CN117171957B - Boom cable force identification method based on dung beetle search algorithm under different boundaries - Google Patents
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Abstract
The invention relates to a boom cable force identification method based on a dung beetle search algorithm under different boundaries, which comprises the following steps of S1, selecting corresponding boundary conditions according to design data in bridge formation, selecting corresponding elastic rotation stiffness value k 1、k2, and approximately selecting an implicit function frequency equation under the boundary; s2, taking a cable length l, a linear density m, a first-order frequency f 1 and a second-order frequency f 2 as input units, taking a cable force T, bending stiffness EI and an elastic rotation stiffness value k 1、k2 as input values to be brought into a formula (1), obtaining a frequency value under the randomly generated numerical value, and finally generating an initial matrix formed by n vectors; s3, taking an initial matrix generated by the n vectors as an initial population of a dung beetle search algorithm. The method provided by the invention can construct a multi-parameter identification frame such as the cable force of the hanging rod by utilizing the frequency matrix under the elastic boundary deduced by the vibration method, and obtain an accurate cable force value through intelligent identification.
Description
Technical Field
The invention belongs to the technical field of bridge health detection and monitoring, and particularly relates to a boom cable force identification method based on a dung beetle search algorithm under different boundaries.
Background
The state of the suspender is directly related to whether the suspender system bridge can work safely, and the safety and the durability of many bridges are not fully considered at the beginning of design, or are limited by technical and economic reasons, so that the heavy economic cost is paid in the operation and maintenance process, and serious engineering accidents sometimes occur, thereby causing bad social influence. Bridge accidents due to the breaking of the boom have been more numerous during the past 60 years. Therefore, accurate recognition of the boom cable force value is a key for avoiding damage to the boom system bridge.
With the continuous application of the dung beetle search algorithm in the traditional industry fields of civil engineering, machinery and the like, the difficult problem of complex multi-element nonlinear optimization is solved, but the hidden equation of the boom under a boundary condition is complex and single in multi-parameter identification through the dung beetle search algorithm.
Disclosure of Invention
First, the technical problem to be solved
Aiming at the existing technical problems, the invention provides a crane jib cable force identification method based on a dung beetle search algorithm under different boundaries, which can construct a crane jib cable force and other multi-parameter identification frame by utilizing a frequency matrix under an elastic boundary deduced by a vibration method, and obtain an accurate cable force value through intelligent identification.
(II) technical scheme
In order to achieve the above purpose, the main technical scheme adopted by the invention comprises the following steps:
The boom cable force identification method S1 based on the dung beetle search algorithm under different boundaries selects corresponding boundary conditions according to design data in bridge formation, selects corresponding elastic rotation stiffness values k 1、k2, and approximately selects an implicit function frequency equation under the boundary; s2, taking a cable length l, a linear density m, a first-order frequency f 1 and a second-order frequency f 2 as input units, taking a cable force T, bending stiffness EI and an elastic rotation stiffness value k 1、k2 as input values to be brought into a formula (1), obtaining a frequency value under the randomly generated numerical value, and finally generating an initial matrix formed by n vectors; s3, taking an initial matrix generated by n vectors as an initial population of a dung beetle search algorithm, establishing n-order frequency and actual measurement frequency of a suspender by using a frequency equation, carrying the n-order frequency and the actual measurement frequency into a formula (2) to calculate a fitness value of the suspender, and finally finding out the minimum fitness value to serve as a parameter solution vector to be identified; s4, iteration is continuously carried out, and the cable force T, the bending stiffness EI and the elastic rotation stiffness value k 1、k2 are output after the iteration convergence criterion is met;
Wherein: g is a determinant value of adequate requirements when A 1、A2、A3、A4 is not 0;
Wherein: And f j is the correspondence between the actual measurement of the boom and the identification value of the parameter.
Preferably, the S1 further includes:
① Selecting corresponding boundary conditions according to the design boundary conditions during bridging;
② The elastic rotational stiffness values k 1 and k 2 under the corresponding boundary conditions are selected.
Preferably, when the two ends are at the hinge boundary, k 1＝k2 =0;
When the fixed connection boundary is positioned, k 1＝k2 is = infinity;
when both ends are at elastic boundaries, k 1、k2 needs to be identified.
Preferably, the S2 further includes:
① Taking the cable length l, the linear density m, the first-order frequency f 1 and the second-order frequency f 2 as input units, taking the cable force T, the bending stiffness EI and the elastic rotation stiffness value k 1、k2 as input values to be brought into a formula (1), and solving a determinant frequency value when G=0 based on a numerical analysis dichotomy;
② The random cable length l, the linear density m, the first-order frequency f 1 and the second-order frequency f 2 are used as input units, the cable force T, the bending stiffness EI, the elastic rotation stiffness value k 1、k2 and corresponding frequency values, and are used as an initial matrix formed by n vectors.
Preferably, the step S3 further includes:
① Parameters of the dung beetle search algorithm are set as follows: nPop =50 (initial population), rd=0.2 (ball dung beetle ratio), bd=0.2 (dancing dung beetle ratio), sm=0.25 (propagation dung beetle ratio), td=0.35 (theft dung beetle ratio);
② Taking the n-dimensional matrix as an initial population of a dung beetle search algorithm;
③ And carrying out iterative updating on the initial population according to an updating strategy of the dung beetle searching algorithm.
Preferably, the S4 further includes:
① Judging whether the iteration times meet the maximum convergence times, if not, continuing to update the iteration, and if so, outputting an optimal result.
(III) beneficial effects
The beneficial effects of the invention are as follows: the crane jib cable force identification method based on the dung beetle search algorithm under different boundaries has the following beneficial effects:
(1) The matrix frequency equation is obtained by adjusting the elastic rotation stiffness value, so that any one of the boom boundary conditions without a shock absorber can be approximately simulated, and the analytic solution of the implicit equation under different boundary conditions is replaced.
(2) The dung beetle search algorithm greatly improves the cable force recognition efficiency, and the error is controlled within 2 percent, so that the method has the potential and wide application prospect of in-depth discussion in the aspects of boom state monitoring and health management in the field of cable bridge engineering.
Drawings
FIG. 1 is a diagram of a boom cable multiple parameter identification framework of the present invention;
FIG. 2 is a diagram illustrating the process of identifying the forces of a virtual boom cable at the hinge boundary in accordance with the present invention;
FIG. 3 is a diagram illustrating the process of identifying the elastic boundary virtual boom cable force according to the present invention;
FIG. 4 is a diagram illustrating the process of identifying the cable force of a virtual boom at a consolidation boundary in accordance with the present invention;
FIG. 5 is a graph of the time and error required for identifying the virtual boom cable force according to the present invention;
FIG. 6 is a diagram illustrating the measured boom data cable force identification process of the present invention.
Detailed Description
The invention will be better explained by the following detailed description of the embodiments with reference to the drawings.
1-6, In this embodiment, a boom cable force identification method S1 based on a dung beetle search algorithm under different boundaries is disclosed, corresponding boundary conditions are selected according to design data during bridge formation, corresponding elastic rotation stiffness values k 1、k2 are selected, and an implicit function frequency equation under the boundary is approximately selected; s2, taking a cable length l, a linear density m, a first-order frequency f 1 and a second-order frequency f 2 as input units, taking a cable force T, bending stiffness EI and an elastic rotation stiffness value k 1、k2 as input values to be brought into a formula (1), obtaining a frequency value under the randomly generated numerical value, and finally generating an initial matrix formed by n vectors; s3, taking an initial matrix generated by n vectors as an initial population of a dung beetle search algorithm, establishing n-order frequency and actual measurement frequency of a suspender by using a frequency equation, carrying the n-order frequency and the actual measurement frequency into a formula (2) to calculate a fitness value of the suspender, and finally finding out the minimum fitness value to serve as a parameter solution vector to be identified; s4, iteration is continuously carried out, and the cable force T, the bending stiffness EI and the elastic rotation stiffness value k 1、k2 are output after the iteration convergence criterion is met;
Wherein: g is a determinant value of adequate requirements when A 1、A2、A3、A4 is not 0;
Wherein: And f j is the correspondence between the actual measurement of the boom and the identification value of the parameter.
In detail, the S1 further includes:
① Selecting corresponding boundary conditions according to the design boundary conditions during bridging;
② The elastic rotational stiffness values k 1 and k 2 under the corresponding boundary conditions are selected.
For example, when the two ends are at a hinge boundary, k 1＝k2 =0;
When the fixed connection boundary is positioned, k 1＝k2 is = infinity;
when both ends are at elastic boundaries, k 1、k2 needs to be identified.
In detail, the S2 further includes:
① Taking the cable length l, the linear density m, the first-order frequency f 1 and the second-order frequency f 2 as input units, taking the cable force T, the bending stiffness EI and the elastic rotation stiffness value k 1、k2 as input values to be brought into a formula (1), and solving a determinant frequency value when G=0 based on a numerical analysis dichotomy;
② The random cable length l, the linear density m, the first-order frequency f 1 and the second-order frequency f 2 are used as input units, the cable force T, the bending stiffness EI, the elastic rotation stiffness value k 1、k2 and corresponding frequency values, and are used as an initial matrix formed by n vectors.
In detail, the S3 further includes:
① Parameters of the dung beetle search algorithm are set as follows: nPop =50 (initial population), rd=0.2 (ball dung beetle ratio), bd=0.2 (dancing dung beetle ratio), sm=0.25 (propagation dung beetle ratio), td=0.35 (theft dung beetle ratio);
② Taking the n-dimensional matrix as an initial population of a dung beetle search algorithm;
③ And carrying out iterative updating on the initial population according to an updating strategy of the dung beetle searching algorithm.
In detail, the S4 further includes:
① Judging whether the iteration times meet the maximum convergence times, if not, continuing to update the iteration, and if so, outputting an optimal result.
In order to more clearly illustrate the solution in this embodiment, the following description is made by way of example, and the data listed in this description belong to the protection scope of the present invention.
The first step: according to boom data in a large number of existing texts, 5 pieces of virtual boom data are selected as identification samples under each boundary condition;
And a second step of: using Matlab programming, taking a boom 1 under a hinged boundary condition as an example, inputting m=56.2, l=3, a corresponding rotational stiffness value k 1＝k2 =0, a corresponding first-order frequency f 1 =30 and a second-order frequency f 2 =92, substituting the values into a frequency matrix equation (the recognition can be completed only by the second-order frequency under the hinged boundary and the consolidation boundary, and the recognition can be completed only by the fifth-order frequency under the elastic boundary);
Thirdly, generating 50 initial populations through a frequency matrix equation;
fourth step: substituting a dung beetle search algorithm program based on Matlab to carry out iterative calculation;
fifth step: judging whether the iteration times reach the preset times, if not, continuing to iterate to the maximum iteration times and outputting a corresponding result.
The cable force identification is completed for 15 virtual booms, the cable force identification process is shown in fig. 2, and the time and error percentage required for cable force completion are shown in fig. 3 and 4. Statistics of prediction errors show that the maximum error is not more than 1%, the minimum error is 0.1%, and the frame model effect of identifying cable force parameters based on a dung beetle search algorithm is ideal, wherein the virtual suspender is shown in table 1.
Table 1 virtual boom parameters
The reliability of the boom is further verified by carrying out cable force identification on the boom which is actually measured, the accurate cable force value is 1635.5kN, the linear density of the boom which is actually measured is m=45.7kg/m, the length is l=9m, the front 2-order actual measurement frequency of the boom is f 1＝12.286Hz、f2 = 26.004Hz, the specific parameters are shown in table 2, and the setting of the parameters of the dung beetle search algorithm is consistent with the foregoing.
TABLE 2 theoretical and measured data
The cable force identification value can be converged to be close to the accurate cable force value in 80-100 iteration steps, the cable force identification value is 1615kN when the iteration is performed for 100 times, and the error is 1.25%. The error is mainly caused by the fact that when the cable force of the actually measured boom is recognized, errors exist in boom parameter values, including linear density, length value errors and the like of the boom. Especially, the measurement of the first two-order frequency errors may be greatly disturbed by the external environment, and the accumulation of the errors leads to the increase of the cable force identification errors. But the identification error of the actually measured boom cable force is still less than 2%, and the requirements of actual engineering can be met.
The technical principles of the present invention have been described in connection with specific embodiments, which are provided for the purpose of explaining the principles of the present invention and are not to be construed in any way as limiting the scope of the present invention. Other embodiments of the invention will be apparent to those skilled in the art from consideration of this specification without undue burden.
Claims (6)
1. A boom cable force identification method based on a dung beetle search algorithm under different boundaries is characterized in that,
S1, selecting a corresponding boundary condition according to design data in bridge formation, selecting a corresponding elastic rotation stiffness value k 1、k2, and approximately selecting an implicit function frequency equation under the boundary;
S2, substituting the cable length l, the linear density m, the cable force T, the bending stiffness EI and the elastic rotation stiffness value k 1、k2 as input values into a formula (1) to obtain a frequency value under a randomly generated numerical value, and finally generating an initial matrix consisting of n vectors;
s3, taking an initial matrix generated by n vectors as an initial population of a dung beetle search algorithm, establishing n-order frequency and actual measurement frequency of a suspender by using a frequency equation, substituting the n-order frequency and the actual measurement frequency into a formula (2) to calculate a fitness value of the suspender, and finally finding the minimum fitness value to serve as a parameter solution vector to be identified;
S4, iteration is continuously carried out, and the cable force T, the bending stiffness EI and the elastic rotation stiffness value k 1、k2 are output after the iteration convergence criterion is met;
Wherein: a 1、A2、A3、A4 is a pending constant; k 1 is the upper end elastic rotational stiffness; k 2 is the lower end elastic rotation rigidity;
T is a cable force value; EI is the stiffness value;
Wherein: f * is the true value of the boom; f i is the ith cable force identification value of the suspension rod; n is the number of input frequencies.
2. The method of claim 1, wherein,
The S1 further includes:
① Selecting corresponding boundary conditions according to the design boundary conditions during bridging;
② The elastic rotational stiffness values k 1 and k 2 under the corresponding boundary conditions are selected.
3. The method of identification of claim 2, wherein,
When the two ends are at the hinge boundary, k 1＝k2 =0;
When the fixed connection boundary is positioned, k 1＝k2 is = infinity;
when both ends are at elastic boundaries, k 1、k2 needs to be identified.
4. The method of claim 1, wherein,
The S2 further includes:
① Taking the cable length l, the linear density m, the cable force T, the bending stiffness EI and the elastic rotation stiffness value k 1、k2 as input values to be brought into a formula (1), and solving a determinant frequency value when G=0 based on a numerical analysis dichotomy;
② The random cable length l, the linear density m, the cable force T, the bending stiffness EI, the elastic rotation stiffness value k 1、k2 and the corresponding frequency value are used as an initial matrix formed by n vectors.
5. The method of claim 1, wherein,
The step S3 further includes:
① Parameters of the dung beetle search algorithm are set as follows: initial population nPop =50, ball dung beetle ratio RD=0.2, dancing dung beetle ratio BD=0.2, propagation dung beetle ratio SM=0.25, and stealing dung beetle ratio TD=0.35;
② Taking the n-dimensional matrix as an initial population of a dung beetle search algorithm;
③ And carrying out iterative updating on the initial population according to an updating strategy of the dung beetle searching algorithm.
6. The method of claim 1, wherein,
The S4 further includes:
① Judging whether the iteration times meet the maximum convergence times, if not, continuing to update the iteration, and if so, outputting an optimal result.
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