CN111652154B - Underdetermined system modal identification method based on automatic frequency band segmentation - Google Patents

Underdetermined system modal identification method based on automatic frequency band segmentation Download PDF

Info

Publication number
CN111652154B
CN111652154B CN202010499791.2A CN202010499791A CN111652154B CN 111652154 B CN111652154 B CN 111652154B CN 202010499791 A CN202010499791 A CN 202010499791A CN 111652154 B CN111652154 B CN 111652154B
Authority
CN
China
Prior art keywords
frequency
time
short
response
mode
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.)
Active
Application number
CN202010499791.2A
Other languages
Chinese (zh)
Other versions
CN111652154A (en
Inventor
姚小俊
杨欣
赵少伟
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hebei University of Technology
Original Assignee
Hebei University of Technology
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Hebei University of Technology filed Critical Hebei University of Technology
Priority to CN202010499791.2A priority Critical patent/CN111652154B/en
Publication of CN111652154A publication Critical patent/CN111652154A/en
Application granted granted Critical
Publication of CN111652154B publication Critical patent/CN111652154B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • 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
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/12—Classification; Matching
    • 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

Abstract

The invention belongs to the technical field of health monitoring data analysis of civil engineering structures, and particularly provides an underdetermined system modal identification method based on automatic frequency band segmentation; according to the method, the response of a vibration system is transformed into a time-frequency domain through short-time Fourier transform, so that the window length of short-time Fourier is adaptively determined by utilizing information entropy, the minimum value of a frequency spectrum is automatically searched according to a scale space peak detection method and is determined as a segmentation point in a frequency range, then single-mode points on a time-frequency plane are detected in each frequency sub-band, and the single-mode points are clustered to obtain a vibration mode matrix, and because the number of measurement in each frequency sub-band is larger than the number of active modes, the time-domain modal response is obtained through short-time Fourier inverse transform, and finally the frequency and damping ratio can be estimated by utilizing a logarithmic attenuation technology; the invention automatically locates the division points on the frequency axis, and uses sparse component analysis in the sub-frequency bands, so that the division points can be accurately identified under the condition of larger underdetermined degree.

Description

Underdetermined system modal identification method based on automatic frequency band segmentation
Technical Field
The invention belongs to the technical field of health monitoring data analysis of civil engineering structures, relates to a mode identification method under the condition of large underdetermined degree, and particularly relates to an underdetermined system mode identification method based on automatic frequency band segmentation.
Background
The modal parameters including modal frequency, vibration mode and damping ratio are important parameters for characterizing the dynamic characteristics of the civil engineering structure. The process of identifying modal parameters from vibration data is consistent with the principle of the blind source separation method, so that a modal identification method based on the blind source separation theory is generated. The number of active modes of the actual structure is often unknown, and the number of sensors may be limited, so the underdetermined blind source separation method is suitable for mode identification of large structures.
Sparse component analysis is suitable for handling underdetermined problems. The time-frequency transformation is a necessary step for realizing the time-frequency response sparsification by sparse component analysis, mainly adopts short-time Fourier transformation to transform time domain data into a time-frequency domain, and then utilizes a clustering technology to estimate the vibration mode after the time-frequency transformation. When the underdetermined degree of the blind source separation system is large, the number of available measurements is far smaller than the number of modes participating in vibration, and the precision of the sparse component analysis method is reduced.
To address this problem, by dividing the frequency range into sub-bands, the accuracy of modal identification at a large underdetermined degree can be improved using sparse component analysis in the sub-bands. However, dividing the frequency range often requires manual selection from the spectrum.
Thus, research into an automatic band segmentation technique is critical for sparse component analysis-based modal identification. .
Disclosure of Invention
The invention aims to provide an underdetermined system mode identification method based on automatic frequency band segmentation so as to improve the mode identification precision of a sparse component analysis method under the condition of larger underdetermined degree.
The invention adopts the following technical scheme:
an underdetermined system modal identification method based on automatic frequency band segmentation comprises the following steps:
the first step: converting the acceleration response to a time-frequency domain;
converting the response of the vibration system to a time-frequency domain through short-time Fourier transform; the expression in the time-frequency domain is
Figure BDA0002524278950000021
In (1) the->
Figure BDA0002524278950000022
And->
Figure BDA0002524278950000023
Response +.>
Figure BDA0002524278950000024
And modality response->
Figure BDA0002524278950000025
Short-time fourier transform at a frequency ω at time i. />
Figure BDA0002524278950000026
Is->
Figure BDA0002524278950000027
The i-th element of (a);
and a second step of: determining the window length of short-time Fourier transform by using information entropy;
time-frequency coefficient
Figure BDA0002524278950000028
Considering as a sequence of probability distributions, the probability of each time-frequency coefficient can be calculated as:
Figure BDA0002524278950000029
then the entropy of the time-frequency representation is obtained: />
Figure BDA00025242789500000210
Calculating entropy values of time-frequency coefficients under different window lengths, determining the window length when the entropy takes the minimum value as an optimal window length parameter, and calculating a short-time Fourier transform coefficient of structural response under the window length;
and a third step of: automatically partitioning frequency subbands using scale space peak detection;
selecting an extremely small value between two peaks of a power spectrum as a dividing point of a frequency band based on a theory that the vicinity of the peak of a frequency response function is dominant in a certain-order mode; t is t k At time, the amplitude of the short-time Fourier transform coefficient at the ith position at frequency ω is
Figure BDA00025242789500000211
Representing the peak picked target amplitude as
Figure BDA00025242789500000212
Wherein AMP i (t k ω) is to find +.>
Figure BDA00025242789500000213
Target amplitude of the minimum value. Automatic detection of AMP using scale space method i (t k ω) to obtain a sub-band divided separation pointFrequency sub-band division is carried out on the corresponding short-time Fourier transform coefficient;
fourth step: selecting a single mode point in each sub-band;
selecting a time-frequency point which mainly contributes to a j-th order mode from a time-frequency plane, and adopting a formula:
Figure BDA00025242789500000214
selection is made where Δθ is a given threshold, re { · } represents the real part of the extracted data, im { · } represents the imaginary part of the extracted data, subscript Ω j Representing the jth time-frequency subspace, marking the single mode point corresponding to the jth order mode as +.>
Figure BDA0002524278950000031
Fifth step: estimating the vibration mode by using the short-time Fourier coefficient of the single-mode point through a clustering technology;
in each sub-frequency band, for the time-frequency coefficient at the single mode point
Figure BDA0002524278950000032
Clustering, wherein N is the number of modes participating in vibration, and the obtained clustering center is the mode shape of each order of mode;
sixth step: frequency and damping ratio identification;
calculating modal response of the time-frequency domain through inverse operation:
Figure BDA0002524278950000033
wherein the method comprises the steps of
Figure BDA0002524278950000034
Indicated is +.>
Figure BDA0002524278950000035
Pseudo-inverse of->
Figure BDA0002524278950000036
The time-frequency coefficient for the j-th order modal response further obtains the time-domain modal response through the short-time inverse Fourier transform, and finallyThe damping ratio is estimated using a logarithmic decay method.
Compared with the prior art, the invention has the following beneficial effects:
according to the invention, the response of the vibration system is transformed into a time-frequency domain through short-time Fourier transform, and the window length of short-time Fourier is determined by utilizing information entropy self-adaptation; automatically searching for a minimum value of a frequency spectrum by using a scale space peak value detection method, and determining the minimum value as a segmentation point in a frequency range; detecting single-mode points on a time-frequency plane in each frequency sub-band, and clustering the single-mode points to obtain a vibration mode matrix; since the number of measurements is greater than the number of active modes in each frequency subband, the time domain modal response is obtained by inverse short time fourier transform, and the frequency and damping ratio is further estimated using a logarithmic decay technique.
According to the method, the frequency range is divided into the sub-bands, the underdetermined problem is converted into the easily-solved overdetermined problem, the segmentation points on the frequency axis can be automatically positioned without manual selection based on the scale space peak detection method, and the accuracy of modal identification under the condition of large underdetermined degree is improved.
Detailed Description
In order to enable those skilled in the art to better understand the technical scheme of the present invention, the present invention will be further described in detail with reference to specific embodiments.
Example 1
Taking a 10-layer linear shear building model, wherein the mass and the interlayer rigidity of each layer of building surface are 1000Kg and 1.76108N/m respectively; mass proportion damping is adopted, the damping coefficient is 2, and the obtained maximum damping ratio is 1.5%. Free vibrational responses are generated by applying initial conditions, and modal identification is performed using the first two structural responses.
Based on the above conditions, the embodiment provides an underdetermined system mode identification method based on automatic frequency band segmentation, which comprises the following steps:
the first step: converting the acceleration response to a time-frequency domain;
the response of the vibration system is converted to the time-frequency domain by a short-time fourier transform. The expression in the time-frequency domain is
Figure BDA0002524278950000041
In (1) the->
Figure BDA0002524278950000042
And->
Figure BDA0002524278950000043
Response +.>
Figure BDA0002524278950000044
And modality response->
Figure BDA0002524278950000045
A short-time fourier transform at a frequency ω at time t; />
Figure BDA0002524278950000046
Is->
Figure BDA0002524278950000047
The i-th element of (a); acceleration data are collected by acceleration sensors in a structural health monitoring system;
and a second step of: determining the window length of short-time Fourier transform by using information entropy;
time-frequency coefficient
Figure BDA0002524278950000048
Considering as a sequence of probability distributions, the probability of each time-frequency coefficient can be calculated as:
Figure BDA0002524278950000049
then the entropy of the time-frequency representation is obtained: />
Figure BDA00025242789500000410
Calculating information entropy values of different window lengths (0.2 s to 5 s), wherein the information entropy is minimum when the window length is 1s, so that the optimal window length is 1s, and calculating a short-time Fourier transform coefficient of the structural response under 1 s;
and a third step of: automatically partitioning frequency subbands using scale space peak detection;
based on the theory that the vicinity of the peak of the frequency response function is dominant for a certain order mode, the minimum value between two peaks of the power spectrum is selected as a dividing point of the frequency band. t is t k At time, the amplitude of the short-time Fourier transform coefficient at the ith position at frequency ω is
Figure BDA00025242789500000411
Representing the peak picked target amplitude as
Figure BDA00025242789500000412
Wherein AMP i (t k ω) is to find +.>
Figure BDA00025242789500000413
Target amplitude of the minimum value. Automatic detection of AMP using scale space method i (t k ω) to obtain a division point of sub-band division, so that the frequency axis is divided into ten frequency bands;
fourth step: selecting a single mode point in each sub-band;
selecting a time-frequency point which mainly contributes to a j-th order mode from a time-frequency plane, and adopting a formula:
Figure BDA00025242789500000414
selecting, marking a single mode point corresponding to a j-th order mode as
Figure BDA0002524278950000051
Fifth step: estimating the vibration mode by using the short-time Fourier coefficient of the single-mode point through a clustering technology;
in each sub-frequency band, for the time-frequency coefficient at the single mode point
Figure BDA0002524278950000052
Clustering, wherein N is the number of modes participating in vibration, and the obtained clustering center is the mode shape of each order of mode;
sixth step: frequency and damping ratio identification;
calculating modal response of the time-frequency domain through inverse operation:
Figure BDA0002524278950000053
estimating the damping ratio by using a logarithmic attenuation method, wherein the finally identified modal frequencies of each order are as follows: 9.97Hz, 29.73Hz, 48.76Hz, 66.75Hz, 83.27Hz, 97.60Hz, 110.34Hz, 120.76Hz, 127.62Hz and 132.26Hz, the damping ratios of the respective steps are: 1.52%, 0.52%, 0.31%, 0.23%, 0.18%, 0.15%, 0.11%, 0.13% and 0.12%.
Seventh step: and determining the health state of the civil engineering structure based on the modal parameters obtained by the identification.
Example two
The embodiment provides a civil engineering structure health state monitoring system based on automatic frequency band segmentation, which comprises a remote server and an acceleration sensor, wherein the acceleration sensor is arranged at a main body part of a civil engineering structure and is used for acquiring acceleration data; the acceleration sensor can comprise a controller, a GPS module, a thermometer, an accelerometer, a gyroscope, a 3D compass, a wireless transceiver and a power module, wherein the controller is respectively connected with the wireless transceiver, the accelerometer and the power module, and the GPS module, the thermometer, the gyroscope and the 3D Luo Panjun are connected with the accelerometer; the acceleration sensor is connected with the remote server in a wired or wireless mode, and acceleration data acquired by the acceleration sensor are transmitted to the remote server for modal identification.
The remote server is configured to perform the steps of:
the first step: converting the acceleration response to a time-frequency domain;
converting the response of the vibration system to a time-frequency domain through short-time Fourier transform; the expression in the time-frequency domain is
Figure BDA0002524278950000054
In (1) the->
Figure BDA0002524278950000055
And->
Figure BDA0002524278950000056
Response +.>
Figure BDA0002524278950000057
And modality response->
Figure BDA0002524278950000058
A short-time fourier transform at a time instant frequency ω; />
Figure BDA0002524278950000059
Is->
Figure BDA00025242789500000510
The i-th element of (a);
and a second step of: determining the window length of short-time Fourier transform by using information entropy;
time-frequency coefficient
Figure BDA0002524278950000061
Considering as a sequence of probability distributions, the probability of each time-frequency coefficient can be calculated as:
Figure BDA0002524278950000062
then the entropy of the time-frequency representation is obtained: />
Figure BDA0002524278950000063
Calculating entropy values of time-frequency coefficients under different window lengths, determining the window length when the entropy takes the minimum value as an optimal window length parameter, and calculating a short-time Fourier transform coefficient of structural response under the window length;
and a third step of: automatically partitioning frequency subbands using scale space peak detection;
selecting an extremely small value between two peaks of a power spectrum as a dividing point of a frequency band based on a theory that the vicinity of the peak of a frequency response function is dominant in a certain-order mode; t is t k At time, the amplitude of the short-time Fourier transform coefficient at the ith position at frequency ω is
Figure BDA0002524278950000064
Representing the peak picked target amplitude as
Figure BDA0002524278950000065
Wherein AMP i (t k ω) is to find +.>
Figure BDA0002524278950000066
Target amplitude of the minimum value. Automatic detection of AMP using scale space method i (t k ω) to obtain sub-band divided separation points, and frequency sub-band dividing the corresponding short-time fourier transform coefficients;
fourth step: selecting a single mode point in each sub-band;
selecting a time-frequency point which mainly contributes to a j-th order mode from a time-frequency plane, and adopting a formula:
Figure BDA0002524278950000067
selection is made where Δθ is a given threshold, re { · } represents the real part of the extracted data, im { · } represents the imaginary part of the extracted data, subscript Ω j Representing the jth time-frequency subspace, marking the single mode point corresponding to the jth order mode as +.>
Figure BDA0002524278950000068
Fifth step: estimating the vibration mode by using the short-time Fourier coefficient of the single-mode point through a clustering technology;
in each sub-frequency band, for the time-frequency coefficient at the single mode point
Figure BDA0002524278950000069
Clustering, wherein N is the number of modes participating in vibration, and the obtained clustering center is the mode shape of each order of mode;
sixth step: frequency and damping ratio identification;
calculating modal response of the time-frequency domain through inverse operation:
Figure BDA00025242789500000610
wherein the method comprises the steps of
Figure BDA00025242789500000611
Indicated is +.>
Figure BDA00025242789500000612
Pseudo-inverse of->
Figure BDA00025242789500000613
And obtaining a time domain modal response for the time-frequency coefficient of the j-th order modal response by further carrying out short-time inverse Fourier transform, and finally estimating the damping ratio by using a logarithmic attenuation method.
And finally, determining the health state of the civil engineering structure based on the modal parameters obtained by the identification.
Finally, it is pointed out that the principles and embodiments of the invention have been described herein with reference to specific examples, which are intended to be merely illustrative of the core idea of the invention, and that several improvements and modifications can be made to the invention without departing from the principles of the invention, which also fall within the scope of protection of the invention.

Claims (1)

1. An underdetermined system modal identification method based on automatic frequency band segmentation is characterized by comprising the following steps:
the first step: converting the acceleration response to a time-frequency domain;
converting the response of the vibration system to a time-frequency domain through short-time Fourier transform; the expression in the time-frequency domain is
Figure FDA0002524278940000011
In (1) the->
Figure FDA0002524278940000012
And->
Figure FDA0002524278940000013
Response +.>
Figure FDA0002524278940000014
And modality response->
Figure FDA0002524278940000015
A short-time fourier transform at a frequency ω at time t; />
Figure FDA0002524278940000016
Is->
Figure FDA0002524278940000017
The i-th element of (a);
and a second step of: determining the window length of short-time Fourier transform by using information entropy;
time-frequency coefficient
Figure FDA0002524278940000018
Considering as a sequence of probability distributions, the probability of each time-frequency coefficient can be calculated as:
Figure FDA0002524278940000019
then the entropy of the time-frequency representation is obtained: />
Figure FDA00025242789400000110
Calculating entropy values of time-frequency coefficients under different window lengths, determining the window length when the entropy takes the minimum value as an optimal window length parameter, and calculating a short-time Fourier transform coefficient of structural response under the window length;
and a third step of: automatically partitioning frequency subbands using scale space peak detection;
selecting an extremely small value between two peaks of a power spectrum as a dividing point of a frequency band based on a theory that the vicinity of the peak of a frequency response function is dominant in a certain-order mode; t is t k At time, the amplitude of the short-time Fourier transform coefficient at the ith position at frequency ω is
Figure FDA00025242789400000111
Representing the peak picked target amplitude as
Figure FDA00025242789400000112
Wherein AMP i (t k ω) is to find +.>
Figure FDA00025242789400000113
Target amplitude of the minimum value; automatic detection of AMP using scale space method i (t k ω) to obtain sub-band divided separation points, and frequency sub-band dividing the corresponding short-time fourier transform coefficients;
fourth step: selecting a single mode point in each sub-band;
selecting a time-frequency point which mainly contributes to a j-th order mode from a time-frequency plane, and adopting a formula:
Figure FDA00025242789400000114
selection is made where Δθ is a given threshold, re { · } represents the real part of the extracted data, im { · } represents the imaginary part of the extracted data, subscript Ω j Representing the jth time-frequency subspace, marking the single mode point corresponding to the jth order mode as +.>
Figure FDA0002524278940000021
Fifth step: estimating the vibration mode by using the short-time Fourier coefficient of the single-mode point through a clustering technology;
in each sub-frequency band, for the time-frequency coefficient at the single mode point
Figure FDA0002524278940000022
j=1, 2, …, N is the number of modes participating in vibration, and the obtained clustering center is the mode shape of each order mode;
sixth step: frequency and damping ratio identification;
calculating modal response of the time-frequency domain through inverse operation:
Figure FDA0002524278940000023
wherein the method comprises the steps of
Figure FDA0002524278940000024
Indicated is +.>
Figure FDA0002524278940000025
Pseudo-inverse of->
Figure FDA0002524278940000026
And obtaining a time domain modal response for the time-frequency coefficient of the j-th order modal response by further carrying out short-time inverse Fourier transform, and finally estimating the damping ratio by using a logarithmic attenuation method. />
CN202010499791.2A 2020-06-04 2020-06-04 Underdetermined system modal identification method based on automatic frequency band segmentation Active CN111652154B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010499791.2A CN111652154B (en) 2020-06-04 2020-06-04 Underdetermined system modal identification method based on automatic frequency band segmentation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010499791.2A CN111652154B (en) 2020-06-04 2020-06-04 Underdetermined system modal identification method based on automatic frequency band segmentation

Publications (2)

Publication Number Publication Date
CN111652154A CN111652154A (en) 2020-09-11
CN111652154B true CN111652154B (en) 2023-05-30

Family

ID=72351135

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010499791.2A Active CN111652154B (en) 2020-06-04 2020-06-04 Underdetermined system modal identification method based on automatic frequency band segmentation

Country Status (1)

Country Link
CN (1) CN111652154B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112348829B (en) * 2020-11-02 2022-06-28 东华理工大学 Method for separating branches and leaves of ground LiDAR point cloud based on modal point evolution
CN115982625B (en) * 2023-01-06 2023-10-03 哈尔滨工业大学（深圳） Priori information-based long-term working mode analysis method and detection method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104809097A (en) * 2015-04-30 2015-07-29 吴伟 Multi-window function selection method for time-frequency domain signal processing
CN108009584A (en) * 2017-12-01 2018-05-08 西安交通大学 Deficient based on the detection of single source point determines blind source separation method
CN108491608A (en) * 2018-03-06 2018-09-04 大连理工大学 The Sparse Component Analysis method of distinguishing structural mode when number of sensors is incomplete

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104809097A (en) * 2015-04-30 2015-07-29 吴伟 Multi-window function selection method for time-frequency domain signal processing
CN108009584A (en) * 2017-12-01 2018-05-08 西安交通大学 Deficient based on the detection of single source point determines blind source separation method
CN108491608A (en) * 2018-03-06 2018-09-04 大连理工大学 The Sparse Component Analysis method of distinguishing structural mode when number of sensors is incomplete

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
基于信息熵的自适应窗长STFT算法在AFVISAR中的应用;苏欣;孟晓风;;现代电子技术(第05期);全文 *
基于模态参数的钢框架螺栓连接节点损伤识别理论与实验研究;贾晓健;尹涛;;武汉大学学报(工学版)(第02期);全文 *

Also Published As

Publication number Publication date
CN111652154A (en) 2020-09-11

Similar Documents

Publication Publication Date Title
CN104166804B (en) A kind of operation mode discrimination method based on time-frequency domain list source point sparse component analysis
CN106844935B (en) Large-damping engineering structure modal parameter identification method
CN111652154B (en) Underdetermined system modal identification method based on automatic frequency band segmentation
CN104112072B (en) Operational modal parameter recognition methods based on the principal component analysis of wavelet threshold denoising
WO2019061439A1 (en) Improved sound source positioning method based on progressive serial orthogonalized blind source separation algorithm, and system for implementing same
CN101701820B (en) Method for extracting optical fiber gyro random error characteristics based on wavelet variance
CN102590553B (en) Temperature compensation method for accelerometer based on wavelet noise elimination
CN101957443B (en) Sound source localizing method
CN108491608B (en) Sparse component analysis method for structural modal identification when sensor number is incomplete
CN110794170B (en) Method for identifying parameters of two-degree-of-freedom dynamic model of accelerometer
CN102023010A (en) MEMS (micro-electromechanical system)-based wavelet field multisensor information fusion system and fusion method
US20190376874A1 (en) A method of estimating the number of modes for the sparse component analysis based modal identification
CN111273297A (en) Horizontal array moving target depth estimation method based on AR wave number spectrum
CN101587007A (en) Output-only wavelet analytical method for recognizing flexible bridge structure kinetic parameter
CN109459745B (en) Method for estimating speed of moving sound source by using radiation noise
CN109060371A (en) A kind of auto parts and components abnormal sound detection device
CN107148553A (en) Method and system for improving Inertial Measurement Unit sensor signal
CN106548031A (en) A kind of Identification of Modal Parameter
CN114187330A (en) Structural micro-amplitude vibration working mode analysis method based on optical flow method
CN115169409A (en) Bridge structure natural vibration frequency identification and early warning method and device based on sliding window
CN108646248B (en) Passive acoustic speed and distance measuring method for low-speed moving sound source
CN116861544A (en) Building abnormal vibration source positioning method based on edge cloud cooperation and related equipment
CN110726981A (en) Radar signal phase difference detection method for fixed target
CN110231403A (en) Long-span bridge online real-time damage identification method supported by mobile load response wavelet packet analysis
CN101509774A (en) ARMA time-series north-searching method based on optical fiber gyroscope

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