Method for measuring air-coupled ultrasonic stress by extracting Lyapunov exponent peak of low signal-to-noise ratio air-coupled ultrasonic signal through moving window

Abstract

A method for measuring an air-coupled ultrasonic stress by extracting a Lyapunov exponent peak of a low signal-to-noise ratio air-coupled ultrasonic signal through a moving window. In view that the ch

Description

TECHNICAL FIELD

[01] The present invention belongs to the technical field of ultrasonic testing, and particularly relates to a method for measuring an air-coupled ultrasonic stress by extracting a Lyapunov exponent peak of a low signal-to-noise ratio air-coupled ultrasonic signal through a moving window that is suitable for composite plates. BACKGROUND ART

[02] Composite materials, due to their high stiffness ratio, high strength ratio, good corrosion resistance, aging resistance, and other features, are widely used in the wings, fuselages and cabins of new airplanes, as well as the fields of automotive, communication, etc. The residual stress or structural bearing capacity inside a composite material might lead to delamination, cracking, or exacerbation thereof, which will greatly reduce the safety performance of composite components. Therefore, precise measurement of the stress state of a composite material is of great significance to ensure the safety of its application to relevant fields.

[03] Non-destructive stress testing methods mainly include X-ray diffraction method, neutron diffraction method, Raman spectroscopy, and ultrasonic method. Judged from the perspectives of application scope, detection accuracy, and operability, ultrasonic method is more suitable for in-situ stress measurement of composite plates. In the ultrasonic stress measurement method, the acoustic elastic effect of elastic waves is used to achieve measurement. Lamb waves, with small energy attenuation in the long distance of propagation, can be widely used for stress detection of carbon fiber composite plates in an efficient manner. For the traditional ultrasonic testing technology, a coupling agent is needed to ensure sufficient acoustic coupling between an energy transducer and a device under test (DUT). However, uneven thickness of the coupling agent might directly affect the measurement of acoustic time, thus leading to stress measurement errors. In addition, the presence of the coupling agent greatly reduces detection flexibility and efficiency. Therefore, the non-contact detection technology for air-coupled ultrasonic Lamb waves is more suitable for achieving automated and rapid in-situ stress measurement of composite plates made up of large-size components. 104] An air-coupled ultrasonic transducer is a key component of the air-coupled ultrasonic Lamb wave detection technology. However, due to serious mismatch between the piezoelectric material and the acoustic impedance of air, the air-coupled ultrasonic transducer suffers from severe energy loss. Air-coupled ultrasonic Lamb wave signals are extremely weak and susceptible to serious interference by environmental noise. The key to achieving stress measurement of composite plates by using air-coupled ultrasonic Lamb waves lies in the extraction of signal-related acoustic time features. At a low signal-to-noise ratio, existing acoustic time calculation methods such as the threshold method, peak-to-peak method, envelope method, and positive correlation method cannot be used to accurately obtain acoustic time features, which will directly affect the accuracy of stress measurement. In addition, the stress resolution directly depends on the acoustic time resolution, and improvement of the traditional acoustic time resolution is limited by hardware conditions such as the maximum sampling rate of sampling equipment. In view that the chaotic system is extremely sensitive to initial conditions and parameters and has strong immunity to noise, the present invention establishes a chaotic system based on Duffing oscillators. The Lyapunov exponent for each moving window is obtained by means of scanning, and acoustic time information of echo is received for the ultrasonic Lamb waves at the moment corresponding to the peak of the Lyapunov exponent. The minimum step size of window function movement is the acoustic time resolution, and can be determined comprehensively based on various indicators such as measurement indicators and computational efficiency. Under the premise of low signal-to-noise ratio, high-resolution and high-precision stress characterization of composite plates based on air-coupled ultrasonic Lamb waves is achieved while ensuring the accuracy of extracting acoustic time resolution and features. SUMMARY 105] To overcome the shortcomings and deficiencies in the prior art, the present invention provides a method for measuring an air-coupled ultrasonic stress by extracting a Lyapunov exponent peak of a low signal-to-noise ratio air-coupled ultrasonic signal through a moving window.

[06] The present invention is achieved by means of the following technical solution. The present invention provides a method for measuring an air-coupled ultrasonic stress by extracting a Lyapunov exponent peak of a low signal-to-noise ratio air-coupled ultrasonic signal through a moving window, and for, under the premise of low signal-to-noise ratio, achieving high-resolution and high-precision stress characterization of composite plates based on air-coupled ultrasonic Lamb waves while ensuring the accuracy of extracting acoustic time resolution and features, and the method includes the following steps:

[07] SI: selecting the anti-symmetric Ao mode as the detection mode for Lamb waves due to the larger out-of-plane displacement of the Ao mode, and determining the center frequency f and inclination angle a of an air-coupled ultrasonic transducer according to the Lamb wave frequency dispersion curve and Snell's law, to achieve ipsilateral in-situ stress measurement of air-coupled ultrasonic Lamb waves;

[08] S2: determining the driving force frequency co of a chaotic system based on a duffing oscillator according to the center frequency of the air-coupled ultrasonic transducer, and subsequently making the chaotic system exist in a critical state of transition from chaotic state to periodic state or from periodic state to chaotic state by adjusting parameters;

[09] S3: after determining the chaotic system, determining the size At of the moving window according to the width of an excitation signal, and determining the minimum step size Ate of the moving window according to the stress measurement resolution index and computational efficiency requirements; and

[10] S4: obtaining the Lyapunov exponent corresponding to each moving window moment through the moving window from an initial position of an ultrasonic Lamb wave signal to be analyzed, receiving acoustic time information of echo for the ultrasonic Lamb waves at the moment corresponding to the peak of any Lyapunov exponent.

[11] Further, the adjusted parameters include a system damping coefficient 5 and an external driving force amplitude F.

[12] Further, the chaotic system is based on a Duffing oscillator. If S(t)=Asincoot is a weak sinusoidal signal to be detected, and is added to the right side of the system as an additional input, then the system is expressed as follows: x + £x-x3 + x5 = F coscot + Jsin<yor = 4f2+ cos(<yf -0)     (2)

[13] where 9 represents an initial phase of the system, satisfying the condition of tan0=J / F; Because the chaotic system is extremely sensitive to initial conditions, as long as the chaotic system exists in a critical state of transition from chaotic state to periodic state or from periodic state to chaotic state by adjusting parameters, the system will undergo a significant change in state when the above sinusoidal signal is inputted to the system, so that the purpose of identifying weak signals can be achieved even if there exists noise in a signal to be detected. Because the noise signal does not have the characteristic of angular frequency of the external driving force of the system, and does not belong to the intrinsic change of the system, the system will not be changed.

[14] Further, after the chaotic system is determined, the moving window (oc(t) is determined: 1, tc — Af / 2 <  / — tc + Af / 2 0, other (3)

[15] where tc is the center position moment of the moving window, the step size Atc of the moving window is determined according to the stress measurement resolution index and computational efficiency requirements, and At as the size of the moving window is set as the length of the excitation signal (so that the moving window is capable to contain most echo signals of Lamb waves, but information of only one echo signal of Lamb wave can be contained once); obtaining the Lyapunov exponent for a signal within the moving window using the following processing method:

[16] For an ^-dimensional nonlinear system, the Lyapunov exponent in the / -direction is as follows:

[17] where ll'll is the Euclidean norm;

[18] for a continuous system, X = F(x) (5)

[19] where X — dx / df, X € R represents the coordinate vector of a midpoint in an 77-dimensional space; the amount of separation between adjacent orbits is represented in a tangent space: Ax = j(x(f))Axz                   (6) . j(x(t)} = dF / dx

[20] where \ ' / / is a Jacobian matrix;

[21] solving the problem of the Jacobian iterative algorithm by continuously substituting and changing new vectors through Schmidt orthogonalization using the following orthogonalization process: 122] where <,> is an inner product, and h is a solved step size; the superscript j ( / -0,1,2,..., 00) represents the times of orthogonalization, which corresponds to the evolution times of a nonlinear system; the GSR method is used to obtain a new orthogonal set {U\,U2,...,Un}', 123] a constant d is used to substitute ||Ax, (0)||(z=0,1,2,...,«) ; to meet the requirements, d is set to be 1 ( ' expressed as: 124] ), and the Lyapunov exponent solution equation can be approximately

[25] after obtaining the Lyapunov exponents corresponding to all moving windows, acoustic time information corresponding to the ultrasonic Lamb wave signals is received at the moment corresponding to the peak, to achieve the air-coupled ultrasonic stress measurement.

[26] The present invention has the beneficial effects as follows:

[27] To solve the problem that it is difficult to accurately extract acoustic time information of air-coupled ultrasonic Lamb wave signals at a low signal-to-noise ratio, the present invention replaces the existing acoustic time extraction technique with a method of extracting the Lyapunov exponent peak through a moving window, to accurately obtain the acoustic time features of air-coupled ultrasonic Lamb waves. In view that the chaotic system is extremely sensitive to initial conditions and parameters and has strong immunity to noise, the present invention reduces the signal-to-noise ratio threshold and improves the accuracy of extracting acoustic time features. The present invention determines the acoustic time resolution through the moving window according to the minimum step size, overcomes the problem that improvement of the traditional acoustic time resolution is limited by hardware conditions such as the maximum sampling rate of sampling equipment, and achieves stress measurement of composite plates based on air-coupled ultrasonic Lamb waves while ensuring the accuracy of extracting acoustic time resolution and features. BRIEF DESCRIPTION OF THE DRAWINGS

[28] FIG. 1 is a flowchart of a method for measuring an air-coupled ultrasonic Lamb wave stress by extracting a Lyapunov exponent peak through a moving window.

[29] FIG. 2 is a schematic diagram of extracting a Lyapunov exponent peak through a moving window. DETAILED DESCRIPTION OF THE EMBODIMENTS

[30] The technical solutions in the embodiments of the present invention will be clearly and completely described below in combination with the accompanying drawings in the embodiments of the present invention. Apparently, the embodiments described are merely some rather than all of the embodiments of the present invention. Based on the embodiment of the present invention, all other embodiments acquired by those of ordinary skill in the art without making creative efforts fall within the scope of protection of the present invention.

[31] With reference to FIGs. 1 and 2, the present invention provides a method for measuring an air-coupled ultrasonic stress by extracting a Lyapunov exponent peak of a low signal-to-noise ratio air-coupled ultrasonic signal through a moving window, and the method includes the following steps: 132] SI: selecting Ao mode as the detection mode for Lamb waves due to the larger out-of-plane displacement of the Ao mode, and determining the center frequency f and inclination angle a of an air-coupled ultrasonic transducer according to the Lamb wave frequency dispersion curve and Snell's law, to achieve ipsilateral in-situ stress measurement of air-coupled ultrasonic Lamb waves; 133] S2: determining the driving force frequency co of a chaotic system according to the center frequency of the air-coupled ultrasonic transducer, and subsequently making the chaotic system exist in a critical state of transition from chaotic state to periodic state or from periodic state to chaotic state by adjusting parameters, where the adjusted parameters include a system damping coefficient S and an external driving force amplitude F;

[34] S3: after determining the chaotic system, determining the size At of the moving window according to the width of an excitation signal, and determining the minimum step size Ate of the moving window according to the stress measurement resolution index and computational efficiency requirements; and

[35] S4: obtaining the Lyapunov exponent corresponding to each moving window moment through the moving window from an initial position of an ultrasonic Lamb wave signal to be analyzed, receiving acoustic time information of echo for the ultrasonic Lamb waves at the moment corresponding to the peak of any Lyapunov exponent, and under the premise of low signal-to-noise ratio, achieving high-resolution and high-precision stress characterization of composite plates based on air-coupled ultrasonic Lamb waves while ensuring the accuracy of extracting acoustic time resolution and features.

[36] Because the Duffing equation has rich dynamic characteristics, and the external driving force of the Duffing Holmes chaotic system is generally determined by sine or cosine, theoretically it is extremely sensitive to sinusoidal periodic signals and has strong immunity to noise.

[37] In mathematics, the Duffing Holmes equation is expressed as

[38] x + dx - axk{ + Pxk2 = F coscot (i)

[39] where 8 represents the damping coefficient of the system; — ax + denotes a nonlinear restoring force; F is an external driving force amplitude; to refers to an angular frequency of the external driving force.

[40] When a=P=l, Ai=3, and fe=5, the above equation is the improved Duffing Holmes equation, and currently is quite sensitive in detection of weak signals. The chaotic system is based on a Duffing oscillator. If S(t)=A sincoot is a weak sinusoidal signal to be detected, and is added to the right side of the system as an additional input, then the system is expressed as follows:

[41] x + ^x-x3 +x5 =Fcos®r + Jsin®or = a / f2 + A2 cos(tur-^) (2)

[42] where 9 represents an initial phase of the system, satisfying the condition of tan0=J / F; through comparing the equation (1) and the equation (2), it can be found that in the equation (2), the amplitude and the initial phase of the external driving force are changed based on the equation (1). because the chaotic system is extremely sensitive to initial conditions, as long as the chaotic system exists in a critical state of transition from chaotic state to periodic state or from periodic state to chaotic state by adjusting parameters (5 and F), the system will undergo a significant change in state when the above sinusoidal signal is inputted to the system, so that the purpose of identifying weak signals can be achieved even if there exists noise in a signal to be detected. Because the noise signal does not have the characteristic of angular frequency of the external driving force of the system, and does not belong to the intrinsic change of the system, the system will not be changed. In summary, based on the sensitivity of non-equilibrium phase transition of the chaotic system based on a Duffing oscillator to system parameters, and its immunity to noise signals, the present invention achieves detection of weak signals in a strong noise background. Quantitative estimation of the state of the chaotic system based on a Duffing oscillator can be achieved by calculating the Lyapunov exponent of the system.

[43] With reference to FIG. 2, the principle of extracting a Lyapunov exponent peak through a moving window is explained in detail.

[44] Lamb waves have symmetric and anti-symmetric modes as well as frequency dispersion characteristics, and may excite multiple symmetric modes (So, Si,...,Sz) and anti-symmetric modes (Ao, Ai, ...,A() at the same excitation frequency. Because the out-of-plane displacement in an anti-symmetric mode is much greater than that in a symmetric mode, in order to achieve ipsilateral in-situ stress measurement of air-coupled ultrasonic Lamb waves, the air-coupled ultrasonic transducer should be capable to excite a relatively pure Ao mode in the composite plates. The excitation frequency f is determined based on the cutoff frequency of Ai mode in the frequency dispersion curve of Lamb waves, and the thickness of a device under test (DUT). The driving force frequency to of a chaotic system is determined according to the center frequency of the air-coupled ultrasonic transducer, and subsequently the chaotic system is arranged to exist in a critical state of transition from chaotic state to periodic state or from periodic state to chaotic state by adjusting parameters (a system damping coefficient S and an external driving force amplitude F).

[45] After the chaotic system is determined, the moving window (£>c(t) is determined: 146] Uc -A? / 2<?<fc +Ar / 2 0, other (3)

[47] where tc is the center position moment of the moving window, the step size Atc of the moving window is determined according to the stress measurement resolution index and computational efficiency requirements, and At as the size of the moving window is set as the length of the excitation signal, so that the moving window is capable to contain most echo signals of Lamb waves, but information of only one echo signal of Lamb wave can be contained once; the following processing method is used to obtain the Lyapunov exponent for a signal within the moving window:

[48] For an ^-dimensional nonlinear system, the Lyapunov exponent in the / -direction is as follows: (4)

[49] where || j| is the Euclidean norm;

[50] for a continuous system, (5)

[51] where X ' , X€ □ represents the coordinate vector of a midpoint in an / / -dimensional space; the amount of separation between adjacent orbits is represented in a tangent space: Ax = J(4 / ))Ax( (6)

[52] where 7 I'D)— ]s a Jacobian matrix; by solving the above equation, Ax,.(0 U • J ' v 7 can be obtained.

[53] According to Gram Schmidt Renormalization (GSR) method, the problem of the Jacobian iterative algorithm is solved by continuously substituting and changing new vectors through Schmidt orthogonalization, and the orthogonalization process is as follows:

[54] where <,> is an inner product, and h is a solved step size; the superscript j ( / -0,1,2,..., 00 ) represents the times of orthogonalization, which corresponds to the evolution times of a nonlinear system; the GSR method is used to obtain a new orthogonal set {U\,Ui,...,Un}',

[55] a constant d is used to substitute ^)11 ( / =0,1,2,...,n); to meet the requirements, d is set to be 1(11 ' II ), and the Lyapunov exponent solution equation can be approximately expressed as: (8) ( / +1)

[56] after obtaining the Lyapunov exponents corresponding to all moving windows, acoustic time information corresponding to the ultrasonic Lamb wave signals is received at the moment corresponding to the peak, to achieve the air-coupled ultrasonic stress measurement.

[57] The method for measuring an air-coupled ultrasonic stress by extracting a Lyapunov exponent peak of a low signal-to-noise ratio air-coupled ultrasonic signal through a moving window proposed by the present invention is described in detail, and the contents, claims, effects, and specific implementations of the present invention are expounded. In addition, in accordance with the ideas of the present invention, various modifications and adjustments can be made by those of ordinary skill in the art to specific forms of the network structure used, the optimization algorithm and hyperparameter selection for model training, specific forms of the loss function, and specific values of weight coefficients according to the actual scenes and condition limitations. Therefore, relevant expressions shall not be construed as limitation to the present invention.

Claims

1. A method for measuring an air-coupled ultrasonic stress by extracting a Lyapunov exponent peak of a low signal-to-noise ratio air-coupled ultrasonic signal through a moving window, andfor, under the premise of low signal-to-noise ratio, achieving high-resolution and high-precision stress characterization of composite plates based on air-coupled ultrasonic Lamb waves while ensuring the accuracy of extracting acoustic time resolution and features, the method comprising the following steps:S1: selecting the anti-symmetric Ao mode as the detection mode for Lamb waves due to the larger out-of-plane displacement of the Ao mode, and determining the center frequency f and inclination angle a of an air-coupled ultrasonic transducer according to the Lamb wave frequency dispersion curve and Snell's law, to achieve ipsilateral in-situ stress measurement of air-coupled ultrasonic Lamb waves;S2: determining the driving force frequency co of a chaotic system based on a duffing oscillator according to the center frequency of the air-coupled ultrasonic transducer, and subsequently making the chaotic system exist in a critical state of transition from chaotic state to periodic state or from periodic state to chaotic state by adjusting parameters;S3: after determining the chaotic system, determining the size At of the moving window according to the width of an excitation signal, and determining the minimum step size Atc of the moving window according to the stress measurement resolution index and computational efficiency requirements; andS4: obtaining the Lyapunov exponent corresponding to each moving window moment through the moving window from an initial position of an ultrasonic Lamb wave signal to be analyzed, receiving acoustic time information of echo for the ultrasonic Lamb waves at the moment corresponding to the peak of the Lyapunov exponent.

2. The method according to claim 1, wherein the adjusted parameters include a system damping coefficient 8 and an external driving force amplitude F.

3. The method according to claim 2, wherein the chaotic system is based on a Duffing oscillator, wherein if S(t)=A sincoot is a weak sinusoidal signal to be detected, and is added to the right side of the system as an additional input, then the system is expressed as follows:x + ^x-x3 + x5 = F cos M + Asin a)ot = F2 + A2 cos(m-0) (2) wherein 0 represents an initial phase of the system, satisfying the condition of tan^=J / F.

4. The method according to claim 3, wherein after the chaotic system is determined, the moving window <nc(t) is determined:( .    1,4 - Ar / 2 < r < 4 + Ar / 20, other(3)wherein tc is the center position moment of the moving window, the step size ^tc of themoving window is determined according to the stress measurement resolution index andcomputational efficiency requirements, and At as the size of the moving window is set as the length of the excitation signal, obtaining the Lyapunov exponent for a signal within the moving window using the following processing method:For an ^-dimensional nonlinear system, the Lyapunov exponent in the / -direction is asfollows:(4)wherein || j| is the Euclidean norm;for a continuous system,(5)wherein x = dx / dr , xe 0 ” represents the coordinate vector of a midpoint in an77-dimensional space; the amount of separation between adjacent orbits is represented in atangent space:(6). j(x(t)} = dF / dxwherein \ ' / / is a Jacobian matrix;solving the problem of the Jacobian iterative algorithm by continuously substituting and changing new vectors through Schmidt orthogonalizationusing the following orthogonalization process :(7)wherein <,> is an inner product, and h is a solved step size; the superscript j ( / =0,1,2,...,00) represents the times of orthogonalization, which corresponds to the evolution times of a nonlinear system; the GSR method is used to obtain a new orthogonal set {U\,Ui,...,Un}',a constant d is used to substitute ||Arz (0)|| ( / =0,1,2,...,«); to meet the requirements, d is set to be l(||t / ^|| = 1), and the Lyapunov exponent solution equation can be approximately expressed as:after obtaining the Lyapunov exponents corresponding to all moving windows, acoustic time information corresponding to the ultrasonic Lamb wave signals is received at the moment corresponding to the peak, to achieve the air-coupled ultrasonic stress measurement.

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