CN113295377A - Non-linear shaking test method and system based on analytic mode decomposition - Google Patents
Non-linear shaking test method and system based on analytic mode decomposition Download PDFInfo
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- 238000000354 decomposition reaction Methods 0.000 title claims abstract description 29
- 238000010998 test method Methods 0.000 title claims description 10
- 238000012360 testing method Methods 0.000 claims abstract description 80
- 239000007788 liquid Substances 0.000 claims abstract description 46
- 238000000034 method Methods 0.000 claims abstract description 33
- 230000004044 response Effects 0.000 claims abstract description 24
- 238000013016 damping Methods 0.000 claims abstract description 19
- 239000011435 rock Substances 0.000 claims abstract description 11
- 238000004458 analytical method Methods 0.000 claims description 17
- 230000005284 excitation Effects 0.000 claims description 14
- 239000000446 fuel Substances 0.000 claims description 9
- 230000001052 transient effect Effects 0.000 claims description 9
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 8
- 230000008569 process Effects 0.000 claims description 7
- 238000013480 data collection Methods 0.000 claims description 3
- 230000014509 gene expression Effects 0.000 claims description 3
- 230000009466 transformation Effects 0.000 claims description 3
- 239000003350 kerosene Substances 0.000 claims description 2
- 238000005192 partition Methods 0.000 abstract description 4
- 230000007547 defect Effects 0.000 abstract description 3
- 239000000295 fuel oil Substances 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 5
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000010355 oscillation Effects 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 239000003921 oil Substances 0.000 description 1
- 238000003672 processing method Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
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- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M10/00—Hydrodynamic testing; Arrangements in or on ship-testing tanks or water tunnels
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Abstract
The invention provides a nonlinear shaking test system and method based on analytic mode decomposition, which comprises a Doppler laser vibrometer, a bracket, a horizontal sliding table of a vibration table, data acquisition equipment, a computer, a test piece and a tool; the test piece passes through the frock and installs at the horizontal slip table of shaking table, the test piece is used for the splendid attire to rock test liquid, doppler laser vibrometer installs on the support, and doppler laser vibrometer is located the top of test piece, doppler laser vibrometer is through data acquisition equipment and computer data connection. The method can solve the strong nonlinear problem of free shaking attenuation vibration in a state of adding a tiny dense well-shaped partition plate in the fuel oil storage tank of the aircraft by adopting an identification method based on analytical mode decomposition, has low requirements on data volume obtained by a test, and can make up the defect of small shaking attenuation response data volume, thereby obtaining the shaking frequency and the damping value of the nonlinear shaking response.
Description
Technical Field
The invention relates to a dynamics test and response analysis, in particular to a nonlinear sloshing test method and a nonlinear sloshing test system based on analytic mode decomposition.
Background
The liquid shaking problem is widely existed in the aerospace field, and scholars at home and abroad have made a lot of researches on the liquid shaking problem, but certain differences exist between certain assumptions in the shaking calculation theory and actual conditions, and the theoretical calculation result needs to be tested and verified, so that the liquid shaking modal test becomes an important means for researching the liquid shaking problem. In the current unmanned vehicles engineering development process, the storage tank fuel rocks the frequency and crosses low and the time-varying, influence the design of pilot filter, in order to solve this problem, can add minimum intensive "well" type baffle in this aircraft fuel storage tank, it rocks the frequency and increases and rocks the damping to improve the fuel, make the fuel rock the frequency and keep away from aircraft rigid body gesture frequency of motion, and accelerate the decay that the fuel rocked in the oil tank, but can lead to the liquid level to rock like this and be difficult to arouse and decay very fast, present strong nonlinear characteristic, decay response data are difficult to test and analysis.
In the chinese patent application publication No. CN105928677A, a method for testing the sloshing frequency of a liquid in a water tank structure is disclosed, which mainly uses a vibrating table to excite the water tank structure, arranges a pressure sensor in the liquid, tests the water pressure data information at the free sloshing stage, and performs FFT analysis on the data to obtain the low-order frequency of sloshing of the liquid in the water tank. For the water tank container with the large ratio of the liquid level width to the liquid level depth, the liquid level shaking is easy to excite, conventional sine excitation can be adopted, the shaking frequency is generally low, the damping ratio is small, the attenuation is slow, the process mainly adopts linear shaking attenuation, and the conventional FFT analysis can be performed on the vibration response time course to obtain the frequency and the damping. However, in the case of adding a very small and dense 'well' -shaped partition plate in an aircraft fuel storage tank, the liquid level sloshing is difficult to excite and attenuates quickly, strong nonlinear characteristics are presented, and the response data samples obtained at the moment are relatively few, so that the conventional FFT method is not completely applicable.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a nonlinear sloshing test method and system based on analytic mode decomposition.
The invention provides a nonlinear sloshing test system based on analytic mode decomposition, which comprises: the device comprises a Doppler laser vibrometer, a bracket, a horizontal sliding table of a vibration table, data acquisition equipment, a computer, a test piece and a tool;
the test piece passes through the frock and installs at the horizontal slip table of shaking table, the test piece is used for the splendid attire to rock test liquid, doppler laser vibrometer installs on the support, and doppler laser vibrometer is located the top of test piece, doppler laser vibrometer is through data acquisition equipment and computer data connection.
Preferably, the doppler laser vibrometer collects a vibration velocity signal of the liquid level and converts the vibration velocity signal into an analog voltage signal, the analog voltage signal is converted into a digital voltage signal through the data collection device, and the digital voltage signal is subjected to signal analysis through the computer.
Preferably, the distance between the Doppler laser vibrometer and the test piece is set to be 1 meter.
Preferably, the sloshing test liquid comprises water or jet fuel.
According to the invention, the nonlinear sloshing test method based on the analytic mode decomposition adopts the nonlinear sloshing test system based on the analytic mode decomposition as claimed in claim 1, and comprises the following steps:
step S1: adding a shaking test liquid into a test piece;
step S2: applying step excitation of a certain magnitude to a test piece by a horizontal sliding table of a vibration table, shaking test liquid after excitation is stopped to enter free attenuation shaking, and collecting nonlinear shaking response data of the liquid level in the whole process by a Doppler laser vibrometer;
step S3: taking out the response data acquired in the step S2, and performing frequency dichotomy on the nonlinear shaking response data by adopting an analytic mode decomposition method to obtain a high-pass signal and a low-pass signal;
step S4: analyzing and identifying the signal obtained in the step S3 by adopting a free vibration analysis method based on Hilbert transform;
step S5: and obtaining the shaking frequency and the damping value of the nonlinear shaking response.
Preferably, the height of the sloshing test liquid in the test piece in the step S1 is 0.9 times of the total liquid filling height of the test piece.
Preferably, in step S2, the step excitation applied by the horizontal sliding table of the vibration table to the test piece is 0.1g to 1 g.
Preferably, in step S2, the time for applying the step excitation to the test piece by the horizontal sliding table of the vibration table is 5S.
Preferably, the frequency halving in the step S3 includes the following steps:
let the vibration signal x (t) acquired by laser Doppler contain n frequency components omega1、ω2、…、ωnOf a single frequency component signal
Then there are several dichotomy frequencies omegabi∈(ωi，ωi+1) I ═ 1, 2, …, n-1), and x (t) is divided into two parts
In the formula, si(t) is frequency less than ωbi∈(ωi，ωi+1) I ═ a (1, 2, …, n-1) signal, i.e., a low-pass signal;
for frequencies above omegabi∈(ωi，ωi+1) I ═ the signal of (1, 2, …, n-1), i.e., the high-pass signal;
si(t)＝sin(ωbit)H[x(t)cos(ωbit)]-cos(ωbit)H[x(t)sin(ωbit)]
i＝1，2，…，n-1 (3)
the single frequency component signal is represented as
xi(t)＝si(t)-si-1(t)
s0(t)＝0 (4)
xiAnd (t) is the intrinsic signal.
Preferably, the analyzing and identifying in step S4 includes the following steps:
let the analytic signal X (t) be composed of the measured vibration signal x ═ x (t) and its Hilbert transform
Composition of
Written in amplitude/phase form
X(t)＝A(t)eiψ(t) (6)
In the formula: a (t) is the transient amplitude or envelope; psi (t) being the transient phase
The first and second derivatives of the transient amplitude and phase with respect to time t are
In the formula (10), ω (t) is the instantaneous circular frequency of the signal;
differential equation of free vibration
H and k are nonlinear damping and rigidity respectively, and Hilbert transformation is performed on the equation to obtain signals
Differential equation of
According to the formula (5), a differential equation of the analytic signal is obtained
The first and second derivatives of the analytic signal with respect to time t are substituted into formula (16)
The real part and the imaginary part of the pair formula (17) are separated to obtain
Equations (18) and (19) are the identified nonlinear damping and stiffness expressions, respectively.
Compared with the prior art, the invention has the following beneficial effects:
1. the vibration table is used for pushing the horizontal sliding table to apply step excitation of a certain magnitude to the test piece, nonlinear free attenuation vibration of the liquid level of the test piece can be easily excited, liquid level response data of the whole process are directly collected through the Doppler laser vibrometer, and the liquid level response data are collected through the data collection equipment and the computer.
2. The identification method based on analytical mode decomposition can be used for solving the strong nonlinear problem of free shaking attenuation vibration in a state of adding an extremely small dense well-shaped partition plate in an aircraft fuel storage tank, meanwhile, the method has low requirements on data volume obtained by tests, can make up the defect of small shaking attenuation response data volume, and further obtains the shaking frequency and the damping value of the nonlinear shaking response.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a layout diagram of a non-linear shaking test system based on analytic mode decomposition according to an embodiment of the present disclosure;
FIG. 2 is a model diagram of a test piece in a non-linear shaking test system based on analytic mode decomposition according to an embodiment of the present disclosure;
FIG. 3 is a flowchart illustrating steps of a method for non-linear jitter testing based on analytic mode decomposition according to an embodiment of the present disclosure;
FIG. 4 is a graph showing liquid level response raw data of a nonlinear oscillation attenuation process in a nonlinear oscillation test method based on analytic mode decomposition according to an embodiment of the present application;
FIG. 5 is effective vibration data obtained through analysis mode decomposition in a nonlinear jitter test method based on analysis mode decomposition according to an embodiment of the present application;
fig. 6 is a first-order frequency diagram of shaking obtained by analyzing effective vibration data obtained after the analysis mode decomposition in the nonlinear shaking test method based on the analysis mode decomposition according to the embodiment of the present application;
fig. 7 is a sway first-order damping diagram obtained by analyzing effective vibration data obtained after an analytic mode is decomposed in a nonlinear sway testing method based on the analytic mode decomposition in the embodiment of the present application.
Description of reference numerals: 1. a Doppler laser vibrometer; 2. a support; 3. a horizontal sliding table of the vibration table; 4. a data acquisition device; 5. a computer; 6. a test piece; 7. assembling; 8. shaking the test liquid.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
A non-linear slosh test system based on analytical model decomposition, comprising: doppler laser vibrometer 1, support 2, shaking table horizontal slip table 3, data acquisition equipment 4, computer 5, test piece 6 and frock 7.
The test piece 6 is fixed on the horizontal sliding table 3 of the vibrating table through the tool 7, and the shaking test liquid 8 is injected into the test piece 6 to a fixed depth, wherein the shaking test liquid 8 can be water, aviation kerosene or other liquid which needs to be subjected to shaking measurement. Doppler's laser vibrometer 1 installs on support 2, and Doppler's laser vibrometer 1 is located the top of test piece 6 and tests shaking test liquid 8, and Doppler's laser vibrometer 1 sets up to 1 meter with the interval of test piece 6. The data acquisition equipment 4 and the computer 5 are connected with the Doppler laser vibration meter 1, the Doppler laser vibration meter 1 acquires vibration speed signals of the liquid level and converts the vibration speed signals into analog voltage signals, the analog voltage signals are converted into digital voltage signals through the data acquisition equipment 4, and the computer 5 carries out signal analysis on the digital voltage signals. The layout of the shaking test system is shown in fig. 1, and fig. 2 is a model diagram of a test piece 6.
A nonlinear sloshing test method based on analytic mode decomposition adopts the system, and specifically comprises the following steps:
step S1: and adding the shaking test liquid 8 into the test piece 6 to a fixed depth, wherein the height of the shaking test liquid 8 in the test piece 6 is 0.9 times of the total liquid filling height of the test piece 6.
Step S2: let shaking table horizontal slip table 3 exert 0.1 ~ 1g of step excitation to test piece 6, excitation time is 5s, rocks test liquid 8 and gets into the free attenuation after the excitation stops and rocks, and Doppler laser vibrometer 1 gathers the nonlinear response data that rocks of whole in-process liquid level, transmits to computer 5 through data acquisition equipment 4, and experimental flow chart refers to figure 3.
Step S3: the acquired shake attenuation response data is taken out from the computer 5, the liquid level response raw data in the shake attenuation process is shown in fig. 4, and the nonlinear shake response data is divided into two parts in frequency by adopting an analytical model decomposition method (AMD) to obtain a high-pass signal and a low-pass signal, and the specific steps are as follows:
let the vibration signal x (t) acquired by laser Doppler contain n frequency components omega1、ω2、…、ωnOf a single frequency component signal
Then there are several dichotomy frequencies omegabi∈(ωi，ωi+1) I ═ 1, 2, …, n-1), and x (t) is divided into two parts
In the formula, si(t) is frequency less than ωbi∈(ωi，ωi+1) I ═ a (1, 2, …, n-1) signal, i.e., a low-pass signal;
for frequencies above omegabi∈(ωi，ωi+1) I ═ the signal of (1, 2, …, n-1), i.e., the high-pass signal;
si(t)＝sin(ωbit)H[x(t)cos(ωbit)]-cos(ωbit)H[x(t)sin(ωbit)]
i＝1，2，…，n-1 (3)
the single frequency component signal can be represented as
xi(t)＝si(t)-si-1(t)
s0(t)＝0 (4)
xiAnd (t) is the intrinsic signal.
The effective vibration data obtained after the analysis mode decomposition is shown in fig. 5.
Step S4: analyzing and identifying the signal obtained in the step S3 by adopting a free vibration analysis method based on Hilbert transform, wherein the method specifically comprises the following steps of:
let the analytic signal X (t) be composed of the measured vibration signal x ═ x (t) and its Hilbert transform
Composition of
Written in amplitude/phase form
X(t)＝A(t)eiψ(t) (6)
In the formula: a (t) is the transient amplitude or envelope; psi (t) being the transient phase
The first and second derivatives of the transient amplitude and phase with respect to time t are
In the formula (10), ω (t) is the instantaneous circular frequency of the signal;
differential equation of free vibration
H and k are nonlinear damping and rigidity respectively, and Hilbert transformation is performed on the equation to obtain signals
Differential equation of
From equation (5), a differential equation of the analytic signal can be obtained
The first and second derivatives of the analytic signal with respect to time t are substituted into formula (16)
The real part and the imaginary part of the pair formula (17) are separated to obtain
Equations (18) and (19) are the identified nonlinear damping and stiffness expressions, respectively.
Step S5: the sway frequency and the damping value of the nonlinear sway response are obtained, and the sway first-order frequency and the damping curve obtained after analysis along with time are shown in figures 6 and 7.
According to the method provided by the invention, the vibration table is used for pushing the horizontal sliding table to apply step excitation of a certain magnitude to the test piece 6, nonlinear free damping vibration of the liquid surface of the test piece 6 is excited, a nonlinear damping curve of the aircraft fuel oil storage tank shaking with the addition of the dense 'well' type partition plate with the extremely small width-depth ratio is obtained, the shaking first-order frequency and damping are obtained by using a data processing method based on analysis mode decomposition, and the problems that the nonlinearity cannot be solved and the sample size is small in the conventional segmented FFT analysis method are solved.
Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, units provided by the present invention as pure computer readable program code, the system and its various devices, modules, units provided by the present invention can be fully implemented by logically programming method steps in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system and various devices, modules and units thereof provided by the invention can be regarded as a hardware component, and the devices, modules and units included in the system for realizing various functions can also be regarded as structures in the hardware component; means, modules, units for performing the various functions may also be regarded as structures within both software modules and hardware components for performing the method.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (10)
1. A non-linear sloshing test system based on analytic mode decomposition is characterized by comprising: the device comprises a Doppler laser vibrometer (1), a bracket (2), a horizontal sliding table (3) of a vibration table, data acquisition equipment (4), a computer (5), a test piece (6) and a tool (7);
the test piece (6) is installed at shaking table horizontal sliding table (3) through frock (7), test piece (6) are used for the splendid attire to rock test liquid (8), install on support (2) doppler laser vibrometer (1), and doppler laser vibrometer (1) is located the top of test piece (6), doppler laser vibrometer (1) is through data acquisition equipment (4) and computer (5) data connection.
2. The system according to claim 1, wherein the system comprises: the Doppler laser vibration meter (1) collects vibration speed signals of the liquid level and converts the vibration speed signals into analog voltage signals, the analog voltage signals are converted into digital voltage signals through the data collection equipment (4), and the computer (5) analyzes the digital voltage signals.
3. The system according to claim 1, wherein the system comprises: the distance between the Doppler laser vibration meter (1) and the test piece (6) is set to be 1 meter.
4. The system according to claim 1, wherein the system comprises: the sloshing test liquid (8) comprises water or aviation kerosene.
5. A nonlinear sloshing test method based on analytic mode decomposition is characterized in that: the analytical model decomposition-based nonlinear sloshing test system of claim 1 is adopted, and comprises the following steps:
step S1: adding a shaking test liquid (8) into the test piece (6);
step S2: applying step excitation of a certain magnitude to a test piece (6) by a horizontal sliding table (3) of a vibration table, shaking test liquid (8) to enter free attenuation shaking after excitation is stopped, and collecting nonlinear shaking response data of a liquid level in the whole process by a Doppler laser vibrometer (1);
step S3: taking out the response data acquired in the step S2, and performing frequency dichotomy on the nonlinear shaking response data by adopting an analytic mode decomposition method to obtain a high-pass signal and a low-pass signal;
step S4: analyzing and identifying the signal obtained in the step S3 by adopting a free vibration analysis method based on Hilbert transform;
step S5: and obtaining the shaking frequency and the damping value of the nonlinear shaking response, thereby being used for researching the fuel shaking problem of the aircraft.
6. The method according to claim 5, wherein the method comprises the following steps: in the step S1, the height of the shaking test liquid (8) in the test piece (6) is 0.9 times of the total liquid filling height of the test piece (6).
7. The method according to claim 5, wherein the method comprises the following steps: in the step S2, the step excitation applied to the test piece (6) by the horizontal sliding table (3) of the vibration table is 0.1 g-1 g.
8. The method according to claim 5, wherein the method comprises the following steps: in the step S2, the time for applying the step excitation to the test piece (6) by the horizontal sliding table (3) of the vibration table is 5S.
9. The method according to claim 5, wherein the method comprises the following steps: the frequency halving in the step S3 includes the following steps:
let the vibration signal x (t) acquired by laser Doppler contain n frequency components omega1、ω2、…、ωnOf a single frequency component signal
Then there are several dichotomy frequencies omegabi∈(ωi，ωi+1) I ═ 1, 2, …, n-1), and x (t) is divided into two parts
In the formula, si(t) is frequency less than ωbi∈(ωi，ωi+1) I ═ a (1, 2, …, n-1) signal, i.e., a low-pass signal;
for frequencies above omegabi∈(ωi，ωi+1) I ═ the signal of (1, 2, …, n-1), i.e., the high-pass signal;
si(t)＝sin(ωbit)H[x(t)cos(ωbit)]-cos(ωbit)H[x(t)sin(ωbit)]
i＝1，2，…，n-1 (3)
the single frequency component signal is represented as
xi(t)＝si(t)-si-1(t)
s0(t)＝0 (4)
xiAnd (t) is the intrinsic signal.
10. The method according to claim 5, wherein the method comprises the following steps: the analyzing and identifying in the step S4 includes the following steps:
let the analytic signal X (t) be composed of the measured vibration signal x ═ x (t) and its Hilbert transform
Composition of
Written in amplitude/phase form
X(t)＝A(t)e1ψ(t) (6)
In the formula: a (t) is the transient amplitude or envelope; psi (t) being the transient phase
The first and second derivatives of the transient amplitude and phase with respect to time t are
ω (t) in equation (10) is the instantaneous circular frequency of the signal;
differential equation of free vibration
H and k are nonlinear damping and rigidity respectively, and Hilbert transformation is performed on the equation to obtain signals
Differential equation of
According to the formula (5), a differential equation of the analytic signal is obtained
The first and second derivatives of the analytic signal with respect to time t are substituted into formula (16)
The real part and the imaginary part of the pair formula (17) are separated to obtain
Equations (18) and (19) are the identified nonlinear damping and stiffness expressions, respectively.
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