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 PDFInfo
- Publication number
- 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
- Authority
- CN
- China
- Prior art keywords
- damping
- nonlinear
- characteristic
- displacement
- linear
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000013016 damping Methods 0.000 title claims abstract description 50
- 238000000034 method Methods 0.000 title claims abstract description 20
- 230000005284 excitation Effects 0.000 title claims abstract description 10
- 238000006073 displacement reaction Methods 0.000 claims abstract description 42
- 230000004044 response Effects 0.000 claims abstract description 21
- 230000001052 transient effect Effects 0.000 claims abstract description 13
- 238000005259 measurement Methods 0.000 claims abstract description 10
- 238000010845 search algorithm Methods 0.000 claims abstract description 6
- 230000009466 transformation Effects 0.000 claims description 3
- 230000001133 acceleration Effects 0.000 description 2
- 230000006399 behavior Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000010399 physical interaction Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/02—Preprocessing
- G06F2218/04—Denoising
- G06F2218/06—Denoising by applying a scale-space analysis, e.g. using wavelet analysis
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/08—Feature extraction
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- General Physics & Mathematics (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Theoretical Computer Science (AREA)
- Operations Research (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
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
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:
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):
Wherein deltacAs characteristic displacement, ωcIn order to be the instantaneous frequency of the frequency,is a characteristic displacement deltacWith respect to the first derivative of time,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:
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,Respectively a linear rigidity term and a damping term of the nonlinear structure;
22) note the bookδ=0.85δc、According to the dynamic equation (3), a damping function relation formula about the characteristic speed is obtained:
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,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:
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):
Wherein deltacAs characteristic displacement, ωcIn order to be the instantaneous frequency of the frequency,is a characteristic displacement deltacWith respect to the first derivative of time,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:
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,respectively a linear rigidity term and a damping term of the nonlinear structure;
and m is 0.05, k2=300、c=0.3;μ=0.25;
22) Remember that delta is 0.85 deltacAndobtaining the damping zeta (v) relative to the characteristic speed according to the dynamic equationc):
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:
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):
Wherein deltacAs characteristic displacement, ωcIn order to be the instantaneous frequency of the frequency,is a characteristic displacement deltacWith respect to the first derivative of time,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:
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,Are respectively as followsA linear stiffness term and a damping term of the nonlinear structure;
22) note the bookδ=0.85δc、According to the dynamic equation (3), a damping function relation formula about the characteristic speed is obtained:
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.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202110445319.5A CN113297907B (en) | 2021-04-23 | 2021-04-23 | Nonlinear damping identification method based on data driving under pulse excitation |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202110445319.5A CN113297907B (en) | 2021-04-23 | 2021-04-23 | Nonlinear damping identification method based on data driving under pulse excitation |
Publications (2)
Publication Number | Publication Date |
---|---|
CN113297907A true CN113297907A (en) | 2021-08-24 |
CN113297907B CN113297907B (en) | 2024-04-30 |
Family
ID=77320128
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202110445319.5A Active CN113297907B (en) | 2021-04-23 | 2021-04-23 | Nonlinear damping identification method based on data driving under pulse excitation |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN113297907B (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN114295359A (en) * | 2022-01-11 | 2022-04-08 | 中国第一汽车股份有限公司 | Method and device for measuring dynamic damping parameters |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN107609221A (en) * | 2017-08-15 | 2018-01-19 | 东南大学 | It is a kind of that hinged structure nonlinear parameter recognition methods is contained based on genetic algorithm |
CN110083920A (en) * | 2019-04-23 | 2019-08-02 | 西南交通大学 | The analysis method of non-proportional damping structural random response under a kind of geological process |
CN112632694A (en) * | 2020-12-02 | 2021-04-09 | 东南大学 | Spacecraft structure nonlinear parameter hybrid identification method |
-
2021
- 2021-04-23 CN CN202110445319.5A patent/CN113297907B/en active Active
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN107609221A (en) * | 2017-08-15 | 2018-01-19 | 东南大学 | It is a kind of that hinged structure nonlinear parameter recognition methods is contained based on genetic algorithm |
CN110083920A (en) * | 2019-04-23 | 2019-08-02 | 西南交通大学 | The analysis method of non-proportional damping structural random response under a kind of geological process |
CN112632694A (en) * | 2020-12-02 | 2021-04-09 | 东南大学 | Spacecraft structure nonlinear parameter hybrid identification method |
Non-Patent Citations (3)
Title |
---|
PRABAKARAN BALASUBRAMANIAN 等: "Identification of the viscoelastic response and nonlinear damping of a rubber plate in nonlinear vibration regime", 《MECHANICAL SYSTEMS AND SIGNAL PROCESSING》, vol. 111, 31 October 2018 (2018-10-31), pages 376 - 398, XP085392250, DOI: 10.1016/j.ymssp.2018.03.061 * |
TENG WANXIU 等: "Improved nonlinear model of a yaw damper for simulating the dynamics of a high-speed train", 《PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS, PART F: JOURNAL OF RAIL AND RAPID TRANSIT》, vol. 233, no. 7, 9 October 2018 (2018-10-09), pages 651 - 665 * |
代煜: "基于小波变换的线性及弱非线性结构动力学***辨识方法", 《中国博士学位论文全文数据库 基础科学辑》, no. 11, 15 November 2011 (2011-11-15) * |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN114295359A (en) * | 2022-01-11 | 2022-04-08 | 中国第一汽车股份有限公司 | Method and device for measuring dynamic damping parameters |
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 |
Also Published As
Publication number | Publication date |
---|---|
CN113297907B (en) | 2024-04-30 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Diez-Ibarbia et al. | Comparison between transfer path analysis methods on an electric vehicle | |
CN104123463A (en) | Time domain identification method of random dynamic loads | |
CN106644519B (en) | Method and device for identifying parameters of vehicle vertical dynamics model | |
Smyth et al. | Surveillance of mechanical systems on the basis of vibration signature analysis | |
CN113297907B (en) | Nonlinear damping identification method based on data driving under pulse excitation | |
CN103336482B (en) | A kind of modal parameter acquisition methods of the structure of numerically controlled machine-tool based on velocity correlation | |
CN115060451A (en) | Multi-mode vibration cooperative inhibition method for wind tunnel model support system | |
Dong et al. | Robust fault diagnosis based on nonlinear model of hydraulic gauge control system on rolling mill | |
Zhao et al. | Robotic grinding process monitoring by vibration signal based on LSTM method | |
CN107561934B (en) | Output-only structure modal parameter identification method based on multi-reference time domain transfer rate | |
CN112632694A (en) | Spacecraft structure nonlinear parameter hybrid identification method | |
Brown et al. | The modern era of experimental modal analysis | |
CN115809575A (en) | Working condition transmission path analysis method | |
CN115455353A (en) | Online parameter identification method based on nonlinear time domain filtering | |
CN113486523B (en) | Global identification method for linear variable parameter vibration system | |
CN113297908B (en) | Nonlinear stiffness identification method based on mode search under pulse excitation | |
JP3495594B2 (en) | Twin shaking table controller | |
CN109117547B (en) | Method for optimizing dynamic characteristics of large part structure of machine tool | |
JP2023015923A (en) | Information processing apparatus, information processing method, and information processing program | |
Pourmostaghimi et al. | Vibration based Assessment of Tool Wear in Hard Turning using Wavelet Packet Transform and Neural Networks. | |
Cheng et al. | Fusing LSTM neural network and expanded disturbance Kalman filter for estimating external disturbing forces of ball screw drives | |
Saad et al. | Transducer (Accelerometer) Modeling and Simulation | |
Shrivastava et al. | Estimation of strain in a rotating shaft using deterministic–stochastic approach | |
CN111259328A (en) | Method for detecting nonlinear characteristics of spacecraft structure driven by free vibration displacement response | |
Kohut et al. | The integration of vision based measurement system and modal analysis for detection and localization of damage |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |