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

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

[05] 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 the method includes the following steps:

[07] 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 / 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 aircoupled ultrasonic Lamb waves;

[08] 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;

[09] S3: after determining the chaotic system, determining the size A / of the moving window according to the width of an excitation signal, and determining the minimum step size A / c 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, 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.

[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)=Asinwo / 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* = Feos 6# +              + A" cos( - 0)    (2)

[13] where 0 represents an initial phase of the system, satisfying the condition of tanFM / 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 coc( / ) is determined: , x f 1, t —     / 2 X t < t, ■+ A / / 2 = s (3) [0, other

[15] where tc is the center position moment of the moving window, the step size A / c 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:

[16] For an w-dimensional nonlinear system, the Lyapunov exponent in the / -direction is as follows: i ||ax.(Y)|| X = lim - In ——4                 (4)

[17] where iHi is the Euclidean norm;

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

[19] where = , X 6 1R represents the coordinate vector of a midpoint in an n- dimensional space; the amount of separation between adjacent orbits is represented in a tangent space: Ax = J ( x (t)) Ax,                      (6) u j(x(t)) = dF / dx . T ,.

[20] where v v 77 ' is a Jacobian matrix;

[21] 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: - Ax, ( / A) M(jh)- (y / ?),U^Yl^! W|4 = ^ / 1^1                                   (7) ^-ax4j70-(MM^-----(¼. j L'W-FvMk'^

[22] 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\,U^---.Un}',

[23] a constant d is used to substitute JAa' Wf!°’1 \ to meet the requirements, d is set to be 1( ■ i I! ), and the Lyapunov exponent solution equation can be approximately expressed as:

[24] In d (8)

[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:

[32] 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 / 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 aircoupled ultrasonic Lamb waves;

[33] 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 8 and an external driving force amplitude F;

[34] S3: after determining the chaotic system, determining the size A / of the moving window according to the width of an excitation signal, and determining the minimum step size 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 + (Jx - axki + 0xk2 - F cosa£            (i)

[39] where 5 represents the damping coefficient of the system; ~ax ± px ~ denotes a nonlinear restoring force; F is an external driving force amplitude; co refers to an angular frequency of the external driving force.

[40] When a=P=l, &i=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)=Asincoo / 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 ~ Feos®#+ .4sin+ J2 cos(^ — #)   (2)

[42] where 0 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 nonequilibrium 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,...,S / ) 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 / 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 co 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 5 and an external driving force amplitude F).

[45] After the chaotic system is determined, the moving window toc(0 is determined:

[46] ,. (lx “A / / 2< / <z. + A / 72 at 1 = 1 (3) 10, other

[47] where tc is the center position moment of the moving window, the step size A / e of the moving window is determined according to the stress measurement resolution index and computational efficiency requirements, and A / 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 ||-|| is the Euclidean norm;

[50] for a continuous system, (5)

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

[52] where J{x{t^~uFjux js a jacobjan matrix; by solving the above equation, Ax (7) 1 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: i (7) ) | 4° - 0½) - (¼ (jA),( / ^ 4 -----(¾ 0A ‘ kzF -^MMI

[54] where <>is an inner product, and A 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 {Ui,U2,...,Un}; IIax (o)||

[55] a constant d is used to substitute 11 ' v 711 ( / =0,1,2,.to meet the requirements, d is M=i set to be 1(11 H ), and the Lyapunov exponent solution equation can be approximately expressed as:

[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, comprising the following steps: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 aircoupled ultrasonic Lamb waves;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;S3: after determining the chaotic system, determining the size A / of the moving window according to the width of an excitation signal, and determining the minimum step size Al 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, 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.

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. If 5’(t)=Jsino)o / 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:wherein 0 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.

4. The method according to claim 3, wherein after the chaotic system is determined, the moving window (oc(t) is determined:wherein tc is the center position moment of the moving window, the step size A / c of the moving window is determined according to the stress measurement resolution index and computational efficiency requirements, and A / 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:For an / / -dimensional nonlinear system, the Lyapunov exponent in the / -direction is as follows:wherein || j| is the Euclidean norm;for a continuous system,wherein X = 6x / At, x e □ ” represents the coordinate vector of a midpoint in an n-dimensional space; the amount of separation between adjacent orbits is represented in a tangent space:Ax = (6), . j(x(t)} = dF / dx .wherein ' v 7 7 is a Jacobian matrix;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:(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\,Uz,--.,Un}',a constant d is used to substitute ||Ax, (o)|| ( / =0,1,2,...,«); to meet the requirements, d is set to be '(||^ ’ ''|| = 1), and the Lyapunov exponent solution equation can be approximately expressed as:after obtaining the Lyapunov exponents corresponding to all moving windows, acoustictime 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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