CN113297907A - Nonlinear damping identification method based on data driving under pulse excitation - Google Patents

Nonlinear damping identification method based on data driving under pulse excitation Download PDF

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CN113297907A
CN113297907A CN202110445319.5A CN202110445319A CN113297907A CN 113297907 A CN113297907 A CN 113297907A CN 202110445319 A CN202110445319 A CN 202110445319A CN 113297907 A CN113297907 A CN 113297907A
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damping
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characteristic
displacement
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张大海
马晗
朱锐
李彦斌
费庆国
马蕾
张利
姜东�
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Southeast University
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Abstract

The invention relates to a nonlinear damping identification method based on data driving under pulse excitation, which comprises the following steps: generating a pulse signal, acting on a two-degree-of-freedom nonlinear vibration system to obtain a response after testing, obtaining characteristic displacement and characteristic speed by utilizing actually measured transient response, extracting instantaneous frequency, and obtaining a damping-speed curve according to the characteristic displacement and the instantaneous frequency; and (3) providing a corresponding dynamic model according to the obtained damping-speed curve, defining damping according to the dynamic model, fitting the damping-speed curve, and determining unknown damping parameters of the system based on a pattern search algorithm. The method obtains the output signal based on the measurement, effectively identifies the nonlinear parameter of the system based on the pattern search algorithm through data processing of actually measured transient response, determines the unknown damping parameter of the two-degree-of-freedom nonlinear vibration system, and has practical engineering significance.

Description

Nonlinear damping identification method based on data driving under pulse excitation
Technical Field
The invention relates to the technical field of nonlinear system parameter identification methods, in particular to a nonlinear damping identification method based on data driving under pulse excitation.
Background
The purpose of nonlinear system parameter identification is to estimate model parameters that describe the dynamics of the system. With the rapid development of engineering machinery, parameter identification and analysis of linear vibration systems gradually mature. However, in practical engineering applications, many systems show complex nonlinear behaviors due to multiple physical interactions, and therefore an effective nonlinear parameter identification method is needed to describe the nonlinear system dynamics.
Disclosure of Invention
The invention provides a nonlinear damping identification method based on data driving under pulse excitation, and aims to effectively identify nonlinear damping parameters.
The technical scheme adopted by the invention is as follows:
a nonlinear damping identification method based on data driving under pulse excitation identifies a multi-degree-of-freedom nonlinear vibration system, wherein the multi-degree-of-freedom nonlinear vibration system comprises a linear structure and a nonlinear structure, and the nonlinear structure comprises a damping term and a linear stiffness term which are connected in parallel:
the identification method comprises the following steps:
(1) applying a pulse signal to the multi-degree-of-freedom nonlinear vibration system to obtain an actually measured transient response after the pulse signal is applied, obtaining characteristic displacement and characteristic speed by using the actually measured transient response, extracting instantaneous frequency, and obtaining a damping-speed curve according to the characteristic displacement and the instantaneous frequency;
(2) and establishing a corresponding dynamic model according to the damping-speed curve, defining damping according to the dynamic model, and fitting the damping-speed curve to finally obtain unknown damping parameters of the nonlinear structure.
The further technical scheme is as follows:
the step (1) specifically comprises the following substeps:
11) applying a pulse signal to a two-degree-of-freedom nonlinear vibration system to obtain an acted actual measurement transient response, and defining characteristic displacement delta according to response datac：
Figure BDA0003034608560000011
Where T denotes time, x (T), y (T) are displacements of the nonlinear structure and the linear structure, respectively, δ (T) ═ x (T) -y (T) is a relative displacement between the nonlinear structure and the linear structure, Δ T is a period of a lowest frequency involved in measurement response, δ (T) is a period of a lowest frequency involved in measurement response, and y (T) is a period of a lowest frequency involved in measurement responsec(T) is the maximum value of | δ (T) | within Δ T time;
12) time-frequency analysis is carried out on the relative displacement delta (t), the instantaneous frequency is extracted according to a time-frequency analysis graph obtained by wavelet transformation, and the damping zeta of the time t is obtained according to the characteristic displacement and the instantaneous frequencyc(t)：
Figure BDA0003034608560000021
Wherein deltacAs characteristic displacement, ωcIn order to be the instantaneous frequency of the frequency,
Figure BDA0003034608560000022
is a characteristic displacement deltacWith respect to the first derivative of time,
Figure BDA0003034608560000023
is the instantaneous frequency omegacA first derivative with respect to time;
in conjunction with the velocity of the nonlinear structure, a damping-velocity curve is established.
The step (2) specifically comprises the following substeps:
21) establishing a dynamic equation for representing the two-degree-of-freedom nonlinear vibration system by a nonlinear structure:
Figure BDA0003034608560000024
wherein m and x are respectively the mass of the nonlinear structure and the displacement of the nonlinear structure, and delta is the relative displacement between the nonlinear structure and the linear structure; k2,
Figure BDA0003034608560000025
Respectively a linear rigidity term and a damping term of the nonlinear structure;
and damping term
Figure BDA0003034608560000026
Representing non-linear damping terms
Figure BDA0003034608560000027
And the linear damping term c;
22) note the book
Figure BDA0003034608560000028
δ＝0.85δc、
Figure BDA0003034608560000029
According to the dynamic equation (3), a damping function relation formula about the characteristic speed is obtained:
Figure BDA00030346085600000210
wherein deltacIs a characteristic displacement, vcIs the characteristic speed;
23) fitting the formula (4) with the damping-speed curve, and finally determining unknown damping parameters C and C of the system based on a pattern search algorithm.
The invention has the following beneficial effects:
the invention only utilizes the measured transient response and the related quality, and does not need to know the prior knowledge of the parent structure in advance. The output signal is obtained based on measurement, the nonlinear damping parameters of the system are effectively identified through data processing of actually measured transient response, the unknown damping parameters of the two-degree-of-freedom nonlinear vibration system are determined, and the method has practical engineering significance.
Drawings
Fig. 1 is a schematic structural diagram of a nonlinear vibration system according to an embodiment of the present invention.
FIG. 2 is a comparison of a measured damping-velocity curve and a fitted damping-velocity curve according to an embodiment of the present invention.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
In the present embodiment, a nonlinear damping identification method based on data driving under pulse excitation identifies damping parameters for a multiple degree of freedom nonlinear vibration system, where the multiple degree of freedom nonlinear vibration system includes at least one linear structure (e.g., a parent structure) and a nonlinear structure (e.g., a local attachment) connected to the linear structure, and the present embodiment takes a two degree of freedom nonlinear vibration system as shown in fig. 1 as an example. In fig. 1, M represents the mass of a linear structure, M represents the mass of a nonlinear structure, and the linear coupling between the two is weak, k1 and k2 represent the linear stiffness terms of the linear structure and the nonlinear structure respectively, c1 represents the linear damping term of the linear structure,
Figure BDA00030346085600000211
represents the damping term of the nonlinear structure, y (t) represents the displacement of the linear structure, and x (t) represents the displacement of the nonlinear structure.
The identification method comprises the following steps:
(1) generating a pulse signal, acting on a two-degree-of-freedom nonlinear vibration system to obtain actual measurement transient response, obtaining characteristic displacement and characteristic speed by utilizing the actual measurement transient response, extracting instantaneous frequency, and obtaining a damping-speed curve according to the characteristic displacement and the instantaneous frequency, wherein the method comprises the following substeps:
11) firstly, a pulse signal is generated by adopting a force hammer structureThe method is used on a two-degree-of-freedom nonlinear vibration system, the transient acceleration response is measured by using an acceleration sensor, and the characteristic displacement delta is defined according to response datac：
Figure BDA0003034608560000031
Wherein, x (T) and y (T) are displacements of the nonlinear structure and the linear structure respectively, δ (T) ═ x (T) -y (T) is a relative displacement between the nonlinear structure and the linear structure, Δ T is a period of the lowest frequency participating in the measurement response, and Δ T ═ 0.1 s; deltac(T) is the maximum value of | δ (T) | within Δ T time;
12) time-frequency analysis is carried out on the relative displacement delta (t), the instantaneous frequency is extracted according to a time-frequency analysis graph obtained by wavelet transformation, and the damping zeta of the time t is obtained according to the characteristic displacement and the instantaneous frequencyc(t)：
Figure BDA0003034608560000032
Wherein deltacAs characteristic displacement, ωcIn order to be the instantaneous frequency of the frequency,
Figure BDA0003034608560000033
is a characteristic displacement deltacWith respect to the first derivative of time,
Figure BDA0003034608560000034
is the instantaneous frequency omegacA first derivative with respect to time; directly measuring or calculating the speed of the nonlinear structure according to the displacement, and establishing a damping-speed curve by combining a formula (2).
(2) Providing a corresponding dynamic model according to the obtained damping-speed curve, defining damping according to the dynamic model, fitting the damping-speed curve, and determining unknown damping parameters of the system based on a pattern search algorithm, wherein the method comprises the following substeps:
21) the dynamic equation of the two-degree-of-freedom nonlinear vibration system structure characterized by the nonlinear structure is as follows:
Figure BDA0003034608560000035
m represents the nonlinear structure mass, x represents the displacement of the nonlinear structure, y represents the displacement of the linear structure, δ ═ x-y represents the relative displacement between the nonlinear structure and the linear structure,
Figure BDA0003034608560000036
respectively a linear rigidity term and a damping term of the nonlinear structure;
wherein the damping term
Figure BDA0003034608560000037
Is made by non-linear damping
Figure BDA0003034608560000038
And linear damping c;
taking coulomb damping as an example, the damping is,
Figure BDA0003034608560000039
equation (3) is written as:
Figure BDA00030346085600000310
and m is 0.05, k2＝300、c＝0.3；μ＝0.25；
22) Remember that delta is 0.85 deltacAnd
Figure BDA00030346085600000311
obtaining the damping zeta (v) relative to the characteristic speed according to the dynamic equationc)：
Figure BDA00030346085600000312
Wherein deltacIs a characteristic displacement, vcIs the characteristic speed;
23) and finally determining unknown damping parameters C and C of the system based on a pattern search algorithm by fitting the formula (5) with the damping-speed curve.
As shown in fig. 2, the measured damping-velocity curve is compared to the fitted damping-velocity curve.

Claims (3)

1. A nonlinear damping identification method based on data driving under pulse excitation identifies a multi-degree-of-freedom nonlinear vibration system, the multi-degree-of-freedom nonlinear vibration system comprises a linear structure and a nonlinear structure, the nonlinear structure comprises a damping term and a linear stiffness term which are connected in parallel, and the method is characterized by comprising the following steps of:
(1) applying a pulse signal to the multi-degree-of-freedom nonlinear vibration system to obtain an actually measured transient response after the pulse signal is applied, obtaining characteristic displacement and characteristic speed by using the actually measured transient response, extracting instantaneous frequency, and obtaining a damping-speed curve according to the characteristic displacement and the instantaneous frequency;
(2) and establishing a corresponding dynamic model according to the damping-speed curve, defining damping according to the dynamic model, and fitting the damping-speed curve to finally determine unknown damping parameters of the nonlinear structure.
2. The method for identifying nonlinear damping based on data driving under pulse excitation according to claim 1, wherein the step (1) comprises the following sub-steps:
11) applying a pulse signal to a two-degree-of-freedom nonlinear vibration system to obtain an acted actual measurement transient response, and defining characteristic displacement delta according to response datac：
Figure FDA0003034608550000011
Wherein t represents time, x (t), y (t) are displacements of the nonlinear structure and the linear structure, respectively, δ (t) ═ x (t) -y (t) is a relative displacement between the nonlinear structure and the linear structure,Δ T is the period of the lowest frequency involved in measuring the response, δc(T) is the maximum value of | δ (T) | within Δ T time;
12) time-frequency analysis is carried out on the relative displacement delta (t), the instantaneous frequency is extracted according to a time-frequency analysis graph obtained by wavelet transformation, and the damping zeta of the time t is obtained according to the characteristic displacement and the instantaneous frequencyc(t)：
Figure FDA0003034608550000012
Wherein deltacAs characteristic displacement, ωcIn order to be the instantaneous frequency of the frequency,
Figure FDA0003034608550000013
is a characteristic displacement deltacWith respect to the first derivative of time,
Figure FDA0003034608550000014
is the instantaneous frequency omegacA first derivative with respect to time;
in conjunction with the velocity of the nonlinear structure, a damping-velocity curve is established.
3. The method for identifying nonlinear damping based on data driving under pulse excitation according to claim 2, wherein the step (2) comprises the following sub-steps:
21) establishing a dynamic equation for representing the two-degree-of-freedom nonlinear vibration system by a nonlinear structure:
Figure FDA0003034608550000015
wherein m and x are respectively the mass of the nonlinear structure and the displacement of the nonlinear structure, and delta is the relative displacement between the nonlinear structure and the linear structure; k2,
Figure FDA0003034608550000016
Are respectively as followsA linear stiffness term and a damping term of the nonlinear structure;
and damping term
Figure FDA0003034608550000017
Representing non-linear damping terms
Figure FDA0003034608550000018
And the linear damping term c;
22) note the book
Figure FDA0003034608550000019
δ＝0.85δc、
Figure FDA00030346085500000110
According to the dynamic equation (3), a damping function relation formula about the characteristic speed is obtained:
Figure FDA0003034608550000021
wherein deltacIs a characteristic displacement, vcIs the characteristic speed;
23) fitting the formula (4) with the damping-speed curve, and finally determining unknown damping parameters C and C of the system based on a pattern search algorithm.
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CN114295359B (en) * 2022-01-11 2024-05-03 中国第一汽车股份有限公司 Method and device for measuring dynamic damping parameters

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