Non-baseline On-line Stress Monitoring System and Monitoring Method Based on Multi-mode Lamb Wave Data Fusion

Abstract

The present disclosure proposes a non-baseline on-line stress monitoring system and monitoring method based on multi-mode Lamb wave data fusion. A Lamb wave dispersion curve is established according to geometric dimensions and material parameters of a measured object, a cut-off frequency of a first-order Lamb wave mode is obtained, an excitation frequency of a Lamb wave signal is determined, and then pure Lamb waves in S0 and A0 modes obtained inside the measured object are obtained; an acoustoelastic equation is established, an elastodynamic equation of the measured object under a prestress condition is solved, and linear relationships between a group velocity and a stress of the Lamb waves in the S0 and A0 modes under the excitation frequency are obtained; data is processed through the on-line monitoring system; a stress gradient in a depth direction is calculated, and finally, a stress state of the measured object is represented. The present disclosure does not require data under a zero stress state as baseline data, does not require designing a wedge block capable of generating a critical refraction longitudinal wave, and combines acoustoelastic effects of Lamb waves in different modes to realize online stress monitoring without the baseline data.

Claims

1. A non-baseline on-line stress monitoring system based on multi-mode Lamb wave data fusion, wherein the on-line monitoring system comprises a waveform generator (1), a power amplifier (2), a piezoelectric wafer exciter (3), a piezoelectric wafer sensor (4), a high-bandwidth receiving and amplifying device (5), a high-speed data acquisition system (6) and a PC (7); the waveform generator (1) generates a low-voltage modulation signal, and generates a Lamb wave for the piezoelectric wafer exciter (3) after amplification by the power amplifier (2), and Lamb waves in S0 and A0 modes propagate inside a measured object and are received by the piezoelectric wafer sensor (4); the piezoelectric wafer sensor (4) inputs an obtained signal into the high-bandwidth receiving and amplifying device (5), and ensures that the signal is amplified into an input range of a digital-to-analog conversion chip through coarse gain tuning and fine gain tuning, and then a lower cut-off frequency and an upper cut-off frequency of a filter are set according to a bandwidth of an excitation signal, the amplified and filtered signal is input into the high-speed data acquisition system (6), the signal is encoded and processed by an FPGA chip, and a sampled signal is transmitted to the PC (7) by using a PXIE bus for storage.

2. A method of non-baseline on-line stress monitoring based on multi-mode Lamb wave data fusion, wherein the method comprises the following steps: step 1: establishing a Lamb wave dispersion curve according to geometric dimensions and material parameters of a measured object, obtaining a cut-off frequency of a first-order Lamb wave mode, determining an excitation frequency of a Lamb wave signal, and then obtaining pure Lamb waves in S0 and A0 modes obtained inside the measured object; step 2: establishing an acoustoelastic equation, and after determining the excitation frequency of the Lamb wave signal, solving an elastodynamic equation of the measured object under a prestress condition, and obtaining linear relationships between a group velocity and a stress of the Lamb waves in the S0 and A0 modes under the excitation frequency; the elastodynamic equation of the measured object under the prestress condition being: $\begin{array}{cc}{A}_{\mathrm{\alpha \beta \gamma \delta }}\frac{{\partial }^2{u}_{\gamma }}{\partial {\xi }_{\delta }\partial {\xi }_{\beta }}={\rho }_0\frac{{\partial }^2{u}_{\alpha }}{\partial t^2}& \left(5\right)\end{array}$ wherein, $\begin{array}{cc}{A}_{\mathrm{\alpha \beta \gamma \delta }}=C_{\mathrm{\beta \delta \gamma \rho }}{e}_{\mathrm{\lambda \rho }}^i{\delta }_{\mathrm{\alpha \gamma }}+C_{\mathrm{\alpha \beta \gamma \delta }}+C_{\mathrm{\alpha \beta \rho \delta }}\frac{\partial u_{\alpha }^i}{\partial {\xi }_{\rho }}+C_{\mathrm{\alpha \beta \gamma \delta \epsilon \eta }}{e}_{\mathrm{\epsilon \eta }}^i& \left(6\right)\end{array}$ in the equation, C.sub.αßγ¢ represents a second-order elastic modulus of the measured object, C.sub.αβγδεη represents a third-order elastic modulus of the measured object, e.sup.i.sub.αß represents an initial strain caused by a prestress, u.sup.i.sub.α an initial displacement caused by the prestress, and ρ.sub.0 represents a density of the measured object; a relationship between the group velocity and a frequency and a wave number of the Lamb wave satisfying: $\begin{array}{cc}{c}_g=\frac{d\omega }{\mathrm{dk}}& \left(7\right)\end{array}$ wherein c.sub.g is the group velocity of the Lamb wave, ω is the frequency of the Lamb wave, and k is the wave number of the Lamb wave; according to the group velocity of the Lamb waves in the S0 and A0 modes without a stress, linear relationships between a uniaxial prestress in a propagation direction and the group velocity of the Lamb waves in the S0 and A0 modes being established as:
c.sub.g(S.sub.0.sub.)=5.5625×10.sup.−7σ+5296.38  (8)
c.sub.g(A.sub.0.sub.)=1.675×10.sup.−7σ+2891.56  (9) wherein c.sub.g(S.sub.0.sub.) is the group velocity of the Lamb wave in the S0 mode, and c.sub.g(A.sub.0.sub.) is the group velocity of the Lamb wave in the A0 mode; according to equations (8) and (9), a relationship between a propagating sound-time ratio and a stress of the Lamb waves in the S0 and A0 modes at a fixed propagation distance being obtained as: $\begin{array}{cc}\frac{L/c_{g\left(A_0\right)}}{L/c_{g\left(s_0\right)}}=\frac{c_{g\left(s_0\right)}}{c_{g\left(A_0\right)}}=\frac{5.5625\times {10}^{-7}\sigma +5296.38}{1.675\times {10}^{-7}\sigma +2891.56}\approx 8.6267\times {10}^{-11}\sigma +1.8317& \left(10\right)\end{array}$ step 3: processing data by an on-line monitoring system, the on-line monitoring system being the on-line monitoring system according to claim 1; and step 4: calculating a stress gradient in a depth direction, performing Hilbert transformation on a signal received by a piezoelectric wafer sensor (4) to extract an amplitude envelope of the received signal, calculating the propagating sound-time ratio of the Lamb waves in the S0 and A0 modes, substituting the acoustoelastic equation established in step two to determine a magnitude and a direction of a uniaxial stress inside the measured object, and finally representing a stress state of the measured object.

3. The method according to claim 2, wherein in step 1, a calculation equation of the Lamb wave dispersion curve is a Rayleigh-Lamb wave dispersion equation: $\begin{array}{cc}\frac{\tan \left(\mathrm{qh}\right)}{\tan \left(\mathrm{ph}\right)}=-\frac{4k^2\mathrm{pq}}{{\left(q^2-k^2\right)}^2}& \left(1\right)\\ \frac{\tan \left(\mathrm{qh}\right)}{\tan \left(\mathrm{ph}\right)}=-\frac{{\left(q^2-k^2\right)}^2}{4k^2\mathrm{pq}}& \left(2\right)\end{array}$ wherein, p and q are respectively expressed as: $\begin{array}{cc}p=\sqrt{\frac{{\omega }^2}{c_L^2}-k^2}& \left(3\right)\\ q=\sqrt{\frac{{\omega }^2}{c_T^2}-k^2}& \left(4\right)\end{array}$ in the equations, c.sub.L and c.sub.T represent velocities of a longitudinal wave and a transverse wave, respectively; h represents half of a plate thickness; w is an angular frequency of an ultrasonic wave; k is the wave number; equations (1) and (2) are solved to obtain a dispersion curve of a structure to be measured, and a cut-off frequency of a first-order Lamb wave mode is determined according to the dispersion curve of the structure to be measured, so that the excitation frequency of the Lamb signal is below the cut-off frequency of the first-order Lamb wave mode.

4. The method according to claim 3, wherein in step 4, a Hilbert transformation formula is: $\begin{array}{cc}\hat{f}\left(t\right)=H\left[f\left(t\right)\right]=\frac{1}{\pi }{\int }_{-\infty }^{\infty }\frac{f\left(t\right)}{t-\tau }& \left(11\right)\end{array}$ wherein f(t) is an original signal and τ is an integration variable.

5. The method according to claim 4, wherein in step 4, a specific method for calculating the propagation sound-time ratio of the Lamb waves in the S0 and A0 modes is: according to different propagation time of the S0 and A0 modes, wave packets of the S0 and A0 modes are distinguished, arrival time of the two wave packets is determined by a peak extraction algorithm, and propagation time of the Lamb waves in the two modes at the fixed distance is determined according to a width of the excitation signal, and a ratio of the propagation time of the two is calculated.

6. An electronic device, comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the steps of the methods according to claim 2 when executing the computer program.

7. A computer-readable storage medium, configured to store a computer instruction, wherein the steps of the methods according to claim 2 are implemented when the computer instruction is executed by a processor.

Description

BRIEF DESCRIPTION OF FIGURES

[0044] FIG. 1 is a group velocity dispersion curve of a mm 6061 aluminum plate of the present disclosure;

[0045] FIG. 2 is time domain curve and frequency diagrams of an excitation signal of the present disclosure, where (a) is a time domain curve diagram and (b) is a frequency diagram;

[0046] FIG. 3 is group velocity changes of Lamb waves in different modes under an uniaxial stress of 100 MPa of the present disclosure;

[0047] FIG. 4 is group velocity changes in S0 and A0 modes caused by a stress of 500 kHz of the present disclosure, where (a) is the group velocity change in the S0 mode and (b) is the group velocity change in the A0 mode; and

[0048] FIG. 5 is an integrated measurement system of the present disclosure, where 1 is a waveform generator, 2 is a power amplifier, 3 is a piezoelectric wafer exciter, 4 is a piezoelectric wafer sensor, 5 is a high-bandwidth receiving and amplifying device, 6 is a high speed data acquisition system, and 7 is a PC.

DETAILED DESCRIPTION

[0049] The technical solutions in the examples of the disclosure will be clearly and completely described below with reference to the drawings in the examples of the disclosure. It is apparent that the described examples are only a part of the examples of the disclosure, but are not all of the examples; based on the examples in the disclosure, all other examples obtained by those skilled in the art without creative efforts fall within the scope of protection of the disclosure.

[0050] With reference to FIG. 1 to FIG. 5,

[0051] at a normal temperature, a measured object is a 6061 aluminum plate with a thickness of 1 mm, which is an isotropic material. An arbitrary waveform generator is used to generate a 500 kHz pulse waveform modulated by a Hanning window. A low-frequency signal generated by a signal generator is first-stage amplified by an Aigtek power amplifier. A high-voltage signal is used to excite a piezoelectric wafer exciter and generate a trigger signal at the same time. A high-speed data acquisition board is used to acquire an ultrasonic signal obtained by a piezoelectric wafer sensor. Before acquiring a received signal, the signal is firstly weakly amplified and band-pass filtered to amplify the signal to an input voltage range of a data acquisition board. The received signal is continuously acquired for 10 times, and the acquired signal is smoothly filtered to filter a part of electronic noise, so as to improve a signal-to-noise ratio of the received signal. Then propagation time of Lamb waves in S0 and A0 modes is determined by Hilbert transformation and a peak extraction algorithm, a ratio of the propagation time is substituted into a pre-calibrated acoustoelastic equation, and an obtained result is an uniaxial stress value of the measured object.

[0052] A non-baseline on-line stress monitoring system based on multi-mode Lamb wave data fusion:

[0053] the on-line monitoring system specifically includes a waveform generator 1, a power amplifier 2, a piezoelectric wafer exciter 3, a piezoelectric wafer sensor 4, a high-bandwidth receiving and amplifying device 5, a high-speed data acquisition system 6 and a PC 7;

[0054] the waveform generator 1 generates a low-voltage modulation signal, and generates a Lamb wave for the piezoelectric wafer exciter 3 after amplification by the power amplifier 2, and Lamb waves in S0 and A0 modes propagate inside the measured object and are received by the piezoelectric wafer sensor 4; the received signal is a weak signal of an order of mV, which is easily interfered by random electronic noise, so it is necessary to perform non-distortion amplification on an original signal, and then perform bandwidth filtering on the amplified signal;

[0055] the piezoelectric wafer sensor 4 inputs an obtained signal into the high-bandwidth receiving and amplifying device 5, and ensures that the signal is amplified into an input range of a digital-to-analog conversion chip through coarse gain tuning and fine gain tuning, and then a lower cut-off frequency and an upper cut-off frequency of a filter are set according to a bandwidth of an excitation signal, the amplified and filtered signal is input into the high-speed data acquisition system 6, the signal is encoded and processed by an FPGA chip, and a sampled signal is transmitted to the PC 7 by using a PXIE bus for storage.

[0056] A non-baseline on-line stress monitoring method based on multi-mode Lamb wave data fusion:

[0057] the method specifically includes the following steps:

[0058] step 1: establishing a Lamb wave dispersion curve according to geometric dimensions and material parameters of a measured object, obtaining a cut-off frequency of a first-order Lamb wave mode, determining an excitation frequency of a Lamb wave signal, and then obtaining pure Lamb waves in S0 and A0 modes obtained inside the measured object;

[0059] step 2: establishing an acoustoelastic equation, and after determining the excitation frequency of the Lamb wave signal, solving an elastodynamic equation of the measured object under a prestress condition, and obtaining linear relationships between a group velocity and a stress of the Lamb waves in the S0 and A0 modes under the excitation frequency;

[0060] further determining linear relationships between a propagating sound-time ratio and the stress in two modes at a fixed propagation distance;

[0061] step 3: processing data by an on-line monitoring system, the on-line monitoring system being the above-mentioned on-line monitoring system; and

[0062] according to the selected excitation frequency, the excitation signal modulated by the Hanning window being loaded inside a signal generator, and driving a transmitting probe after passing through a power amplifier, a signal of a receiving probe at the other end being received by a high-speed acquisition board card after being subjected to first-stage weak signal amplification, and being transmitted to an upper computer through a PXIE bus, and data processing being performed after the signal is stored;

[0063] step 4: calculating a stress gradient in a depth direction, performing Hilbert transformation on a signal received by a piezoelectric wafer sensor 4 to extract an amplitude envelope of the received signal, calculating the propagating sound-time ratio of the Lamb waves in the S0 and A0 modes, substituting the acoustoelastic equation established in step two to determine a magnitude and a direction of a uniaxial stress inside the measured object, and finally representing a stress state of the measured object.

[0064] In step one,

[0065] a calculation equation of the Lamb wave dispersion curve is a Rayleigh-Lamb wave dispersion equation:

[00008]$\begin{array}{cc}\frac{\tan \left(\mathrm{qh}\right)}{\tan \left(\mathrm{ph}\right)}=-\frac{4k^2\mathrm{pq}}{{\left(q^2-k^2\right)}^2}& \left(1\right)\\ \frac{\tan \left(\mathrm{qh}\right)}{\tan \left(\mathrm{ph}\right)}=-\frac{{\left(q^2-k^2\right)}^2}{4k^2\mathrm{pq}}& \left(2\right)\end{array}$

[0066] where, p and q are respectively expressed as:

[00009]$\begin{array}{cc}p=\sqrt{\frac{{\omega }^2}{c_L^2}-k^2}& \left(3\right)\\ q=\sqrt{\frac{{\omega }^2}{c_T^2}-k^2}& \left(4\right)\end{array}$

[0067] in the equations, c.sub.L and C.sub.T represent velocities of a longitudinal wave and a transverse wave, respectively; h represents half of a plate thickness; w is an angular frequency of an ultrasonic wave; k is the wave number;

[0068] equations (1) and (2) are solved to obtain a dispersion curve of a structure to be measured, and a cut-off frequency of a first-order Lamb wave mode is determined according to the dispersion curve of the structure to be measured, so that the excitation frequency of the Lamb signal is below the cut-off frequency of the first-order Lamb wave mode.

[0069] In this example, it is assumed that the object to be measured is an aluminium plate with a thickness of 1 mm and a trade mark of 6061, according to the dispersion curve, it can be determined that the cut-off frequency of the first-order Lamb wave mode is 1.6 MHz, and therefore, a modulation signal with a frequency of 500 kHz is selected to excite the Lamb wave.

[0070] In step two,

[0071] the elastodynamic equation of the measured object under the prestress condition being:

[00010]$\begin{array}{cc}{A}_{\mathrm{\alpha \beta \gamma \delta }}\frac{{\partial }^2{u}_{\gamma }}{\partial {\xi }_{\delta }\partial {\xi }_{\beta }}={\rho }_0\frac{{\partial }^2{u}_{\alpha }}{\partial t^2}& \left(5\right)\end{array}$

[0072] where,

[00011]$\begin{array}{cc}{A}_{\mathrm{\alpha \beta \gamma \delta }}=C_{\mathrm{\beta \delta \gamma \rho }}{e}_{\mathrm{\lambda \rho }}^i{\delta }_{\mathrm{\alpha \gamma }}+C_{\mathrm{\alpha \beta \gamma \delta }}+C_{\mathrm{\alpha \beta \rho \delta }}\frac{\partial u_{\alpha }^i}{\partial {\xi }_{\rho }}+C_{\mathrm{\alpha \beta \gamma \delta \epsilon \eta }}{e}_{\mathrm{\epsilon \eta }}^i& \left(6\right)\end{array}$

[0073] in this example, C.sub.αβγδ represents a second-order elastic modulus of 6061 aluminum, C.sub.αβγδεη represents a third-order elastic modulus of the 6061 aluminum, e.sup.i.sub.αβ represents an initial strain caused by a prestress, u.sup.i.sub.α represents an initial displacement caused by the prestress, and ρ.sub.0 represents a density of the 6061 aluminum.

[0074] In order to establish the dispersion curve of the measured object, the elastodynamic equation of equation (5) is solved by a semi-analytical finite element method, it is assumed that a displacement of the Lamb wave in the propagation direction is represented in a vibration mode of a simple harmonic wave, it is only necessary to discretize a finite element on a cross section of a waveguide, and then a characteristic equation is solved in a target frequency range to obtain wave numbers at different frequencies. Finally, the dispersion curve of the Lamb wave can be drawn completely, and the relationship between the group velocity wave and the frequency and the wave number of the Lamb wave satisfies:

[00012]$\begin{array}{cc}{c}_g=\frac{d\omega }{\mathrm{dk}}& \left(7\right)\end{array}$

[0075] where c.sub.g is the group velocity of the Lamb wave, ω is the frequency of the Lamb wave, and k is the wave number of the Lamb wave;

[0076] a uniaxial prestress is applied to the measured object in the propagation direction of the Lamb wave, the prestress is 100 MPa, and group velocity changes of Lamb waves in different modes at different frequencies are obtained. The effects of the same stress on the group velocity of the Lamb waves in different modes are different, and effect results of the same stress on the Lamb wave in the same mode at different frequencies are also different, which shows that the effect of the stress on the Lamb waves is complex due to the dispersion characteristics of the Lamb waves.

[0077] In this example, the effects of the stress on the Lamb waves in different modes at the same frequency are considered, it is set that the prestress of the measured object starts from 20 MPa, and linearly increases to 100 MPa, taking 20 MPa as stepping, and the relationships between the stress and the group velocity change at 500 kHz in S0 and A0 modes are respectively obtained,

[0078] according to the group velocity of the Lamb waves in the S0 and A0 modes without a stress, linear relationships between a uniaxial prestress in a propagation direction and the group velocity of the Lamb waves in the S0 and A0 modes being established as:

c.sub.g(S.sub.0.sub.)=5.5625×10.sup.−7σ+5296.38  (8)

c.sub.g(A.sub.0.sub.)=1.675×10.sup.−7σ+2891.56  (9)

[0079] where c.sub.g(S.sub.0.sub.) is the group velocity of the Lamb wave in the S0 mode, and c.sub.g(A.sub.0.sub.) is the group velocity of the Lamb wave in the A0 mode;

[0080] according to equations (8) and (9), a relationship between a propagating sound-time ratio and a stress of the Lamb waves in the S0 and A0 modes at a fixed propagation distance being obtained as:

[00013]$\begin{array}{cc}\frac{L/c_{g\left(A_0\right)}}{L/c_{g\left(s_0\right)}}=\frac{c_{g\left(s_0\right)}}{c_{g\left(A_0\right)}}=\frac{5.5625\times {10}^{-7}\sigma +5296.38}{1.675\times {10}^{-7}\sigma +2891.56}\approx 8.6267\times {10}^{-11}\sigma +1.8317.& \left(10\right)\end{array}$

[0081] It can be determined from equation (10) that at the fixed propagation distance, the ratio of the propagating acoustic time in the A0 and S0 modes has an approximate linear relationship with the stress, and thus by using the data fusion of the S0 and A0 modes, average stress measurement on a propagation path of the Lamb wave can be achieved without the baseline data.

[0082] In step four,

[0083] a Hilbert transformation formula is:

[00014]$\begin{array}{cc}\hat{f}\left(t\right)=H\left[f\left(t\right)\right]=\frac{1}{\pi }{\int }_{-\infty }^{\infty }\frac{f\left(t\right)}{t-\tau }& \left(11\right)\end{array}$

[0084] where f(t) is an original signal and τ is an integration variable.

[0085] In step four,

[0086] a specific method for calculating the propagation sound-time ratio of the Lamb waves in the S0 and A0 modes is:

[0087] according to different propagation time of the S0 and A0 modes, wave packets of the S0 and A0 modes are distinguished, arrival time of the two wave packets is determined by a peak extraction algorithm, and propagation time of the Lamb waves in the two modes at the fixed distance is determined according to a width of the excitation signal, and a ratio of the propagation time of the two is calculated.

[0088] An electronic device, includes a memory and a processor, the memory storing a computer program, where the processor implements the steps of the above method when executing the computer program.

[0089] A computer-readable storage medium, configured to store the computer instructions, where the steps of the above method are implemented when the computer instructions are executed by the processor.

[0090] The non-baseline on-line stress monitoring method based on multi-mode Lamb wave data fusion provided by the present disclosure is described in detail as above. The principles and implementation methods of the present disclosure are described. The description of the above examples is only used to help understand the method and core idea of the present disclosure. Meanwhile, for those skilled in the art, according to the idea of the present disclosure, there will be changes in the specific implementation mode and application scope of the disclosure. Based on the above, the content of the description shall not be construed as limiting the present disclosure.