CN108763656B - Method for identifying rigidity of hinge-structure-containing interval based on response surface model - Google Patents

Method for identifying rigidity of hinge-structure-containing interval based on response surface model Download PDF

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CN108763656B
CN108763656B CN201810415540.4A CN201810415540A CN108763656B CN 108763656 B CN108763656 B CN 108763656B CN 201810415540 A CN201810415540 A CN 201810415540A CN 108763656 B CN108763656 B CN 108763656B
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姜东�
秦福溶
费庆国
周李真辉
曹芝腑
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Abstract

The invention discloses a method for identifying rigidity of an interval containing a hinge structure based on a complete second-order polynomial response surface model. The identification method comprises the following steps: step 1, a free mode test of a hinge-containing structure is developed, a CBUSH unit is used for simulating spherical hinge connection, and a correction model of the hinge-containing structure is established; step 2, describing interval rigidity of spherical hinge connection by adopting an interval model, carrying out normalization processing on the interval rigidity, constructing a complete second-order polynomial response surface model of the interval rigidity, constructing an optimized objective function through the deviation of a response surface value and a modal test value, and identifying the rigidity of the interval containing a hinge structure; the modal test values include a natural frequency and a modal shape. The method utilizes the interval model to describe the uncertainty of the spherical hinge connection, combines the complete second-order polynomial response surface model to optimize the interval rigidity of the hinge-containing structure, and is convenient and accurate.

Description

Method for identifying rigidity of hinge-structure-containing interval based on response surface model
Technical Field
The invention relates to a method for identifying parameters containing a hinge structure, in particular to a method for identifying rigidity of an interval containing the hinge structure based on a complete second-order polynomial response surface model.
Background
With the rapid development of aerospace industry, deployable structures have been widely used in space missions, such as solar sails, solar arrays, and space antenna support mechanisms.
The components of the expandable structure are connected through hinges, and due to the simultaneous existence of the stay cable, the spherical hinge and the like, the complexity of structural dynamics analysis is increased, so that the research on the dynamics characteristics of the hinge structure is very important. The spherical hinge mechanism integrates the auxiliary function of the movable mechanism and the connecting function, and the connecting rigidity of the hinge is highly uncertain due to various factors such as clearance, slippage, elastic contact and the like. The main working state of the expandable structure is considered to be after the expandable structure is unfolded and locked, the influence of factors such as a zipper, a driving device and the like is omitted, and the main source of uncertainty of the expandable structure is the spherical hinge connecting part. The interval model is a method commonly used in engineering to describe the problem of structural uncertainty, but in the process of identifying the interval rigidity of the spherical hinge, the optimization of the interval rigidity needs to be realized by using more numerical simulation correction methods.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a hinge structure-containing interval rigidity identification method based on a complete second-order polynomial response surface model, which utilizes the interval model to describe the uncertainty of spherical hinge connection and combines the complete second-order polynomial response surface model to optimize the interval rigidity of a hinge structure.
In order to solve the problems of the prior art, the invention adopts the technical scheme that:
a rigidity identification method for hinge-containing structure intervals based on a complete second-order polynomial response surface model comprises the following steps:
step 1, a free mode test of a hinge-containing structure is developed, a CBUSH unit is used for simulating spherical hinge connection, and a correction model of the hinge-containing structure is established;
step 2, describing interval rigidity of spherical hinge connection by adopting an interval model, carrying out normalization processing on the interval rigidity, constructing a complete second-order polynomial response surface model of the interval rigidity, constructing an optimized objective function through the deviation of a response surface value and a modal test value, and identifying the rigidity of the interval containing a hinge structure; the modal test values include a natural frequency and a modal shape.
The improvement is that the establishment of the correction model of the hinge-containing structure in the step 1 comprises the following steps:
the method comprises the following steps that firstly, a free mode test is developed by adopting a single-point vibration pickup test method, and the natural frequency and the mode vibration mode of the free mode of the hinge-containing structure are measured;
and secondly, selecting a beam unit, adding mass blocks at corresponding angle ends, simulating spherical hinge connection by using a spring damping connection CBUSH unit in Patran/Nastran, and establishing a correction model containing a hinge structure.
As an improvement, the step 2 of identifying the rigidity of the hinge structure-containing interval comprises the following steps:
step i, selecting the three-way translational rigidity of the CBUSH unit as an equivalent rigidity Ke＝K1＝K2＝K3And three rotational rigidities are added for correction,describing interval rigidity of the spherical hinge connection by adopting an interval model, and assuming a value range of the interval rigidity;
step ii, calculating the frequency of a sample point of a correction model of the hinge-containing structure, extracting the inherent frequency of the corresponding mode shape through matching the mode shape with the MAC value of the simulation mode shape, and eliminating jump step frequencies in all samples after the samples are obtained according to full factor test design and calculation, wherein the simulation model is a finite element model of the hinge-containing structure;
step iii, carrying out design parameter normalization processing on the equivalent stiffness and the three rotational stiffnesses, wherein the ith interval stiffness xiHas a value range of [ xi l,xi u]Then the normalized variable is
Figure BDA0001649234910000021
Step iv, constructing a complete second-order polynomial response surface model of interval rigidity through normalization processing, and using a complex correlation coefficient R2And a modified complex correlation coefficient Radj 2And (3) checking the fitting accuracy of the modal test value, and finally optimizing the value range of the spherical hinge connection rigidity by a step-by-step correction method, wherein the input-output relationship of the complete second-order polynomial response surface model description system is
Figure BDA0001649234910000022
Formula (III) β0，βiAnd βijConstant term, primary term and secondary term coefficient of the response surface model respectively; epsilon is the error of the response surface model;
and v, continuously optimizing iteration and adjusting the initial value-taking interval until the corrected interval rigidity and the rigidity actually measured by the free mode reach satisfactory precision.
In a further improvement, a complex correlation coefficient R is used in said step iv2And a modified complex correlation coefficient Radj 2Checking the fitting precision of the modal test value, and judging whether a fitted response surface model is availableReliable, complex correlation coefficient R2The evaluation criterion is defined as
Figure BDA0001649234910000031
Wherein SSY is the sum of the squares of the differences between the response values and the response mean values; SSE is the sum of the squares of the differences between the response values and the response estimate values; SSR is the sum of squares of the difference between the response estimation value and the response mean value, and the expressions are respectively
Figure BDA0001649234910000032
Figure BDA0001649234910000033
Figure BDA0001649234910000034
Where n is the number of trials, the superscript (l) indicates the first trial,
Figure BDA0001649234910000035
mean, y, of n test responseseIn order to test the column vector of the response,
Figure BDA0001649234910000036
for the response surface function, I (1, n) is a unit column vector of 1 × n; defined modified complex correlation coefficient Radj 2Is composed of
Figure BDA0001649234910000037
As an improvement, the step iv of determining the intermediate value of the interval stiffness and the interval radius by a step correction method comprises the following steps:
a, constructing an objective function of the residual error between the midpoint value of the test result and the calculated value interval of the response surface model, and correcting the midpoint value of the parameters by adopting a genetic algorithm, wherein the objective function defined by the midpoint value is
Figure BDA0001649234910000038
b, constructing an objective function of the residual error between the test result interval and the calculated value interval
Figure BDA0001649234910000041
r(ΔpI) Calculating a value interval by combining the uncertainty parameter interval radius and a response surface and a Monte Carlo method, wherein a parameter sample for calculating the response interval in the iteration process is pc+samples×r(ΔpI) Wherein p iscFor the corrected parameter midpoint values in step a, the samples are of sufficient number and obey [ -1,1 [ ]]Uniformly distributed samples; calculating the response interval after iteration to meet the precision, and obtaining the interval radius r (delta p) of the corrected parameterI)。
It is further preferred that in the step iv, a complex correlation coefficient is used to determine whether the fitted response surface model is reliable, wherein the complex correlation coefficient R2The value interval is [0,1 ]]The closer to 1, the smaller the error is, namely the more accurate the response surface model is; if R is2When the number is equal to 1, the sample points are all located on the curved surface determined by the regression equation; modified complex correlation coefficient Radj 2The influence of m on the number of terms of the response surface model can be considered, and when the number of terms is increased, Radj 2Not necessarily increased, so the response surface accuracy with different regression models can be compared; if R isadj 2And R2If the difference is large, the response surface model has unimportant items, and the step-by-step regression method can be adopted to remove redundant items.
Has the advantages that:
compared with the prior art, the hinge-structure-containing interval rigidity identification method based on the complete second-order polynomial response surface model has the advantages that the precision can be guaranteed, and meanwhile, the calculation efficiency is high; meanwhile, the uncertainty of the structure is described by adopting an interval model, a large amount of test data is not needed for supporting, and only the upper and lower bounds of uncertain parameters are required to be given, so that the method is convenient to realize.
Drawings
FIG. 1 is a detailed flow chart of a rigidity identification method of an interval containing hinge structures based on a complete second-order polynomial response surface model;
FIG. 2 is a multi-frame truss structure used in example 1 of the present invention;
FIG. 3 is a graph of excitation point distribution;
FIG. 4 is a spherical hinge connection model;
fig. 5 is a comparison of the natural frequency range before and after identification with the test sample.
Detailed Description
The fermentation process of the present invention is described and illustrated in detail below with reference to specific examples. The content is to explain the invention and not to limit the scope of protection of the invention.
As shown in fig. 2, taking a multi-frame aluminum truss structure as an example, interval stiffness identification considering uncertainty of hinge connection stiffness is performed. The number of the corner blocks of the truss is 52, the number of the cross rods is 48, the total length is 36m, and the total mass is 13.8 kg. The excitation point in fig. 3 is a point where the load is applied in the mode test.
The invention relates to a method for identifying rigidity of an interval containing a hinge structure based on a complete second-order polynomial response surface model, which comprises the following steps of:
step 1, a free modal test of a multi-frame truss is unfolded, and a CBUSH unit is used for establishing a correction model of a unit truss basically comprising a hinge structure as shown in figure 2;
step 1.1: according to the multi-frame truss shown in fig. 2, a free mode test is developed by adopting a single-point vibration pickup test method to obtain the first seven-order and first six-order natural frequency mode arrays.
Step 1.2: selecting beam units to establish a correction model of a multi-frame truss structure, simulating spherical hinge connection by using CBUSH units, and defining a six-direction stiffness value between two nodes connected by the units by editing cards, wherein the six-direction stiffness comprises stiffness (K) in three translation directions1、K2、K3) And three rotation directions (K)4、K5、K6) The three translation directions respectively represent translation along x, y and z axes, the three rotation directions respectively represent rotation around the x, y and z axes, and mass blocks are added at corresponding corner ends.
Step 2: the interval stiffness of the spherical hinge connection is described by adopting an interval model, the interval stiffness is normalized, a complete second-order polynomial response surface model of the interval stiffness is constructed, an optimized objective function is constructed through the deviation of a response surface value and a modal test value, and the stiffness of the interval containing the hinge structure is identified.
Step 2.1: considering that the uncertainty of the aluminum material is small, the uncertainty of the spherical hinge connection rigidity of the truss structure is considered to cause the difference of the inherent frequency of the truss structure, and the CBUSH three-dimensional translational rigidity is selected as an equivalent parameter number Ke＝K1＝K2＝K3Correcting by adding three rotational rigidities, describing uncertainty of spherical hinge connection rigidity by adopting an interval model, and describing spherical hinge connection rigidity Ke、K4、K5、K6Is [0.1,2.1 ] respectively]×2627668.31、[0.1,2.1]×833.93、[0.1,2.1]×175.54、[0.1,2.1]×2.51。
Step 2.2: calculating the modal frequency of a sample point of a correction model of a hinge-containing structure, extracting the inherent frequency of a corresponding array form through matching the modal vibration form with the MAC value of a simulation array form, and eliminating the jump step frequency in all samples after the samples are obtained according to full factor test design and calculation, wherein the simulation model is a finite element model of the hinge-containing structure.
Step 2.3: carrying out design parameter normalization processing on equivalent stiffness and three rotational stiffness, wherein the ith interval stiffness xiHas a value range of [ xi l,xi u]Then the normalized variables are:
Figure BDA0001649234910000061
step 2.4: through normalization processing, a complete second-order polynomial response surface model of interval rigidity is constructed, and a complex correlation coefficient R is used2And a modified complex correlation coefficient Radj 2And (3) checking the fitting accuracy of the modal test value, and finally optimizing the value range of the spherical hinge connection rigidity by a step-by-step correction method, wherein the input-output relationship of the complete second-order polynomial response surface model description system is
Figure BDA0001649234910000062
Formula III β0，βiAnd βijConstant term, primary term and secondary term coefficient of the response surface model respectively; ε is the error of the surrogate model. Wherein, in step 2.4, the complex correlation coefficient R is used2And a modified complex correlation coefficient Radj 2And (3) testing the fitting accuracy of the two standards to the sample data, and judging whether the fitted response surface model is credible or not, wherein the specific operation is as follows: multiple correlation coefficient R2The evaluation criterion is defined as
Figure BDA0001649234910000063
Wherein SSY is the sum of the squares of the differences between the response values and the response mean values; the sum of the squares of the SSE response value and the response estimate value differences; SSR is the sum of squares of the difference between the response estimation value and the response mean value, and the expressions are respectively
Figure BDA0001649234910000064
Figure BDA0001649234910000065
Figure BDA0001649234910000066
Where n is the number of trials, the superscript (l) indicates the first trial,
Figure BDA0001649234910000067
mean, y, of n test responseseIn order to test the column vector of the response,
Figure BDA0001649234910000068
for the response surface function, I (1, n) is a unit column vector of 1 × n;
a modified complex correlation coefficient defined as
Figure BDA0001649234910000071
Wherein the complex correlation coefficient R2The value interval is [0,1 ]]Closer to 1 indicates less error, i.e., more accurate surrogate model. If R is2When the number is equal to 1, the sample points are all located on the curved surface determined by the regression equation; modified complex correlation coefficient Radj 2The influence of m on the number of terms of the response surface model can be considered, and when the number of terms is increased, Radj 2Not necessarily increased, and therefore the response surface accuracy with different regression models may be compared. If R isadj 2And R2If the difference is large, the response surface approximation model is indicated to have unimportant terms, and a stepwise regression method can be adopted to remove redundant terms. The response surface model test is shown in the following table.
TABLE 1 response surface model test
Figure BDA0001649234910000072
In the step 2.4, the value range of the spherical hinge connection stiffness is optimized by a distribution correction method, and the method specifically comprises the following steps: a, constructing an objective function of a residual error between a midpoint value of a test result and a calculated value interval of a response surface model, and correcting the midpoint value of a parameter by adopting a genetic algorithm, wherein the objective function defined by the midpoint value is
Figure BDA0001649234910000073
b constructing an objective function of the residual between the test result interval and the calculated value interval
Figure BDA0001649234910000074
r(ΔpI) The uncertainty parameter interval radius. The calculation value interval is obtained by combining the response surface and a Monte Carlo method, and the parameter sample of the calculation response interval in the iteration process is pc+samples×r(ΔpI) Wherein p iscFor the corrected parameter midpoint value of step a, sampleThe points are of sufficient number and obey [ -1,1 [ ]]Uniformly distributed samples; calculating the response interval after iteration to meet the precision, and obtaining the interval radius r (delta p) of the corrected parameterI)；
Step 2.5: the initial value range is continuously optimized and adjusted in an iterative mode until the corrected range parameter and the test result range reach satisfactory precision, the range rigidity obtained by final recognition is shown in the following table, and the range of the inherent frequency before and after recognition is compared with the test sample as shown in fig. 5.
Table 2 identified parameter value intervals
Figure BDA0001649234910000081
The hinge-structure-containing interval rigidity identification method based on the complete second-order polynomial response surface model has the advantages that the precision can be guaranteed, and meanwhile, the calculation efficiency is high; meanwhile, the uncertainty of the structure is described by adopting an interval model, a large amount of test data is not needed for supporting, and only the upper and lower bounds of uncertain parameters are required to be given, so that the method is convenient to realize.

Claims (4)

1. A rigidity identification method for an articulated structure-containing interval based on a response surface model is characterized by comprising the following steps: step 1, unfolding a free modal test of a hinge-containing structure, unfolding the free modal test by adopting a single-point vibration pickup test method, measuring the natural frequency and the modal vibration mode of the free modal of the hinge-containing structure, selecting a beam unit, adding a mass block at a corresponding angle end, simulating spherical hinge connection by utilizing a spring damping connection CBUSH unit in Patran/Nastran, and establishing a correction model of the hinge-containing structure; step 2, describing interval rigidity of spherical hinge connection by adopting an interval model, carrying out normalization processing on the interval rigidity, constructing a complete second-order polynomial response surface model of the interval rigidity, constructing an optimized objective function through the deviation of a response surface value and a modal experiment value, and identifying the rigidity of the interval containing a hinge structure; the modal test value comprises a natural frequency and a modal shape; the step 2 of identifying the rigidity of the hinge structure-containing interval comprises the following steps: step i, selecting the three-way translational rigidity of the CBUSH unit as an equivalent rigidityKe＝K1＝K2＝K3Correcting by adding three rotational rigidities, describing interval rigidity of spherical hinge connection by adopting an interval model, and assuming a value range of the interval rigidity; step ii, calculating the modal frequency of a sample point of a correction model of the hinge-containing structure, extracting the inherent frequency of the corresponding mode through matching the modal mode and the MAC value of the simulated mode, and eliminating jump step frequencies in all samples after designing and calculating the samples according to a full-factor test, wherein the simulated model is a finite element model of the hinge-containing structure; step iii, carrying out design parameter normalization processing on the equivalent stiffness and the three rotational stiffnesses, wherein the ith interval stiffness xiHas a value interval of
Figure FDA0002312579680000011
The normalized variable is
Figure FDA0002312579680000012
(ii) a Step iv, constructing a complete second-order polynomial response surface model of interval rigidity through normalization processing, and using a complex correlation coefficient R2And a modified complex correlation coefficient Radj 2And (3) checking the fitting accuracy of the modal test value, and finally optimizing the value range of the spherical hinge connection rigidity by a step-by-step correction method, wherein the input-output relationship of the complete second-order polynomial response surface model description system is
Figure FDA0002312579680000013
In the formula, β0，βiAnd βijConstant terms, primary terms and secondary term coefficients of the response surface model are respectively included, epsilon is the error of the response surface model, and the iteration and the initial value interval are continuously optimized and adjusted until the corrected interval stiffness and the stiffness actually measured by the free mode reach satisfactory accuracy.
2. The method for identifying the rigidity of the hinge-containing structure interval based on the response surface model as claimed in claim 1, wherein the method is characterized in thatSaid step iv using a complex correlation coefficient R2And a modified complex correlation coefficient Radj 2Checking the fitting precision of the modal test value, and judging whether the fitted response surface model is credible; multiple correlation coefficient R2The evaluation criterion is defined as
Figure FDA0002312579680000021
Wherein SSY is the sum of the squares of the differences between the response values and the response mean values; SSE is the sum of the squares of the differences between the response values and the response estimate values; SSR is the sum of squares of the difference between the response estimation value and the response mean value, and the expressions are respectively
Figure FDA0002312579680000022
Figure FDA0002312579680000023
Figure FDA0002312579680000024
Where n is the number of trials, the superscript (l) indicates the first trial,
Figure FDA0002312579680000025
mean, y, of n test responseseIn order to test the column vector of the response,
Figure FDA0002312579680000026
for the response surface function, I (1, n) is a unit column vector of 1 × n; defined modified complex correlation coefficient Radj 2Is composed of
Figure FDA0002312579680000027
3. The method for identifying the rigidity of the hinge-containing structure interval based on the response surface model as claimed in claim 1, wherein the step iv is performed by stepsThe correction method optimizes the value interval of the spherical hinge connection rigidity, and comprises the following steps: a, constructing an objective function of the residual error between the midpoint value of the test result and the calculated value interval of the response surface model, and correcting the midpoint value of the parameters by adopting a genetic algorithm, wherein the objective function defined by the midpoint value is
Figure FDA0002312579680000028
b, constructing an objective function of the residual error between the test result interval and the calculated value interval
Figure FDA0002312579680000031
r(ΔpI) Calculating a value interval by combining the uncertainty parameter interval radius and a response surface and a Monte Carlo method, wherein a parameter sample for calculating the response interval in the iteration process is pc+samples×r(ΔpI) Wherein p iscFor the corrected parameter midpoint values in step a, the samples are of sufficient number and obey [ -1,1 [ ]]Uniformly distributed samples; calculating the response interval after iteration to meet the precision, and obtaining the interval radius r (delta p) of the corrected parameterI)。
4. The method for identifying rigidity of interval containing hinge structure based on response surface model as claimed in claim 1, wherein in the step iv, a complex correlation coefficient is used to determine whether the fitted response surface model is credible, wherein the complex correlation coefficient R2The value interval is [0,1 ]]The closer to 1, the smaller the error is, namely the more accurate the response surface model is; if R is2When the number is equal to 1, the sample points are all located on the curved surface determined by the regression equation; modified complex correlation coefficient Radj 2The influence of m on the number of terms of the response surface model can be considered, and when the number of terms is increased, Radj 2Not necessarily increased, so the response surface accuracy with different regression models can be compared; if R isadj 2And R2If the difference is large, the response surface model has unimportant items, and the step-by-step regression method can be adopted to remove redundant items.
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