Cable network antenna manufacturing error sensitivity analysis method based on proxy model - Google Patents
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Abstract
The invention belongs to the field of structural parameter sensitivity analysis, and particularly relates to a cable network antenna manufacturing error sensitivity analysis method based on a proxy model, which comprises the following steps: classifying and combining manufacturing error variables according to structural symmetry characteristics; performing initial sampling on the manufacturing error variable, and calculating corresponding antenna precision; constructing a Kriging proxy model based on the current sample point, and simulating a function relation between manufacturing errors and antenna precision; calculating a sensitivity index by using a global sensitivity analysis strategy based on the current agent model; adding a new sample point based on a dynamic point adding strategy, updating a Kriging agent model and calculating a new sensitivity index; calculating weighted relative errors of sensitivity indexes of two adjacent steps; if the weighted relative error converges, ending the analysis flow; otherwise, continuing to add points and updating the proxy model. The invention can accurately and efficiently obtain the sensitivity of different manufacturing errors in the cable network antenna, is beneficial to screening key factors and lays a foundation for the subsequent antenna structural design.
Description
Technical Field
The invention belongs to the field of structural parameter sensitivity analysis, and particularly relates to a cable network antenna manufacturing error sensitivity analysis method based on a proxy model, which is used for screening importance factors influencing antenna precision and providing technical support for antenna structural design.
Background
The antenna system is a special electromechanical device which aims at acquiring, transmitting, processing and other electromagnetic performances of electromagnetic signals and takes a mechanical structure as a carrier, and structural factors often restrict the realization of electrical performances. The design requirements of large caliber, high frequency band and high gain make the influence of structural factors on the surface accuracy of the cable net antenna more serious, and the design index requirements of the antenna are more severe. However, various uncertain error factors are inevitably present in the mesh antenna structure, and are generally derived from material parameters, section geometry, cable mesh boundary point positions and the like of the cable. The mesh antenna is a typical geometrical nonlinear structure, and the characteristics of large displacement and small strain of the mesh structure cause the small fluctuation of the structure to cause large change of shape, which in turn causes the reflecting surface of the antenna to deviate from an ideal position, thus causing deterioration of accuracy. Such uncertainty severely restricts the improvement of the antenna performance and even leads to the antenna not being normally in service, and thus must be considered in design. The number of cable segments and boundary points in the cable network antenna is numerous, and all error factors appearing in practice cannot be completely considered in the design stage, so that factors affecting the antenna precision obviously need to be determined through sensitivity analysis and are subjected to important treatment in structural design.
Aiming at the problem of sensitivity analysis, the current methods can be divided into the following two types:
① Partial derivative based local sensitivity strategies. The method can only characterize the sensitivity of the error parameter at the nominal value, cannot embody the influence of the integral fluctuation of the error on the antenna precision, and cannot process the structure with higher nonlinearity degree like a cable network antenna.
② Global sensitivity policy based on ideas such as variance decomposition. The global sensitivity method can obtain more accurate and comprehensive sensitivity information than the local sensitivity method. In view of the large amount of computation required to calculate the sensitivity information, a proxy model approach based on sequence dotting is also often used to improve efficiency. However, how to determine the convergence criterion of the sequence point adding iterative process is an important problem, such as inaccurate convergence state judgment, which often results in insufficient accuracy of the proxy model and inaccurate sensitivity index; or the accuracy of the proxy model exceeds the actual demand, and the waste of calculation resources is caused. The existing agent model convergence criterion does not consider the convergence condition of sensitivity indexes constructed by the agent model, and can not meet the two requirements of accuracy and high efficiency.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a cable-net antenna manufacturing error sensitivity analysis method based on a proxy model, so that sensitivity information of antenna manufacturing error factors can be efficiently and accurately obtained, accurate control of a point adding iteration process can be realized, and an accurate global sensitivity index can be obtained on the premise of ensuring calculation efficiency.
The technical scheme of the invention is as follows: a cable network antenna manufacturing error sensitivity analysis method based on a proxy model is characterized by comprising the following steps: at least comprises the following steps:
step 1: performing error sensitivity analysis;
Step 2: classifying and combining manufacturing error variables according to structural symmetry characteristics;
Step 3: performing initial sampling on the manufacturing error, and calculating corresponding antenna precision;
step 4: constructing a Kriging agent model based on the current sample points;
Step 5: calculating sensitivity indexes of each type of error factors according to the current Kriging agent model based on a global sensitivity analysis strategy;
Step 6: based on a point adding strategy, adding new sample points and calculating the corresponding antenna precision;
Step 7: updating the Kriging proxy model according to the new sample point set;
Step 8: calculating a new sensitivity index, and obtaining a sensitivity index weighted relative error;
Step 9: if the relative error convergence condition is satisfied, the analysis flow is ended, otherwise, the step 6 is returned.
Step 2 comprises the following steps:
Aiming at the front cable length error, the rear cable length error, the adjusting cable length error and the boundary point position error of the cable network antenna, the four error types are respectively classified into n types according to the cable section or the boundary point position related to the error and the symmetry of the cable network antenna.
The step 3 comprises the following steps:
step 3a: determining the number of initial sample points according to the size of an error variable N in a specific cable network antenna and N initial =8n;
Step 3b: sampling the N-dimensional variable by using a Latin hypercube method to obtain N initial sample points;
Step 3c: obtaining the structural precision index corresponding to the sample point through finite element analysis Wherein/>And (3) the axial deformation value corresponding to the ith node of the front cable net is NUM, and the NUM is the number of all nodes of the front cable net.
Step 5, comprising the following steps:
Step 5a: according to the joint probability distribution of the vector X formed by all error factors, two groups of input samples (the sample number of each group is M) are extracted, namely, the matrix A and the matrix B are obtained:
Step 5b: constructing a matrix C i which is the matrix after the ith column in B is replaced by the ith column in matrix A, i.e
Step 5c: calculating the sensitivity index of the ith manufacturing error as
Wherein,And/>The sample matrices a, B and C i are taken as inputs, respectively, and are substituted into the antenna accuracy vector obtained in the proxy model constructed in step 4, and g 0 is the average value of all elements in R A.
Step 6, comprising the following steps:
In order to ensure the accuracy of the obtained sensitivity index, the agent model needs to be ensured to better approach the real physical model in the full feasible domain, so that the sample points need to be uniformly distributed. The invention utilizes the minimum distance to maximize thinking, and constructs an optimization model for searching new sample points as follows
Dnew＝argmax min(||D-Di||2)
Where D new is the newly added sample point and D i is the sample in the current sample library.
Step 8, comprising the following steps:
step 8a: calculating sensitivity index of each manufacturing error based on current agent model by using step 5
Step 8b: definition of the q-th iteration step weighted relative error
Wherein the relative errorIt can be seen that the relative error γ i,q characterizes the relative error of the ith manufacturing error in the q-th iteration step, and the absolute value of sensitivity |s i,q | is used to weight the relative error, so as to obtain a weighted relative error index epsilon q. Compared with the indexes of the traditional convergence criterion, epsilon q can represent the convergence degree of each sensitivity index on one hand, and meanwhile, by utilizing the weighting of the sensitivity indexes, the relative error fluctuation of individual non-important factors can be avoided to interfere with the convergence process, so that the stability of the convergence process is ensured.
The step 9 of meeting the relative error convergence condition criteria is defined as follows:
εQ≤0.01，Q＝q，q-1，q-2，q≥4
As can be seen, if the weighted relative error epsilon q is smaller than 0.01 for all three consecutive iteration steps, the iteration is ended, and the current sensitivity index is considered to be converged; otherwise, it is necessary to return to step 6 to continue adding new sample points.
Analytical methods not described in detail in this example, such as Kriging proxy model construction method, latin hypercube sampling method, etc., are common means in the industry and are not described here.
The invention provides a cable network antenna manufacturing error sensitivity analysis method based on a proxy model, which constructs a new convergence criterion through weighted relative errors of sensitivity indexes between adjacent iteration steps and can efficiently and accurately obtain sensitivity information of antenna manufacturing error factors.
Accuracy means that the convergence criterion provided by the invention is based on sensitivity relative errors, so that the basic stability of each sensitivity index during convergence can be essentially ensured; the high efficiency means that the relative error of the important factors obtains larger weight through weighting, but the relative error of the non-important factors has smaller weight, so that the relative error fluctuation of the non-important factors can be avoided to interfere with the convergence process of the whole iteration, and redundant iteration of the iteration process is avoided.
Drawings
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
FIG. 1 is a flow chart showing the implementation of the sensitivity analysis method according to the present invention
Fig. 2 is a schematic diagram of a cable network antenna structure related to the cable in this aspect
FIG. 3 is a diagram showing the classification of the front cable and the variables of a cable-network antenna with a caliber of 3 meters
FIG. 4 is a graph comparing the iteration history of the convergence index with the non-weighted convergence criterion method of the present invention.
Detailed Description
As shown in fig. 1, a global sensitivity analysis method based on a proxy model at least includes the following steps:
step 1: performing error sensitivity analysis;
step 2: classifying and combining manufacturing error variables according to structural symmetry characteristics; comprises the following contents:
Aiming at the front cable length error, the rear cable length error, the adjusting cable length error and the boundary point position error of the cable network antenna, the four error types are respectively classified into n types according to the cable section or the boundary point position related to the error and the symmetry of the cable network antenna.
Step 3: performing initial sampling on the manufacturing error, and calculating corresponding antenna precision; comprises the following steps:
step 3a: determining the number of initial sample points according to the size of an error variable N in a specific cable network antenna and N initial =8n;
Step 3b: sampling the N-dimensional variable by using a Latin hypercube method to obtain N initial sample points;
Step 3c: obtaining the structural precision index corresponding to the sample point through finite element analysis Wherein/>And (3) the axial deformation value corresponding to the ith node of the front cable net is NUM, and the NUM is the number of all nodes of the front cable net.
Step 4: constructing a Kriging agent model based on the current sample points;
Step 5: calculating sensitivity indexes of each type of error factors according to the current Kriging agent model based on a global sensitivity analysis strategy; the method comprises the following steps:
Step 5a: according to the joint probability distribution of the vector X formed by all error factors, two groups of input samples (the sample number of each group is M) are extracted, namely, the matrix A and the matrix B are obtained:
Step 5b: constructing a matrix C i which is the matrix after the ith column in B is replaced by the ith column in matrix A, i.e
Step 5c: calculating the sensitivity index of the ith manufacturing error as
Wherein,And/>The sample matrices a, B and C i are taken as inputs, respectively, and are substituted into the antenna accuracy vector obtained in the proxy model constructed in step 4, and g 0 is the average value of all elements in R A.
Step 6: based on a point adding strategy, adding new sample points and calculating the corresponding antenna precision; in order to ensure the accuracy of the obtained sensitivity index, the agent model needs to be ensured to better approach the real physical model in the full feasible domain, so that sample points need to be uniformly distributed, and an optimal model for searching new sample points is constructed by utilizing the minimum distance maximization thinking as follows
Dnew＝argmax min(||D-Di||2)
Where D new is the newly added sample point and D i is the sample in the current sample library.
Step 7: updating the Kriging proxy model according to the new sample point set;
Step 8: calculating a new sensitivity index, and obtaining a sensitivity index weighted relative error; comprises the following contents:
step 8a: calculating sensitivity index of each manufacturing error based on current agent model by using step 5
Step 8b: definition of the q-th iteration step weighted relative error
Wherein the relative errorIt can be seen that the relative error γ i,q characterizes the relative error of the ith manufacturing error in the q-th iteration step, and the absolute value of sensitivity |s i,q | is used to weight the relative error, so as to obtain a weighted relative error index epsilon q. Compared with the indexes of the traditional convergence criterion, epsilon q can represent the convergence degree of each sensitivity index on one hand, and meanwhile, by utilizing the weighting of the sensitivity indexes, the relative error fluctuation of individual non-important factors can be avoided to interfere with the convergence process, so that the stability of the convergence process is ensured.
Step 9, the criterion meeting the relative error convergence condition is defined as follows:
εQ≤0.01，Q＝q，q-1，q-2，q≥4
As can be seen, if the weighted relative error epsilon q is smaller than 0.01 for all three consecutive iteration steps, the iteration is ended, and the current sensitivity index is considered to be converged; otherwise, it is necessary to return to step 6 to continue adding new sample points.
Analytical methods not described in detail in this example, such as Kriging proxy model construction method, latin hypercube sampling method, etc., are common means in the industry and are not described here.
The advantages of the invention can be further illustrated by the following simulation experiments:
1. Simulation conditions
The general structure of a cable net antenna is shown in fig. 2. The specific parameters of a cable network antenna are as follows:
caliber of 3m
Front cable net focal length 1.2m
The number of the front (back) cable net cable segments is 72
Number of adjusting ropes 19
The maximum length of the front (back) cable net cable segment is 1.149m
The minimum length of the front (back) cable net cable section is 0.480m
The maximum length of the adjusting rope is 1.000m
The minimum length of the adjusting rope is 0.563m
Front (back) cable net cable section tension 20N
The simulation experiment only considers the length error of the cable section in the cable network before the cable network antenna, and specific variables are summarized in fig. 3.
The cable segments in the cable network antenna front cable network can be divided into 8 types in consideration of structural symmetry. From the conventional processing and manufacturing precision of the cable net antenna, the fluctuation range of each cable length is determined to be [ -0.15,0.15] mm.
2. Simulation results
The sensitivity index of the cable length error variable of the cable segment 8 class in the cable network in front of the cable network antenna is obtained by the method (the specific flow is shown in figure 1), and the sensitivity index is compared with the traditional method in two aspects.
The comparison of the first aspect is that of a non-proxy model method, and the calculated sensitivity index and calculation cost are shown in table 1. The non-proxy model method is that in the step 5c of the invention, the finite element method is directly adopted to calculate the antenna precision, instead of using the proxy model, and the result obtained by the method can be regarded as an accurate value.
Step 5c: calculating the sensitivity index of the ith manufacturing error as
Wherein,And/>The sample matrices a, B and C i are used as inputs, respectively, and are substituted into the antenna accuracy vector obtained in the proxy model constructed in step 104, and g 0 is the average value of all the elements in R A.
The method can obtain quite accurate results with extremely low calculation cost, and the accuracy of the method is verified.
Table 1 shows the sensitivity index comparison of the method of the present invention and the non-proxy model method
The second aspect of comparison is an iteration history comparing the weighted convergence criterion and the non-weighted convergence criterion proposed by the present invention.
In order to avoid relative error fluctuation of individual non-important factors interfering with the convergence process and thereby ensure the stability of the convergence process, the invention proposes a convergence criterion based on weighting, see:
step 8a: calculating sensitivity index of each manufacturing error based on current agent model by using step 5
Step 8b: definition of the q-th iteration step weighted relative error
Wherein the relative errorIt can be seen that the relative error γ i,q characterizes the relative error of the ith manufacturing error in the q-th iteration step, and the absolute value of sensitivity |s i,q | is used to weight the relative error, so as to obtain a weighted relative error index epsilon q. Compared with the indexes of the traditional convergence criterion, epsilon q can represent the convergence degree of each sensitivity index on one hand, and meanwhile, by utilizing the weighting of the sensitivity indexes, the relative error fluctuation of individual non-important factors can be avoided to interfere with the convergence process, so that the stability of the convergence process is ensured.
To compare the advantages of the present invention, it is compared to the unweighted relative error γ i,q in the iterative process, see in detail fig. 4. It can be seen that epsilon q has met the convergence requirement after q=36 iterations, but it is apparent that the individual relative error gamma i,q values are still large, especially gamma 3,q. As can be seen from table 1, the sensitivity index of the third class of cable length error is the smallest:
3 0.0120 0.0094
About 0.01. The small sensitivity index is subject to unstable numerical value in the calculation process, and large fluctuation is always easy to generate in the iteration process, and the weighted convergence criterion provided by the invention can effectively avoid the influence of the fluctuation on the overall convergence, so that the high efficiency of the iteration process is ensured.
Claims (4)
1. A cable network antenna manufacturing error sensitivity analysis method based on a proxy model is characterized by comprising the following steps: at least comprises the following steps:
step 1: performing error sensitivity analysis;
Step 2: classifying and combining manufacturing error variables according to structural symmetry characteristics;
Step 3: performing initial sampling on the manufacturing error, and calculating corresponding antenna precision;
step 4: constructing a Kriging agent model based on the current sample points;
Step 5: calculating sensitivity indexes of each type of error factors according to the current Kriging agent model based on a global sensitivity analysis strategy;
Step 6: based on a point adding strategy, adding new sample points and calculating the corresponding antenna precision;
Step 7: updating the Kriging proxy model according to the new sample point set;
Step 8: calculating a new sensitivity index, and obtaining a sensitivity index weighted relative error;
step 9: if the relative error convergence condition is met, ending the analysis flow, otherwise returning to the step 6;
Step 5, comprising the following steps:
step 5a: according to the joint probability distribution of the vector X formed by all error factors, two groups of input samples are extracted, and the sample number of each group is M, namely, the matrix A and the matrix B:
Step 5b: constructing a matrix C i which is the matrix after the ith column in B is replaced by the ith column in matrix A, i.e
Step 5c: calculating the sensitivity index of the ith manufacturing error as
Wherein,And/>Taking sample matrixes A, B and C i as inputs, substituting the sample matrixes A, B and C i into the antenna precision vector obtained in the proxy model constructed in the step 4, wherein g 0 is the average value of all elements in R A;
Step 6, comprising the following steps:
The minimum distance is utilized to maximize thinking, and an optimization model for searching new sample points is constructed as follows
DneW＝argmax min(||D-Di||2)
Wherein, D new is the newly added sample point, and D i is the sample in the current sample library;
Step 8, comprising the following steps:
step 8a: calculating sensitivity index of each manufacturing error based on current agent model by using step 5
Step 8b: definition of the q-th iteration step weighted relative error
Wherein the relative errorAs can be seen, the relative error γ i,q represents the relative error of the ith manufacturing error in the q-th iteration step, and the absolute value |s i,q | of the sensitivity is used to weight the relative error, so as to obtain a weighted relative error index epsilon q; compared with the indexes of the traditional convergence criterion, epsilon q can represent the convergence degree of each sensitivity index on one hand, and meanwhile, by utilizing the weighting of the sensitivity indexes, the relative error fluctuation of individual non-important factors can be avoided to interfere with the convergence process, so that the stability of the convergence process is ensured.
2. The cable network antenna manufacturing error sensitivity analysis method based on the proxy model as claimed in claim 1, wherein the method comprises the following steps: step 2 comprises the following steps:
Aiming at the front cable length error, the rear cable length error, the adjusting cable length error and the boundary point position error of the cable network antenna, the four error types are respectively classified into n types according to the cable section or the boundary point position related to the error and the symmetry of the cable network antenna.
3. The cable network antenna manufacturing error sensitivity analysis method based on the proxy model as claimed in claim 1, wherein the method comprises the following steps: the step 3 comprises the following steps:
step 3a: determining the number of initial sample points according to the size of an error variable N in a specific cable network antenna and N initial =8n;
Step 3b: sampling the N-dimensional variable by using a Latin hypercube method to obtain N initial sample points;
Step 3c: obtaining the structural precision index corresponding to the sample point through finite element analysis Wherein/>And (3) the axial deformation value corresponding to the ith node of the front cable net is NUM, and the NUM is the number of all nodes of the front cable net.
4. The cable network antenna manufacturing error sensitivity analysis method based on the proxy model as claimed in claim 1, wherein the method comprises the following steps: the step 9 of meeting the relative error convergence condition criteria is defined as follows:
εQ≤0.01,Q＝q,q-1,q-2,q≥4
As can be seen, if the weighted relative error epsilon q is smaller than 0.01 for all three consecutive iteration steps, the iteration is ended, and the current sensitivity index is considered to be converged; otherwise, it is necessary to return to step 6 to continue adding new sample points.
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