CN108491578B - A kind of Random dynamic loads recognition methods based on perturbative matrix - Google Patents
A kind of Random dynamic loads recognition methods based on perturbative matrix Download PDFInfo
- Publication number
- CN108491578B CN108491578B CN201810148292.1A CN201810148292A CN108491578B CN 108491578 B CN108491578 B CN 108491578B CN 201810148292 A CN201810148292 A CN 201810148292A CN 108491578 B CN108491578 B CN 108491578B
- Authority
- CN
- China
- Prior art keywords
- matrix
- random
- uncertain
- dynamic
- dynamic loads
- 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
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The Random dynamic loads recognition methods based on perturbative matrix that the present invention provides a kind of, structure containing uncertain parameters is carried out with modal test multiple under operating condition, calculate uncertainty rigidity, quality and damping matrix, to uncertain rigidity, quality and damping matrix are unfolded, calculate Green's function matrix, establish the uncertain kinetic model based on perturbative matrix, measure the random file response sample of the structure containing uncertain parameters under Random dynamic loads effect, utilize the mean value of suffered Random dynamic loads in random file response sample mean value identification structure, calculate the approximation for only considering the response covariance of random file caused by dynamic loading randomness, identification obtains the statistical nature of Random dynamic loads.Utilize the method for the present invention, the uncertainty of dynamic response, structural system and dynamic loading can be considered simultaneously, the statistical nature of structure dynamic loading is obtained using actual measurement dynamic response specimen discerning, dynamic loading information abundant can be provided for engineering structure, be more advantageous to the security evaluation and optimization design of engineering structure.
Description
Technical field
The present invention relates to a kind of dynamic loading indirect identification methods, and in particular to a kind of Random dynamic loads recognition methods.
Background technique
Dynamic loading suffered by engineering structure is most important to the design and security evaluation of structure.In many cases, some engineerings
External load suffered by structure is difficult to obtain by method measured directly, such as suffered aerodynamic loading, sea in aircraft flight course
Storm load suffered by foreign platform, wheel and the contact load on ground etc. on driving vehicle, therefore, using surveying dynamic response in structure
Carry out indirect gain dynamic loading information as a kind of technology being widely adopted, also referred to as dynamic loading indirect identification technology.
Current dynamic loading indirect identification method does not consider the uncertainty of structural system parameter mostly, uses certainty
The structure that can be obtained by single measurement of Dynamic Load Identification method on dynamic response identification when the dynamic load that time act in structure
Lotus.However, dynamic loading such as wind load, seismic (seismal, aerodynamic loading, acoustic loads etc. suffered on engineering structure, Chang Cheng
Now random feature, what certainty Dynamic Load Identification method obtained only works as time approximation of effect dynamic loading, can not provide reality
The statistical nature of border dynamic loading is easy not lead to " cross and design " comprehensively since dynamic loading information understands in structured design process
Or " owing design "；On the other hand, engineering structure itself is made due to the discreteness of error and material itself in manufacture and measurement
The system parameter for obtaining structure is sometimes not appropriate for being described with a determining value, does not consider the uncertainty of system parameter
It will lead to the distortion even mistake of Dynamic Load Identification result.
Summary of the invention
Goal of the invention: in view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of limited based on perturbation stochastic
The Random dynamic loads recognition methods of member, this method can consider the uncertainty of dynamic loading and system parameter simultaneously, utilize reality
Geodesic structure dynamic response sample identifies the statistical nature that Random dynamic loads are acted on structural system.
Technical solution: the Random dynamic loads recognition methods based on perturbative matrix that the present invention provides a kind of, including
Following steps:
(1) structure containing uncertain parameters is carried out with modal test multiple under operating condition, obtains uncertain system parameter
Random distribution field；
(2) K-L expansion is carried out to system random parameter field, calculates uncertainty rigidity, quality and damping matrix；
(3) uncertain rigidity, quality and damping matrix are unfolded using perturbation method, calculate Green's function matrix,
Establish the uncertain kinetic model based on perturbative matrix；
(4) the random file response sample of the structure containing uncertain parameters under measurement Random dynamic loads act on；
(5) mean value of suffered Random dynamic loads in random file response sample mean value identification structure is utilized；
(6) structure random file when only considering system parameter uncertainty is solved using the Random dynamic loads mean value of identification
Response；
(7) approximation for only considering the response covariance of random file caused by dynamic loading randomness is calculated；
(8) identification obtains the statistical nature of Random dynamic loads.
Further, in step (2) uncertain stiffness matrix K, mass matrix M and damping matrix C respectively by element stiffness
Matrix Ke, element mass matrix MeWith unit damping matrix CeAssemble:
Element mass matrix MeWith element stiffness matrix KeIt is calculate by the following formula respectively:
In formula,WithThe respectively desired value of density and elastic parameter, λρWithRespectively containing uncertain density parameter
Covariance function eigenvalue and eigenfunction, λDWithThe spy of covariance function respectively containing uncertain elastic parameter
Value indicative and characteristic function, KρAnd KDItem number respectively after density and elastic parameter K-L truncation, HeAnd BeThe respectively shape of unit
Jacobian matrix and strain matrix, D are elastic matrix, veFor unit volume, ξiFor irrelevant standard gaussian stochastic variable, under
Marking i indicates i-th of ingredient of randomness part；
Unit damping matrix CeAccording to Rayleigh damping model, by MeAnd KeIt is calculated.
Further, step (3) the following steps are included:
(31) the Green's function matrix G (η) of uncertain kinetic model is calculated:
Green's function matrix G (η) is assembled using the form of Green's function g (t, η) according to the following formula:
Time t in Green's function g (t, η) is wherein subjected to discrete, tQIndicate the Q discrete time in Green's function
Step；Green's function matrix is unfolded using perturbation method:
Wherein, ηdThe mean value for the stochastic variable η for including in system parameter and dynamic loading is represented, n is the quantity of stochastic variable,
Gi' be Green's function matrix the corresponding coefficient matrix in randomness part；
(32) matrix G (η when uncertain parameters take mean value is calculatedd):
Uncertain parameters take Green's function D when mean valued(t) it is obtained by solving following equation:
In formula, subscript d represents certainty part, i.e., acquired results when stochastic variable takes desired, and δ (t) is impulse response letter
Number, the transposition of T representing matrix or vector.
According to formula (3), g (t, η) is replaced with into Dd(t), it can solve and obtain matrix G (ηd)；
(33) Green's function matrix randomness part G is calculatedi′；
In formula, Mi、CiAnd KiThe respectively randomness part of mass matrix M, damping matrix C and stiffness matrix K, by unit
Mass matrix Me, unit damping matrix CeWith element stiffness matrix KeAssembling obtains；
Solution formula (6) respectively obtains stochastic variable ξiThe variation D of caused response when variationi(t), according to formula (3), by g
(t, η) replaces with Di(t), it can solve and obtain matrix Gi′；
(34) Random dynamic loads and random file response are used into chaos polynomial expansion, established limited based on perturbation stochastic
The uncertainty structure kinetic model of member.
Further, step (5) utilizes random file response sample mean valueIdentify suffered Random dynamic loads in structure
Mean valueSpecific method be:
Further, step (6) is based on the kinetic model based on perturbative matrix that step (3) are established, solution side
Journey (8) calculates Random dynamic loads mean valueThe random file acted on uncertain system responds corresponding vector u(P)
(t):
In formula, P is the item number of the chaos polynomial expansion of system random file response, and,
Wherein, Ψj, Ψk(j, k=1,2 ... P) is respectively jth and k rank chaos multinomial, and expectation is asked in<>expression.
Further, step (7) the following steps are included:
(71) system that uncertain parameters ask expectation corresponding is defined as deterministic system, by the equal of Random dynamic loads
Value is defined as corresponding certainty dynamic loading；Remember that Random dynamic loads act on lower uncertain system with the covariance matrix of kinematical displacement
Dynamic displacement covariance matrix for [R], the lower corresponding deterministic system of Random dynamic loads effect is [R]d, corresponding certainty dynamic loading
The dynamic displacement covariance matrix for acting on lower uncertain system is [R]s, above three covariance matrix is with following relational expression:
In formula,WithRespectively indicate only as dynamic loading uncertainty and only as system parameter it is uncertain caused by
Uncertain dynamic respond is in jth rank chaos multinomial at the projection vector in random space；
(72) since the uncertainty of dynamic loading and uncertain the two correlation of system parameter are weak, formula (10) equation is left
Side Section 3 contributes very little, calculates [R]dApproximation:
[R]d≈[R]-[R]s (11)。
Further, step (8) the following steps are included:
(81) covariance matrix [R] is askeddCharacteristic valueAnd feature vectorCalculate its K-L vectorIdentify vector f corresponding to Random dynamic loads in structure(j)(t):
(82) the mean μ F (t) and variance of Random dynamic loads are solved using vector corresponding to Random dynamic loads
The utility model has the advantages that 1, existing Dynamic Load Identification method does not consider the uncertainty of structural system parameter mostly, know
The precision of other result will be completely dependent on when time dynamic response measurement accuracy and structural system modeling accuracy, be obtained using duplicate measurements
Dynamic response identification dynamic loading result it is inconsistent, it is difficult to give engineering staff to provide accurate dynamic loading information, be also unfavorable for determining
Plan；Using the method for the present invention, the uncertainty of dynamic response, structural system and dynamic loading can be considered simultaneously, utilize the actual measurement sound of something astir
It answers specimen discerning to obtain the statistical nature of structure dynamic loading, dynamic loading information abundant can be provided for engineering structure, more favorably
In the security evaluation and optimization design of engineering structure；
2, existing Dynamic Load Identification method is only used for simple structure mostly, and the present invention is according to the Green's function of system
The Random dynamic loads information acted in identifying system, it is effective to improve computational efficiency and anti-noise ability and can be used in complicated work
Random dynamic loads identification in journey structure.
Detailed description of the invention
Fig. 1 is the logical procedure diagram of the method for the present invention；
Fig. 2 is FEM model schematic diagram in embodiment；
Fig. 3 is the comparison diagram of load mean value and reference value that identification obtains；
Fig. 4 is the comparison diagram of load variance and reference value that identification obtains.
Specific embodiment
Technical solution of the present invention is described in detail below, but protection scope of the present invention is not limited to the implementation
Example.
For a composite material cantilever beam structure comprising uncertain parameters, as shown in Figure 1, using the method for the present invention base
Go out the statistical nature of suffered Random dynamic loads in the structure in the dynamic displacement specimen discerning of actual measurement on beam, specifically includes the following steps:
S1, carry out for a batch of more composite material cantilever beams with modal test multiple under operating condition, modal test
System is using conventional mode experiment system；Structural finite element model as shown in Figure 2 is established, cantilever beam is divided into 14 sections
Point, wherein number 1~14 is respectively cantilever beam node serial number in figure, and it is close that the model modification method based on frequency response function obtains structure
The sample for spending parameter and elastic parameter, calculates the statistical property of structural parameters, including mean value and covariance；
S2, system parameter random field is unfolded using K-L expansion, calculates uncertainty rigidity, quality and damping
Matrix；Wherein element mass matrix and element stiffness matrix can be calculated by following formula:
In formula: I is cantilever beam cross sectional moment of inertia.
Unit damping matrix C is calculated according to Rayleigh damping modele。
Assembling obtains the certainty part K of global stiffness, quality and damping matrixd、MdAnd Cd, and uncertain part
Ki、MiAnd Ci。
S3, it is unfolded using uncertain rigidity, quality and damping matrix of the perturbation method to system, and is calculated not
The Green's function matrix of certainty structure.
Green's function matrix G (η) can be used the form of Green's function g (t, η) according to the following formula and be assembled:
Time t in Green's function g (t, η) is wherein subjected to discrete, tQIndicate the Q discrete time in Green's function
Step.Green's function matrix is unfolded using perturbation method:
Wherein, ξiFor irrelevant standard gaussian stochastic variable, n is the quantity of structural uncertainty parameter
Wherein, ηdRepresent the mean value for the stochastic variable η for including in system parameter and dynamic loading, Gi' it is Green's function matrix
The corresponding coefficient matrix in randomness part.
Green's function matrix can be calculated by formula (7) and (8):
Solution formula (7) and (8) obtain Dd(t) and Di(t), the g (t, η) in alternate form (4) can solve to obtain Green respectively
The mean value G of Jacobian matrix0With randomness part coefficient of correspondence Gi′。
S4, the single-point arbitrary excitation for applying given statistical property to every cantilever beam using vibration excitor, use laser displacement
On meter measurement beam set point with kinematical displacement, calculate using with kinematical displacement sample with kinematical displacement mean value
S5, suffered Random dynamic loads mean value in random file response sample mean value identification structure is utilized
S6, the random dynamic response of structure is unfolded using chaos multinomial, is established based on perturbative matrix not
Certainty kinetic model solves equation (10), calculates Random dynamic loads mean valueIt acts on uncertain system
Random file responds corresponding vector u(j)(t), wherein equation (10) are as follows:
In formula, P is the item number after the chaos polynomial expansion of system random file response.
Wherein, Ψj, Ψk(j, k=1,2 ... P) is respectively jth and k rank chaos multinomial, and expectation is asked in<>expression.
It is [R] that S7, note Random dynamic loads, which act on lower uncertain system (cantilever beam) with the covariance matrix of kinematical displacement,
The dynamic displacement covariance matrix of the lower corresponding deterministic system of Random dynamic loads effect is [R]d, correspond under certainty dynamic load effect
The dynamic displacement covariance matrix of uncertain system is [R]s, above three covariance matrix is with following relational expression:
In formula,WithRespectively indicate only as dynamic loading uncertainty and only as system parameter it is uncertain caused by
Uncertain dynamic respond is in jth rank chaos multinomial at the projection vector in random space；
Weaker, formula (12) equation as the uncertainty of dynamic loading with uncertain the two Relativity of system parameter
Left side Section 3 relative contribution very little calculates [R]dApproximation:
[R]d≈[R]-[R]s (13)
S8, covariance matrix [R] is askeddCharacteristic valueAnd feature vectorCalculate its K-L vectorIdentify vector corresponding to Random dynamic loads in structure:
The mean μ of Random dynamic loads is solved using vector corresponding to Random dynamic loadsF(t) and variance
It is set forth in Fig. 3 and Fig. 4 when the coefficient of variation of random systematical and Random dynamic loads amplitude is equal to
10%, the Random dynamic loads mean value and variance and reference value identified using technology in the present invention is compared, and is illustrated in the present invention
The statistical nature of Random dynamic loads can be recognized accurately in technology using the random file response in structure.
The present invention can be using the dynamic loading information acted in the dynamic response data identification structure of actual measurement, not only can be because same
When consider system parameter uncertainty and load randomness, and labyrinth a fairly large number of for freedom degree also have compared with
Good applicability has important theory and application value.
Claims (2)
1. a kind of Random dynamic loads recognition methods based on perturbative matrix, it is characterised in that: the following steps are included:
(1) structure containing uncertain parameters is carried out with modal test multiple under operating condition, obtain uncertain system parameter with
Machine distribution field；
(2) K-L expansion is carried out to system random parameter field, calculates uncertainty rigidity, quality and damping matrix；
(3) uncertain rigidity, quality and damping matrix are unfolded using perturbation method, calculate Green's function matrix, established
Uncertain kinetic model based on perturbative matrix；
(4) the random file response sample of the structure containing uncertain parameters under measurement Random dynamic loads act on；
(5) mean value of suffered Random dynamic loads in random file response sample mean value identification structure is utilized；
(6) it is rung using the structure random file that the Random dynamic loads mean value of identification solves when only considering system parameter uncertainty
It answers；
(7) approximation for only considering the response covariance of random file caused by dynamic loading randomness is calculated；
(8) identification obtains the statistical nature of Random dynamic loads；
Wherein；
Uncertain stiffness matrix K, mass matrix M and damping matrix C are respectively by element stiffness matrix K in step (2)e, unit matter
Moment matrix MeWith unit damping matrix CeAssemble:
Element mass matrix MeWith element stiffness matrix KeIt is calculate by the following formula respectively:
In formula,WithThe respectively desired value of density and elastic parameter, λρWithAssociation respectively containing uncertain density parameter
The eigenvalue and eigenfunction of variance function, λDWithThe characteristic value of covariance function respectively containing uncertain elastic parameter
And characteristic function, KρAnd KDItem number respectively after density and elastic parameter K-L truncation, HeAnd BeThe respectively shape function of unit
Matrix and strain matrix, D are elastic matrix, veFor unit volume, ξiFor irrelevant standard gaussian stochastic variable, subscript i table
Show i-th of ingredient of randomness part；
Unit damping matrix CeAccording to Rayleigh damping model, by MeAnd KeIt is calculated；
Step (3) the following steps are included:
(31) the Green's function matrix G (η) of uncertain kinetic model is calculated:
Green's function matrix G (η) is assembled using the form of Green's function g (t, η) according to the following formula:
Time t in Green's function g (t, η) is wherein subjected to discrete, tQIndicate the Q discrete time step in Green's function；Benefit
Green's function matrix is unfolded with perturbation method:
Wherein, ηdThe mean value for the stochastic variable η for including in system parameter and dynamic loading is represented, n is the quantity of stochastic variable, Gi' be
The corresponding coefficient matrix in randomness part of Green's function matrix；
(32) matrix G (η when uncertain parameters take mean value is calculatedd):
Uncertain parameters take Green's function D when mean valued(t) it is obtained by solving following equation:
In formula, subscript d represents certainty part, i.e., acquired results when stochastic variable takes desired, and δ (t) is impulse response function, T
The transposition of representing matrix or vector；
According to formula (3), g (t, η) is replaced with into Dd(t), it can solve and obtain matrix G (ηd)；
(33) Green's function matrix randomness part G is calculatedi′；
In formula, Mi、CiAnd KiThe respectively randomness part of mass matrix M, damping matrix C and stiffness matrix K, by element quality
Matrix Me, unit damping matrix CeWith element stiffness matrix KeAssembling obtains；
Solution formula (6) respectively obtains stochastic variable ξiThe variation D of caused response when variationi(t), according to formula (3), by g (t,
η) replace with Di(t), it can solve and obtain matrix Gi′；
(34) Random dynamic loads and random file response are used into chaos polynomial expansion, established based on perturbative matrix
Uncertainty structure kinetic model；
Step (5) utilizes random file response sample mean valueIdentify the mean value of suffered Random dynamic loads in structure's
Specific method is:
Step (6) be based on step (3) establish the kinetic model based on perturbative matrix, solve equation (8), calculate with
Maneuver load mean valueThe random file acted on uncertain system responds corresponding vector u(P)(t):
In formula, P is the item number of the chaos polynomial expansion of system random file response, and,
Wherein, Ψj,ΨkExpectation is asked in respectively jth and k rank chaos multinomial, j=1,2 ... P, k=1,2 ... P,<>expression；
Step (7) the following steps are included:
(71) system that uncertain parameters ask expectation corresponding is defined as deterministic system, the mean value of Random dynamic loads is determined
Justice is corresponding certainty dynamic loading；Note Random dynamic loads act on lower uncertain system with the covariance matrix of kinematical displacement
The dynamic displacement covariance matrix of [R], the lower corresponding deterministic system of Random dynamic loads effect are [R]d, corresponding certainty dynamic loading work
It is [R] with the dynamic displacement covariance matrix of lower uncertain systems, above three covariance matrix is with following relational expression:
In formula,WithIt respectively indicates only by dynamic loading uncertainty and only uncertain caused not true by system parameter
Qualitative dynamic respond is in jth rank chaos multinomial at the projection vector in random space；
(72) since the uncertainty of dynamic loading and uncertain the two correlation of system parameter are weak, formula (10) equation left side the
Three contribution very littles calculate [R]dApproximation:
[R]d≈[R]-[R]s (11)。
2. the Random dynamic loads recognition methods according to claim 1 based on perturbative matrix, it is characterised in that: step
Suddenly (8) the following steps are included:
(81) covariance matrix [R] is askeddCharacteristic valueAnd feature vectorCalculate its K-L vectorIdentify vector f corresponding to Random dynamic loads in structure(j)(t):
(82) mean μ of Random dynamic loads is solved using vector corresponding to Random dynamic loadsF(t) and variance
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810148292.1A CN108491578B (en) | 2018-02-13 | 2018-02-13 | A kind of Random dynamic loads recognition methods based on perturbative matrix |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810148292.1A CN108491578B (en) | 2018-02-13 | 2018-02-13 | A kind of Random dynamic loads recognition methods based on perturbative matrix |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108491578A CN108491578A (en) | 2018-09-04 |
| CN108491578B true CN108491578B (en) | 2019-03-12 |
Family
ID=63340410
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810148292.1A Active CN108491578B (en) | 2018-02-13 | 2018-02-13 | A kind of Random dynamic loads recognition methods based on perturbative matrix |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108491578B (en) |
Families Citing this family (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109490983B (en) * | 2018-11-02 | 2019-12-17 | 西南石油大学 | reservoir geomechanical parameter automatic fitting method and system |
| CN110008530B (en) * | 2019-03-15 | 2020-04-24 | 东南大学 | Distributed probability modeling method for space flexible composite material |
| CN110020467B (en) * | 2019-03-20 | 2020-12-08 | 东南大学 | Method for identifying annularly distributed dynamic loads |
| CN110287534B (en) * | 2019-05-24 | 2023-04-18 | 上海宇航系统工程研究所 | Robustness topology optimization method of thin-shell structure considering thickness uncertainty |
| CN110569549B (en) * | 2019-08-07 | 2023-09-19 | 宁波大学 | Dynamic load identification method of truss structure based on interval perturbation |
| CN111027133B (en) * | 2019-10-16 | 2021-06-22 | 北京航空航天大学 | Structure dynamic distribution load identification method based on radial basis function neural network |
| CN111563338B (en) * | 2020-04-24 | 2023-04-07 | 宁波大学 | Truss structure dynamic load identification method considering bounded measurement error |
| CN111832102B (en) * | 2020-06-19 | 2024-02-06 | 浙江大学 | Novel composite material structure optimization design method under high-dimensional random field condition |
| CN112818449B (en) * | 2021-01-29 | 2022-08-02 | 中南大学 | Method and device for analyzing structure random eigenvalue under consideration of parameter uncertainty |
| CN113392547B (en) * | 2021-05-31 | 2024-01-05 | 东南大学 | Frequency domain distribution random dynamic load identification method considering spatial correlation |
| CN113392545B (en) * | 2021-05-31 | 2024-01-30 | 东南大学 | Time domain distribution random dynamic load identification method considering spatial correlation |
| CN115859796B (en) * | 2022-11-24 | 2024-01-26 | 东南大学 | Multi-target structure safety monitoring sensor arrangement method, equipment and storage medium |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102567567A (en) * | 2011-11-15 | 2012-07-11 | 北京宇航系统工程研究所 | Finite element analysis based pipeline random-vibration fatigue life analyzing method |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9088905B2 (en) * | 2012-04-23 | 2015-07-21 | Hughes Network Systems, Llc | Method and apparatus for load balancing on a priority level basis over shared communications channels of a communications system |
| US10432298B2 (en) * | 2012-04-30 | 2019-10-01 | Hughes Network Systems, Llc | Method and apparatus for dynamic load balancing of communications channels for controlling traffic load in a communications system |
| CN107423487B (en) * | 2017-06-21 | 2018-06-12 | 东南大学 | A kind of recognition methods of Random dynamic loads spatial distribution and statistical nature |
| CN107341297B (en) * | 2017-06-21 | 2018-04-24 | 东南大学 | A kind of distribution Random dynamic loads recognition methods based on KL expansion |
| CN107451338B (en) * | 2017-07-12 | 2018-05-11 | 东南大学 | A kind of distribution Random dynamic loads recognition methods based on finite element |
-
2018
- 2018-02-13 CN CN201810148292.1A patent/CN108491578B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102567567A (en) * | 2011-11-15 | 2012-07-11 | 北京宇航系统工程研究所 | Finite element analysis based pipeline random-vibration fatigue life analyzing method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108491578A (en) | 2018-09-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108491578B (en) | A kind of Random dynamic loads recognition methods based on perturbative matrix | |
| CN108038315B (en) | A kind of Random dynamic loads recognition methods based on spectrum stochastic finite meta-model | |
| Hu et al. | Damage assessment of structures using modal test data | |
| WO2012130237A1 (en) | Method for improving determination of mode shapes for a mechanical structure and applications hereof | |
| CN102759573B (en) | Based on the construction damage positioning of frequency change and the appraisal procedure of degree of injury | |
| CN107862170B (en) | Finite element model correction method based on dynamic polycondensation | |
| Pingle et al. | Full field dynamic stress/strain from limited sets of measured data | |
| Pingle et al. | Prediction of full field dynamic stress/strain from limited sets of measured data | |
| Shyamala et al. | Numerical and experimental investigation for damage detection in FRP composite plates using support vector machine algorithm | |
| Ong et al. | Determination of damage severity on rotor shaft due to crack using damage index derived from experimental modal data | |
| CN115879331A (en) | Kelvin model-based spring-damping vibration attenuation structure parameter optimization analysis method | |
| Zimmerman | Looking into the crystal ball: The continued need for multiple viewpoints in damage detection | |
| Shahbaznia et al. | An improved time-domain damage detection method for railway bridges subjected to unknown moving loads | |
| Bagherahmadi et al. | Structural damage detection using a damage probability index based on frequency response function and strain energy concept | |
| Garesci et al. | Experimental results of a damage detection methodology using variations in modal parameters | |
| Patil et al. | Experimental modal analysis on a tyre–lessons learned | |
| CN111428342B (en) | Random dynamic load identification method based on frequency domain spectrum decomposition | |
| Almeida et al. | Evaluation of the performance of three different methods used in the identification of rigid body properties | |
| Chen et al. | Reduced-order modeling of unsteady hypersonic aerodynamics in multi-dimensional parametric space | |
| Sun et al. | Parameter identification of composite materials based on spectral model by using model updating method | |
| Zhang | Effect of damping coefficients on structural damage identification | |
| Martins et al. | In-Situ Health Monitoring of Aerospace Structures via Dynamic Strain Measurements | |
| Sellami et al. | 3D Finite Volume model for free and forced vibrations computation in on-shore wind turbines | |
| Sinha et al. | Enhancing damping estimation accuracy of exponential windowed responses of a GFRP plate through Finite Element Model Updating approach | |
| El-Kafafy et al. | Modal parameter identification using particle swarm optimization |
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 |