CN111781275A - Steel rail ultrasonic guided wave defect identification and positioning method and device based on Lyapunov index - Google Patents

Steel rail ultrasonic guided wave defect identification and positioning method and device based on Lyapunov index Download PDF

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CN111781275A
CN111781275A CN202010547249.XA CN202010547249A CN111781275A CN 111781275 A CN111781275 A CN 111781275A CN 202010547249 A CN202010547249 A CN 202010547249A CN 111781275 A CN111781275 A CN 111781275A
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signal
time
steel rail
ultrasonic guided
rail
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CN111781275B (en
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马宏伟
曾紫焰
林荣
武静
刘仲铭
廖斌
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Dongguan Rail Transit Co ltd
Dongguan University of Technology
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Dongguan Rail Transit Co ltd
Dongguan University of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04Analysing solids
    • G01N29/07Analysing solids by measuring propagation velocity or propagation time of acoustic waves
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/4409Processing the detected response signal, e.g. electronic circuits specially adapted therefor by comparison
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00Indexing codes associated with group G01N29/00
    • G01N2291/02Indexing codes associated with the analysed material
    • G01N2291/023Solids
    • G01N2291/0234Metals, e.g. steel
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention discloses a method and a device for identifying and positioning defects of steel rail ultrasonic guided waves based on Lyapunov exponent, wherein the method comprises the following steps: acquiring a time-course signal propagated by the ultrasonic guided wave in the steel rail; constructing a multi-frequency driving duffin vibrator detection system and determining the optimal driving force amplitude; inputting the time-course signal into the constructed multi-frequency curating duffin oscillator detection system, defining a time-shifting window function, scanning the actually-measured signal through the time-shifting window function, and calculating the Lyapunov index of each section of signal; if the maximum Lyapunov index between the incident wave and the end face echo is less than or equal to 0, the steel rail is intact, if the maximum Lyapunov index is greater than 0, the steel rail has defects, the time when the incident wave, the end face echo and the defect echo are received is determined by using the curve peak value of the Lyapunov index, and the defect of the steel rail is positioned according to the time proportion relation among the incident wave, the end face echo and the defect echo. The invention improves the sensitivity of the ultrasonic guided wave detection method to the rail defect identification, thereby effectively prolonging the detection range.

Description

Steel rail ultrasonic guided wave defect identification and positioning method and device based on Lyapunov index
Technical Field
The invention relates to an ultrasonic guided wave detection technology, in particular to a method and a device for identifying and positioning defects of steel rail ultrasonic guided waves based on Lyapunov index, and belongs to the technical field of nondestructive testing.
Background
With the development of rail transit systems and railway systems, safety must be the primary consideration, and detection of rail damage is a necessary link for guaranteeing safe operation of trains. At present, steel rail flaw detection in China is based on a traditional ultrasonic detection technology, and flaw detection blind areas exist in a steel rail bottom area, so that missed detection and misjudgment are easily caused. The ultrasonic guided wave nondestructive testing technology has the advantages of long testing distance, full-section testing, high testing efficiency and the like, is particularly suitable for testing slender members, and has important theoretical and practical significance for guaranteeing safe operation of railway and rail transit systems and improving the testing level of infrastructure if the technology can be applied to rail flaw detection.
The current ultrasonic guided wave detection technology for steel rails can be mainly divided into three parts: 1) the research on the propagation characteristics of the ultrasonic guided waves in the steel rail is specifically shown in the research on the frequency dispersion characteristics, the attenuation characteristics, the propagation mode and mode conversion and the like of the ultrasonic guided waves in the steel rail; 2) ultrasonic guided wave excitation reception and device research, such as design and application of contact transducers based on piezoelectric effect and non-contact transducers based on magnetostrictive effect, pulse laser type and air coupling type; 3) and (3) ultrasonic guided wave signal characteristic extraction and defect identification, such as analysis methods of short-time Fourier transform, wavelet transform, correlation analysis and the like. The related literature shows that the research results are abundant in the three aspects. However, in the engineering application of the actual ultrasonic guided wave nondestructive testing technology, due to irresistible factors such as complexity of the service environment of the steel rail, the unknown defect size and the like, the reflected signal of the ultrasonic guided wave at the defect part is often submerged in the noise signal, and meanwhile, the reflected signal of the small defect is difficult to observe due to the attenuation of the ultrasonic guided wave in the long-distance detection, so that the defect characteristic extraction of the echo signal of the ultrasonic guided wave containing the noise is increasingly emphasized by scholars at home and abroad.
Because the chaotic system has sensitivity to the initial value and is resistant to external interference, the weak signal can be effectively identified from the phase state response of the chaotic system by inputting the weak signal as the initial value into a proper chaotic system.
The duffin array subsystem driving force item is a single frequency driving, while the ultrasonic guided wave signal is a multi-frequency pulse signal after being modulated, therefore, when the duffin array subsystem detects the ultrasonic guided wave signal, the influence of the multi-frequency signal on the detection system is no longer just to increase the original system driving force amplitude, because of the complexity of the nonlinear system and the sensitivity to the initial value, the multi-frequency signal can generate uncertain influence on the phase change law of the duffin array subsystem, thereby influencing the detection result.
Disclosure of Invention
In view of the above, the present invention provides a method, an apparatus, a system, a computer device, and a storage medium for identifying and positioning defects of a steel rail based on a lyapunov index, which can detect specific multi-frequency signals, reduce or eliminate uncertain influences generated when a single-frequency actuation duffing oscillator system detects multi-frequency signals when detecting the ultrasonic guided-wave multi-frequency signals, and effectively identify and position small micro defects with different damage degrees in the steel rail by using the lyapunov index as a quantitative index, thereby improving the sensitivity of the ultrasonic guided-wave detection method to the identification of the defects of the steel rail, and effectively extending the detection range.
The invention aims to provide a rail ultrasonic guided wave defect identification and positioning method based on Lyapunov exponent.
The invention aims to provide a rail ultrasonic guided wave defect identification and positioning device based on the Lyapunov exponent.
The third purpose of the invention is to provide a steel rail ultrasonic guided wave defect identification and positioning system based on the Lyapunov exponent.
It is a fourth object of the invention to provide a computer apparatus.
It is a fifth object of the present invention to provide a computer-readable storage medium.
The first purpose of the invention can be achieved by adopting the following technical scheme:
a rail ultrasonic guided wave defect identification and positioning method based on Lyapunov exponent comprises the following steps:
acquiring a time-course signal propagated by the ultrasonic guided wave in the steel rail;
constructing a multi-frequency driving duffing oscillator detection system based on a duffing equation and an ultrasonic guided wave signal expansion mode, and determining an optimal driving force amplitude value;
inputting the time-course signal into the constructed multi-frequency curating duffin oscillator detection system, defining a time-shifting window function, scanning the actually-measured signal through the time-shifting window function, and calculating the Lyapunov index of each section of signal;
if the maximum Lyapunov index between the incident wave and the end face echo is less than or equal to 0, the steel rail is intact; if the maximum Lyapunov index between the incident wave and the end face echo is larger than 0, the steel rail has defects;
when the steel rail has defects, determining the time when the incident wave, the end face echo and the defect echo are received by utilizing the curve peak value of the Lyapunov exponent, and positioning the defects of the steel rail according to the time proportional relation of the incident wave, the end face echo and the defect echo.
Further, the constructing of the multi-frequency policy duffing oscillator detection system based on the duffing equation and the ultrasonic guided wave signal expansion specifically includes:
selecting a Du-Feng equation as follows:
Figure BDA0002541160030000021
wherein, for damping ratio, F0cos ω t is the driving force term, F0For driving force, (-x) for driving force angular frequency, (-x)3+x5) Is a non-linear restoring force term;
representation of ultrasonic waveguide signal
Figure BDA0002541160030000031
Performing a triangular transformation, and expanding the following formula:
Figure BDA0002541160030000032
wherein, ω iscIs an angular frequency, and ωc=2πfcN is the number of modulation signal cycles, fcIs the excitation signal center frequency;
recalling cos ω t in the driving force term of the duffing equation as the same form as the ultrasonic waveguide signal
Figure BDA0002541160030000033
And setting the signal to be detected as
Figure BDA0002541160030000034
The duffin equation is rewritten as follows:
Figure BDA0002541160030000035
so as to complete the construction of the multi-frequency driving duffing oscillator signal detection system.
Further, the time shift window function is defined as follows:
Figure BDA0002541160030000036
Sm=g(t-nτ)S
wherein S is a time domain signal to be detected, SmThe signal intercepted by the time shift window, N is the length of the time domain signal to be detected, the length of the time shift window is 2, the moving interval is tau, and r tau is the time of the center of the time shift window.
Further, the lyapunov exponent is calculated as follows:
constructing an n-dimensional infinitesimal sphere space, and deforming the sphere into a shape of delta x in the evolution process of the target orbit along the reference orbiti(t) is an ellipsoid of the length of the main shaft, and along with the evolution of the orbit, the main shaft of the ellipsoid will be continuously changed, and the Lyapunov exponent of the multi-frequency-drive duffing oscillator detection system is as follows:
Figure BDA0002541160030000037
the n-dimensional system corresponds to n Lyapunov index values, if the maximum Lyapunov index is larger than 0, the multi-frequency actuation duffin oscillator detection system is in a chaotic state, and the two-dimensional non-autonomous duffin oscillator signal detection system is rewritten into a three-dimensional autonomous duffin oscillator signal detection system, which has the following formula:
Figure BDA0002541160030000038
the three-dimensional autonomous duffing oscillator signal detection system solves the Lyapunov exponent through a fourth-order Longge-Kutta method, and calculates the three Lyapunov exponents L under the three-dimensional autonomous duffing oscillator signal detection system1、L2、L3And L is1≥L2≥L3
Further, the rail defect positioning is carried out by adopting the following calculation formula:
Figure BDA0002541160030000041
wherein lcThe distance between the rail defect and the excitation end, l is the length of the rail, t1、t2And t3Respectively the time of receiving the incident wave, the defect echo and the end face echo.
The second purpose of the invention can be achieved by adopting the following technical scheme:
a rail ultrasonic guided wave defect identification and positioning device based on Lyapunov exponent, the device comprises:
the acquisition module is used for acquiring a time-course signal propagated by the ultrasonic guided wave in the steel rail;
the construction module is used for constructing a multi-frequency driving duffin oscillator detection system based on a duffing equation and an ultrasonic guided wave signal expansion mode and determining an optimal driving force amplitude value;
the calculation module is used for inputting the time-course signals into the constructed multi-frequency driving duffing oscillator detection system, defining a time-shifting window function, scanning the actually-measured signals through the time-shifting window function, and calculating the Lyapunov exponent of each section of signals;
the identification module is used for enabling the steel rail to be intact if the maximum Lyapunov index between the incident wave and the end face echo is less than or equal to 0; if the maximum Lyapunov index between the incident wave and the end face echo is larger than 0, the steel rail has defects;
and the positioning module is used for determining the incident wave, the end face echo and the moment of receiving the defect echo by utilizing the curve peak value of the Lyapunov index when the steel rail has defects, and positioning the defects of the steel rail according to the time proportional relation of the incident wave, the end face echo and the defect echo.
The third purpose of the invention can be achieved by adopting the following technical scheme:
a rail ultrasonic guided wave defect identification and positioning system based on Lyapunov exponent comprises an arbitrary waveform generator, a power amplifier, an exciter, a receiver, a digital oscilloscope and a computer, wherein the exciter and the receiver are arranged on the end face of one side of the rail bottom of a rail, the arbitrary waveform generator, the power amplifier and the exciter are sequentially connected, and the receiver, the digital oscilloscope and the computer are sequentially connected;
the computer is used for executing the rail ultrasonic guided wave defect identification and positioning method.
Further, the exciter and the receiver are respectively a piezoelectric excitation probe and a piezoelectric receiving probe.
The fourth purpose of the invention can be achieved by adopting the following technical scheme:
the computer equipment comprises a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program stored in the memory to realize the rail ultrasonic guided wave defect identification and positioning method.
The fifth purpose of the invention can be achieved by adopting the following technical scheme:
a computer readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for identifying and positioning the defects of the steel rail ultrasonic guided waves is realized.
Compared with the prior art, the invention has the following beneficial effects:
1. when the multi-frequency driving duffing array sub-detection system is constructed, the single-frequency item form in the driving force of the original duffing array sub-system is rewritten into the form consistent with the multi-frequency item form in the ultrasonic guided wave excitation signal, and the multi-frequency signal is detected by the multi-frequency driving duffing array system, so that the uncertain influence generated when the multi-frequency signal is detected by the single-frequency driving duffing array sub-system can be reduced or eliminated.
2. When the weak ultrasonic guided wave signals obtained by reflecting the defects in the steel rail are detected, the signals to be detected are input into the constructed multi-frequency planning duffin array detection system, the Lyapunov index is calculated, and the system phase state of the duffin system can be quantitatively judged, so that whether the echo signals have the defects or not is shown, and the defect identification is further completed.
3. According to the invention, a time shifting window function is constructed to scan a signal to be detected, and a Lyapunov exponent quantitative criterion is combined to determine whether a defect signal exists in the time shifting window, so that the defect position is determined through the position of the time shifting window, and thus defect positioning is realized.
4. The invention can effectively identify and position small micro defects with different damage degrees in the steel rail, thereby improving the sensitivity of the ultrasonic guided wave detection method to the identification of the defects of the steel rail and effectively prolonging the detection range.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
Fig. 1 is a schematic structural diagram of a rail ultrasonic guided-wave defect identification and positioning system in embodiment 1 of the present invention.
Fig. 2 is a flowchart of a method for identifying and positioning defects of a steel rail by using ultrasonic guided waves in embodiment 1 of the present invention.
Fig. 3 is a schematic diagram of a time-shift window function of scanning a measured signal according to embodiment 1 of the present invention.
Fig. 4 is a flowchart of a method for identifying and positioning defects of a steel rail by using ultrasonic guided waves in embodiment 2 of the present invention.
Fig. 5 is a schematic diagram of the lyapunov exponent and the original time domain signal under the condition that the steel rail of embodiment 2 of the invention is defect-free.
Fig. 6 is a schematic diagram of the lyapunov exponent and the original time domain signal under the condition of the defect of the 3mm rail foot of the steel rail in embodiment 2 of the invention.
Fig. 7 is a schematic diagram of the lyapunov exponent and the original time domain signal under the condition of the defect of 4.5mm of the rail foot of the steel rail in embodiment 2 of the invention.
Fig. 8 is a structural block diagram of a rail ultrasonic guided-wave defect identification and positioning device according to embodiment 3 of the present invention.
Fig. 9 is a block diagram of a computer device according to embodiment 4 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer and more complete, the technical solutions in the embodiments of the present invention will be described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by a person of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the protection scope of the present invention.
Example 1:
as shown in fig. 1, the present embodiment provides a rail ultrasonic guided wave defect identification and location system, which includes an arbitrary waveform generator 101, a power amplifier 102, an exciter 103, a receiver 104, a digital oscilloscope 105 and a computer 106.
Further, the exciter 103 and the receiver 104 of the present embodiment are respectively a piezoelectric exciting probe and a piezoelectric receiving probe, and are disposed on an end surface of a rail bottom side of the steel rail 107, the arbitrary waveform generator 101, the power amplifier 102 and the exciter 103 are sequentially connected, the receiver 104, the digital oscilloscope 105 and the computer 106 are sequentially connected, the arbitrary waveform generator 101 generates a pulse signal modulated by a hanning window, the pulse signal is amplified by the power amplifier 102, an ultrasonic guided wave signal is excited in the steel rail 107 by the exciter 103, the ultrasonic guided wave signal propagates along the steel rail 107 and travels through all positions of the steel rail 107, an echo signal is received by the receiver 104, a time-course signal of the ultrasonic guided wave propagating in the steel rail 107 is sampled by the digital oscilloscope 105, and the sampled time-course signal is transmitted to the computer 106 by the digital oscilloscope 105.
As shown in fig. 2, the embodiment further provides a method for identifying and positioning defects of a steel rail by using ultrasonic guided waves, which is implemented by the computer and includes the following steps:
s201, acquiring time-course signals of the ultrasonic guided waves propagating in the steel rail.
Specifically, the computer receives the signals transmitted by the digital oscilloscope, so that the time-course signals propagated by the ultrasonic guided waves in the steel rail are obtained.
S202, constructing a multi-frequency driving duffing oscillator detection system based on the duffing equation and the ultrasonic guided wave signal expansion mode, and determining the optimal driving force amplitude.
Specifically, an actual ultrasonic guided wave pulse excitation signal and a numerical simulation noise signal are set, a multi-frequency driving duffing oscillator signal detection system is constructed according to the central frequency, the sampling frequency and the characteristics of the duffing equation of the actual ultrasonic guided wave pulse excitation signal, and the optimal driving force amplitude F is determined0
S203, inputting the time-course signal into the constructed multi-frequency driving duffing oscillator detection system, defining a time-shifting window function, scanning the actually-measured signal through the time-shifting window function, and calculating the Lyapunov exponent of each section of signal.
Wherein, define the time shift window function, scan the measured signal through the time shift window function, specifically: a time-shift window function is defined, and the window length and the window moving speed are determined, and the measured signal is scanned by the time-shift window function, as shown in fig. 3.
S204, if the maximum Lyapunov index between the incident wave and the end face echo is less than or equal to 0, the steel rail is intact; if the maximum Lyapunov index between the incident wave and the end face echo is larger than 0, the steel rail has defects.
Wherein, the maximum lyapunov exponent between the incident wave and the end face echo is the maximum lyapunov exponent calculated by the signal in the window in step S203, and if the maximum lyapunov exponent L is calculated by the signal in the window1<If the value is 0, the steel rail is intact; if the calculated Lyapunov exponent L of the signal in the window is1>0, the rail has a defect at the position corresponding to the window, and the process goes to step S205.
S205, determining the receiving time of the incident wave, the end face echo and the defect echo by using the curve peak value of the Lyapunov exponent, and positioning the rail defect according to the time proportional relation of the incident wave, the end face echo and the defect echo.
Example 2:
as shown in fig. 4, in this embodiment, a specific experiment is taken as an example, and the ultrasonic guided wave defect identification and positioning is performed on a steel rail in a laboratory, and the specific implementation process is as follows:
1) the steel rail adopts a 60kg/m standard steel rail, the length of the steel rail is 6m, artificial cracks with the width of 3mm and 4.5mm are respectively manufactured at the position 2.5m away from the end surface of the steel rail, and three working conditions, namely no defect, cracks with the width of 3mm at the bottom of the rail and cracks with the width of 4.5mm at the bottom of the rail are set.
2) The arbitrary waveform generator generates a pulse signal modulated by a Hanning window, the pulse signal is amplified by a power amplifier and then passes through a piezoelectric excitation probe to excite an ultrasonic guided wave signal in the steel rail, and the ultrasonic guided wave is transmitted along the steel rail and passes through all positions of the steel rail.
The expression of the ultrasonic guided wave pulse signal modulated by the Hanning window is as follows:
Figure BDA0002541160030000071
where n is the number of modulation signal cycles, fcIs the excitation signal center frequency.
Rewriting formula (1) as:
Figure BDA0002541160030000072
wherein, ω iscIs an angular frequency, and ωc=2πfc
Carrying out triangular transformation on the formula (2), and expanding the following formula:
Figure BDA0002541160030000073
3) the method comprises the steps of receiving actual measurement signals of three working conditions through a piezoelectric receiving probe on the steel rail, sampling time-course signals propagated in the steel rail by ultrasonic guided waves through a digital oscilloscope, and transmitting the sampled time-course signals to a computer through the digital oscilloscope.
4) Construction of multi-frequency driving duffin vibrator detection system
4.1) selecting a Dufen equation (namely a Dufen vibrator mathematical model) as follows:
Figure BDA0002541160030000081
wherein, for damping ratio, F0cos ω t is the driving force term, F0For driving force, (-x) for driving force angular frequency, (-x)3+x5) Is a non-linear restoring force term.
When cos ω t in the driving force term of equation (4) is rewritten to the same form as that of the ultrasonic waveguide signal, equation (4) is changed to:
Figure BDA0002541160030000082
4.2) setting the signal to be detected as s- (t), the center frequency of the signal to be detected as 50KHz, the sampling frequency of the digital oscilloscope as 50M times/second, setting omega of the duffin equation as 0.34159 rad/mus, the integration step length as 0.02 mus, the damping ratio as 0.5, and rewriting the formula (5) into the following form:
Figure BDA0002541160030000083
and (3) completing construction of the multi-frequency driving duffing oscillator signal detection system, inputting the ultrasonic guided wave signal, namely changing the amplitude of the driving force term of the formula (4), and causing the change of the output characteristic of the multi-frequency driving duffing oscillator signal detection system, thereby realizing the analysis of the input signal.
5) Calculating Lyapunov exponent
The lyapunov exponent is an average exponential rate used to measure the convergence or divergence over time of two adjacent trajectories in phase space where the initial conditions are different.
In this embodiment, an n-dimensional infinitesimal sphere space is constructed, and during the evolution of the target orbit along the reference orbit, the sphere will be deformed into a shape of Δ xi(t) is an ellipsoid of major axis length, and the major axis of the ellipsoid will change continuously with the evolution of the orbit. Then, the lyapunov exponent of the multi-frequency actuation duffing oscillator signal detection system is as follows:
Figure BDA0002541160030000084
the n-dimensional system corresponds to n Lyapunov index values, if the maximum Lyapunov index is larger than 0, the multi-frequency actuation duffin oscillator detection system is in a chaotic state, and the two-dimensional non-autonomous duffin oscillator signal detection system of the formula (5) is rewritten into a three-dimensional autonomous duffin oscillator signal detection system, which has the following formula:
Figure BDA0002541160030000091
the formula (8) solves the Lyapunov exponent by a fourth-order Runge-Kutta method, and calculates three plums under the three-dimensional autonomous duffin oscillator signal detection systemYaponov index L1、L2、L3And L is1≥L2≥L2I.e. L1Is the maximum lyapunov index.
The original state of the system is a periodic state, when a defect signal is added, the phase state is changed into a chaotic state, and the Lyapunov exponent recognition damage is shown in Table 1.
Figure BDA0002541160030000092
TABLE 1 evaluation criteria for Lyapunov exponent to defects
6) And defining a time shifting window function, and identifying and positioning the defects of the steel rail under different working conditions.
6.1) definition of the time-shift window function, as follows:
Figure BDA0002541160030000093
Sm=g(t-nτ)S#(10)
wherein S is a time domain signal to be detected, SmThe signal intercepted by the time shift window, N is the length of the time domain signal to be detected, the length of the time shift window is 2, the moving interval is tau, and r tau is the time of the center of the time shift window.
6.2) time-shift Window function scanning of the measured Signal
And scanning the measured signals through a time-shifting window function, calculating the Lyapunov index corresponding to each window, and comparing the accuracy of the method for identifying and positioning the defects of the steel rail.
FIG. 5 is a plot of echo signals under a complete rail versus the corresponding Lyapunov exponent, and the results show that in a complete rail, the maximum Lyapunov exponent L is only at the incident wave and end echo, due to the absence of defects, at1>0, and between the incident wave and the end echo, the maximum lyapunov exponent L, despite the presence of noise1<0; as shown in FIG. 6, when the rail foot defect is 3mm, it is difficult to determine whether there is a defect in the time domain signal due to the small defect, and the Lyapunov exponential curveDisplay at the lesion L1>0, so that the presence of a defect can be judged, and since the Lyapunov exponent becomes significantly larger than 0 even if the signal is incomplete as long as a weak signal is present, the calculated Lyapunov exponent L1>0 is a range time region; as shown in FIG. 7, when the rail bottom defect is 4.5mm, the result in the figure is consistent with the conclusion of 3mm, and the description is omitted here.
6.3) locating the position of the rail defect
Determining the time of a time shifting window received by incident waves, end surface echoes and defect echoes by utilizing the curve peak value of the Lyapunov exponent, and positioning the defects of the steel rail according to the time proportional relation among the incident waves, the end surface echoes and the defect echoes, wherein the specific expressions of the defect positions and the error percentages are as follows:
Figure BDA0002541160030000101
Figure BDA0002541160030000102
wherein lcThe distance between the rail defect and the excitation end, l is the length of the rail, t1、t2And t3The time corresponding to the wave crest of the Lyapunov exponent curve at the incident wave, the defect echo and the end surface echo wave packet respectively.
The calculation results are shown in table 2 below, and since the piezoelectric probe itself has a certain size and a certain distance exists between the piezoelectric receiving probe and the piezoelectric excitation probe, the positioning error is within an acceptable range.
Figure BDA0002541160030000103
TABLE 2 Defect location of rails under different conditions
Example 3:
as shown in fig. 8, the present embodiment provides a rail ultrasonic guided wave defect identification and positioning apparatus, which includes an obtaining module 801, a constructing module 802, a calculating module 803, an identifying module 804, and a positioning module 805, and the specific functions of each module are as follows:
the acquisition module 801 is configured to acquire a time-course signal propagated by the ultrasonic guided wave in the steel rail.
The building module 802 is configured to build a multi-frequency driving duffing oscillator detection system based on the duffing equation and an ultrasonic guided wave signal expansion formula, and determine an optimal driving force amplitude.
The calculating module 803 is configured to input the time-course signal into the constructed multi-frequency curating duffin oscillator detection system, define a time-shift window function, scan the actually-measured signal through the time-shift window function, and calculate the lyapunov index of each segment of the signal.
The identification module 804 is used for enabling the steel rail to be intact if the maximum Lyapunov index between the incident wave and the end face echo is smaller than or equal to 0; if the maximum Lyapunov index between the incident wave and the end face echo is larger than 0, the steel rail has defects.
And the positioning module 805 is used for determining the incident wave, the end echo and the moment of receiving the defect echo by using the curve peak value of the Lyapunov exponent when the steel rail has the defect, and positioning the steel rail defect according to the time proportional relation among the incident wave, the end echo and the defect echo.
It should be noted that the system provided in this embodiment is only illustrated by the division of the functional modules, and in practical applications, the functions may be distributed by different functional modules according to needs, that is, the internal structure is divided into different functional modules to complete all or part of the functions described above.
Example 4:
as shown in fig. 9, the present embodiment provides a computer apparatus, which is a computer and includes a processor 902, a memory, an input device 903, a display 904 and a network interface 905 connected by a system bus 901, wherein the processor is used for providing computing and controlling capabilities, the memory includes a nonvolatile storage medium 906 and an internal memory 907, the nonvolatile storage medium 906 stores an operating system, a computer program and a database, the internal memory 907 provides an environment for the operation of the operating system and the computer program in the nonvolatile storage medium, and when the processor 902 executes the computer program stored in the memory, the method for identifying and locating a defect in a steel rail ultrasonic guided wave defect of embodiment 1 is implemented as follows:
acquiring a time-course signal propagated by the ultrasonic guided wave in the steel rail;
constructing a multi-frequency driving duffing oscillator detection system based on a duffing equation and an ultrasonic guided wave signal expansion mode, and determining an optimal driving force amplitude value;
inputting the time-course signal into the constructed multi-frequency curating duffin oscillator detection system, defining a time-shifting window function, scanning the actually-measured signal through the time-shifting window function, and calculating the Lyapunov index of each section of signal;
if the maximum Lyapunov index between the incident wave and the end face echo is less than or equal to 0, the steel rail is intact; if the maximum Lyapunov index between the incident wave and the end face echo is larger than 0, the steel rail has defects;
when the steel rail has defects, determining the time when the incident wave, the end face echo and the defect echo are received by utilizing the curve peak value of the Lyapunov exponent, and positioning the defects of the steel rail according to the time proportional relation of the incident wave, the end face echo and the defect echo.
Example 5:
the present embodiment provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the method for identifying and positioning a defect of a steel rail ultrasonic guided wave according to embodiment 1 is implemented as follows:
acquiring a time-course signal propagated by the ultrasonic guided wave in the steel rail;
constructing a multi-frequency driving duffing oscillator detection system based on a duffing equation and an ultrasonic guided wave signal expansion mode, and determining an optimal driving force amplitude value;
inputting the time-course signal into the constructed multi-frequency curating duffin oscillator detection system, defining a time-shifting window function, scanning the actually-measured signal through the time-shifting window function, and calculating the Lyapunov index of each section of signal;
if the maximum Lyapunov index between the incident wave and the end face echo is less than or equal to 0, the steel rail is intact; if the maximum Lyapunov index between the incident wave and the end face echo is larger than 0, the steel rail has defects;
when the steel rail has defects, determining the time when the incident wave, the end face echo and the defect echo are received by utilizing the curve peak value of the Lyapunov exponent, and positioning the defects of the steel rail according to the time proportional relation of the incident wave, the end face echo and the defect echo.
It should be noted that the computer readable storage medium of the present embodiment may be a computer readable signal medium or a computer readable storage medium or any combination of the two. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples of the computer readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present disclosure, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In contrast, in the present disclosure, a computer readable signal medium may include a data signal propagating in a baseband or as part of a carrier wave, in which a computer readable program is carried. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable storage medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. The computer program embodied on the computer readable storage medium may be transmitted using any appropriate medium, including but not limited to: electrical wires, optical cables, RF (radio frequency), etc., or any suitable combination of the foregoing.
The computer-readable storage medium may be written with a computer program for performing the present embodiments in one or more programming languages, including an object oriented programming language such as Java, Python, C + +, and conventional procedural programming languages, such as C, or similar programming languages, or combinations thereof. The program may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of methods, apparatus, and computer devices according to various embodiments described above. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions. The modules described in the above embodiments may be implemented by software or hardware.
The foregoing description is only exemplary of the preferred embodiments of the invention and is illustrative of the principles of the technology employed. It will be appreciated by those skilled in the art that the scope of the disclosure in the embodiments described above is not limited to the particular combination of features described above, and that other embodiments can be made by any combination of features described above or their equivalents without departing from the spirit of the disclosure. For example, the above features and (but not limited to) the features with similar functions disclosed in the above embodiments are mutually replaced to form the technical solution.
It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described above, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims (10)

1. A rail ultrasonic guided wave defect identification and positioning method based on Lyapunov exponent is characterized by comprising the following steps:
acquiring a time-course signal propagated by the ultrasonic guided wave in the steel rail;
constructing a multi-frequency driving duffing oscillator detection system based on a duffing equation and an ultrasonic guided wave signal expansion mode, and determining an optimal driving force amplitude value;
inputting the time-course signal into the constructed multi-frequency curating duffin oscillator detection system, defining a time-shifting window function, scanning the actually-measured signal through the time-shifting window function, and calculating the Lyapunov index of each section of signal;
if the maximum Lyapunov index between the incident wave and the end face echo is less than or equal to 0, the steel rail is intact; if the maximum Lyapunov index between the incident wave and the end face echo is larger than 0, the steel rail has defects;
when the steel rail has defects, determining the time when the incident wave, the end face echo and the defect echo are received by utilizing the curve peak value of the Lyapunov exponent, and positioning the defects of the steel rail according to the time proportional relation of the incident wave, the end face echo and the defect echo.
2. The method for identifying and positioning the defects of the steel rail through the ultrasonic guided wave according to claim 1, wherein the multi-frequency curated duffin oscillator detection system is constructed based on a duffing equation and an ultrasonic guided wave signal expansion formula, and specifically comprises the following steps:
selecting a Du-Feng equation as follows:
Figure FDA0002541160020000011
wherein, for damping ratio, F0cos ω t is the driving force term, F0For driving force, (-x) for driving force angular frequency, (-x)3+x5) Is a non-linear restoring force term;
representation of ultrasonic waveguide signal
Figure FDA0002541160020000012
Performing a triangular transformation, and expanding the following formula:
Figure FDA0002541160020000013
wherein, ω iscIs an angular frequency, and ωc=2πfcN is the number of modulation signal cycles, fcIs the excitation signal center frequency;
recalling cos ω t in the driving force term of the duffing equation as the same form as the ultrasonic waveguide signal
Figure FDA0002541160020000014
And setting the signal to be detected as
Figure FDA0002541160020000016
The duffin equation is rewritten as follows:
Figure FDA0002541160020000015
so as to complete the construction of the multi-frequency driving duffing oscillator signal detection system.
3. The method for identifying and locating defects by ultrasonic guided wave of steel rail according to claim 1, wherein the time-shift window function is defined as follows:
Figure FDA0002541160020000021
Sm=g(t-nτ)S
wherein S is a time domain signal to be detected, SmThe signal intercepted by the time shift window, N is the length of the time domain signal to be detected, the length of the time shift window is 2, the moving interval is tau, and r tau is the time of the center of the time shift window.
4. A rail flaw identification and location method by ultrasonic guided waves according to any one of claims 1 to 3, wherein the Lyapunov exponent is calculated as follows:
constructing an n-dimensional infinitesimal sphere space, and deforming the sphere into a shape of delta x in the evolution process of the target orbit along the reference orbiti(t) is an ellipsoid of the length of the main shaft, and along with the evolution of the orbit, the main shaft of the ellipsoid will be continuously changed, and the Lyapunov exponent of the multi-frequency-drive duffing oscillator detection system is as follows:
Figure FDA0002541160020000022
the n-dimensional system corresponds to n Lyapunov index values, if the maximum Lyapunov index is larger than 0, the multi-frequency actuation duffin oscillator detection system is in a chaotic state, and the two-dimensional non-autonomous duffin oscillator signal detection system is rewritten into a three-dimensional autonomous duffin oscillator signal detection system, which has the following formula:
Figure FDA0002541160020000023
the three-dimensional autonomous duffing oscillator signal detection system solves the Lyapunov exponent through a fourth-order Longge-Kutta method, and calculates the three Lyapunov exponents L under the three-dimensional autonomous duffing oscillator signal detection system1、L2、L3And L is1≥L2≥L3
5. A rail defect identification and location method by ultrasonic guided wave according to any one of claims 1 to 3, wherein the rail defect location is calculated by the following formula:
Figure FDA0002541160020000024
wherein 1 iscThe distance between the rail defect and the excitation end, 1 is the length of the rail, t1、t2And t3Respectively the time of receiving the incident wave, the defect echo and the end face echo.
6. A rail ultrasonic guided wave defect identification and positioning device based on Lyapunov exponent is characterized by comprising:
the acquisition module is used for acquiring a time-course signal propagated by the ultrasonic guided wave in the steel rail;
the construction module is used for constructing a multi-frequency driving duffin oscillator detection system based on a duffing equation and an ultrasonic guided wave signal expansion mode and determining an optimal driving force amplitude value;
the calculation module is used for inputting the time-course signals into the constructed multi-frequency driving duffing oscillator detection system, defining a time-shifting window function, scanning the actually-measured signals through the time-shifting window function, and calculating the Lyapunov exponent of each section of signals;
the identification module is used for enabling the steel rail to be intact if the maximum Lyapunov index between the incident wave and the end face echo is less than or equal to 0; if the maximum Lyapunov index between the incident wave and the end face echo is larger than 0, the steel rail has defects;
and the positioning module is used for determining the incident wave, the end face echo and the moment of receiving the defect echo by utilizing the curve peak value of the Lyapunov index when the steel rail has defects, and positioning the defects of the steel rail according to the time proportional relation of the incident wave, the end face echo and the defect echo.
7. A rail ultrasonic guided wave defect identification and positioning system based on Lyapunov exponent is characterized by comprising an arbitrary waveform generator, a power amplifier, an exciter, a receiver, a digital oscilloscope and a computer, wherein the exciter and the receiver are arranged on the end face of one side of the rail bottom of a rail, the arbitrary waveform generator, the power amplifier and the exciter are sequentially connected, and the receiver, the digital oscilloscope and the computer are sequentially connected;
the computer is used for executing the steel rail ultrasonic guided wave defect identification and positioning method of any one of claims 1 to 5.
8. The steel rail ultrasonic guided wave defect identification and location system of claim 7, wherein the exciter and receiver are a piezoelectric excitation probe and a piezoelectric receiving probe, respectively.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the method for identifying and locating defects in steel rail ultrasonic guided waves according to any one of claims 1 to 5 when executing the computer program stored in the memory.
10. A computer readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the method for identifying and locating a rail flaw according to any one of claims 1 to 5.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112505155A (en) * 2020-12-09 2021-03-16 暨南大学 Pipeline guided wave damage identification and positioning method, device and system based on information entropy
CN112697877A (en) * 2020-11-07 2021-04-23 西南交通大学 Turnout steel rail damage detection method based on nonlinear ultrasonic guided waves
CN112697881A (en) * 2020-12-09 2021-04-23 东莞理工学院 Steel rail guided wave defect identification and positioning method, device and system based on K-S entropy
JP7309236B2 (en) 2021-12-10 2023-07-18 東莞理工学院 Dual Chaos Analysis System Detection Method for Weak Ultrasonic Guided Wave Signals

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103323538A (en) * 2013-05-23 2013-09-25 暨南大学 Duffing equation Lyapunov index based ultrasonic guided wave detection method
CN103512955A (en) * 2013-09-25 2014-01-15 暨南大学 Ultrasonic guided-wave method for identifying inclined crack of steel rail by using chaotic oscillator system
CN104101648A (en) * 2014-04-10 2014-10-15 太原科技大学 Ultrasonic guided-wave defect locating method based on Liapunov index
CN104777222A (en) * 2015-03-30 2015-07-15 暨南大学 Pipeline defect identification and visualization method based on three-dimensional phase trajectory of Duffing system
US20190086370A1 (en) * 2017-09-18 2019-03-21 Quanta Associates, L.P. Statistical analysis of chaotic response signals for tubulars

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103323538A (en) * 2013-05-23 2013-09-25 暨南大学 Duffing equation Lyapunov index based ultrasonic guided wave detection method
CN103512955A (en) * 2013-09-25 2014-01-15 暨南大学 Ultrasonic guided-wave method for identifying inclined crack of steel rail by using chaotic oscillator system
CN104101648A (en) * 2014-04-10 2014-10-15 太原科技大学 Ultrasonic guided-wave defect locating method based on Liapunov index
CN104777222A (en) * 2015-03-30 2015-07-15 暨南大学 Pipeline defect identification and visualization method based on three-dimensional phase trajectory of Duffing system
US20190086370A1 (en) * 2017-09-18 2019-03-21 Quanta Associates, L.P. Statistical analysis of chaotic response signals for tubulars

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
JING WU ET AL.: "Defect detection of pipes using Lyapunov dimension of Duffing oscillator based on ultrasonic guided waves", 《MECHANICAL SYSTEMS AND SIGNAL PROCESSING》 *
WEIWEI ZHANG ET AL.: "Detection of minor damage in structures with guided wave signals and nonlinear oscillator", 《MEASUREMENT》 *
XIAOFENG LIU: "Detection of micro-cracks using nonlinear lamb waves based on the Duffing-Holmes system", 《JOURNAL OF SOUNDAND VIBRATION》 *
张伟伟 等: "基于Lyapunov指数的超声导波检测技术", 《振动、测试与诊断》 *
林荣: "基于超声导波的钢轨探伤技术研究", 《中国优秀博硕士学位论文全文数据库(博士) 工程科技Ⅱ辑》 *
武静 等: "基于Lyapunov 指数的管道超声导波小缺陷定位实验研究", 《振动与冲击》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112697877A (en) * 2020-11-07 2021-04-23 西南交通大学 Turnout steel rail damage detection method based on nonlinear ultrasonic guided waves
CN112505155A (en) * 2020-12-09 2021-03-16 暨南大学 Pipeline guided wave damage identification and positioning method, device and system based on information entropy
CN112697881A (en) * 2020-12-09 2021-04-23 东莞理工学院 Steel rail guided wave defect identification and positioning method, device and system based on K-S entropy
JP7309236B2 (en) 2021-12-10 2023-07-18 東莞理工学院 Dual Chaos Analysis System Detection Method for Weak Ultrasonic Guided Wave Signals

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