CN107633132A - The equivalent recognition methods of spatial distribution dynamic load - Google Patents
The equivalent recognition methods of spatial distribution dynamic load Download PDFInfo
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- CN107633132A CN107633132A CN201710839583.0A CN201710839583A CN107633132A CN 107633132 A CN107633132 A CN 107633132A CN 201710839583 A CN201710839583 A CN 201710839583A CN 107633132 A CN107633132 A CN 107633132A
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Abstract
The present invention discloses a kind of equivalent recognition methods of spatial distribution dynamic load suffered by structure.First, a series of sub- load that the distribution dynamic load of time and space coupling is resolved into time and space independences is decomposed using Proper Orthogonal；Secondly, structural response is measured, modal response is obtained by modal transformation, and combine regularization method and accurate stable identification is carried out to mode load；Again, blind source separating is carried out to the mode load of identification, obtains the time history of dynamic load in limited individual equal set, and calculate its aliased coefficient；Finally, consider that aliased coefficient is load space distribution function and the inner product of the structural modal vibration shape, Its Sparse Decomposition is carried out to it, identifies the locus of equivalent concentrfated load.The present invention provides a kind of effective equivalent recognition methods to be difficult to the spatial distribution dynamic load measured, when the equivalent concentrfated load identified puts on structure, can produce and be responded with the output of former spatial distribution dynamic load identical.
Description
Technical field
The invention belongs to parameter identification technology field, more particularly to a kind of equivalent knowledge of spatial distribution dynamic load suffered by structure
Other method.
Background technology
Distribution dynamic load is widely present in Practical Project, such as the wind load suffered by building or aircraft, dykes and dams or
Wave load suffered by boat etc..For engineering structure, analyze and research its vibration problem, grasp as caused by distribution dynamic load are shaken
Motivation is managed, and effectively can be prevented or be eliminated and vibrate the harmful effect that brings, reasonably using vibrating favourable one side.However,
This is needed premised on determining the distribution dynamic load suffered by structure.Distribution dynamic load was both related to time history, and in sky
Between it is upper distribution form is presented, due to being limited by technology or economic condition, it is difficult or even at all can not be by direct measurement pair
Its determination.The measurement of structure dynamic displacement response is relatively easily and accurate, therefore utilizes limited individual structure measurement response identification knot
The distribution dynamic load that structure is subject to, there will be important practical usage.
The content of the invention
It is difficult to difficulty measured directly for distribution dynamic load, the present invention proposes a kind of point based on structure dynamic response
The equivalent recognition methods of cloth dynamic load, accurately have so as to be provided for structural vibration control, Dynamic Modification and dynamics Optimization Design
The external load parameter of effect.
The present invention provides a kind of spatial distribution based on Proper Orthogonal decomposition, model analysis, blind source separating and Its Sparse Decomposition
The equivalent recognition methods of dynamic load, comprises the following steps：
1st, a kind of equivalent recognition methods of spatial distribution dynamic load, it is characterised in that comprise the following steps：
Step 1：By suffered by structure unknown distribution dynamic load carry out Proper Orthogonal decomposition, be converted into a series of times with
The sub- load of space independence；
Step 2：Structural finite element model is established, and carries out model analysis, obtains Mode Shape coefficient matrix, the mould of structure
State quality, modal damping, modal stiffness, undamped natural frequency of a mechanical system, damped natural frequency and damping ratio；
Step 3：Using the dynamic response of the lower structure of sensor measurement distribution dynamic load effect, and carry out modal transformation and obtain
Take and block modal response accordingly；
Step 4：Based on modal response and mode Green's kernel function, the mode load using regularization method to limited order
Carry out accurate stable identification；
Step 5：It is the limited aliasing for concentrating dynamic load by mode load-transfer mechanism, using blind source separate technology from identification
Mode load in obtain the time history of equivalent concentrfated load, and calculate corresponding aliased coefficient；
Step 6：It is load space distribution and the inner product of the structural modal vibration shape to consider aliased coefficient, and aliased coefficient vector is entered
Row Its Sparse Decomposition, identify the space behavior position of equivalent concentrfated load.
Preferably, in the step 1, spatial distribution dynamic load form to be identified can be that time and space are mutual
It is independent, can also time and space intercouple., will by Proper Orthogonal resolution when time and space intercouple
It is converted into a series of sub- load of time and space independences as shown in formula (1).
In formula, F (x, t) represent act in structure the time and space coupling distribution dynamic load, by it is intrinsic just
Hand over the sub- load sum that decomposition can be approximately L item times and space independence, ψn(x) space point of n-th of sub- load is represented
Cloth function, sn(t) time history of n-th of sub- load is represented.
Preferably, in the step 3, the measurement response for spatial distribution dynamic state loading identification can be displacement, speed
Degree or acceleration.
Preferably, in the step 4, the forward model of structural modal load reverse is established based on Green's KERNEL FUNCTION METHOD
, and pass through the precision and stability of regularization raising recognition result.
Preferably, in the step 5, the time history of each rank mode load can be equivalent to the limited individual concentrfated load time
The aliasing of course, it has following expression,
In formula, pi(t) the i-th rank mode load is represented,Represent structure the i-th rank Mode Shape, subscript T represent vector or
The transposition of matrix,Represent time history sn(t) i-th of aliased coefficient, its be the i-th rank Mode Shape vector with
The inner product of n-th of spatially distributed functions vector.
Preferably, in the step 6, the formula (7) for solving sub- load space distribution function is the underdetermined system of equations, therefore load
Solve be present in the reverse result of spatially distributed functions more.By most sparse solution as reverse result, i.e., determined by Its Sparse Decomposition equivalent
The active position of concentrfated load.
In formula,The aliased coefficient of n-th of spatially distributed functions of correspondence that solution obtains is represented, H is
Mode number is blocked, N represents the discrete points of structure loading area, and it typically much deeper than blocks mode number H,(j=1,2 ...,
N the Mode Shape coefficient under structure the i-th rank mode at j-th of discrete point, ψ) are representednjRepresent n-th of spatially distributed functions in jth
Equivalence value at individual discrete point.
The present invention innovatively proposes a kind of side that the identification of distribution dynamic load-transfer mechanism is realized using structure dynamic response
Method.The identification of the distribution dynamic load of time and Space Coupling is equivalent to the identification of limited individual concentrfated load time history by this method
And its determination of space behavior position, what structure was subject to etc. is identified using the structure dynamic response accurate stable for being easy to measurement
Imitate concentrfated load.
According to above-mentioned technical proposal, beneficial effects of the present invention include：
(1) engineering structure is acted on by the continuous distribution dynamic load in space, tested equipment and economic technology condition
Limitation, conventional method of testing are difficult to carry out direct measurement to distribution dynamic load.Identification of the invention by distribution dynamic load
Be equivalent to the identification of limited individual concentrfated load time history and active position, for the structure design in Practical Project, optimization and
Tool is assessed to be of great significance.
(2) present invention takes full advantage of the knot relatively easily measured when carrying out the identification of distribution dynamic load history
Structure Dynamic Response Information and accurate structural modal information, and regularization and blind source separate technology are combined, realize concentration and carry
The stable identification of lotus time history.
(3) present invention, by Its Sparse Decomposition technology, has asked for sky when distributed load spatially distributed functions are identified
Between distribution function most sparse solution, realize the determination of concentrfated load active position.
Brief description of the drawings
Accompanying drawing is only used for showing the purpose of specific embodiment, and is not considered as limitation of the present invention, in whole accompanying drawing
In, identical reference symbol represents identical part.
Fig. 1 is the step flow chart of distribution dynamic load-transfer mechanism recognition methods in the present invention；
Fig. 2 is the distribution dynamic load of time and space coupling；
Fig. 3 is that Proper Orthogonal decomposes to obtain the distribution dynamic load of time and space independence；
Fig. 4 is the bonnet inner panel acted on by distribution dynamic load；
Fig. 5 is the preceding 6 rank mode load of identification；
Fig. 6 a are load histories in the equal set that blind source separating obtains；
Fig. 6 b are load space positions in the equal set that Its Sparse Decomposition obtains；
Fig. 6 c are dynamic loads in the equal set identified；
Fig. 7 is the lower structure dynamic response of equivalent load effect and checking.
Embodiment
1-7 is right by taking the distribution dynamic load that equivalent certain car bonnet inner panel edge of identification is subject to as an example below in conjunction with the accompanying drawings
The embodiment of the present invention is described in detail.
The distribution dynamic load that structure is subject to can not generally be obtained by means measured directly, and structure is dynamic because being distributed
The relatively easy measurement of response caused by state load.Therefore, decomposed first by Proper Orthogonal, by time and point of Space Coupling
Cloth dynamic load is decoupled into a series of sub- distribution dynamic load of time and space independences；Secondly, reverse knot is responded using measurement
Simultaneously limited rank mode load is identified in Modal Space for the modal response of structure；Again, being obtained based on blind source separate technology is had
The time history of limit concentrfated load；The space behavior position of concentrfated load is determined finally by Its Sparse Decomposition.
Fig. 1 shows the step flow of distribution dynamic load-transfer mechanism recognition methods in the specific embodiment of the invention, specifically
Implementation steps are as follows：
Step 1：By suffered by structure unknown distribution dynamic load carry out Proper Orthogonal decomposition, be converted into a series of times with
The sub- load of space independence；
Consider distribution dynamic load F (x, t)=1000sin (20 π xt) of time and space coupling as shown in Figure 2,0≤
X≤1m, 0≤t≤0.1s.It is only that a series of time and spaces as shown in formula (1) are translated into by Proper Orthogonal resolution
Vertical sub- load,
In formula, F (x, t) represent act in structure the time and space coupling distribution dynamic load, by it is intrinsic just
Hand over the sub- load sum that decomposition can be approximately L item times and space independence, ψn(x) space point of n-th of sub- load is represented
Cloth function, sn(t) time history of n-th of sub- load is represented.In this embodiment, distribution dynamic load to be identified can be equivalent
To convert the sub- load sum of 4 time and space independences as shown in Figure 3.
Step 2：Structural finite element model is established, and carries out model analysis, obtains Mode Shape coefficient matrix, the mould of structure
State quality, modal damping, modal stiffness, undamped natural frequency of a mechanical system, damped natural frequency and damping ratio；
As shown in figure 4, Slab in certain automobile engine cover by the effect of distribution dynamic load is employed in the embodiment, altogether
Comprising 10775 shell units, 10685 nodes, uniform thickness 0.8mm, four angles are by fixed constraint, the modulus of elasticity of material
For E=210GPa, Poisson's ratio is μ=0.3, and density is ρ=7.65 × 103kg/m3.Distribution dynamic load acts on its front end edge
The intermediate region of edge.The intrinsic frequency of the Mode Shape coefficient matrix of structure, modal mass, modal damping, modal stiffness, undamped
Rate, damped natural frequency and damping ratio are obtained by analysis of finite element method.
Step 3：Using the dynamic response of the lower structure of sensor measurement distribution dynamic load effect, and carry out modal transformation and obtain
Take and block modal response accordingly；
Due to contribution very little of the high order mode to structure physical responses, thus it is actual calculate in frequently with mode truncation, this
For Rigen according to the actual modal information of structure, mode truncation number is H=6., can by arranging 6 sensors on bonnet inner panel
The dynamic response of structure is measured, it can be displacement, speed or acceleration.In the embodiment, dynamic respond is measured, then accordingly
Response of mode displacement can be tried to achieve by following inverse transformation formula,
In formula, qi(t) (i=1,2 ..., H) represents the i-th rank response of mode displacement of structure,Represent j-th measuring point
I-th rank Mode Shape coefficient, μ(j)(t) dynamic respond of j-th of measuring point is represented,The generalized inverse of representing matrix.
Step 4：Based on modal response and mode Green's kernel function, the mode load using regularization method to limited order
Carry out accurate stable identification；
Under each rank mode, the forward model that mode load reverse is established based on Green's KERNEL FUNCTION METHOD is
In formula, qi(t) the i-th rank response of mode displacement of structure, g are representedi(t) system Green's core under the i-th rank mode is represented
Function, pi(t) the i-th rank mode load is represented, response of mode displacement is the convolution point of mode load and system Green's kernel function.Should
In embodiment, the response measurement time is 0.1s, sampling time interval 0.0002s, and system Green kernel function can parse as follows to be obtained
,
In formula, mi,And ξiRespectively represent structure the i-th rank mode under modal mass, undamped natural frequency of a mechanical system,
Damped natural frequency and damping ratio.By being dissipated in the first-class separation of time-domain, above-mentioned convolution point (3) can be written as matrix form,
It is as shown in Figure 5 using 6 rank mode load before the regularization method identification based on truncated singular value decomposition.
Step 5：It is the limited aliasing for concentrating dynamic load by mode load-transfer mechanism, using blind source separate technology from identification
Mode load in obtain the time history of equivalent concentrfated load, and calculate corresponding aliased coefficient；
According to modal transformation, each rank mode load has following aliasing expression formula,
In formula, pi(t) the i-th rank mode load is represented,Represent structure the i-th rank Mode Shape, subscript T represent vector or
The transposition of matrix,Represent time history sn(t) i-th of aliased coefficient, its be the i-th rank Mode Shape vector with
The inner product of n-th of spatially distributed functions vector.
By carrying out principal component analysis to the mode load (Fig. 5 shows) of reconstruct, it is found that 6 rank mode load are mainly only by 3
Vertical time history aliasing forms.Because in mode loading is built by (6) formula, there is the amplitude phase of a system number
To very little, corresponding time history is caused to be submerged.By the blind source separation method based on global optimum, 3 times are obtained
As shown in Figure 6 a, aliased coefficient is then calculated course by least square method.
Step 6：It is load space distribution and the inner product of the structural modal vibration shape to consider aliased coefficient, and aliased coefficient vector is entered
Row Its Sparse Decomposition, identify the space behavior position of equivalent concentrfated load.
According to the composition of aliased coefficient,The forward model of following spatially distributed functions reverse is established,
In formula,The aliased coefficient of n-th of spatially distributed functions of correspondence that solution obtains is represented,(j
=1,2 ..., N) the Mode Shape coefficient at j-th of discrete point under structure the i-th rank mode is represented, N represents structure loading area
Discrete points, it, which is typically much deeper than, blocks mode number H, N=49, H=6, ψ in the embodimentnjRepresent n-th of spatially distributed functions
Equivalence value at j-th of discrete point.Because the equation group of above-mentioned solution room distribution function is to owe fixed, therefore have countless more
Solution.
Using Its Sparse Decomposition algorithm, ψ is obtainednjThe minimum most sparse solution of nonzero value number is as shown in Figure 6 b.It is originally continuous
Distribution dynamic load-transfer mechanism is reconstructed into multi-source dynamic load as fig. 6 c.The distributed load of equivalent reconstruct is applied to engine
Lid inner panel calculates response and carries out Accuracy Verification, and the dynamic respond of 3 measuring points picked out at random with original response as shown in fig. 7, intend
Close very good.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art the invention discloses technical scope in, the change or replacement that can readily occur in,
It should all be included within the scope of the present invention.
Claims (6)
1. a kind of equivalent recognition methods of spatial distribution dynamic load, it is characterised in that it is characterised in that it includes following steps：
Step 1：Unknown distribution dynamic load suffered by structure is subjected to Proper Orthogonal decomposition, is converted into a series of time and spaces
Independent sub- load；
Step 2：Structural finite element model is established, and carries out model analysis, obtains Mode Shape coefficient matrix, the mode matter of structure
Amount, modal damping, modal stiffness, undamped natural frequency of a mechanical system, damped natural frequency and damping ratio；
Step 3：Using the dynamic response of the lower structure of sensor measurement distribution dynamic load effect, and carry out modal transformation and obtain phase
That answers blocks modal response；
Step 4：Based on modal response and mode Green's kernel function, the mode load of limited order is carried out using regularization method
Accurate stable identifies；
Step 5：By mode load-transfer mechanism for the limited aliasing for concentrating dynamic load, the mould using blind source separate technology from identification
The time history of equivalent concentrfated load is obtained in state load, and calculates corresponding aliased coefficient；
Step 6：It is load space distribution and the inner product of the structural modal vibration shape to consider aliased coefficient, aliased coefficient vector is carried out dilute
Dredge and decompose, identify the space behavior position of equivalent concentrfated load.
2. according to the method for claim 1, it is characterised in that in the step 1, spatial distribution to be identified dynamic carries
Lotus form can be that time and space are separate, can also time and space intercouple；When time and space are mutual
During coupling, a series of sub- load for the time and space independences being translated into by Proper Orthogonal resolution as shown in formula (1)：
<mrow>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>&ap;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>&psi;</mi>
<mi>n</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>s</mi>
<mi>n</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, F (x, t) represents to act on the distribution dynamic load of the time and space coupling in structure, passes through Proper Orthogonal point
Solution can be approximately the sub- load sum of L item times and space independence, ψn(x) the spatial distribution letter of n-th of sub- load is represented
Number, sn(t) time history of n-th of sub- load is represented.
3. according to the method for claim 1, it is characterised in that in the step 3, know for spatial distribution dynamic load
Other measurement response can be displacement, speed or acceleration.
4. according to the method for claim 1, it is characterised in that in the step 4, the forward direction of structural modal load reverse
Model is established based on Green's KERNEL FUNCTION METHOD, and the precision and stability of recognition result is improved by regularization.
5. according to the method for claim 1, it is characterised in that in the step 5, the time history of each rank mode load
The aliasing of limited individual concentrfated load time history can be equivalent to, it has following expression,
In formula, pi(t) the i-th rank mode load is represented,The i-th rank Mode Shape of structure is represented, subscript T represents vector or matrix
Transposition,Represent time history sn(t) i-th of aliased coefficient, it is the i-th rank Mode Shape vector and n-th
The inner product of spatially distributed functions vector.
6. according to the method for claim 1, it is characterised in that in the step 6, solve sub- load space distribution function
Formula (7) be the underdetermined system of equations, therefore there is solve in the reverse result of load space distribution function more；By most sparse solution as reverse knot
Fruit, i.e., the active position of equivalent concentrfated load is determined by Its Sparse Decomposition：
In formula,The aliased coefficient of n-th of spatially distributed functions of correspondence that solution obtains is represented, H is to block
Mode number, N represent the discrete points of structure loading area, and it typically much deeper than blocks mode number H,(j=1,2 ..., N) table
Show the Mode Shape coefficient at j-th of discrete point, ψ under structure the i-th rank modenjRepresent n-th of spatially distributed functions j-th from
Equivalence value at scatterplot.
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| CN109238447A (en) * | 2018-09-12 | 2019-01-18 | 西北工业大学 | A kind of blind source separation method of tether vibration signal |
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| CN110986843A (en) * | 2019-11-12 | 2020-04-10 | 浙江大学 | Subway tunnel displacement and longitudinal strain approximate calculation method based on discontinuous multi-point monitoring data |
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