Method for detecting low-frequency-band cut-off frequency of piezoelectric type shock wave pressure sensing system

Abstract

The invention relates to a low-frequency cut-off frequency detection method for a piezoelectric shock wave pressure sensing system. Comprising the following steps: connecting a standard pressure monitoring system and a piezoelectric shock wave pressure sensing system to the same excitation pressure; applying excitation pressure; acquiring output signals of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system; adopting a frequency spectrum refining algorithm based on Chirp-Z transformation to calculate amplitude spectrums of output signals of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system under the same excitation; and an output signal of the standard pressure monitoring system is used as an excitation signal of the piezoelectric type shock wave pressure sensing system, and the ratio of the amplitude spectrum of the piezoelectric type shock wave pressure sensing system to the amplitude spectrum output by the standard pressure monitoring system is calculated to obtain an amplitude-frequency characteristic curve of the detected pressure sensor at a low-frequency part. According to the invention, the frequency resolution is improved by adopting a frequency spectrum refining method, and the amplitude-frequency characteristic of the piezoelectric shock wave pressure sensing system at a low-frequency part is obtained.

Description

Technical Field

[0001] The invention belongs to the field of measurement and testing, and in particular relates to a low-frequency cutoff frequency detection method for a piezoelectric shock wave pressure sensor system. Background Art

[0002] Piezoelectric shock wave pressure sensors have excellent dynamic characteristics and perform well in dynamic signal tests, and are often used to test shock wave pressure. However, since the impedance of the conditioning circuit cannot be infinite, the piezoelectric shock wave pressure sensor system is often accompanied by charge leakage when performing shock wave pressure testing, which usually leads to the static characteristics of the piezoelectric shock wave pressure sensor system being unsatisfactory. The low-frequency cutoff frequency of the shock wave pressure sensor system determines the lower limit of its operating frequency band, which directly affects the measurement of the pressure signal. Calibration of the low-frequency cutoff frequency of the piezoelectric pressure sensor system can determine the lower limit of the operating frequency band, which is of great significance for ensuring accurate testing of shock wave pressure.

[0003] The existing calibration and detection technologies for shock wave pressure sensor systems mainly include quasi-static calibration and dynamic calibration. Quasi-static calibration is mainly aimed at the static working characteristic parameters of the sensor system, and cannot obtain the low-frequency characteristics of the sensor. Dynamic calibration includes calibration methods such as shock tube calibration and sinusoidal pressure generator calibration. Shock tube tests are mostly performed on high-frequency characteristics such as the natural frequency of the sensor, and due to the limited platform time of the shock tube excitation signal, the frequency resolution of the test results is low, generally tens of hertz to hundreds of hertz. The low-frequency cutoff frequency of the piezoelectric shock wave pressure sensor system is mostly below 1Hz, and it is difficult to obtain the low-frequency cutoff frequency by relying on shock tube tests. The sinusoidal pressure generator can generate sinusoidal pressures of different frequencies, thereby obtaining the gain of the piezoelectric shock wave pressure sensor system at different frequencies. However, it is difficult for a sinusoidal pressure generator to generate a low-frequency sinusoidal pressure signal, which makes it difficult to obtain the amplitude-frequency characteristics of the piezoelectric shock wave pressure sensor system in the low-frequency band using a sinusoidal pressure generator. Summary of the invention

[0004] The purpose of the present invention is to provide a calibration method for the low-frequency characteristics of a piezoelectric shock wave pressure sensing system. The method is based on a comparative calibration method, using a large pulse width near half-sine pressure with a pulse width of more than 10ms as the excitation pressure, and relying on a strain gauge pressure sensor or a piezoresistive pressure sensor with good static characteristics as a standard pressure sensor to form a standard pressure monitoring system. A spectrum refinement algorithm based on Chirp-Z transform is used to calculate the amplitude spectrum of the output signal of the piezoelectric shock wave pressure sensing system and the standard pressure monitoring system under the excitation pressure to improve the frequency resolution of the calculation result. In order to reduce the influence of spectrum leakage on the amplitude spectrum calculation, the signal is windowed using a Hanning window before calculating the amplitude spectrum. The output of the standard pressure monitoring system is used as the input pressure of the piezoelectric shock wave pressure sensing system, and the amplitude-frequency characteristic curve of the detected pressure sensor in the low-frequency part can be obtained by calculating the ratio of the amplitude spectrum of the piezoelectric shock wave pressure sensing system to the amplitude spectrum output by the standard pressure detection monitoring system. Furthermore, this method uses the least squares method to fit the amplitude-frequency characteristic curve obtained from the test with the theoretical model to obtain the amplitude-frequency characteristic parameter model of the shock wave pressure sensing system, and more accurately obtains the cutoff frequency of the piezoelectric shock wave pressure sensing system, thereby realizing the detection of the low-frequency characteristics of the piezoelectric shock wave pressure sensing system.

[0005] The technical solution to achieve the purpose of the present invention is: a method for detecting the low-frequency cutoff frequency of a piezoelectric shock wave pressure sensor system, comprising the following steps:

[0006] Step (1): connecting the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system to the same excitation pressure, and connecting the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system to a data acquisition system;

[0007] Step (2): using a quasi-static pressure signal with a large pulse width of more than 10 ms and a nearly half-sine pulse width as the excitation pressure p(t);

[0008] Step (3) The data acquisition system acquires the output signal x(n) of the standard pressure monitoring system and the output signal y(n) of the piezoelectric shock wave pressure sensing system;

[0009] Step (4): Use a spectrum refinement algorithm based on Chirp-Z transform to calculate the amplitude spectra X(r) and Y(r) of the output signals of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system under the same excitation; use the output signal x(n) of the standard pressure monitoring system as the excitation signal of the piezoelectric shock wave pressure sensing system, and calculate the ratio of the amplitude spectrum Y(r) of the piezoelectric shock wave pressure sensing system to the amplitude spectrum X(r) output by the standard pressure monitoring system to obtain the amplitude-frequency characteristic curve A(r) of the detected pressure sensor in the low-frequency part.

[0010] Furthermore, the standard pressure sensor of the standard pressure monitoring system in step (1) is a piezoresistive pressure sensor or a strain gauge pressure sensor.

[0011] Furthermore, in step (2), the excitation pressure is generated by a pendulum-type quasi-static pressure generating device.

[0012] Furthermore, the pendulum-type quasi-static pressure generating device includes a pendulum, a piston rod and a pressure-building cylinder. The standard pressure sensor and the piezoelectric shock wave pressure sensor connected to the piezoelectric shock wave pressure sensing system are installed on the pressure-building cylinder through the mounting hole on the side of the pressure-building cylinder. The pendulum compresses the liquid pressure-building oil inside the cylinder by striking the piston rod of the pressure-building cylinder, thereby generating a nearly semi-sinusoidal excitation pressure in the cylinder. The standard pressure sensor and the piezoelectric shock wave pressure sensor are simultaneously excited by the pressure signal inside the pressure-building cylinder.

[0013] Furthermore, in step (4), a Hanning window w(n) is used to perform windowing processing on the signal before calculating the amplitude spectrum.

[0014] Furthermore, step (4) is specifically as follows:

[0015] The Hanning window w(n) is used to perform windowing on the output signals x(n) and y(n) of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system under the same excitation pressure p(t), and the spectrum refinement algorithm based on Chirp-Z transform is used to calculate the amplitude spectra X(r) and Y(r) of the two in the low-frequency part; the calculation formula is as follows:

[0016]

[0017] In the formula, j is an imaginary unit, is the digital frequency interval of the amplitude spectrum calculated by the spectrum refinement algorithm, expressed as follows

[0018]

[0019] Where D is the refinement factor and N is the signal length;

[0020] The amplitude-frequency characteristic curve A(r) of the piezoelectric shock wave pressure sensing system is calculated by the following formula:

[0021]

[0022] The analog frequency f(r) corresponding to A(r) can be calculated by the following formula:

[0023]

[0024] Among them, F s is the sampling frequency of the data acquisition system;

[0025] The transfer function of the shock wave pressure sensor system in the low frequency band is approximately a first-order high-pass system, and its amplitude-frequency characteristic is expressed as follows:

[0026]

[0027] Furthermore, step (4) further includes the following steps: relying on the non-parametric model calculated by formula (3) and the simulation frequency f(r) corresponding to formula (4), the least square method is used to fit the theoretical model shown in formula (5) to obtain the parameter model of the low-frequency amplitude-frequency characteristics of the piezoelectric shock wave pressure sensor system. Relying on the parameter model obtained by fitting, its -3dB cutoff frequency is calculated by formula (6):

[0028]

[0029] Compared with the prior art, the present invention has the following significant advantages:

[0030] A large pulse width nearly half-sine pressure with a pulse width of more than 10ms is used as the excitation pressure, and a piezoresistive pressure sensor or a strain gauge pressure sensor with good low-frequency and static characteristics is used as the standard pressure sensor. The spectrum refinement algorithm based on Chirp-Z transform is used to calculate the amplitude spectrum of the output signal of the piezoelectric shock wave pressure sensing system and the standard pressure monitoring system under the excitation pressure. The amplitude-frequency characteristic curve of the piezoelectric shock wave pressure sensing system in the low-frequency part is obtained through comparative calibration.

[0031] When calculating the amplitude spectrum, the Hanning window is used to perform windowing on the signal, which reduces the impact of spectrum leakage during amplitude spectrum calculation.

[0032] The amplitude-frequency characteristic curve obtained from the test was fitted with the theoretical model using the least squares method, and the parameter model of the amplitude-frequency characteristic of the shock wave pressure sensing system in the low-frequency band was obtained. Based on the fitted parameter model, the cutoff frequency of the sensing system in the low-frequency band was obtained more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 System block diagram of the calibration method for the low-frequency characteristics of a piezoelectric shock wave pressure sensor system.

[0034] Figure 2 A low-frequency characteristic calibration system based on a pendulum-type quasi-static pressure generator.

[0035] Figure 3 Standard pressure monitoring system as well as shock wave pressure sensing system outputs.

[0036] Figure 4 Standard pressure monitoring system as well as shock wave pressure sensing system refine the amplitude spectrum.

[0037] Figure 5Amplitude-frequency characteristic curve and fitting results of shock wave pressure sensing system.

[0038] Description of Reference Numerals

[0039] 1-Pendulum, 2-Piston rod, 3-Pressure cylinder, 4-Standard pressure sensor, 5-Piezoelectric shock wave pressure sensor. DETAILED DESCRIPTION

[0040] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0041] The present invention proposes a calibration method for the low-frequency characteristics of a piezoelectric shock wave pressure sensing system. The method is based on a comparative calibration method, using a large pulse width near half-sine pressure with a pulse width of more than 10ms as the excitation pressure, and relying on a strain gauge pressure sensor or a piezoresistive pressure sensor with good static characteristics as a standard pressure sensor to form a standard pressure monitoring system. A spectrum refinement algorithm based on Chirp-Z transform is used to calculate the amplitude spectrum of the output signal of the piezoelectric shock wave pressure sensing system and the standard pressure monitoring system under the excitation pressure to improve the frequency resolution of the calculation result. In order to reduce the influence of spectrum leakage on the amplitude spectrum calculation, the signal is windowed by a Hanning window before calculating the amplitude spectrum. The output of the standard pressure monitoring system is used as the input pressure of the piezoelectric shock wave pressure sensing system, and the amplitude-frequency characteristic curve of the detected pressure sensor in the low-frequency part can be obtained by calculating the ratio of the amplitude spectrum of the piezoelectric shock wave pressure sensing system to the amplitude spectrum output by the standard pressure detection monitoring system. Furthermore, this method uses the least squares method to fit the amplitude-frequency characteristic curve obtained from the test with the theoretical model to obtain the amplitude-frequency characteristic parameter model of the shock wave pressure sensing system, and more accurately obtains the cutoff frequency of the piezoelectric shock wave pressure sensing system, thereby realizing the detection of the low-frequency characteristics of the piezoelectric shock wave pressure sensing system.

[0042] The present invention proposes a method for calibrating the low-frequency characteristics of a piezoelectric shock wave pressure sensor system, which can obtain the amplitude-frequency characteristic curve of the piezoelectric shock wave pressure sensor system in the low-frequency part. The process of the detection and calibration method is as follows: Figure 1 As shown:

[0043] 1. A quasi-static pressure signal with a pulse width of more than 10 ms and a nearly half-sine pulse width is used as the excitation pressure p(t).

[0044] 2. Use a piezoresistive pressure sensor or a strain gauge pressure sensor with good static characteristics as a standard pressure sensor to form a standard pressure monitoring system

[0045] 3 The standard pressure monitoring system and the piezoelectric shock wave pressure sensing system are connected to the same excitation pressure p(t), and are excited by the excitation pressure p(t) at the same time, and the data acquisition system is used to obtain their output signals x(n) and y(n).

[0046] 4 The spectrum refinement algorithm based on Chirp-Z transform is used to calculate the amplitude spectra X(r) and Y(r) of the output signals of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system under the same excitation. To reduce the influence of spectrum leakage on the amplitude spectrum calculation, the Hanning window w(n) is used to perform windowing on the signal before calculating the amplitude spectrum. The output x(n) of the standard pressure monitoring system is used as the excitation signal of the piezoelectric shock wave pressure sensing system. By calculating the ratio of the amplitude spectrum Y(r) of the piezoelectric shock wave pressure sensing system to the amplitude spectrum X(r) output by the standard pressure monitoring system, the amplitude-frequency characteristic curve A(r) of the detected pressure sensor in the low-frequency part can be obtained, thereby realizing the detection of the low-frequency characteristics of the piezoelectric shock wave pressure sensing system.

[0047] The excitation pressure can be generated by a pendulum-type quasi-static pressure generator. The calibration system based on the low-frequency characteristics of the pendulum-type quasi-static pressure generator is as follows: Figure 2 As shown. The core components of the pendulum-type quasi-static pressure generating device are composed of a pendulum 1 and a pressure-generating cylinder 3. The pendulum 1 compresses the liquid pressure-generating oil inside the cylinder by striking the piston rod 2 of the pressure-generating cylinder 3, thereby generating a nearly semi-sine excitation pressure in the cylinder. The standard pressure sensor 4 and the piezoelectric shock wave pressure sensor 5 are installed on the pressure-generating cylinder through the mounting hole on the side of the pressure-generating cylinder, and can be excited by the pressure signal inside the pressure-generating cylinder at the same time. The standard pressure monitoring system is composed of a strain gauge pressure sensor or a piezoresistive pressure sensor with good static characteristics as a standard pressure sensor to ensure accurate measurement of low-frequency and zero-frequency signals. The standard pressure monitoring system is used to monitor the pressure changes in the cylinder, and its monitoring results are used as the excitation signal of the piezoelectric shock wave pressure sensing system. The standard pressure monitoring system and the piezoelectric shock wave pressure sensing system are connected to the data acquisition system through cables, and the output signal will be collected by the data acquisition system.

[0048] After obtaining the output x(n) and y(n) of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system under the same excitation pressure p(t) by the above method, the signal is windowed using the Hanning window w(n), and the spectrum refinement algorithm based on Chirp-Z transform is used to calculate the amplitude spectra X(r) and Y(r) of the two in the low-frequency part.

[0049] The calculation method is shown in formula (1), and the calculation result is Figure 4 shown.

[0050]

[0051] j is an imaginary unit, where x(n) is the output of the standard pressure monitoring system under the excitation pressure, and y(n) is the output of the piezoelectric shock wave pressure sensing system under the excitation pressure. is the digital frequency interval of the amplitude spectrum calculated by the spectrum refinement algorithm, which can be expressed as follows

[0052]

[0053] Where D is the refinement factor and N is the signal length.

[0054] The amplitude-frequency characteristic curve A(r) of the piezoelectric shock wave pressure sensor system can be calculated by formula (3). The calculation result is as follows: Figure 5 shown.

[0055]

[0056] The analog frequency f(r) corresponding to A(r) can be calculated by formula (4):

[0057]

[0058] Among them, F s is the sampling frequency of the data acquisition system.

[0059] The transfer function of the shock wave pressure sensor system in the low frequency band can be approximated as a first-order high-pass system, and its amplitude-frequency characteristic can be expressed by formula (5).

[0060]

[0061] In order to obtain the cutoff frequency in the low frequency band more accurately, the non-parametric model calculated by formula (3) and the corresponding simulation frequency f(r) are fitted with the theoretical model shown in formula (5) using the least squares method to obtain the parameter model of the low-frequency amplitude-frequency characteristics of the piezoelectric shock wave pressure sensor system. The fitting results are shown in Figure 5 As shown. Based on the parameter model obtained by fitting, its -3dB cutoff frequency can be calculated using formula (6).

[0062]

[0063] When the low-frequency characteristics of the piezoelectric shock wave pressure sensing system are tested by the above method, the sensor, pressure generating device, signal cable, etc. are installed in place. Start the sensor and the data acquisition system. Then start the quasi-static pressure generating device to generate an excitation pressure p(t) in the pressure-generating cylinder. The output signals x(n) and y(n) of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system are obtained through the data acquisition system. The excitation pressure of the pendulum-type quasi-static pressure generating device is a quasi-static pressure that is approximately half-sine. The outputs of the standard pressure sensing system and the piezoelectric shock wave pressure sensing system are as follows: Figure 3As shown. Using the above spectrum refinement method, the amplitude spectra X(r) and Y(r) output by the standard pressure detection system and the piezoelectric shock wave pressure sensing system can be calculated. Then, according to formula (3), the monitoring pressure of the standard pressure detection system is used as the input pressure of the piezoelectric shock wave pressure sensing system to calculate the amplitude-frequency characteristic curve A(r) of the piezoelectric shock wave pressure sensing system in the low-frequency part, as shown in Figure 4 As shown. By fitting, the parameter model of the amplitude-frequency characteristics of the piezoelectric shock wave pressure sensing system in the low frequency band can be obtained. The test and fitting results of the amplitude-frequency characteristics of the piezoelectric shock wave pressure sensing system in the low frequency band are shown in Figure 5 According to formula (6), it can be calculated that the -3dB cutoff frequency of the sensor system in the low frequency band is 0.1Hz.

Claims

1. A method for detecting the low-frequency cutoff frequency of a piezoelectric shock wave pressure sensing system. It is characterized in that The steps include: Step (1): connecting the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system to the same excitation pressure, and connecting the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system to a data acquisition system; Step (2): using a quasi-static pressure signal with a large pulse width of more than 10 ms and a nearly half-sine pulse width as the excitation pressure p(t); Step (3): the data acquisition system acquires the output signal x(n) of the standard pressure monitoring system and the output signal y(n) of the piezoelectric shock wave pressure sensing system; Step (4): Use a spectrum refinement algorithm based on Chirp-Z transform to calculate the amplitude spectra X(r) and Y(r) of the output signals of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system under the same excitation; use the output signal x(n) of the standard pressure monitoring system as the excitation signal of the piezoelectric shock wave pressure sensing system, and calculate the ratio of the amplitude spectrum Y(r) of the piezoelectric shock wave pressure sensing system to the amplitude spectrum X(r) output by the standard pressure monitoring system to obtain the amplitude-frequency characteristic curve A(r) of the detected pressure sensor in the low-frequency part.

2. The method according to claim 1, It is characterized in that The standard pressure sensor of the standard pressure monitoring system in step (1) is a piezoresistive pressure sensor or a strain gauge pressure sensor.

3. The method according to claim 2, It is characterized in that In step (2), the excitation pressure is generated by a pendulum-type quasi-static pressure generating device.

4. The method according to claim 3, It is characterized in that The pendulum-type quasi-static pressure generating device comprises a pendulum (1), a piston rod (2) and a pressure-generating cylinder (3); a standard pressure sensor (4) and a piezoelectric shock wave pressure sensor (5) connected to a piezoelectric shock wave pressure sensing system are installed on the pressure-generating cylinder (3) through a mounting hole on the side of the pressure-generating cylinder; the pendulum (1) compresses the liquid pressure-generating oil inside the cylinder by striking the piston rod (2) of the pressure-generating cylinder (3), thereby generating a nearly semi-sine excitation pressure inside the cylinder; the standard pressure sensor (4) and the piezoelectric shock wave pressure sensor (5) are simultaneously excited by the pressure signal inside the pressure-generating cylinder.

5. The method according to claim 4, It is characterized in that Step (4) uses a Hanning window w(n) to perform windowing on the signal before calculating the amplitude spectrum.

6. The method according to claim 5, It is characterized in that Step (4) is specifically as follows: The Hanning window w(n) is used to perform windowing on the output signals x(n) and y(n) of the standard pressure monitoring system and the piezoelectric shock wave pressure sensing system under the same excitation pressure p(t), and the spectrum refinement algorithm based on Chirp-Z transform is used to calculate the amplitude spectra X(r) and Y(r) of the two in the low-frequency part; the calculation formula is as follows: In the formula, j is an imaginary unit, is the digital frequency interval of the amplitude spectrum calculated by the spectrum refinement algorithm, expressed as follows Where D is the refinement factor and N is the signal length; The amplitude-frequency characteristic curve A(r) of the piezoelectric shock wave pressure sensing system is calculated by the following formula: The analog frequency f(r) corresponding to A(r) can be calculated by the following formula: where F s is the sampling frequency of the data acquisition system; The transfer function of the shock wave pressure sensor system in the low frequency band is approximately a first-order high-pass system, and its amplitude-frequency characteristic is expressed as follows:

7. The method according to claim 6, It is characterized in that Step (4) further includes the following steps: relying on the non-parametric model calculated by formula (3) and the simulation frequency f(r) corresponding to formula (4), the least square method is used to fit the theoretical model shown in formula (5) to obtain the parameter model of the low-frequency amplitude-frequency characteristics of the piezoelectric shock wave pressure sensor system. Relying on the parameter model obtained by fitting, its -3dB cutoff frequency is calculated by formula (6):

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