CN110889336A - Quasi-static long-gauge strain extraction method based on EMD decomposition - Google Patents

Quasi-static long-gauge strain extraction method based on EMD decomposition Download PDF

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CN110889336A
CN110889336A CN201911084732.2A CN201911084732A CN110889336A CN 110889336 A CN110889336 A CN 110889336A CN 201911084732 A CN201911084732 A CN 201911084732A CN 110889336 A CN110889336 A CN 110889336A
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丁李
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Nanjing Southeast Building Electrical And Mechanical Shock Research Institute Co Ltd
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Abstract

The invention discloses a quasi-static long gauge length strain extraction method based on EMD decomposition, which comprises the following steps: extracting the strain time course of the structural unit; EMD decomposition is carried out on the extracted strain signals, and a plurality of intrinsic mode functions IMF and a residual component which can not be decomposed any more are decomposed; performing spectrum analysis on each decomposed IMF component to obtain IMF components and residual components with characteristic frequencies lower than the fundamental frequency; and adding the IMF component with the characteristic frequency lower than the fundamental frequency and the residual component to obtain the quasi-static strain time course of the structural unit. According to the invention, the EMD technology is adopted to carry out dynamic and static strain separation on the long gauge length strain signal, and the quasi-static long gauge length strain time course of the structural unit is extracted, so that the moving load can be more accurately identified, and meanwhile, the damage of the monitoring structure can be rapidly evaluated.

Description

Quasi-static long-gauge strain extraction method based on EMD decomposition
Technical Field
The invention belongs to the field of structural vibration analysis, and particularly relates to a quasi-static long gauge length strain extraction method based on EMD decomposition.
Background
With the development of signal processing technology, damage identification and load identification methods based on signal processing are rapidly developed in the field of structural health monitoring, and the existing signal separation analysis technology comprises Fourier change, short-time Fourier, wavelet analysis, empirical mode analysis and the like.
The long-gauge strain sensor is widely applied to a structural health monitoring system at present, and has the main advantage that the long-gauge strain sensor is different from a traditional point strain gauge, the point strain gauge can only monitor the strain response of a certain point, and the long-gauge strain sensor can obtain the structural average response in a section of gauge. Meanwhile, in the monitoring process, because the monitored targets are inconsistent, some targets are focused on damage identification, and some targets are focused on load identification. However, no matter what kind of monitoring target is, the data collected on site are inevitably doped with environmental change factors, and if we directly analyze signals, the monitored data are likely to be seriously distorted, so that the real state of the structure cannot be obtained.
Disclosure of Invention
The quasi-static long gauge strain extraction method based on EMD adopts the EMD technology to separate dynamic and static strain of a long gauge strain signal, extracts the quasi-static long gauge strain time range of a structural unit, can more accurately identify a moving load, and can also quickly evaluate the damage of a monitoring structure.
In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:
the quasi-static long gauge length strain extraction method based on EMD decomposition comprises the following steps:
(1) extracting the strain time course of the structural unit;
(2) EMD decomposition is carried out on the extracted strain signals, and a plurality of intrinsic mode functions IMF and a residual component which can not be decomposed any more are decomposed;
(3) performing spectrum analysis on each decomposed IMF component to obtain IMF components and residual components with characteristic frequencies lower than the fundamental frequency;
(4) and adding the IMF component with the characteristic frequency lower than the fundamental frequency and the residual component to obtain the quasi-static strain time course of the structural unit.
As a further improved technical solution of the present invention, the step (1) specifically comprises:
and carrying out data acquisition on the corner time courses of the two nodes of the structural unit through numerical simulation, and calculating the long gauge length strain time course of the structural unit through the relation between the corner time courses and the strain time courses.
As a further improved technical solution of the present invention, the calculation formula for calculating the long gauge length strain time of the structural unit is as follows:
Figure BDA0002265041310000021
in the formula, hmIs the distance L from the pasting position of the long gauge length strain sensor to the neutral axis of the structuremIs the length of the structural unit, θi(t)，θjAnd (t) are the corner time courses of the two nodes of the structural unit respectively.
As a further improved technical scheme of the invention, the step (2) is specifically as follows:
(1) finding original strain signals
Figure BDA0002265041310000022
All maximum value points are interpolated into an upper envelope V of the original data sequence by a cubic spline function1(t); finding out signals
Figure BDA0002265041310000023
All minimum value points are interpolated into a lower envelope V of the original data sequence by a cubic spline function2(t) obtaining an average value m of upper and lower envelope lines thereof1(t)：
Figure BDA0002265041310000024
(2) The original data sequence is processed
Figure BDA0002265041310000025
Minus the average envelope m1After (t), a new data sequence with low frequency removed is obtained:
Figure BDA0002265041310000026
judgment h1(t) whether or not IMF is satisfied, if IMF is not satisfied, determining whether or not IMF is satisfiedh1(t) is regarded as novel
Figure BDA0002265041310000027
Repeating the step (1) and the step (2) until h1(t) if IMF conditions are satisfied, then h is1(t) as the 1 st eigenmode function c1(t) is expressed as c1(t) is IMF (1):
c1(t)＝h1(t)；
(3) then, the following steps are carried out:
Figure BDA0002265041310000028
will r is1(t) is regarded as novel
Figure BDA0002265041310000029
And repeating the screening process from the step (1) to the step (3), and sequentially obtaining n intrinsic mode functions IMF in the screening process: c. C1(t)、c2(t)、c3(t)、c4(t)……cn(t) until a residual component rn(t) stopping the screening when it cannot be decomposed;
raw strain signal
Figure BDA00022650413100000210
I.e. n eigenmode functions IMF and a mean or trend term rn(t) is expressed as:
Figure BDA00022650413100000211
as a further improved technical solution of the present invention, the quasi-static strain time course of the structural unit in step (4) is:
Figure BDA0002265041310000031
wherein f is1Is the first order frequency of the structural unit, i.e. the fundamental frequency, f (c)i(t)) is the frequency of the ith eigenmode function IMF,
Figure BDA0002265041310000032
is a quasi-static strain time course.
The invention has the beneficial effects that: according to the method, dynamic and static strain separation is carried out on the long gauge length strain signal based on the EMD technology, the quasi-static strain time range of the structural unit is extracted, the characteristic frequency of the component is obtained by carrying out frequency spectrum analysis on the separated IMF component, and the IMF time domain component lower than the structural fundamental frequency can be extracted through a judgment criterion. And performing signal reconstruction on the extracted IMF time domain component and the residual component to obtain the long gauge length quasi-static strain time course of the unit. The method can be used for more accurately identifying the moving load and can be used for quickly evaluating the damage of the monitoring structure. The method has the advantages of clear principle, high calculation speed and good calculation precision, can be used for quasi-static strain extraction of common infrastructure of large buildings, traffic and the like under the action of dynamic load, analyzes the extracted quasi-static strain, and can obtain the real state of the structure.
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FIG. 1 is a system workflow diagram of the present invention;
FIG. 2 is a schematic view of a simply supported beam of the present invention under a moving load;
FIG. 3 is a long gauge length strain response time course diagram of the monitoring unit of the present invention;
FIG. 4 is a time domain plot of IMF components and residual components obtained after EMD decomposition of the original long gauge length strain response;
FIG. 5 is a frequency domain diagram of IMF components;
fig. 6 is a graph comparing a cell long gauge length quasi-static strain time course obtained by time course signal reconstruction after quasi-static strain determination with a real static strain time course.
Detailed Description
The following further describes embodiments of the present invention with reference to fig. 1 to 6:
the structural unit of this embodiment is a key part of a simply supported beam bridge, and fig. 1 is a flowchart of this embodiment, which is mainly implemented as follows: acquiring a key part corner time course of the simply supported beam bridge through numerical simulation (the key part corner time course refers to the corner time course of each node of a unit with a long gauge length strain sensor), and acquiring the long gauge length strain time course of the unit through the relation between corners and strain; performing empirical mode decomposition processing on the extracted strain signal, specifically analyzing a plurality of Intrinsic Mode Function (IMF) components obtained by the empirical mode decomposition, and sequentially performing frequency spectrum analysis on each IMF component; and finally, adding the IMF component with the frequency lower than the first-order frequency of the simply-supported beam bridge and the time domain signal of the residual component for signal reconstruction, thereby obtaining the quasi-static strain influence line of the simply-supported beam bridge.
The process of extracting the quasi-static strain time course by EMD decomposition is that the long gauge length strain time course of the structural unit calculated by the relationship between the rotation angle and the strain can be expressed by the following formula:
Figure BDA0002265041310000041
in the formula, hmIs the distance L from the pasting position of the long gauge length strain sensor to the neutral axis of the structuremIs the length of the structural unit, θi(t)，θjAnd (t) are the corner time courses of the two nodes of the structural unit respectively.
Decomposing the unit strain signal from a high frequency band to a low frequency band to decompose a plurality of intrinsic mode functions IMF: c. C1(t)、c2(t)、c3(t)、c4(t)……cn(t) and a residual component r which cannot be decomposed any moren(t); decomposing an original strain response signal into the sum of a plurality of intrinsic mode functions, wherein the decomposition steps are as follows:
(1) finding original strain signals
Figure BDA0002265041310000042
All maximum value points are interpolated into an upper envelope V of the original data sequence by a cubic spline function1(t); finding out signals
Figure BDA0002265041310000043
All minimum value points are interpolated into a lower envelope V of the original data sequence by a cubic spline function2(t) obtaining an average value m of upper and lower envelope lines thereof1(t)：
Figure BDA0002265041310000044
(2) The original data sequence is processed
Figure BDA0002265041310000045
Minus the average envelope m1After (t), a new data sequence with low frequency removed is obtained:
Figure BDA0002265041310000046
judgment h1(t) whether it is IMF, if it does not satisfy the IMF condition, h1(t) is regarded as novel
Figure BDA0002265041310000047
Repeating the step (1) and the step (2) until h1(t) if IMF conditions are satisfied, then h is1(t) as the 1 st eigenmode function c1(t) is expressed as c1(t) is IMF (1):
c1(t)＝h1(t)；
(3) then, the following steps are carried out:
Figure BDA0002265041310000048
will r is1(t) is regarded as novel
Figure BDA0002265041310000049
And repeating the screening process from the step (1) to the step (3), and sequentially obtaining n intrinsic mode functions IMF in the screening process: c. C1(t)、c2(t)、c3(t)、c4(t)……cn(t) until a residual component rn(t) when it cannot be decomposed, stopping the screening, wherein the residual component rn(t) is the mean or trend term of the original strain signal;
raw strain signal
Figure BDA00022650413100000410
I.e. n eigenmode functions IMF and a mean or trend term rn(t) is expressed as:
Figure BDA00022650413100000411
performing spectrum analysis on the decomposed IMF component, and performing spectrum analysis on the IMF with characteristic frequency lower than fundamental frequency and the residual component rn(t) is attributed to the quasi-static strain component, and the quasi-static strain acquisition and determination criteria can be expressed as follows:
Figure BDA0002265041310000051
wherein f is1First order frequency of structure, f (c)i(t)) is the frequency of the ith eigenmode function IMF,
Figure BDA0002265041310000052
in order to achieve a time course of the dynamic strain,
Figure BDA0002265041310000053
is a quasi-static strain time course.
Fig. 2 is a schematic diagram of a rectangular simply supported beam under the action of a moving load, and the model parameters are as follows: width b 0.3m, height h 0.6m, length L20 m, density 7800kg/m 3, modulus of elasticity E2.1E 11 pa, Poisson's ratio 0.3. Assuming a mass of 6000N, a moving load at a speed of 10m/s acts on the simply supported beam. The time of the moving load acting on the simply supported beam bridge is 2s, and ten long-gauge strain sensors are adopted to monitor the strain response of the structure.
FIG. 3 shows the calculation result of the long gauge length strain response time course, wherein the unit length is 2 m.
Fig. 4 is a time domain result of the IMF component and the residual component obtained after the EMD decomposition of the long gauge length strain response shown in fig. 3.
FIG. 5 is the frequency domain result of the IMF components shown in FIG. 4, wherein the fundamental frequency of the structure is 3.5Hz, and the frequency of IMF3 is 3.5Hz equal to the fundamental frequency of the structure, so that the backward component of IMF3 is the quasi-static strain component, and only the residual component r3 is present, so that the quasi-static strain of the structure can be extracted in the time domain.
Fig. 6 is a comparison graph of the quasi-static strain time course of the unit long gauge length obtained by time-course strain signal reconstruction after the quasi-static strain determination and the real static strain time course. According to the method, the quasi-static strain of the structure is successfully extracted by adopting an EMD decomposition method through a quasi-static strain extraction rule, and results show that the method is good in effect and can effectively extract the quasi-static strain time course of the structure under the action of moving load.
The scope of the present invention includes, but is not limited to, the above embodiments, and the present invention is defined by the appended claims, and any alterations, modifications, and improvements that may occur to those skilled in the art are all within the scope of the present invention.

Claims (5)

1. The quasi-static long gauge length strain extraction method based on EMD decomposition is characterized by comprising the following steps of:
(1) extracting the strain time course of the structural unit;
(2) EMD decomposition is carried out on the extracted strain signals, and a plurality of intrinsic mode functions IMF and a residual component which can not be decomposed any more are decomposed;
(3) performing spectrum analysis on each decomposed IMF component to obtain IMF components and residual components with characteristic frequencies lower than the fundamental frequency;
(4) and adding the IMF component with the characteristic frequency lower than the fundamental frequency and the residual component to obtain the quasi-static strain time course of the structural unit.
2. The EMD decomposition-based quasi-static long-gauge strain extraction method according to claim 1, wherein the step (1) specifically comprises:
and carrying out data acquisition on the corner time courses of the two nodes of the structural unit through numerical simulation, and calculating the long gauge length strain time course of the structural unit through the relation between the corner time courses and the strain time courses.
3. The EMD decomposition-based quasi-static long gauge length strain extraction method of claim 2, wherein the calculation formula for calculating the long gauge length strain time course of the structural unit is as follows:
Figure FDA0002265041300000011
in the formula, hmIs the distance L from the pasting position of the long gauge length strain sensor to the neutral axis of the structuremIs the length of the structural unit, θi(t)，θjAnd (t) are the corner time courses of the two nodes of the structural unit respectively.
4. The EMD decomposition-based quasi-static long-gauge strain extraction method according to claim 3, wherein the step (2) is specifically as follows:
(1) finding original strain signals
Figure FDA0002265041300000012
All maximum value points are interpolated into an upper envelope V of the original data sequence by a cubic spline function1(t); finding out signals
Figure FDA0002265041300000013
All minimum value points are interpolated into a lower envelope V of the original data sequence by a cubic spline function2(t) obtaining an average value m of upper and lower envelope lines thereof1(t)：
Figure FDA0002265041300000014
(2) The original data sequence is processed
Figure FDA0002265041300000015
Minus the average envelope m1After (t), a new data sequence with low frequency removed is obtained:
Figure FDA0002265041300000016
judgment h1(t) whether it is IMF, if it does not satisfy the IMF condition, h1(t) is regarded as novel
Figure FDA0002265041300000017
Repeating the step (1) and the step (2) until h1(t) if IMF conditions are satisfied, then h is1(t) as the 1 st eigenmode function c1(t) is expressed as c1(t) is IMF (1):
c1(t)＝h1(t)；
(3) then, the following steps are carried out:
Figure FDA0002265041300000021
will r is1(t) is regarded as novel
Figure FDA0002265041300000022
And repeating the screening process from the step (1) to the step (3), and sequentially obtaining n intrinsic mode functions IMF in the screening process: c. C1(t)、c2(t)、c3(t)、c4(t)……cn(t) until a residual component rn(t) stopping the screening when it cannot be decomposed;
raw strain signal
Figure FDA0002265041300000023
I.e. n eigenmode functions IMF and a mean or trend term rn(t) is expressed as:
Figure FDA0002265041300000024
5. the EMD decomposition-based quasi-static long-gauge-distance strain extraction method of claim 4, wherein the quasi-static strain time course of the structural unit in the step (4) is as follows:
Figure FDA0002265041300000025
wherein f is1Is the first order frequency of the structural unit, i.e. the fundamental frequency, f (c)i(t)) is the frequency of the ith eigenmode function IMF,
Figure FDA0002265041300000026
is a quasi-static strain time course.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104568493A (en) * 2015-01-27 2015-04-29 南京工业大学 Quick structure damage identification method based on displacement time-course area under vehicle load
CN105973627A (en) * 2016-05-26 2016-09-28 东南大学 Long-gauge-length-strain-influence-envelope-based bridge damage identification method
CN108564046A (en) * 2018-04-19 2018-09-21 南京大学 Based on the steel construction dynamic strain signal processing method for improving EEMD
US20190120995A1 (en) * 2017-10-20 2019-04-25 Jilin University Method for random noise reduction from mrs oscillating signal using joint algorithms of emd and tfpf

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104568493A (en) * 2015-01-27 2015-04-29 南京工业大学 Quick structure damage identification method based on displacement time-course area under vehicle load
CN105973627A (en) * 2016-05-26 2016-09-28 东南大学 Long-gauge-length-strain-influence-envelope-based bridge damage identification method
US20190120995A1 (en) * 2017-10-20 2019-04-25 Jilin University Method for random noise reduction from mrs oscillating signal using joint algorithms of emd and tfpf
CN108564046A (en) * 2018-04-19 2018-09-21 南京大学 Based on the steel construction dynamic strain signal processing method for improving EEMD

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