CN112149308B - Method for quickly and automatically adjusting excitation force - Google Patents
Method for quickly and automatically adjusting excitation force Download PDFInfo
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- CN112149308B CN112149308B CN202011059206.3A CN202011059206A CN112149308B CN 112149308 B CN112149308 B CN 112149308B CN 202011059206 A CN202011059206 A CN 202011059206A CN 112149308 B CN112149308 B CN 112149308B
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- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Abstract
The invention discloses a method for quickly and automatically adjusting excitation force, which comprises the following steps: firstly, according to the characteristics of a tested structure or by using an impact force hammering method, determining the number of exciting forces and the position of an exciting point by enabling a vibration exciter to be positioned at a point where each interested order mode has enough displacement; step two, carrying out multipoint sine frequency sweep or multipoint random excitation test on the tested structure to obtain a frequency response function matrix and modal frequency of the structure; thirdly, a purity indication function is used as a fitness function in the algorithm, and a group of optimal excitation force amplitudes can be obtained after the particle swarm optimization iteration; and step four, sending the optimal excitation force amplitude to the vibration exciter to enable the vibration exciter to quickly and automatically adjust the excitation force. The invention provides a new method for quickly and automatically adjusting exciting force in a modal test, which uses an optimization algorithm to realize the automatic adjustment of exciting force, the force adjustment process is simple, and the test time is greatly shortened.
Description
Technical Field
The application relates to the technical field of automatic adaptive exciting force in pure modal tests, in particular to a method for quickly and automatically adapting exciting force.
Background
The automatic adjustment of the exciting force in the pure modal test is always a difficult problem, and the traditional Dark method and the like cannot solve the problem of the automatic adjustment of the exciting force in the pure modal test of a large complex structure because the optimal distribution of the exciting force cannot be searched globally.
The method for adjusting the vibration force developed based on the idea that the modal force of the adaptive mode is not zero and the modal force of the non-adaptive mode is zero is to obtain the approximate distribution of the modal shape by a frequency domain modal parameter identification method.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a novel method for quickly and automatically adjusting the exciting force in a modal test, the force adjusting process of automatically adjusting the exciting force by using an optimization algorithm is simple, and the test time is greatly shortened.
The invention relates to a method for quickly and automatically adjusting excitation force, which is characterized by comprising the following steps of:
firstly, according to the characteristics of a tested structure or by using an impact force hammering method, determining the number of exciting forces and the position of an exciting point by enabling a vibration exciter to be positioned at a point where each interested order mode has enough displacement;
step two, carrying out multipoint sine frequency sweep or multipoint random excitation test on the tested structure to obtain a frequency response function matrix and modal frequency of the structure;
thirdly, a purity indication function is used as a fitness function in the algorithm, and a group of optimal excitation force amplitudes can be obtained after the particle swarm optimization iteration;
step four, the optimal excitation force amplitude is sent to the vibration exciter, so that the vibration exciter can quickly and automatically adjust the excitation force;
the automatic excitation force optimization based on the particle swarm optimization specifically comprises the following steps: setting the number of exciting forces in a test as d, and setting the number of exciting force vectors of each group in an optimization algorithm as m; each group of exciting force vector is F ═ F1，F2，…，Fm) (ii) a Single excitation force vector is Fi＝(fi，1，fi，2，…，fi，d) (ii) a Velocity vector corresponding to excitation force vector is Vi＝(vi，1，vi，2，…，vi，d) (ii) a The excitation force vector only corresponds to a pure mode indication function value P ═1，P2，…，Pm) Wherein the optimal excitation force vector is Pi＝(pi，1，pi，2，…，pi，d) (ii) a The global optimal excitation force vector is Pg＝(pg，1，pg，2，…，pg，d) (ii) a Each generation of excitation force vector update and corresponding velocity update is as follows:
vi，j(t+1)＝vi，j(t)+c1r1[Pi，j-fi，j(t)]+c2r2[Pg，j-fi，j(t)]
fi，j(t+1)＝fi，j(t)+vi，j(t+1)，j＝1，…，d
fi，j(t) is the exciting force vector at the moment t; v. ofi，j(t) is the speed corresponding to the exciting force vector at the moment t; f. ofi，j(t +1) is an exciting force vector at the moment (t + 1); v. ofi，j(t +1) is the speed corresponding to the excitation force vector at the moment (t + 1);
c1and c2A learning factor that is a non-negative constant; r is1And r2Are mutually independent pseudo-random numbers; d is the number of exciting forces in the modal test; pi，jThe optimal excitation force vector at the moment t; pg，jSetting an optimal excitation force vector for all excitation force vectors until the moment t;
and obtaining the optimal excitation force vector through the iteration of an automatic optimization algorithm.
Further, the differential equation of vibration of the structure under test is expressed as follows
Wherein M, C and K are a mass matrix, a damping matrix and a rigidity matrix of the tested structure respectively; { x (t) } and { f (t) } are respectively the displacement vector of the structure under test and the simple harmonic excitation to which the system is subjected.
Further, the second step specifically includes the following steps:
step 2.1, the system is set to be subjected to simple harmonic excitation
{f(t)}＝Fejωt
In the formula: f is an exciting force amplitude array;
the displacement vector of the system can be expressed as
{x(t)}＝X(ω)ejωt
In the formula: x (omega) is the frequency spectrum of the system displacement;
step 2.2, substituting the system displacement expression into the vibration differential equation to obtain a system displacement frequency spectrum:
X(ω)＝(K-ω2M+jωC)-1·F＝H(ω)·F
wherein the frequency response function is H (omega) ═ K-omega2M+jωC)-1。
Further, the purity indication function in the third step is as follows:
as a preferable selection, the particle swarm algorithm in step three has the characteristics of intuitive background, simplicity and easy implementation, and wide adaptability to different types of functions, and is often used for optimizing complex nonlinear functions, combinatorial optimization and the like.
The particle swarm optimization is used for the automatic excitation force optimization in the patent and specifically comprises the following steps: setting the number of exciting forces in a test as d, and setting the number of exciting force vectors of each group in an optimization algorithm as m; each group of exciting force vector is F ═ F1，F2，…，Fm) (ii) a Single excitation force vector is Fi＝(fi，1，fi，2，…，fi，d) (ii) a Velocity vector corresponding to excitation force vector is Vi＝(vi，1，vi，2，…，vi，d) (ii) a Each excitation force vector uniquely corresponds to a pure mode indication function value P ═ P1，P2，…，Pm) Wherein the optimal excitation force vector is Pi＝(pi，1，pi，2，…，pi，d) (ii) a The global optimal excitation force vector is Pg＝(pg，1，pg，2，…，pg，d) (ii) a Each generation of excitation force vector update and corresponding velocity update is as follows:
vi，j(t+1)＝vi，j(t)+c1r1[Pi，j-fi，j(t)]+c2r2[Pg，j-fi，j(t)]
fi，j(t+1)＝fi，j(t)+vi，j(t+1)，j＝1，…，d
fi，j(t) is the exciting force vector at the moment t; v. ofi，j(t) is the speed corresponding to the exciting force vector at the moment t; f. ofi，j(t +1) is an exciting force vector at the moment (t + 1); v. ofi，j(t +1) is time (t +1)A velocity corresponding to an excitation force vector;
c1and c2A learning factor that is a non-negative constant; r is1And r2Are mutually independent pseudo-random numbers; d is the number of exciting forces in the modal test; pi，jThe optimal excitation force vector at the moment t; pg，jAnd (4) setting the optimal excitation force vector for all the excitation force vectors until the moment t. And obtaining the optimal excitation force vector through the iteration of an automatic optimization algorithm.
Compared with the prior art, the method for quickly and automatically adjusting the excitation force has the following beneficial effects: the force adjusting process in the pure mode test is simpler, and the exciting force amplitude which enables the pure mode indicating function to be very high can be obtained in a short time.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the present invention will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without inventive labor.
FIG. 1 is a schematic diagram of simulation structure meshing.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The method is explained in detail by the simulation of the double U-shaped beam and the attached drawings as follows:
when the number of the exciting forces of the tested structure and the positions of the exciting points are determined, a group of exciting force amplitudes must exist in the exciting force amplitude combination in the range of the vibration exciter, so that the purity indicating function reaches the maximum value. The method provided by the invention is to use an optimization algorithm to perform optimization in the amplitude and phase combination of the exciting force so as to realize automatic adjustment of the exciting force.
The invention relates to a method for quickly and automatically adjusting excitation force, which comprises the following steps:
firstly, according to the characteristics of a tested structure or by using an impact force hammering method, determining the number of exciting forces and the position of an exciting point by enabling a vibration exciter to be positioned at a point where each interested order mode has enough displacement;
step two, carrying out multipoint sine frequency sweep or multipoint random excitation test on the tested structure to obtain a frequency response function matrix and modal frequency of the structure;
thirdly, a purity indication function is used as a fitness function in the algorithm, and a group of optimal excitation force amplitudes can be obtained after the particle swarm optimization iteration;
and step four, sending the optimal excitation force amplitude to the vibration exciter to enable the vibration exciter to quickly and automatically adjust the excitation force.
Wherein the differential equation of vibration of the structure under test is expressed as follows
Wherein M, C and K are a mass matrix, a damping matrix and a rigidity matrix of the tested structure respectively; { x (t) } and { f (t) } are the displacement vector of the structure under test and the external force vector acting on the structure, respectively.
Further, the second step specifically includes the following steps:
step 2.1, the system is excited by simple harmonic as
{f(t)}＝Fejωt
In the formula: f is an excitation force amplitude array, and the steady-state response of the system can be expressed as
{x(t)}＝X(ω)ejωt
In the formula: x (omega) is a steady-state response amplitude array;
step 2.2, substituting the steady state response into the vibration differential equation to obtain a system response:
X(ω)＝(K-ω2M+jωC)-1·F＝H(ω)·F
wherein the frequency response function is H (omega) ═ K-omega2M+jωC)-1。
Further, the purity indication function in the third step is as follows:
as a preferable selection, the particle swarm algorithm in step three has the characteristics of intuitive background, simplicity and easy implementation, and wide adaptability to different types of functions, and is often used for optimizing complex nonlinear functions, combinatorial optimization and the like.
The particle swarm optimization is used for the automatic excitation force optimization in the patent and specifically comprises the following steps: setting the number of exciting forces in a test as d, and setting the number of exciting force vectors of each group in an optimization algorithm as m; each group of exciting force vector is F ═ F1，F2，…，Fm) (ii) a Single excitation force vector is Fi＝(fi，1，fi，2，…，fi，d) (ii) a Velocity vector corresponding to excitation force vector is Vi＝(vi，1，vi，2，…，vi，d) (ii) a The excitation force vector only corresponds to a pure mode indication function value P ═1，P2，…，Pm) Wherein the optimal excitation force vector is Pi＝(pi，1，pi，2，…，pi，d) (ii) a The global optimal excitation force vector is Pg＝(pg，1，pg，2，…，pg，d) (ii) a Each generation of excitation force vector update and corresponding velocity update is as follows:
vi，j(t+1)＝vi，j(t)+c1r1[Pi，j-fi，j(t)]+c2r2[Pg，j-fi，j(t)]
fi，j(t+1)＝fi，j(t)+vi，j(t+1)，j＝1，…，d
fi，j(t) is the exciting force vector at the moment t; v. ofi，j(t) is the speed corresponding to the exciting force vector at the moment t; f. ofi，j(t +1) is an exciting force vector at the moment (t + 1); v. ofi，j(t +1) is the speed corresponding to the excitation force vector at the moment (t + 1);
c1and c2A learning factor that is a non-negative constant; r is1And r2Are mutually independent pseudo-random numbers; d is the number of exciting forces in the modal test; pi，jThe optimal excitation force vector at the moment t; pg，jAnd (4) setting the optimal excitation force vector for all the excitation force vectors until the moment t. And obtaining the optimal excitation force vector through the iteration of an automatic optimization algorithm.
Example 1
As shown in fig. 1, the measured structure provided in this example is a double U-shaped beam, which is made of steel, and has a density of 7.8, an elastic modulus of 210Gpa, and a poisson's ratio of 0.31. Its total length is 2500, height is 100, width is 100, and thickness is 10. And (3) deriving an overall mass matrix and an overall stiffness matrix of the model by using workbench, and introducing matrix data of the model and a modal damping matrix with a modal damping ratio of 0.05 into an algorithm for calculation. Since the first six-order mode of the simulation structure is a rigid body mode, we take the first five-order bending mode to verify the method.
Since we only need to obtain the ratio of the excitation forces of the excitation points, one of the excitation force amplitudes is set to 1 or-1. The results obtained with the method of this patent are as follows:
| order of mode | 1 | 2 | 3 | 4 | 5 |
| Mode frequency Hz | 7.54 | 7.68 | 10.87 | 22.22 | 33.86 |
| Indicating function T | 0.94 | 0.99 | 0.99 | 0.99 | 0.99 |
| Excitation force 1 | 1 | 1 | -1 | 1 | -1 |
| |
1.02 | -0.99 | -0.99 | -0.94 | 0.98 |
| Excitation point 1 | 7 | 7 | 4 | 15 | 7 |
| |
19 | 19 | 40 | 21 | 19 |
It can be seen that the method of the present patent can be used to quickly and automatically adjust the exciting force. And through inspection, the normalized excitation array is basically consistent with the theoretical array.
The above description is only exemplary of the present application and should not be taken as limiting the present application, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims (5)
1. A method for fast and automatic tuning of excitation forces, characterized in that the method comprises the steps of:
firstly, according to the characteristics of a tested structure or by using an impact force hammering method, determining the number of exciting forces and the position of an exciting point by enabling a vibration exciter to be positioned at a point where each interested order mode has enough displacement;
step two, carrying out multipoint sine frequency sweep or multipoint random excitation test on the tested structure to obtain a frequency response function matrix and modal frequency of the structure;
thirdly, a purity indication function is used as a fitness function in the algorithm, and a group of optimal excitation force amplitudes can be obtained after the particle swarm optimization iteration;
step four, the optimal excitation force amplitude is sent to the vibration exciter, so that the vibration exciter can quickly and automatically adjust the excitation force;
the automatic excitation force optimization based on the particle swarm optimization specifically comprises the following steps: setting the number of exciting forces in a test as d, and setting the number of exciting force vectors of each group in an optimization algorithm as m; each group of exciting force vector is F ═ F1，F2，…，Fm) (ii) a Single excitation force vector is Fi＝(fi，1，fi，2，…，fi，d) (ii) a Velocity vector corresponding to excitation force vector is Vi＝(vi，1，vi，2，…，vi，d) (ii) a The excitation force vector only corresponds to a pure mode indication function value P ═1，P2，…，Pm) Wherein the optimal excitation force vector is Pi＝(pi，1，pi，2，…，pi，d) (ii) a The global optimal excitation force vector is Pg＝(pg，1，pg，2，…，pg，d) (ii) a Each generation of excitation force vector update and corresponding velocity update is as follows:
vi，j(t+1)＝vi，j(t)+c1r1[Pi，j-fi，j(t)]+c2r2[Pg，j-fi，j(t)]
fi，j(t+1)＝fi，j(t)+vi，j(t+1)，j＝1，…，d
fi，j(t) is the exciting force vector at the moment t; v. ofi，j(t) is the speed corresponding to the exciting force vector at the moment t; f. ofi，j(t +1) is an exciting force vector at the moment (t + 1); v. ofi，j(t +1) is the speed corresponding to the excitation force vector at the moment (t + 1);
c1and c2A learning factor that is a non-negative constant; r is1And r2Are mutually independent pseudo-random numbers; d is the number of exciting forces in the modal test; pi，jThe optimal excitation force vector at the moment t; pg，jSetting an optimal excitation force vector for all excitation force vectors until the moment t;
and obtaining the optimal excitation force vector through the iteration of an automatic optimization algorithm.
2. The method of claim 1, wherein the differential equation of the vibration of the structure under test is expressed as follows
Wherein M, C and K are a mass matrix, a damping matrix and a rigidity matrix of the tested structure respectively; { x (t) } and { f (t) } are respectively the displacement vector of the structure under test and the simple harmonic excitation to which the system is subjected.
3. The method for rapidly and automatically adjusting excitation force according to claim 2, wherein the second step specifically comprises the following steps:
step 2.1, the system is set to be subjected to simple harmonic excitation
{f(t)}＝Fejωt
In the formula: f is an exciting force amplitude array;
the displacement vector of the system can be expressed as
{x(t)}＝X(ω)ejωt
In the formula: x (omega) is the frequency spectrum of the system displacement;
step 2.2, substituting the system displacement expression into the vibration differential equation to obtain a system displacement frequency spectrum:
X(ω)＝(K-ω2M+jωC)-1·F＝H(ω)·F
wherein the frequency response function is H (omega) ═ K-omega2M+jωC)-1。
4. The method according to claim 3, wherein the purity indicator function in step three is:
5. the method according to claim 4, wherein the particle swarm algorithm in the third step is to generate a group of particles at random, that is, an excitation force vector and a velocity vector corresponding to the particle, and after a system frequency response function and a purity indication function are programmed into the particle swarm algorithm, each particle uniquely corresponds to a system response value and a purity indication function value, and an optimal particle is determined by the purity indication function value; the next generation of particles can be generated after the position and speed of the particles are updated in the algorithm.
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| US20050155431A1 (en) * | 2004-01-19 | 2005-07-21 | Mayumi Fukuyama | Vibration test system and method for structures |
| CN101598632A (en) * | 2009-07-07 | 2009-12-09 | 华中科技大学 | The measuring method of strong point axial rigidity and damping in the screw rod drive feeding system |
| CN106570264A (en) * | 2016-10-28 | 2017-04-19 | 南京航空航天大学 | Method for quickly adjusting excitation force in pure modal test |
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| US20050155431A1 (en) * | 2004-01-19 | 2005-07-21 | Mayumi Fukuyama | Vibration test system and method for structures |
| CN101598632A (en) * | 2009-07-07 | 2009-12-09 | 华中科技大学 | The measuring method of strong point axial rigidity and damping in the screw rod drive feeding system |
| CN106570264A (en) * | 2016-10-28 | 2017-04-19 | 南京航空航天大学 | Method for quickly adjusting excitation force in pure modal test |
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