CN109254321A - Quick Bayes's Modal Parameters Identification under a kind of seismic stimulation - Google Patents
Quick Bayes's Modal Parameters Identification under a kind of seismic stimulation Download PDFInfo
- Publication number
- CN109254321A CN109254321A CN201810842715.XA CN201810842715A CN109254321A CN 109254321 A CN109254321 A CN 109254321A CN 201810842715 A CN201810842715 A CN 201810842715A CN 109254321 A CN109254321 A CN 109254321A
- Authority
- CN
- China
- Prior art keywords
- indicate
- frequency
- bayes
- quick
- modal
- 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
- 230000000638 stimulation Effects 0.000 title claims abstract description 28
- 238000013016 damping Methods 0.000 claims abstract description 16
- 230000004044 response Effects 0.000 claims abstract description 12
- 238000001228 spectrum Methods 0.000 claims abstract description 4
- 230000001133 acceleration Effects 0.000 claims description 14
- 239000011159 matrix material Substances 0.000 claims description 12
- 230000017105 transposition Effects 0.000 claims description 7
- 238000012546 transfer Methods 0.000 claims description 5
- 238000005259 measurement Methods 0.000 claims description 4
- 230000003595 spectral effect Effects 0.000 claims description 3
- 238000000034 method Methods 0.000 abstract description 14
- 230000008569 process Effects 0.000 abstract description 6
- 238000004458 analytical method Methods 0.000 abstract description 5
- 238000012360 testing method Methods 0.000 abstract description 5
- 238000007796 conventional method Methods 0.000 abstract description 2
- 230000009466 transformation Effects 0.000 description 4
- 238000009795 derivation Methods 0.000 description 3
- 238000005457 optimization Methods 0.000 description 3
- 230000008859 change Effects 0.000 description 2
- 238000007405 data analysis Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 230000005284 excitation Effects 0.000 description 1
- 230000036541 health Effects 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 230000021715 photosynthesis, light harvesting Effects 0.000 description 1
- 235000015170 shellfish Nutrition 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
- G01V1/30—Analysis
- G01V1/307—Analysis for determining seismic attributes, e.g. amplitude, instantaneous phase or frequency, reflection strength or polarity
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/60—Analysis
- G01V2210/63—Seismic attributes, e.g. amplitude, polarity, instant phase
Landscapes
- Engineering & Computer Science (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- Life Sciences & Earth Sciences (AREA)
- Acoustics & Sound (AREA)
- Environmental & Geological Engineering (AREA)
- Geology (AREA)
- General Life Sciences & Earth Sciences (AREA)
- General Physics & Mathematics (AREA)
- Geophysics (AREA)
- Geophysics And Detection Of Objects (AREA)
Abstract
The present invention relates to Bayes's Modal Parameters Identifications quick under a kind of seismic stimulation, comprising the following steps: S1, collects Seismic input and structural response data under known seismic stimulation；S2, one frequency-domain segment of selection and the initial value that intrinsic frequency is obtained from the singular value spectrum of data in step S1, set the initial value of damping ratio；S3, the objective function obtained by minimum by Bayesian formula, obtain the optimal value of intrinsic frequency and damping ratio；S4, the modal contribution factor is obtained by the optimal value of intrinsic frequency and damping ratio.Compared with prior art, use process of the present invention is convenient, it only needs to select frequency-domain segment, then inputting original frequency and damping ratio can directly be calculated, it does not need professional person and carries out empirical analysis, it is faster than conventional method calculating speed, as long as being generally completed several seconds of analysis, can directly be used in test.
Description
Technical field
The present invention relates to modal parameter identification technologies under seismic stimulation, more particularly, to quick pattra leaves under a kind of seismic stimulation
This Modal Parameters Identification.
Background technique
Under seismic stimulation, parameter when carrying out Modal Parameter Identification based on collected structural vibration response mainly includes
The intrinsic frequency of structure damps the when vibration shape.These three parameters due to be structure build-in attribute, be usually to keep substantially
Constant, if there is variation, it is meant that be likely to occur structural damage, therefore these parameters correct structural model, damage
Identification and monitoring structural health conditions play important function.Modal idenlification under seismic stimulation can help solution structure in larger vibration
Energy dissipation capacity under dynamic amplitude, while also effective method is provided for the analysis of vibrostand experiment data.
Existing technology has following two problem.First problem is that current recognition methods step is comparatively laborious, often
It needs professional person just and can be carried out data analysis, calculating process is slower, cannot carry out in time data analysis in test site.
Second Problem be random load due to the seismic stimulation of input, the modal parameter of output certainly exists certain uncertain
Property, however at present there is no the accuracy evaluation that modal parameter under seismic stimulation may be implemented in effective ways, need to build frame,
Platform is provided for modal parameter assessment.
Summary of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide fast under a kind of seismic stimulation
Fast Bayes's Modal Parameters Identification.
The purpose of the present invention can be achieved through the following technical solutions:
Quick Bayes's Modal Parameters Identification under a kind of seismic stimulation, comprising the following steps:
S1, Seismic input and structural response data under known seismic stimulation are collected；
S2, one frequency-domain segment of selection and the initial value that intrinsic frequency is obtained from the singular value spectrum of data in step S1, if
Determine the initial value of damping ratio；
S3, the objective function obtained by minimum by Bayesian formula, obtain the optimal value of intrinsic frequency and damping ratio；
S4, the modal contribution factor is obtained by the optimal value of intrinsic frequency and damping ratio.
Preferably, the objective function obtained by Bayesian formula are as follows:
Wherein, fiIndicate the intrinsic frequency of the i-th rank mode, ζiIndicate the damping ratio of the i-th rank mode,When indicating k-th
The Fast Fourier Transform (FFT) for the acceleration responsive that domain sample measures, k=2,3 ..., Nq, Nq=int [N/2]+1, int [N/2] table
Showing and is rounded to immediate integer downwards to N/2, N indicates the number that sample is measured in time domain scale,It indicatesConjugation turn
It sets,
Wherein, fk=(k-1)/N Δ t, Δ t indicate the time interval between sampled point, Fg(fk) indicate known seismic stimulationFast Fourier Transform (FFT),Indicate Kronecker product, Re indicate in bracket to measuring real part, InIndicate a n
× n unit matrix, n indicate the number for the Degree of Structure Freedom that measurement obtains, Rnm×nmIndicate nm × nm rank real number matrix,It indicates
hkConjugate transposition, hkAre as follows:
hk=[h1k,h2k,...,hmk]∈R1×m
Wherein, hikIt indicates in frequency fkThe i-th rank mode transfer equation, 1≤i≤m, m indicate contribution mode quantity,
Wherein,Indicate Fg(fk) conjugate matrices, RnmIndicate the rank real number matrix of nm × 1.
Preferably, the modal contribution factor are as follows:
γi=| | Φγ(i)||
Wherein, | | Φγ(i) | | indicate that canonical turns to 1 Φγ(i), Φγ(i) by from (Φγ:) optimal value in extract
It obtains, in which:
(the Φγ:) optimal value pass through the optimal value of P and QWithIt obtains.
Preferably, the described (Φγ:) optimal value are as follows:
Wherein,Respectively the minimization of object function when P and Q.
Preferably, the Fast Fourier Transform (FFT) for the acceleration responsive that k-th of time domain samples measureAre as follows:
Wherein, Fk(θ) indicates the Fast Fourier Transform (FFT) of acceleration responsive theoretical value, FekIt is in quick Fu for predict error
Leaf transformation:
Wherein, SeIndicate the amplitude of the power spectral density of prediction error, Z1kAnd Z2kIndicate the Gauss reality vector of two standards,
i2=-1.
Preferably, described in frequency fkThe i-th rank mode transfer equation hikAre as follows:
hik=[(βik 2-1)+i(2ζiβik)]-1
Wherein, βik=fi/fk, i2=-1.Compared with prior art, the invention has the following advantages that
1, use process is convenient, it is only necessary to select frequency-domain segment, then input original frequency and damping ratio can directly into
Row calculates, and does not need professional person and carries out empirical analysis, faster than conventional method calculating speed, as long as being generally completed several seconds of analysis
Clock can be used directly in test.
2, the data under the seismic response that vibrostand experiment data and real structure measure can be analyzed simultaneously, had preferable
Robustness.
3, the frame proposed based on this method is provided platform for modal parameter assessment, the prior art may be implemented and do not accomplish
Modal parameter uncertain assessment.
Detailed description of the invention
Fig. 1 is the flow diagram of the method for the present invention.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention
Premised on implemented, the detailed implementation method and specific operation process are given, but protection scope of the present invention is not limited to
Following embodiments.
Present applicant proposes one kind under bayesian theory frame, is carried out based on known seismic stimulation and structural response quick
The method of Modal Parameter Identification.It is primarily based on the earthquake motion of collected structural vibration response and input, including acceleration, speed
Degree, displacement etc. construct the likelihood function under Bayesian frame according to Structural Dynamics basic principle, priori probability density function,
Posterior probability density function is constructed, negative log-likelihood function is finally obtained, by excellent to negative log-likelihood function derivation and iteration
Change algorithm, can quickly identify modal parameter optimal value.The Bayesian frame of this method development can also join for later period mode
Number assessment provides platform.
Embodiment
As shown in Figure 1, quick Bayes's Modal Parameters Identification under a kind of seismic stimulation, comprising the following steps:
S1, Seismic input and structural response data under known seismic stimulation are collected；
One S2, selection frequency-domain segment simultaneously obtain intrinsic frequency f from the singular value spectrum of data in step S1iInitial value,
Set dampingratioζiInitial value, 1% can be set as, single mode is can choose in frequency-domain segment also and can choose multiple mode；
S3, the objective function obtained by minimum by Bayesian formula, obtain the optimal value of intrinsic frequency and damping ratio；
S4, the modal contribution factor is obtained by the optimal value of intrinsic frequency and damping ratio.
The acceleration responsive of n freedom degree of structure that step S1 measurement obtains is usedIt indicates,
Here N indicates that the number that sample is measured in time domain scale is reduced to for convenienceJ-th of acceleration responsive measured can
To indicate are as follows:
In formulaIt is the theoretical value of acceleration responsive, ej∈RnIt is prediction error, indicates acceleration measurement and reason
By the difference of value, it is made of model error, noise etc..
In frequency domain,Fast Fourier Transform (FFT) (FFT) can be with is defined as:
In formula, i2=-1；Δ t indicates the time interval between sampled point；K=2,3 ..., Nq, correspond to frequency fk=
(k-1)/N Δ t FFT data, Nq=int [N/2]+1.The FFT data in frequency range only selected at one can be used to carry out
Modal idenlification.
Fourier transformation is carried out to equation (1) both sides,Fourier transformation can be represented as:
Wherein, FkThe FFT, F of (θ) expression acceleration responsive theoretical valueekIt is the FFT for predicting error.Generally, prediction misses
Difference can be modeled as white Gaussian noise, therefore, predict that the power spectral density of error can be assumed to be the frequency selected at one
It is constant, amplitude S in the section of domaine, FekIt can indicate are as follows:
Wherein, Z1kAnd Z2kIndicate the Gauss reality vector of two standards, the value inside them is independent.
The process for obtaining objective function by Bayesian formula is as follows:
Consider a structure under known seismic stimulation, seismic stimulation is represented asAssuming that due to seismic stimulation
The structural response of generation is occupied an leading position, and the response that environmental excitation generates can be modeled as prediction error.Assuming that classical damping,
The acceleration responsive of one linear structure can indicate are as follows:
Wherein, m indicates the mode quantity of contribution；Φi∈RnIndicate the vibration shape vector for corresponding to test freedom degree；Table
The modal response for showing the i-th rank mode, meets following equation:
ω in formulai=2 π fi, fiIndicate the intrinsic frequency of the i-th rank mode；ζiIndicate the i-th rank damping ratio；pi(t) i-th is indicated
Rank modal forces can indicate under seismic stimulation are as follows:
Wherein,Indicate the vibration shape comprising all freedom degrees of structure；M is mass matrix；1 indicates the vector of n × 1, the inside
All elements are equal to 1.Definition:
It is then available for the modal contribution factor:
Fourier transformation is carried out to formula (9), and is rearranged, modal acceleration responseFFT can indicate are as follows:
It can substitute into obtain by following two relationship:
In formula, Fg(fk) beFFT；WithIt is respectivelyAnd ηi(t) FFT；And
hik=[(βik 2-1)+i(2ζiβik)]-1 (13)
It is a plural number, it is indicated in frequency fkThe i-th rank mode transfer equation, βik=fi/fkIndicate the ratio of frequency
Value.
Formula (10) are substituted into (5), the FFT of modal response can be indicated are as follows:
D is allowed to indicate the FFT data in the frequency-domain segment selected at one, it comprises our interested mode.Based on shellfish
This is theoretical for leaf, and the posterior probability density function for the modal parameter θ for needing to identify can indicate are as follows:
P (θ) is priori probability density function in formula；P (D | θ) indicate likelihood function；P (D) can be seen as a constant.
It is compared with p (θ), due to the influence of data D, p (D | θ) change comparatively fast.Thus, it is supposed that single prior information, posteriority
Probability density function is directly proportional with likelihood function, that is to say, that
p(θ|D)∝p(D|θ) (16)
Likelihood function p (D | θ) it can be constructed by following derivation.
DefinitionFor a vector being made of the real and imaginary parts of FFT data；Including
Select the FFT data in frequency-domain segment.It can prove for big N and small Δ t,It is independent in different frequency, and takes
From Gaussian Profile.Based on the fact that, likelihood function p (D | θ) can be indicated are as follows:
C in formulakIt indicatesCovariance matrix；Det () indicates determinant；μk=[ReFk(θ)+ImFk(θ)] be
Theoretical value, F herek(θ) is a complex vector, can be indicated are as follows:
Fk(θ)=ReFk(θ)+iImFk(θ) (18)
ReFk(θ) and ImFk(θ) respectively indicates FkThe real and imaginary parts of (θ).
According to formula (4),Variance be equal to Se/ 2, therefore likelihood function can indicate are as follows:
Simultaneously:
Therefore, above-mentioned equation can be write as:
Wherein target " * " indicates to correspond to the conjugate transposition of character on character.
In order to optimize conveniently, we convert minimum problems for max problem with negative log-likelihood function, as follows:
p(θ|D)∝exp(-L(θ)) (22)
In above formula
According to formula (23), theoretically the optimal value of modal parameter can be by minimizing negative log-likelihood function come real
It is existing.Will be very time-consuming however, directly optimizing, computational efficiency will be in the number of the freedom degree of test and selection frequency-domain segment
Mode number be greatly reduced.In order to improve computational efficiency, some parameters can be obtained by analytic solutions, they are expressed as it
The function of his modal parameter, remaining modal parameter can be obtained by optimization.
In formula (23), SeIt is independent from each other with other modal parameters, defined parameters set θ={ fi,ζi,γi,Φ
(i): i=1 ..., m }, γ herei∈ R, Φ (i) ∈ Rn；θ does not include Se.Objective function:
Therefore:
Wherein, terms that do not depend on SeExpression and SeUnrelated parameter, because of the shape of alnx+b/x
Formula has unique minimum value, S in x=b/aeOptimal value can be obtained from following formula:
In formula (25), when J (θ) reaches its minimum value, L (θ) is also up to minimum value.Therefore, because J (θ) is disobeyed
Rely in Se, the optimal value of θ can obtain by minimizing J (θ).
For the vibration shape inside θ, it usually needs standardization constraint, that is to say, that | | Φi| |=1.When the optimization is performed,
Want these constraints of reasonable contemplation.In formula (14), γiAlways with ΦiOccur together, therefore define a new variables:
Φγ(i)=γiΦi (27)
This is one without constrained vector.To which formula (14) can be written to:
Due to ΦγIt (i) is n × m matrix, as m > 1, J (θ) is to Φγ(i) derivative solution will be extremely difficult.For
Solution this problem, formula (28) can be reconfigured as:
In formula, InIndicate n × n unit matrix,Indicate Kronecker product,
hk=[h1k,h2k,...,hmk]∈R1×m (30)
And:
Formula (29) are substituted into the J (θ) in formula (24), available:
In formula,
Wherein, Rnm×nmIndicate nm × nm rank real number matrix,Indicate hkConjugate transposition, Re indicate in bracket to
Real part is measured,Indicate seismic stimulationFast Fourier Transform (FFT) conjugate transposition, RnmIndicate that the rank of nm × 1 is real
Matrix number.
By J (θ) to (Φγ:) derivation and derivative is made to be equal to zero, available (Φγ:) optimal value:
Wherein,The optimal value of respectively P and Q, because P and Q only depend on { fi,ζi, therefore (Φγ:) it is also this
Sample, is substituted into formula (32), and objective function can indicate are as follows:
It indicatesConjugate transposition.
{fi,ζiOptimal value can pass through minimize J ({ fi,ζi) obtain, once after obtaining, it is available (Φγ:) can also be obtained by formula (35).In step S4, ΦγIt (i) can be from (Φγ:) in extract obtain, so mode
Contribution factor γi=| | Φγ(i) | | it can be by the way that Φ be arrangediCanonical turns to 1 and obtains.
For a large amount of data, usually optimization process be can be global identifiable.For not being that the overall situation can be known
Other problem, some more advanced tools, such as Markov chain Monte-Carlo (MCMC) can be used to solve these problems, this
Not within that scope of the present invention.
Claims (6)
1. quick Bayes's Modal Parameters Identification under a kind of seismic stimulation, which comprises the following steps:
S1, Seismic input and structural response data under known seismic stimulation are collected；
S2, one frequency-domain segment of selection and the initial value that intrinsic frequency is obtained from the singular value spectrum of data in step S1, setting resistance
The initial value of Buddhist nun's ratio；
S3, the objective function obtained by minimum by Bayesian formula, obtain the optimal value of intrinsic frequency and damping ratio；
S4, the modal contribution factor is obtained by the optimal value of intrinsic frequency and damping ratio.
2. quick Bayes's Modal Parameters Identification under a kind of seismic stimulation according to claim 1, which is characterized in that
The objective function obtained by Bayesian formula are as follows:
Wherein, fiIndicate the intrinsic frequency of the i-th rank mode, ζiIndicate the damping ratio of the i-th rank mode,Indicate k-th of time domain samples
The Fast Fourier Transform (FFT) of the acceleration responsive measured, k=2,3 ..., Nq, Nq=int [N/2]+1, int [N/2] is indicated to N/
2 are rounded to downwards immediate integer, and N indicates the number that sample is measured in time domain scale,It indicatesConjugate transposition,
Wherein, fk=(k-1)/N Δ t, Δ t indicate the time interval between sampled point, Fg(fk) indicate known seismic stimulation's
Fast Fourier Transform (FFT),Indicate Kronecker product, Re indicate in bracket to measuring real part, InIndicate that a n × n is mono-
Bit matrix, n indicate the number for the Degree of Structure Freedom that measurement obtains, Rnm×nmIndicate nm × nm rank real number matrix,Indicate hkBe total to
Yoke transposition, hkAre as follows:
hk=[h1k,h2k,...,hmk]∈R1×m
Wherein, hikIt indicates in frequency fkThe i-th rank mode transfer equation, 1≤i≤m, m indicate contribution mode quantity,
Wherein,Indicate Fg(fk) conjugate matrices, RnmIndicate the rank real number matrix of nm × 1.
3. quick Bayes's Modal Parameters Identification under a kind of seismic stimulation according to claim 2, which is characterized in that
The modal contribution factor are as follows:
γi=| | Φγ(i)||
Wherein, | | Φγ(i) | | indicate that canonical turns to 1 Φγ(i), Φγ(i) by from (Φγ:) optimal value in extract
It arrives, in which:
(the Φγ:) optimal value pass through the optimal value of P and QWithIt obtains.
4. quick Bayes's Modal Parameters Identification under a kind of seismic stimulation according to claim 3, which is characterized in that
(the Φγ:) optimal value are as follows:
Wherein,Respectively the minimization of object function when P and Q.
5. quick Bayes's Modal Parameters Identification under a kind of seismic stimulation according to claim 2, which is characterized in that
The Fast Fourier Transform (FFT) for the acceleration responsive that k-th of time domain samples measureAre as follows:
Wherein, Fk(θ) indicates the Fast Fourier Transform (FFT) of acceleration responsive theoretical value, FekIt is to predict that the fast Fourier of error becomes
It changes:
Wherein, SeIndicate the amplitude of the power spectral density of prediction error, Z1kAnd Z2kIndicate the Gauss reality vector of two standards, i2
=-1.
6. quick Bayes's Modal Parameters Identification under a kind of seismic stimulation according to claim 2, which is characterized in that
It is described in frequency fkThe i-th rank mode transfer equation hikAre as follows:
hik=[(βik 2-1)+i(2ζiβik)]-1
Wherein, βik=fi/fk, i2=-1.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810842715.XA CN109254321B (en) | 2018-07-27 | 2018-07-27 | Method for identifying rapid Bayesian modal parameters under seismic excitation |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810842715.XA CN109254321B (en) | 2018-07-27 | 2018-07-27 | Method for identifying rapid Bayesian modal parameters under seismic excitation |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109254321A true CN109254321A (en) | 2019-01-22 |
| CN109254321B CN109254321B (en) | 2020-06-26 |
Family
ID=65049817
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810842715.XA Active CN109254321B (en) | 2018-07-27 | 2018-07-27 | Method for identifying rapid Bayesian modal parameters under seismic excitation |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109254321B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109884985A (en) * | 2019-03-11 | 2019-06-14 | 上海理工大学 | The measurement method of numerically-controlled machine tool complete machine machining state dynamic characteristic |
| CN112345184A (en) * | 2020-09-28 | 2021-02-09 | 同济大学 | Structural earthquake damage identification method based on real-time monitoring data |
| CN113155384A (en) * | 2020-08-28 | 2021-07-23 | 盐城工学院 | Sensor arrangement method for reducing uncertainty of structural damping ratio identification |
| CN115061203A (en) * | 2022-05-25 | 2022-09-16 | 华北科技学院 | Mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition and application |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106897717A (en) * | 2017-02-09 | 2017-06-27 | 同济大学 | Bayesian model modification method under multiple test based on environmental excitation data |
| CN107687872A (en) * | 2017-08-14 | 2018-02-13 | 深圳市智能机器人研究院 | Bridge structure health state monitoring method and system based on dynamic model renewal |
| CN108052958A (en) * | 2017-11-09 | 2018-05-18 | 同济大学 | Consider based on known excitation and simultaneously Bayes's modal identification method of environmental excitation influence |
-
2018
- 2018-07-27 CN CN201810842715.XA patent/CN109254321B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106897717A (en) * | 2017-02-09 | 2017-06-27 | 同济大学 | Bayesian model modification method under multiple test based on environmental excitation data |
| CN107687872A (en) * | 2017-08-14 | 2018-02-13 | 深圳市智能机器人研究院 | Bridge structure health state monitoring method and system based on dynamic model renewal |
| CN108052958A (en) * | 2017-11-09 | 2018-05-18 | 同济大学 | Consider based on known excitation and simultaneously Bayes's modal identification method of environmental excitation influence |
Non-Patent Citations (6)
| Title |
|---|
| FENG‐LIANG ZHANG ET AL.: "Bayesian structural model updating using ambient vibration data collected by multiple setups", 《STRUCT CONTROL HEALTH MONIT》 * |
| FENG-LIANG ZHANG ET AL.: "Fundamental two-stage formulation for Bayesian system identification, Part II: Application to ambient vibration data", 《MECHANICAL SYSTEMS AND SIGNAL PROCESSING》 * |
| Y. C. NI ET AL.: "Series of Full-Scale Field Vibration Tests and Bayesian Modal Identification of a Pedestrian Bridge", 《JOURNAL OF BRIDGE ENGINEERING》 * |
| YAN-CHUN NI ET AL.: "Field dynamic test and Bayesian modal identification of a special structure – the Palms Together Dagoba", 《STRUCTURAL CONTROL AND HEALTH MONITORING》 * |
| 俞云书: "《结构模态试验分析》", 31 July 2000, 北京：宇航出版社 * |
| 周云等: "基于贝叶斯理论的多模型结构识别的试验研究", 《湖南大学学报（自然科学版）》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109884985A (en) * | 2019-03-11 | 2019-06-14 | 上海理工大学 | The measurement method of numerically-controlled machine tool complete machine machining state dynamic characteristic |
| CN113155384A (en) * | 2020-08-28 | 2021-07-23 | 盐城工学院 | Sensor arrangement method for reducing uncertainty of structural damping ratio identification |
| CN112345184A (en) * | 2020-09-28 | 2021-02-09 | 同济大学 | Structural earthquake damage identification method based on real-time monitoring data |
| CN115061203A (en) * | 2022-05-25 | 2022-09-16 | 华北科技学院 | Mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition and application |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109254321B (en) | 2020-06-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109254321A (en) | Quick Bayes's Modal Parameters Identification under a kind of seismic stimulation | |
| Gaumond et al. | Evaluation of the wind direction uncertainty and its impact on wake modeling at the Horns Rev offshore wind farm | |
| US11580280B2 (en) | Computational framework for modeling of physical process | |
| Peña et al. | On the application of the Jensen wake model using a turbulence‐dependent wake decay coefficient: the Sexbierum case | |
| Hua et al. | Modeling of temperature–frequency correlation using combined principal component analysis and support vector regression technique | |
| Shabri et al. | Streamflow forecasting using least-squares support vector machines | |
| CN110427654B (en) | Landslide prediction model construction method and system based on sensitive state | |
| CN105444923A (en) | Mechanical temperature instrument error prediction method based on genetic-algorithm optimized least square support vector machine | |
| Rouchier | Solving inverse problems in building physics: An overview of guidelines for a careful and optimal use of data | |
| Zhang et al. | RUL prediction and uncertainty management for multisensor system using an integrated data-level fusion and UPF approach | |
| CN106897717A (en) | Bayesian model modification method under multiple test based on environmental excitation data | |
| Achatz et al. | A two-layer model with empirical linear corrections and reduced order for studies of internal climate variability | |
| Shan et al. | Modeling of temperature effect on modal frequency of concrete beam based on field monitoring data | |
| Pumir et al. | Smoothed analysis of the low-rank approach for smooth semidefinite programs | |
| Yao et al. | Damage and noise sensitivity evaluation of autoregressive features extracted from structure vibration | |
| CN114498619A (en) | Wind power prediction method and device | |
| Yang et al. | Estimation of physical parameters under location uncertainty using an ensemble2–expectation–maximization algorithm | |
| Carratu et al. | Smart water meter based on deep neural network and undersampling for pwnc detection | |
| Zhang et al. | A right-hand side function surrogate model-based method for the black-box dynamic optimization problem | |
| Balcombe et al. | An analysis of the impact of research and development on productivity using Bayesian model averaging with a reversible jump algorithm | |
| Zhang et al. | The method for determining optimal analysis length of vibration data based on improved multiscale permutation entropy | |
| CN116522121A (en) | Transformer online fault diagnosis method under unbalanced small sample condition | |
| Zhang et al. | Deep multi-fidelity bayesian data fusion for probabilistic distribution system voltage estimation with high penetration of pvs | |
| Bishop et al. | Optimization of the fixed global observing network in a simple model | |
| Arras | On the use of Frequency Response Functions in the finite element model updating |
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 |