CN112763241A - Method for acquiring modal vibration of railway vehicle - Google Patents

Method for acquiring modal vibration of railway vehicle Download PDF

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CN112763241A
CN112763241A CN202011589242.0A CN202011589242A CN112763241A CN 112763241 A CN112763241 A CN 112763241A CN 202011589242 A CN202011589242 A CN 202011589242A CN 112763241 A CN112763241 A CN 112763241A
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CN112763241B (en
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宫岛
赵阔
周劲松
张俊泽
周锦柯
刘广宇
王泽根
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Tongji University
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Abstract

The invention relates to a rail vehicle modal vibration acquisition method, which comprises the following steps: 1) determining the truncation modal order of the target structure according to the rail vehicle structure to be subjected to modal vibration; 2) arranging a sensor at a proper position of a target structure to acquire a physical vibration response of the sensor; 3) and (3) decoupling operation is carried out on the physical vibration response of the structure based on a modal superposition theory, and the modal vibration of the structure is extracted. Compared with the prior art, the method has the advantages of reducing the error between the fitting value and the observed value, along with high precision and the like.

Description

Method for acquiring modal vibration of railway vehicle
Technical Field
The invention relates to the technical field of rail transit, in particular to a rail vehicle modal vibration acquisition method.
Background
In the technical field of rail transit, improving the running speed and riding comfort of rail vehicles is a research hotspot of various scholars. In order to ensure the safety of the motor train unit train during high-speed running and operation, a large amount of light high-strength materials are adopted. The influence of the vehicle body lightweight technology on the elastic mode vibration problem is increasingly prominent, so that the riding comfort of passengers is greatly reduced.
In order to achieve both high-speed and comfortable ride of a railway vehicle, it is necessary to take effective control measures against modal vibration of a vehicle body. If effective control is required to be exerted on the vibration of the vehicle body, firstly, the overall or local modal vibration characteristics are required to be accurately mastered, the contribution degree of each order of mode to the vibration of the structure is analyzed, and then, accurate control is carried out according to the characteristics of the modal vibration.
So far, the prior art directly solves the problem by directly using the relation between the physical vibration and the modal shape and modal vibration, and the calculation efficiency is not high, which leads to redundancy of the calculated vibration modal information and poor precision.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a rail vehicle modal vibration acquisition method, which comprises the steps of developing a calculated or tested rail vehicle vibration physical space response into various orders of modal responses, setting the minimum residual error between a target fitting value and a physical vibration observation value as an optimization target, and converting the optimization target into a matrix two-norm calculation form, so that the error between the fitting value and the observation value can be reduced to the greatest extent, and more reliable precision is achieved.
The purpose of the invention can be realized by the following technical scheme:
a rail vehicle modal vibration acquisition method comprises the following steps:
s1: and determining the truncation modal order of the target structure according to the rail vehicle structure to be subjected to modal vibration.
S2: the sensors are placed at appropriate locations on the target structure to acquire their physical vibrational response.
S3: and (3) decoupling operation is carried out on the physical vibration response of the structure based on a modal superposition theory, and the modal vibration of the structure is extracted.
Step S1 specifically includes the following steps:
11) determining the elastic modal order of the target structure in the frequency range according to the frequency range of the vibration of the target structure; further, the order of the elastic mode of the target structure in the vibration frequency range of the target structure is the first 15 orders.
12) And determining the total order of the vibration response and the truncated modal order of the target structure based on the two aspects of the elastic mode and the rigid mode.
Further, for the vertical degree of freedom z vibration response, in addition to the first 15-order elastic mode, the vehicle body floating and sinking and nodding head vibration mode related to the vertical direction are considered, and at the moment, the mode vibration mode matrix is [ phi ]z]n×17Similarly, for the vibration response of the transverse degree of freedom y, in addition to the first 15-order elastic mode, the transverse and shaking modes related to the transverse direction are considered, and then the mode matrix is [ phi ]y]n×17。
Step S2 specifically includes the following steps:
21) based on an observability principle, arranging a plurality of sensors of which the number is greater than the truncation modal order of the target structure on the target structure along the length direction of the vehicle body and the surface of the vehicle body;
22) acquiring the relation between physical vibration and modal shape and modal vibration according to the determined truncation modal order of the target structure;
23) and obtaining the vibration response of any degree of freedom at the jth point of the target structure according to the relational expression in the step 22).
In step 22), the relationship between the physical vibration and the modal shape and modal vibration is as follows:
{U}＝[Φ]{q}
in the formula, { U } represents physical vibration, [ phi ] represents mode shape, and { q } represents mode vibration.
Vibration response u of any degree of freedom at jth point of target structurejThe expression of (a) is:
Figure BDA0002866585100000021
where n is the total number of sensors arranged, phijiTo be aComparing the modal shape vector value of the ith order mode at the jth point,
Figure BDA0002866585100000022
for modal vibration response of the ith order mode or as a factor participating in the ith order mode, QiThe modal vibration amplitude of the ith order mode, omega the external excitation frequency, thetaiThe phase difference between the modal vibration of the ith order mode and the external excitation is obtained.
And further, according to the SVD, performing least square fitting on the fitting value and the observed value, and calculating modal vibration according to the vibration response of any degree of freedom at the jth point of the target structure.
Step S3 specifically includes the following steps:
31) setting the residual error between the fitting value of the jth point of the target structure and the observed value of the physical vibration as
Figure BDA0002866585100000031
Then there is the following formula:
Figure BDA0002866585100000032
where n is the total number of sensors arranged, n' is the order of the truncated mode, phijiIs the modal shape vector value of the ith order mode of the system at the jth point,
Figure BDA0002866585100000033
for modal vibration response of the ith order mode or as a factor participating in the ith order mode, QiThe modal vibration amplitude of the ith order mode, omega the external excitation frequency, thetaiIs the phase difference between the modal vibration of the ith order mode and the external excitation, ujThe vibration response of any degree of freedom at the jth point of the target structure;
from the singular value decomposition, for any one matrix A ∈ Rn×n′It is decomposed into:
SVD(A)＝[P][S][VT]
wherein: p is belonged to Rn×n，S∈Rn×n′，V∈Rn′×n′The column vector of P is the left singular vector of A, i.e. AATThe feature vector of (2); vTIs the right singular vector of A, i.e. ATA feature vector; s is [ sigma 0 ]]TΣ is a diagonal matrix whose values are the singular values σ, P and V of the matrix aTIs an orthogonal matrix;
32) according to the two-norm form, the E formula is converted to the following formula:
Figure BDA0002866585100000034
will [ phi ] of]n×n′Represented by formula (6), the two-norm in formula (7) can be written as formula (8):
Figure BDA0002866585100000035
resolving P into [ P ]n′,Pn-n′]Thus, the formula can be written as:
Figure BDA0002866585100000036
namely when
Figure BDA0002866585100000037
The above formula takes equal sign, at this time
Figure BDA0002866585100000038
Taking the minimum value, solving the modal vibration as follows:
Figure BDA0002866585100000041
compared with the prior art, the method can expand the physical space response of the vibration of the railway vehicle obtained by calculation or test into various orders of modal response; meanwhile, when the calculation data is huge or the fitting matrix is a singular matrix, the minimum residual error between the target fitting value and the physical vibration observation value is set as an optimization target according to a least square method target function, and the optimization target is converted into a matrix two-norm calculation form, so that the error between the fitting value and the observation value is reduced to the maximum extent, and the method has more reliable precision.
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FIG. 1 is a schematic flow chart of a method for acquiring modal vibration of a rail vehicle according to an embodiment;
FIG. 2 is a diagram showing the arrangement positions of sensors in the embodiment;
FIG. 3 is the amplitude-frequency response curve of the vertical vibration acceleration of the floor of the vehicle body and the amplitude-frequency curve result of the front 7-order mode vibration (the front 7-order mode is taken as an example) which are respectively expanded;
FIG. 4 is the lateral vibration acceleration response amplitude-frequency curve of the square vehicle body floor in the embodiment, and the result of the amplitude-frequency curve of the front 7-order mode vibration (the front 7-order mode is taken as an example) which is respectively expanded;
FIG. 5 is a diagram illustrating the error between the fitting values and the observed values of physical vibrations at the detection points of the vehicle body floor in the example.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
Examples
The invention relates to a rail vehicle modal vibration acquisition method, which acquires various orders of modal vibration of a vehicle body by using a physical vibration response reverse line, and as shown in figure 1, the method comprises the following specific steps:
step one, determining the truncation modal order of the target structure according to the research requirement. The truncation order may be a certain order mode or a certain order mode. The method comprises the following specific steps:
1.1) the explicit study requirement, i.e. the explicitly studied frequency range, determines the elastic modal order of the target structure within this range. Specifically, the method comprises the following steps: for the vibration expansion problem of the body structure of the railway vehicle, the elastic mode vibration problem of the body is gradually highlighted due to the adoption of a lightweight technology. In order to ensure the ride comfort of the rail vehicle, main low-order (front 15-order, i.e., 1 st order to 15 th order) modal vibration of the vehicle body is focused.
1.2) determining the total order of the vibration response from two aspects of the elastic mode and the rigid mode, and determining the truncated mode order n' of the target structure. Specifically, the method comprises the following steps: for the vertical degree of freedom z vibration response, in addition to the first 15-order elastic mode, the floating and sinking and nodding vibration modes of the vehicle body related to the vertical direction should be considered, and the mode vibration mode matrix is [ phi ] at the momentz]n×17Similarly, for the vibration response of the transverse degree of freedom y, in addition to the first 15-order elastic mode, the transverse and shaking modes related to the transverse direction should be considered, and then the mode matrix is [ phi ]y]n×17. According to [ phi ]z]n×17And [ phi ]y]n×17The truncated modal order n' is determined. In this embodiment, n' is 17.
And secondly, arranging sensors at proper positions of the target structure according to an observability principle, wherein the number of the mounted sensors is at least larger than the total order of the truncation mode, and acquiring the physical response of the sensors. The second step specifically comprises the following steps:
2.1) to obtain the vibrational response of the n 'order mode according to the observability principle, at least n' actuators should be arranged at appropriate positions of the study structure. However, in order to reflect the vibration of the main vibration mode of the vehicle body more comprehensively, n (n > n') sensors are generally installed. The method specifically comprises the following steps: according to the observability principle, at least 17 sensors are arranged on the surface of the vehicle body along the length direction of the vehicle body to obtain the vibration response of the 17-order mode. However, the 17 sensors are considered to be unable to completely reflect the vibration of the principal mode of the vehicle body. For this reason, the present embodiment dispersedly arranges 40 sensors on the surface of the vehicle body in the longitudinal direction of the vehicle body. The 40 sensor placement points are shown in fig. 2.
2.2) determining the truncation order n', for the structure studied, its physical vibration { U } and mode shape [ phi ] & lt & gt]n×n'And modal vibration { q } is:
{U}＝[Φ]{q} (1)
using equation (2), the vibration response u for any degree of freedom at the jth point of the study structurejIs (u)jAny of the six degrees of freedom in formula (3):
Figure BDA0002866585100000051
the formula (2) shows that the vibration response of any degree of freedom at any position of the vehicle body is weighted superposition of modal vibration of each order.
Wherein: phi is ajiIs the modal shape vector value of the ith order mode of the system at the jth point,
Figure BDA0002866585100000052
is the modal vibration response of the ith order mode, also referred to as the participation factor of the ith order mode, QiThe modal vibration amplitude of the ith order mode, omega the external excitation frequency, thetaiThe phase difference between the modal vibration, which is the i-th order mode, and the external excitation is related to the ratio of the excitation frequency to the modal frequency and also to the modal damping.
uj＝[xj yj zj αj βj γj]T (3)
Wherein: x is the number ofj,yj,zjThe node j has freedom degrees along the longitudinal direction, the transverse direction and the vertical direction; alpha is alphaj,βj,γjThe rotational degrees of freedom of the node around longitudinal, transverse and vertical coordinate axes, respectively.
According to the formula (1), if the truncation mode order is n', the truncated mode shape matrix is [ phi ]]n×n′. At this time, the modal vibration { q }can be obtained by equation (4)n'×1：
{U}n×1＝[Φ]n×n'{q}n'×1(n'＜n) (4)
And step three, decoupling the physical vibration response based on a modal superposition theory, and extracting the modal vibration of the structure based on SVD decomposition and least square fitting. The third step specifically comprises the following steps:
and according to the SVD, performing least square fitting on the fitting value and the observed value, and calculating modal vibration. The method comprises the following steps:
3.1) there is a target function according to the least square method, and the residual error between the fitting value at the point j and the observed value of the physical vibration is
Figure BDA0002866585100000061
The expression of the objective function is shown in equation (5):
Figure BDA0002866585100000062
from the singular value decomposition, for any one matrix A ∈ Rn×n′Can be decomposed into formula (6):
SVD(A)＝[P][S][VT] (6)
wherein: p, S, V is the new matrix formed after decomposing matrix A, P is the Rn×n，S∈Rn×n′，V∈Rn′×n′. The column vector of P is the left singular vector of A, also known as AATThe feature vector of (2); vTThe column vector of (A) is the right singular vector of A, i.e. ATA feature vector; s is [ sigma 0 ]]TΣ is a diagonal matrix whose values are the singular values σ, P and V of the matrix aTAre all orthogonal matrices.
3.2) formula (5) is written according to the two-norm form as formula (7):
Figure BDA0002866585100000063
will [ phi ] of]n×n′Represented by formula (6), the two-norm in formula (7) can be written as formula (8):
Figure BDA0002866585100000064
p can be resolved into [ P ]n′,Pn-n′]Thus, formula (8) can be written as formula (9):
Figure BDA0002866585100000071
namely when
Figure BDA0002866585100000072
When the formula (9) is equal, at this time
Figure BDA0002866585100000073
Taking the minimum value, solving to obtain:
Figure BDA0002866585100000074
finally, the results are shown in fig. 3 and fig. 4, and fig. 3 and fig. 4 are respectively the amplitude-frequency curves of the vertical and lateral vibration acceleration response of the vehicle body floor, and the amplitude-frequency curves of the vibration of the first 7 th order mode (taking the first 7 th order mode as an example). From the results it can be seen that: the modal vibration extraction method based on the least square method can effectively decouple physical response into each order of modal vibration, and judge the contribution degree of each order of vibration to the whole vibration by visually comparing and analyzing the amplitude-frequency curve result of each order of modal vibration.
To illustrate the reliable accuracy of the method of the present invention, the mode extraction method was subjected to error analysis. The error between the fitted values at the measurement points on the vehicle body floor and the observed values of physical vibrations is shown in fig. 5. It can be seen that the error between the fitting value and the observed value is small (the magnitude of the error is about one percent of the magnitude of the vibration of the vehicle body floor under the normal condition), which shows that the method has reliable precision.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and those skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. A rail vehicle modal vibration acquisition method is characterized by comprising the following steps:
1) determining the truncation modal order of the target structure according to the rail vehicle structure to be subjected to modal vibration;
2) arranging a sensor at a proper position of a target structure to acquire a physical vibration response of the sensor;
3) and (3) decoupling operation is carried out on the physical vibration response of the structure based on a modal superposition theory, and the modal vibration of the structure is extracted.
2. The rail vehicle modal vibration acquisition method according to claim 1, wherein the step 1) specifically comprises the following steps:
11) determining the elastic modal order of the target structure in the frequency range according to the frequency range of the vibration of the target structure;
12) and determining the total order of the vibration response and the truncated modal order of the target structure based on the two aspects of the elastic mode and the rigid mode.
3. The rail vehicle modal vibration acquisition method according to claim 1, wherein the step 2) specifically comprises the following steps:
21) arranging a plurality of sensors at appropriate positions of the target structure based on observability principles;
22) acquiring the relation between physical vibration and modal shape and modal vibration according to the determined truncation modal order of the target structure;
23) and obtaining the vibration response of any degree of freedom at the jth point of the target structure according to the relational expression in the step 22).
4. The rail vehicle modal vibration acquisition method as recited in claim 3, wherein a plurality of sensors greater than the truncated modal order of the target structure are arranged on the surface of the target structure in the longitudinal direction of the vehicle body.
5. The rail vehicle modal vibration acquisition method according to claim 3, wherein the relation between the physical vibration and the modal shape and the modal vibration is as follows:
{U}＝[Φ]{q}
in the formula, { U } represents physical vibration, [ phi ] represents mode shape, and { q } represents mode vibration.
6. The method according to claim 5, wherein the vibration response u of any degree of freedom at the jth point of the target structure is obtained according to the vibration response u of any degree of freedomjThe expression of (a) is:
Figure FDA0002866585090000011
where n is the total number of sensors arranged, phijiIs the modal shape vector value of the ith order mode of the system at the jth point,
Figure FDA0002866585090000021
for modal vibration response of the ith order mode or as a factor participating in the ith order mode, QiThe modal vibration amplitude of the ith order mode, omega the external excitation frequency, thetaiThe phase difference between the modal vibration of the ith order mode and the external excitation is obtained.
7. The method for acquiring modal vibration of railway vehicle according to claim 1, wherein in step 3), the least square fitting is performed on the fitting value and the observed value according to SVD, and the modal vibration is calculated according to the vibration response of any degree of freedom at the jth point of the target structure.
8. The rail vehicle modal vibration acquisition method according to claim 7, wherein the step 3) specifically comprises the following steps:
31) setting the residual error between the fitting value of the jth point of the target structure and the observed value of the physical vibration as
Figure FDA0002866585090000022
Then there is the following formula:
Figure FDA0002866585090000023
where n is the total number of sensors arranged, n' is the order of the truncated mode, phijiIs the modal shape vector value of the ith order mode of the system at the jth point,
Figure FDA0002866585090000024
for modal vibration response of the ith order mode or as a factor participating in the ith order mode, QiThe modal vibration amplitude of the ith order mode, omega the external excitation frequency, thetaiIs the phase difference between the modal vibration of the ith order mode and the external excitation, ujThe vibration response of any degree of freedom at the jth point of the target structure;
from the singular value decomposition, for any one matrix A ∈ Rn×n′It is decomposed into:
SVD(A)＝[P][S][VT]
wherein: p is belonged to Rn×n，S∈Rn×n′，V∈Rn′×n′The column vector of P is the left singular vector of A, i.e. AATThe feature vector of (2); vTIs the right singular vector of A, i.e. ATA feature vector; s is [ sigma 0 ]]TΣ is a diagonal matrix whose values are the singular values σ, P and V of the matrix aTIs an orthogonal matrix;
32) according to the two-norm form, the E formula is converted to the following formula:
Figure FDA0002866585090000025
will [ phi ] of]n×n′Represented by formula (6), the two-norm in formula (7) can be written as formula (8):
Figure FDA0002866585090000026
resolving P into [ P ]n′,Pn-n′]Thus, the formula can be written as:
Figure FDA0002866585090000031
namely when
Figure FDA0002866585090000032
The above formula takes equal sign, at this time
Figure FDA0002866585090000033
Taking the minimum value, solving the modal vibration as follows:
Figure FDA0002866585090000034
9. the rail vehicle modal vibration acquisition method as recited in claim 2, wherein in step 11), the elastic modal order of the target structure in the target structure vibration frequency range is the first 15 orders.
10. The method for acquiring modal vibration of railway vehicle according to claim 9, wherein in step 12), for the vertical degree of freedom z vibration response, in addition to the first 15-order elastic modes, the vehicle body sinking and floating and nodding head vibration modes related to the vertical direction are considered, and the mode vibration mode matrix is [ Φ ]z]n×17Similarly, for the vibration response of the transverse degree of freedom y, in addition to the first 15-order elastic mode, the transverse and shaking modes related to the transverse direction are considered, and then the mode matrix is [ phi ]y]n×17。
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