CN107423487B - A kind of recognition methods of Random dynamic loads spatial distribution and statistical nature - Google Patents
A kind of recognition methods of Random dynamic loads spatial distribution and statistical nature Download PDFInfo
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Abstract
The invention discloses the recognition methods of a kind of Random dynamic loads spatial distribution and statistical nature.The method of the present invention includes steps：S1. carry out modal test, the modal parameter of structure is obtained, including intrinsic frequency and Mode Shape；S2. Structure Random Vibration response using Mode Shape is unfolded, obtains dynamic response of the structure in Modal Space；S3. it is unfolded using Mode Shape, Modal Space will be projected to the Random dynamic loads of spatial distribution；S4. in Modal Space, by random dynamic response sample inverting Random dynamic loads sample；S5. the spatial distribution and statistical nature of Random dynamic loads in structure are solved by Random dynamic loads sample in Modal Space and model function of vibration.The present invention can solve the problems, such as that, using the statistical property and distribution characteristics for surveying Random dynamic loads in structure dynamic response specimen discerning structure in time domain, Structural Design and security evaluation to be served under distributed random dynamic loading environment provide accurately and reliably dynamic loading information.
Description
Technical field：
The present invention relates to the recognition methods of a kind of Random dynamic loads spatial distribution and statistical nature, and it is anti-to belong to Structural Dynamics
Problem Technical field.
Background technology：
Dynamic loading information in engineering structure is the foundation of structure design and security evaluation.The acquisition methods of dynamic loading are substantially
It is divided into and directly measures and two kinds of indirect identification.In many cases, dynamic loading is difficult to by directly measuring acquisition, general using survey
The dynamic response in structure is measured, in the case that known to structural system, identifies dynamic loading information needed for obtaining.
Traditional Dynamic Load Identification method is that the structure dynamic response data identification surveyed using single causes the secondary dynamic response
Excitation information, being to determine property Dynamic Load Identification method.Existing certainty Dynamic Load Identification method be used to obtain engineering knot
Concentration dynamic loading on structure, the information such as mobile load and distributed dynamic loading.It is worth noting that, distributed Dynamic Load Identification
Problem is equivalent to the infinite multiple concentration dynamic loadings of identification, and difficulty bigger is generally required distributed Dynamic Load Identification problem dimensionality reduction
It solves.
The dynamic loading acted on engineering structure, the wave load born such as the wind load on building, ocean platform
And aerodynamic loading of aircraft surface etc., it is not only distributed in structure, but also with randomness.Random dynamic loads are applied to
During structure, " randomness " will be also presented in dynamic response therewith；Therefore, the structure dynamic response of single actual measurement can only be the random sound of something astir of structure
One of sample of information is answered, the dynamic loading information of certainty Dynamic Load Identification method acquisition is utilized based on some response sample
Also it can only partly reflect that the Random dynamic loads encourage；In addition, the dynamic response error included in single measurement is in certainty dynamic loading
The deviation of load recognition result is also caused by the part as " true response " in identification.It is moved for such distributed random
The identification problem of load, traditional certainty distribution Dynamic Load Identification method and the recognition methods suitable for concentrating Random dynamic loads
It can not use, need to develop a kind of new method for distributed random Dynamic Load Identification, there is actual measurement structure dynamic response sample
Identify the spatial distribution and statistical nature of Random dynamic loads.
Invention content
The object of the present invention is to provide the recognition methods of a kind of Random dynamic loads spatial distribution and statistical nature, solve when
Using the statistical property of Random dynamic loads and distribution characteristics problem in structure dynamic response specimen discerning structure is surveyed in domain, to be on active service
Structural Design under distributed random dynamic loading environment provides accurately and reliably dynamic loading information with security evaluation.
Above-mentioned purpose is achieved through the following technical solutions：
The recognition methods of a kind of Random dynamic loads spatial distribution and statistical nature, this method comprises the following steps：
S1. carry out modal test, the modal parameter of structure is obtained, including intrinsic frequency and Mode Shape；
S2. Structure Random Vibration response using Mode Shape is unfolded, obtains dynamic response of the structure in Modal Space；
S3. it is unfolded using Mode Shape, Modal Space will be projected to the Random dynamic loads of spatial distribution；
S4. in Modal Space, by random dynamic response sample inverting Random dynamic loads sample；
S5. the spatial distribution of Random dynamic loads in structure is solved by Random dynamic loads sample in Modal Space and model function of vibration
And statistical nature.
The recognition methods of Random dynamic loads spatial distribution and the statistical nature, it is described in step S2 that structure is random
Vibratory response is unfolded using Mode Shape, obtains dynamic response of the structure in Modal Space, the specific steps are：
S21：Utilize the sample set that measurement method acquisition PSD response is repeated several times：
(the x in structure1,x2,…xn) measure for the r times at position and obtain dynamic respond sample vector WrIt is expressed as：
Wr={ wr(x1,t) wr(x2,t)…wr(xn,t)}T, r=1 ..., N (1),
Wherein wr(xj, t) and it represents to measure the displacement structure obtained in x the r timesjLocating the value of t moment, N is the number measured,
It is also contemplated that response sample capacity；
S22：For single sample, i.e. single actual measurement structural vibration response, it is unfolded to obtain structural vibration using Mode Shape
It is responded in Modal Space：
The corresponding modal displacement vector of the r times measurement in Modal Space is calculated using Mode Shape function：
Wherein qi,r(t) modal displacement of the displacement structure obtained in the i-th rank Modal Space is measured for the r times,Table
Show the i-th rank Mode Shape function in xjThe value at place, the upper right corner+number expression generalized inverse.
The recognition methods of Random dynamic loads spatial distribution and the statistical nature, the utilization mode described in step S3 are shaken
Type is unfolded, and will project to Modal Space with the Random dynamic loads of spatial distribution, specifically includes following steps：
S31：Random dynamic loads distribution is enabled independently of its stochastic behaviour and time history, by its distribution function and random time
Course is unfolded using Mode Shape, is as follows：Distribution Random dynamic loads f (x, t, θ) is expressed as its distribution function T
(x) it with the product of random time course P (t, θ), is shown below：
F (x, t, θ)=T (x) P (t, θ) (3),
Distribution function T (x) is unfolded using Mode Shape：
Formula (4) is substituted into formula (3), can be obtained：
Wherein ak(t, θ)=dkP(t,θ)。
Random dynamic loads f in i-th rank Modal Spacei(t, θ) can be expressed as：
Wherein L represents the length of beam；
S32：Using the orthogonality of Mode Shape function, establish random between dynamic response and Random dynamic loads in Modal Space
Relationship.It is as follows：
Kinetics equation of the structure in Modal Space be：
Wherein qi(t, θ),WithStructure random file respectively in Modal Space, speed and acceleration,
ζiAnd miRespectively the i-th rank damping ratios and modal mass.Formula (6) is substituted into formula (7), utilizes the orthogonal of the structural modal vibration shape
Property condition, random relational expression between dynamic response and Random dynamic loads can be obtained in Modal Space, it is as follows：
The recognition methods of Random dynamic loads spatial distribution and the statistical nature, described in step S4 in Modal Space
It is interior, Random dynamic loads are solved by random dynamic response, specifically include following steps：
S41：According to displacement structure, the derivative relation between speed and acceleration measures the structural modal obtained by the r times
Displacement qi,r(t), corresponding modal velocity and modal acceleration are obtained to time derivation；If measure acquisition is structure acceleration
Mode acquisition speed and the displacement of integration equally can be used in signal；
S42：By random file q in the Modal Space in formula (8)iThe sample q of (t, θ)i,r(t) and its derivative, solution obtain
Random dynamic loads a in Modal SpaceiThe sample a of (t, θ)i,r(t)。
The recognition methods of Random dynamic loads spatial distribution and the statistical nature, described in step S5 by Modal Space
Interior Random dynamic loads sample and model function of vibration solve the spatial distribution and statistical nature of Random dynamic loads in structure, specifically include with
Lower step：
S51：The spatial distribution of Random dynamic loads can be calculated by following formula：
Wherein t1For any time；
S52：The mean μ of Random dynamic loadsf(x, t) can be calculated by following formula：
S53：The variance Var of Random dynamic loadsf(x, t) can be calculated by following formula：
Advantageous effect：
Compared with prior art, the present invention it has the following advantages：
1st, existing Random dynamic loads identification technology generally can only be by random in actual measurement structure dynamic response specimen discerning structure
Dynamic loading is concentrated, the distribution Random dynamic loads recognition methods occurred at present can not be suitable for the knowledge of non-stationary Random dynamic loads
Not, the distribution Random dynamic loads time domain identification technology provided in the present invention can utilize the actual measurement structure sound of something astir at limited measure node
It answers the spatial distribution of specimen discerning Random dynamic loads and statistical nature changes with time rule, there is certain advance；
2nd, using Mode Shape functional expansion, the identification problem for being distributed Random dynamic loads is converted into dynamic load in Modal Space
The estimation problem of lotus random process greatly reduces the dimension and difficulty of load identification problem, has easy to operate and computational efficiency
The characteristics of high.
Description of the drawings
Fig. 1 is the logical procedure diagram of the method for the present invention.
Fig. 2 is the lower simply supported beam schematic diagram of distribution Random dynamic loads effect.
Fig. 3 is Random dynamic loads spatial distribution recognition result schematic diagram.
Fig. 4 (a) is Random dynamic loads time-varying mean value recognition result schematic diagram.
Fig. 4 (b) is Random dynamic loads time-varying variance recognition result schematic diagram.
Fig. 4 (c) is Random dynamic loads correlation function recognition result schematic diagram.
Specific embodiment
Below by the mode of embodiment, technical solution of the present invention is described in detail, but embodiment is only the present invention
One of which embodiment, it should be pointed out that：To those of ordinary skill in the art, the principle of the invention is not being departed from
Under the premise of, several improvement and equivalent replacement can also be made in a manner of structure and loading etc. to change, these weigh the present invention
Profit requirement be improved with the technical solution after equivalent replacement, each fall within protection scope of the present invention.
Embodiment：To acted on simple beam structure as shown in Figure 2 distribution Random dynamic loads using the present invention method into
Row identification.Beam length L=40m, cross-sectional area A=4.8m2, cross sectional moment of inertia I=2.5498m4, the damping of structure is using Rayleigh resistance
Buddhist nun, each rank damping ratios ξi=0.02, elastic modulus E=5 × 10 of material10N/m2, density p=2.5 × 103kg/m3.It treats
The trapezoidal profile Random dynamic loads distribution function of identification is：
The randomness dynamic loading component F (t, θ) of distributed random dynamic loading is divided into certainty dynamic loading and randomness dynamic load
Two parts of lotus.
The certainty dynamic loading part of F (t, θ)：
Fd(t)=20000 [1+0.1sin (2 π t)] N (2)
The randomness dynamic loading part of F (t, θ) is assumed to zero-mean non-stationary Gaussian random process, power spectrum function S
(ω, t) is：
S (ω, t)=CfPd(t)Φ(ω) (3)
Wherein：CfIt represents Random Level, takes Cf=0.2；Φ (ω) represents the power of zero-mean non-stationary Gaussian random process
Spectral density function has Φ (ω)=(1/2 π) (2/ ω2+1)。
Using technology of the invention by the spatial distribution and system of the random dynamic response specimen discerning Random dynamic loads of actual measurement structure
Feature is counted, specifically includes following steps：
S1：Modal test is carried out to simply supported beam, first five the rank intrinsic frequency for obtaining structure is respectively 3.9Hz, 15.6Hz,
35.1Hz, 62.5Hz and 97.6Hz, while obtain the Mode Shape corresponding to each rank intrinsic frequency；
S2：Structure Random Vibration response using Mode Shape is unfolded, dynamic respond signal is obtained using multiple measure, asks
Solution structure includes the following steps in the dynamic response of Modal Space：
S21：It is evenly arranged 19 measuring points in girder construction, the dynamic displacement signal at each measuring point of duplicate measurements obtains
It is distributed the sample set of PSD response under arbitrary excitation；
S22：For single sample, i.e. single actual measurement structural vibration response, it is unfolded to obtain structural vibration using Mode Shape
It is responded in Modal Space.It is as follows：
The r times measurement in position obtains dynamic respond sample vector W in girder constructionrIt is expressed as：
Wr={ wr(x1,t) wr(x2,t)…wr(xn,t)}T, r=1 ..., N (4),
Wherein wr(xj, t) and it represents to measure the displacement structure obtained in x the r timesjLocating the value of t moment, N is the number measured,
Using 5000 times in the present embodiment, as total sample number is 5000.The r times survey in Modal Space is calculated using Mode Shape function
Measure corresponding modal displacement vector：
Wherein qi,r(t) modal displacement of the displacement structure obtained in the i-th rank Modal Space is measured for the r times,Table
Show the i-th rank Mode Shape function in xjThe value at place, the upper right corner+number expression generalized inverse.At this point, measuring point number n=19, mode number m=
5。
S3：It is unfolded using Mode Shape, Modal Space will be projected to the Random dynamic loads of spatial distribution, including following step
Suddenly：
S31：Random dynamic loads distribution is enabled independently of its stochastic behaviour and time history, by its distribution function and random time
Course is unfolded using Mode Shape.It is as follows：
By taking the non-stationary Random dynamic loads f (x, t, θ) of a trapezoidal profile as an example, can be expressed as its distribution function T (x) with
The product of random time course P (t, θ), is shown below：
F (x, t, θ)=T (x) P (t, θ) (6),
Preceding 5 rank natural mode of vibration functional expansion distribution function T (x), i.e. k=5 are utilized according to the following formula：
The vibration shape in (7) formula of utilization is unfolded, and identifies that the distribution function of dynamic loading can be exchanged into migration index dkThe problem of,
Substantially reduce identification difficulty.Formula (7) is substituted into formula (6), can be obtained
Wherein ak(t, θ)=dkP(t,θ)。
Random dynamic loads f in i-th rank Modal Spacei(t, θ) can be expressed as：
Wherein L represents the length of beam.
S32：Using the orthogonality of Mode Shape function, establish random between dynamic response and Random dynamic loads in Modal Space
Relationship.It is as follows：
Kinetics equation of the simply supported beam in Modal Space be：
Wherein qi(t, θ),WithStructure random file respectively in Modal Space, speed and acceleration,
ζiAnd miRespectively the i-th rank damping ratios and modal mass.Formula (9) is substituted into formula (10), using simply supported beam Mode Shape just
The property handed over condition：
Wherein δijFor Kronecker function.It can then obtain in Modal Space random between dynamic response and Random dynamic loads
Relational expression is as follows：
Wherein ρ A are the line density of beam.
S4：In Modal Space, Random dynamic loads are solved by random dynamic response.It is as follows：
S41：According to displacement structure, the derivative relation between speed and acceleration measures the structural modal obtained by the r times
Displacement qi,r(t), corresponding modal velocity and modal acceleration are obtained to time derivation；If measure acquisition is structure acceleration
Mode acquisition speed and the displacement of integration equally can be used in signal；
S42：By random file q in the Modal Space in formula (12)iThe sample q of (t, θ)i,r(t) and its derivative it, solves
Random dynamic loads a in Modal SpaceiThe sample a of (t, θ)i,r(t)。
S5：The spatial distribution and system of Random dynamic loads in structure are solved by Random dynamic loads in Modal Space and model function of vibration
Count feature.It is as follows：
S51：Using proposed method, identification obtains each moment Random dynamic loads spatial distribution, with true profiles versus
As shown in Figure 3；
S52：Identification obtains the mean value that changes over time of Random dynamic loads, in girder span Random dynamic loads identification mean value with very
Real value comparison is as shown in Figure 4；
S53：Identification obtains the variance that changes over time of Random dynamic loads and correlation function, Random dynamic loads side in girder span
Difference and correlation function discre value and actual value comparison are as shown in Figure 4；
From the foregoing, it will be observed that the recognition methods in the present invention can utilize response sample at limited measure node to accurately identify Random Dynamic Loads
The statistical nature that lotus changes over time suitable for the situation of non-stationary Random dynamic loads, has certain advanced.
Claims (2)
1. the recognition methods of a kind of Random dynamic loads spatial distribution and statistical nature, which is characterized in that this method includes following step
Suddenly：
S1. carry out modal test, the modal parameter of structure is obtained, including intrinsic frequency and Mode Shape；
S2. Structure Random Vibration response using Mode Shape is unfolded, obtains dynamic response of the structure in Modal Space；
S3. it is unfolded using Mode Shape, Modal Space will be projected to the Random dynamic loads of spatial distribution；
S4. in Modal Space, by random dynamic response sample inverting Random dynamic loads sample；
S5. the spatial distribution and system of Random dynamic loads in structure are solved by Random dynamic loads sample in Modal Space and model function of vibration
Count feature；
Structure Random Vibration response being unfolded using Mode Shape described in step S2, obtains the sound of something astir of the structure in Modal Space
Should, the specific steps are：
S21：Utilize the sample set that measurement method acquisition PSD response is repeated several times：
(the x in structure1,x2,…xn) measure for the r times at position and obtain dynamic respond sample vector WrIt is expressed as：
Wr={ wr(x1,t) wr(x2,t) … wr(xn,t)}T, r=1 ..., N (1),
Wherein wr(xj, t) and it represents to measure the displacement structure obtained in x the r timesjLocate the value of t moment, N is the number measured；
S22：For single sample, i.e. single actual measurement structural vibration response, it is unfolded to obtain structural vibration in mould using Mode Shape
It is responded in state space：
The corresponding modal displacement vector of the r times measurement in Modal Space is calculated using Mode Shape function：
Wherein qi,r(t) modal displacement of the displacement structure obtained in the i-th rank Modal Space is measured for the r times,Represent the
I rank Mode Shape functions are in xjThe value at place, the upper right corner+number expression generalized inverse；
Utilization Mode Shape expansion described in step S3, will project to Modal Space with the Random dynamic loads of spatial distribution, has
Body includes the following steps：
S31：Random dynamic loads distribution is enabled independently of its stochastic behaviour and time history, by its distribution function and random time course
It is unfolded using Mode Shape, is as follows：Distribution Random dynamic loads f (x, t, θ) is expressed as its distribution function T (x)
With the product of random time course P (t, θ), it is shown below：
F (x, t, θ)=T (x) P (t, θ) (3),
Distribution function T (x) is unfolded using Mode Shape：
Formula (4) is substituted into formula (3), is obtained：
Wherein ak(t, θ)=dkP (t, θ),
Random dynamic loads f in i-th rank Modal Spacei(t, θ) is expressed as：
Wherein L represents the length of beam；
S32：Using the orthogonality of Mode Shape function, random pass between dynamic response and Random dynamic loads in Modal Space is established
System, is as follows：
Kinetics equation of the structure in Modal Space be：
Wherein qi(t, θ),WithStructure random file respectively in Modal Space, speed and acceleration, ζiWith
miFormula (6) is substituted into formula (7), utilizes the orthogonality item of the structural modal vibration shape by respectively the i-th rank damping ratios and modal mass
Part obtains random relational expression between dynamic response and Random dynamic loads in Modal Space, as follows：
Random dynamic loads in structure are solved by Random dynamic loads sample in Modal Space and model function of vibration described in step S5
Spatial distribution and statistical nature, specifically include following steps：
S51：The spatial distribution of Random dynamic loads is calculated by following formula：
Wherein t1For any time；
S52：The mean μ of Random dynamic loadsf(x, t) is calculated by following formula：
S53：The variance Var of Random dynamic loadsf(x, t) is calculated by following formula：
2. the recognition methods of Random dynamic loads spatial distribution according to claim 1 and statistical nature, which is characterized in that step
Described in rapid S4 in Modal Space, by random dynamic response sample inverting Random dynamic loads sample, specifically include following steps：
S41：According to displacement structure, the derivative relation between speed and acceleration measures the structural modal displacement obtained by the r times
qi,r(t), corresponding modal velocity and modal acceleration are obtained to time derivation；If measure acquisition is structure acceleration signal,
Similary acquisition speed and displacement by the way of integration；
S42：By random file q in the Modal Space in formula (8)iThe sample q of (t, θ)i,r(t) and its derivative, solution obtain mode
Random dynamic loads a in spaceiThe sample a of (t, θ)i,r(t)。
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| CN108038315B (en) * | 2017-12-15 | 2019-04-09 | 东南大学 | A kind of Random dynamic loads recognition methods based on spectrum stochastic finite meta-model |
| CN108491578B (en) * | 2018-02-13 | 2019-03-12 | 东南大学 | A kind of Random dynamic loads recognition methods based on perturbative matrix |
| CN110083886A (en) * | 2019-04-08 | 2019-08-02 | 西北工业大学 | A kind of helicopter vibration load simulating analysis based on finite element |
| CN113392545B (en) * | 2021-05-31 | 2024-01-30 | 东南大学 | Time domain distribution random dynamic load identification method considering spatial correlation |
| CN113392547B (en) * | 2021-05-31 | 2024-01-05 | 东南大学 | Frequency domain distribution random dynamic load identification method considering spatial correlation |
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| EP2500836A2 (en) * | 2011-03-16 | 2012-09-19 | Airbus Operations Limited | Stresses induced by random loading |
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