A method for obtaining dynamic characteristic representation performance of a pulse pressure sensor

Abstract

The application discloses a kind of dynamic characteristic characterization performance acquisition methods of pulse pressure sensor, belongs to pressure sensor metrological calibration field.The application provides a kind of dynamic characteristic characterization performance acquisition methods of pulse pressure sensor, utilizes high-order constant coefficient differential equation with zero output to characterize the dynamic response characteristics of pulse pressure sensor, with the minimum residual error square sum as the basis to carry out system identification, the quantitative differential equation obtained can reflect the influence of measurement system drift;Compared with high-order constant coefficient differential equation of the same order without zero output, smaller system error and random error can be obtained.

Description

Technical Field

[0001] This invention relates to the field of pressure sensor metrology and calibration technology, and more specifically, to a method for obtaining dynamic characteristic performance of a pulse pressure sensor. Background Technology

[0002] Systematic and random errors are important factors affecting the dynamic testing accuracy of pulse pressure sensors. The systematic error of a pulse pressure sensor is mainly determined by its dynamic characteristics, and the quality of these dynamic characteristics depends primarily on the mathematical model characterizing them. The random error of a pulse pressure sensor is obtained by subtracting the systematic error from the dynamic testing error; therefore, the quality of the mathematical model characterizing the dynamic characteristics of the pulse pressure sensor also indirectly affects the magnitude of the random error.

[0003] The traditional time-domain mathematical model for characterizing the dynamic properties of pulse pressure sensors is a differential equation. However, this differential equation is an idealized mathematical model that cannot reflect the influence of drift on the output response of the pulse pressure sensor, which severely restricts further improvement of the dynamic testing accuracy of pulse pressure sensors.

[0004] A search revealed that the paper "Research on Sectional Nominal Mathematical Model of Piezoelectric Pressure Measurement System Based on Quasi-Static Calibration" (IEEE Transactions on Instrumentation and Measurement) was the first to characterize the response characteristics of a pulse pressure sensor and its measurement system using a second-order constant-coefficient differential equation with zero-position output, and established a piecewise mathematical model. The accuracy of this piecewise mathematical model is higher than that of the linear equation obtained by fitting the pulse amplitude response. However, it is unknown whether the accuracy of the second-order constant-coefficient differential equation with zero-position output is superior to that of the traditional non-second-order constant-coefficient differential equation, and the optimal model order for the pulse pressure sensor and its measurement system is not necessarily second-order. Summary of the Invention

[0005] 1. The technical problem that the invention aims to solve

[0006] The purpose of this invention is to obtain a better characterization model of the dynamic response characteristics of a pulse pressure sensor that can reflect the effect of drift, and to provide a method for obtaining the dynamic characteristic characterization performance of a pulse pressure sensor.

[0007] 2. Technical Solution

[0008] To achieve the above objectives, the technical solution provided by the present invention is as follows:

[0009] The present invention provides a method for obtaining the dynamic characteristic performance of a pulse pressure sensor, comprising the following steps:

[0010] S1: Using a drop hammer hydraulic pulse generator or a pendulum hydraulic pulse generator as the pressure source, select a high-performance pressure sensor as the standard pressure sensor, and install the calibrated pulse pressure sensor and the standard pressure sensor symmetrically at the same height on the wall of the pressure-generating cylinder.

[0011] S2: Select m pressure calibration points uniformly within the full-scale range of the pulse pressure sensor being calibrated, and conduct C dynamic calibration experiments at each pressure calibration point.

[0012] S3: Taking the i-th pressure calibration point as an example, the average value of the pressure curve measured by the standard pressure sensor in C dynamic calibration experiments is used as the reference pressure curve, and the average value of the voltage curve measured by the calibrated pulse pressure sensor in C dynamic calibration experiments is used as the voltage response curve.

[0013] The reference pressure curve p measured at the i-th pressure calibration point i (t) and voltage response curve y i (t) can be calculated from equations (1) and (2) respectively.

[0014]

[0015]

[0016] In the above two equations, p ij (t) and y ij (t) represents the pressure curve and voltage curve measured in the j-th calibration experiment at the i-th pressure calibration point, respectively.

[0017] S4: At the i-th pressure calibration point, the dynamic response characteristics of the pulse pressure sensor are characterized by an n-order constant coefficient differential equation with zero-position output. The expression of this differential equation is shown in equation (3):

[0018]

[0019] In the above formula, a n ,a n-1 ..., a1, a0 are constant coefficients, b0 is the zero-position output, d n y i (t) / dt n It is y i The nth derivative of (t) with respect to time t, d n-1 y i (t) / dt n-1 It is y iThe (n-1)th order differential of (t) with respect to time t, dy i (t) / dt is y i (t) is the first-order differential of time t.

[0020] S5: Based on the principle of minimizing the sum of squared residual errors J, use the least squares method to analyze the dataset {d}. n y i (t) / dt n ,d n- 1 y i (t) / dt n-1 ,...,y i (t),p i By performing multivariate linear fitting on (t)}, the order, constant coefficients and quantitative values ​​of the zero-position output of the pulse pressure sensor mathematical model shown in equation (3) can be identified.

[0021] S6: Repeat steps S3 to S5 to obtain quantitative values ​​of the pulse pressure sensor order, constant coefficient, and zero-point output at the other m-1 pressure calibration points.

[0022] S7: Taking the i-th pressure calibration point as an example, assume that the dataset {d} n y i (t) / dt n ,d n-1 y i (t) / dt n-1 ,...,y i Substituting (t)} into equation (3), the pressure prediction curve obtained is p′ i (t), then, the system error curve of the pulse pressure sensor is p si :

[0023] p si (t)=p i (t)-p′ i (t) (4)

[0024] If the number of sampling points for the pressure prediction curve is N, the residual standard deviation s for pressure prediction is calculated using the quantitative model in Equation 3. i for:

[0025]

[0026] S8: The dataset {d} obtained from the j-th repeated experiment n y ij (t) / dt n ,d n-1 y ij (t) / dt n-1 ,...,y ijSubstituting (t) into equation (3), we can obtain the pressure measurement curve p′ based on the mathematical model of the nth-order constant coefficient differential equation with zero-position output. ij (t), and thus the dynamic test error curve Δp can be obtained. ij (t) is:

[0027] Δp ij (t)=p ij (t)-p′ ij (t) (6)

[0028] S9: Use the dynamic test error curve Δp ij (t) minus the system error curve p si The random error curve p of the j-th experiment can be obtained. rij (t).

[0029] p rij (t)=Δp ij (t)-p si (t) (7)

[0030] S10: Repeat steps S8 and S9 to obtain the random error curves for the remaining C-1 experiments. At this point, the population standard deviation q, which characterizes the magnitude of the random error, is... i It can be calculated from equation (8).

[0031]

[0032] In the above formula, p rijl (t) is the random error curve p measured in the j-th experiment. rij (t) is the data at the l-th sampling point. It is the average value of the random error data obtained from C repeated experiments at the l-th sampling point.

[0033] S11: Repeat steps S7 to S10 to calculate the residual standard deviation and total standard deviation data for the other m-1 pressure calibration points.

[0034] Furthermore, in step S3, the monitoring of the reference pressure curve can also be indirectly measured by a high-precision force sensor, an acceleration sensor, or a laser velocity interferometer.

[0035] 3. Beneficial effects

[0036] Compared with the prior art, the technical solution provided by this invention has the following advantages:

[0037] The present invention discloses a method for obtaining the dynamic characteristics of a pulse pressure sensor. The method uses a high-order constant coefficient differential equation with zero-position output to characterize the dynamic response characteristics of the pulse pressure sensor. The system identification is based on minimizing the sum of squared residual errors. The obtained quantitative differential equation can reflect the influence of drift on the response of the pulse pressure sensor. Compared with a high-order constant coefficient differential equation of the same order without zero-position output, it can obtain smaller system errors and random errors. Attached Figure Description

[0038] Figure 1 This is a schematic diagram illustrating the working principle of a drop hammer hydraulic pulse generator based on direct comparison calibration.

[0039] Figure 2 This is a schematic diagram of a typical pulse pressure waveform generated by a drop hammer hydraulic pulse generator.

[0040] Figure 3 This is a schematic diagram showing the results of the residual standard deviation calculation.

[0041] Figure 4 This is a schematic diagram of the overall standard deviation calculation results.

[0042] Figure label:

[0043] 1- The pulse pressure sensor being calibrated; 2- The standard pressure sensor; 3- The pressure-generating cylinder; 4- The counterweight; 5- The piston rod assembly; 6- The pressure transmission medium; 7- The typical pulse pressure curve measured by the standard pressure sensor; 8- The typical voltage response curve of the pressure sensor being calibrated; 9- The residual standard deviation calculation result of the mathematical model of the third-order constant coefficient differential equation with zero output; 10- The residual standard deviation calculation result of the mathematical model of the third-order constant coefficient differential equation without zero output; 11- The overall standard deviation calculation result obtained by participating in the measurement based on the mathematical model of the third-order constant coefficient differential equation with zero output; 12- The overall standard deviation calculation result obtained by participating in the measurement based on the mathematical model of the third-order constant coefficient differential equation without zero output. Detailed Implementation

[0044] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings.

[0045] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0046] The present invention will be further described below with reference to embodiments.

[0047] Example

[0048] Combination Figures 1 to 4 This embodiment of a method for obtaining the dynamic characteristic performance of a pulse pressure sensor includes the following steps:

[0049] S1: As if Figure 1 The drop hammer hydraulic calibration device shown is a pressure source, and the typical pulse pressure curve generated by this device is as follows: Figure 2 As shown, a Kistler 211M0160 piezoelectric pressure sensor is used as the calibrated pulse pressure sensor 1, with an upper limit of 6.90 MPa. The standard pressure sensor 2 is a Kistler 4045A100 piezoresistive pressure sensor manufactured in Switzerland. Both the calibrated pressure sensor 1 and the standard pressure sensor 2 are installed at the same height on the wall of the pressure-generating cylinder 3. The process of the weight 4 falling freely and impacting the piston rod assembly 5, compressing the pressure-transmitting medium 6, and rebounding can generate a pressure pulse similar to a half-sine wave within the pressure-generating cylinder 3.

[0050] S2: Seven pressure calibration points were uniformly selected within the full-scale range of the pulse pressure sensor being calibrated. These pressure calibration points were 1.86 MPa, 2.47 MPa, 3.64 MPa, 4.37 MPa, 5.45 MPa, 6.36 MPa, and 6.98 MPa, respectively. Under the condition of a pulse width of 6 ms ± 0.6 ms, three dynamic calibration experiments were carried out for each pressure calibration point.

[0051] S3: Taking the first pressure calibration point as an example, the average value of the three pressure curves measured by the standard pressure sensor in the three dynamic calibration experiments is used as the reference pressure curve, and the average value of the three voltage curves measured by the calibrated pulse pressure sensor in the three dynamic calibration experiments is used as the voltage response curve.

[0052] The reference pressure curve p1(t) and voltage response curve y1(t) measured at the first pressure calibration point can be calculated by equations (1) and (2), respectively.

[0053]

[0054]

[0055] In the above two equations, p 1j (t) and y 1j (t) represents the pressure curve and voltage curve measured in the j-th calibration experiment at the first pressure calibration point, respectively.

[0056] S4: At the first pressure calibration point, the dynamic response characteristics of the pulse pressure sensor are characterized by an nth-order constant-coefficient differential equation with zero-point output. The expression of this differential equation is shown in equation (3):

[0057]

[0058] In the above formula, a n ,a n-1 ..., a1, a0 are constant coefficients, b0 is the zero-position output, d n y1(t) / dt n It is the nth derivative of y1(t) with respect to time t, d n-1 y i (t) / dt n-1 It is y i The (n-1)th order differential of (t) with respect to time t, dy i (t) / dt is y i (t) is the first-order differential of time t.

[0059] To demonstrate the effectiveness of the constant coefficient differential equation shown in equation (3), the dynamic response characteristics of the pulse pressure sensor are also characterized by the traditional nth-order constant coefficient differential equation without zero-position output shown in equation (4).

[0060]

[0061] S5: Based on the principle of minimizing the sum of squared residual errors J, use the least squares method to analyze the dataset {d}. n y1(t) / dt n ,d n- 1 y1(t) / dt n-1 By performing multivariate linear fitting on the mathematical model of the pulse pressure sensor, the order, constant coefficients, and quantitative values ​​of the zero-point output can be identified.

[0062] S6: Repeat steps S3 to S5 to obtain the quantitative values ​​of the pulse pressure sensor order, constant coefficients, and zero-point output at the other 6 pressure calibration points. At this point, the order of the constant coefficient differential equation model obtained through system identification at the 7 pressure calibration points is 3 for both the model with and without zero-point output. The quantitative data of the constant coefficients and zero-point output of the 3rd-order differential equation with zero-point output are shown in Table 1. The quantitative data of the constant coefficients of the 3rd-order differential equation without zero-point output are shown in Table 2.

[0063] Table 1. Quantitative data on the parameters of the third-order constant coefficient differential equation model with zero-position output.

[0064]

[0065] Table 2. Quantitative data on the parameters of the third-order constant coefficient differential equation model with zero-position output.

[0066]

[0067] S7: Taking the first pressure calibration point as an example, assume that the dataset {d} n y1(t) / dt n ,d n-1 y1(t) / dt n-1 Substituting y1(t) into equation (3), the pressure prediction curve obtained is p′1(t). Then, the system error curve of the pulse pressure sensor is p. s1 :

[0068] p s1 (t)=p1(t)-p′1(t) (5)

[0069] The number of sampling points for the pressure prediction curve is N = 917. Substituting the quantitative data of the model parameters at the 1.86MPa pressure calibration point in Table 1 into equation (3) for pressure prediction, the residual standard deviation s1 can be obtained as follows:

[0070]

[0071] Similarly, the dataset {d n y1(t) / dt n ,d n-1 y1(t) / dt n-1 Substituting y1(t) into equation (4), the pressure prediction curve obtained is p″1(t). Then, the system error curve of the pulse pressure sensor is p′. s1 :

[0072] p′ s1 (t)=p1(t)-p″1(t) (7)

[0073] The number of sampling points for the pressure prediction curve is N = 917. Substituting the quantitative data of the model parameters at the 1.86MPa pressure calibration point in Table 2 into equation (4) for pressure prediction, the residual standard deviation s1 can be obtained as follows:

[0074]

[0075] S8: The dataset {d} obtained from the first repeated experiment. n y 11 (t) / dt n ,d n-1 y 11 (t) / dt n-1 ,...,y 11Substituting (t) into equation (3), we can obtain the pressure measurement curve p based on the mathematical model of a third-order constant coefficient differential equation with zero-position output. 11 (t), and thus the dynamic test error curve Δp can be obtained. 11 (t) is:

[0076] Δp 11 (t)=p 11 (t)-p′ 11 (t) (9)

[0077] The dataset {d} obtained from the first repeated experiment n y 11 (t) / dt n ,d n-1 y 11 (t) / dt n-1 ,...,y 11 Substituting (t) into equation (4), we can obtain the pressure measurement curve p″ based on the mathematical model of a third-order constant coefficient differential equation without zero-position output. 11 (t), and thus the dynamic test error curve Δp′ can be obtained. 11 (t) is:

[0078] Δp′ 11 (t)=p 11 (t)-p″ 11 (t) (10)

[0079] S9: Use the dynamic test error curve Δp 11 (t) minus the system error curve p s1 The random error curve p of the first experiment can be obtained. r11 (t).

[0080] p r11 (t)=Δp 11 (t)-p s1 (t) (11)

[0081] Similarly, the dynamic test error curve Δp′ is used. 11 (t) minus the system error curve p′ s1 The random error curve p′ of the first experiment can be obtained. r11 (t).

[0082] p′ r11 (t)=Δp′ 11 (t)-p′ s1 (t) (12)

[0083] S10: Repeat steps S8 and S9 to obtain the random error curves for the other two experiments. At this point, the overall standard deviation q1, which characterizes the magnitude of the random error, obtained by using the mathematical model of the third-order constant coefficient differential equation with zero output to participate in the measurement, can be calculated by equation (13).

[0084]

[0085] In the above formula, p r11l (t) is the random error curve p obtained in the first experiment. r11 (t) is the data at the l-th sampling point. It is the average value of the random error data obtained from three repeated experiments at the l-th sampling point.

[0086] Similarly, the overall standard deviation q1, which characterizes the magnitude of random error, obtained by using a mathematical model of a third-order constant coefficient differential equation without zero output, can be calculated by equation (14).

[0087]

[0088] In the above formula, p′ r11l (t) is the random error curve p′ obtained in the first experiment. r11 (t) is the data at the l-th sampling point. It is the average value of the random error data obtained from three repeated experiments at the l-th sampling point.

[0089] S11: Repeat steps S7 to S10 to calculate the residual standard deviation and total standard deviation data for the other 6 pressure calibration points. At this point, the residual standard deviations corresponding to the mathematical models of the 3rd-order constant-coefficient differential equations with and without zero-point output at the 7 pressure calibration points can be obtained as follows: Figure 3 As shown. Additionally, the overall standard deviation obtained at seven pressure calibration points using third-order constant-coefficient differential equation mathematical models with and without zero-point output is as follows: Figure 4 As shown. By Figure 3 and Figure 4 It is evident that, compared with the traditional third-order constant coefficient differential equation mathematical model without zero-position output, using the third-order constant coefficient differential equation mathematical model with zero-position output in pulse pressure measurement can achieve smaller systematic error (residual standard deviation) and random error (population standard deviation).

[0090] The present invention and its embodiments have been described above illustratively. This description is not restrictive and is merely one embodiment of the present invention, and is not actually limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method of obtaining a dynamic characterization performance of a pulse pressure sensor, characterized in that: The method comprises the following steps: S1, using a hydraulic pulse generator as a pressure source, symmetrically installing the pulse pressure sensor to be calibrated and the standard pressure sensor on the wall surface of the pressure source at the same height; S2, selecting m pressure calibration points uniformly in the full range of the pulse pressure sensor to be calibrated, and carrying out C dynamic calibration experiments at each pressure calibration point; S3, taking the i-th pressure calibration point as an example, the average value of the pressure curve measured by the standard pressure sensor in the C times dynamic calibration experiment is taken as the reference pressure curve p i (t), the average value of the voltage curve measured by the calibrated pulse pressure sensor in the C times dynamic calibration experiment is taken as the voltage response curve y i (t). S4, at the i-th pressure calibration point, using an n-order constant coefficient differential equation with zero output to represent the dynamic response characteristic mathematical model of the pulse pressure sensor; S5, according to the principle of minimum residual error square sum J, using the least square method to carry out multivariate linear fitting on the data set obtained in S4, and identifying the quantitative values of the order, constant coefficient and zero output of the pulse pressure sensor mathematical model; S6, repeating S3-S5 to obtain the quantitative values of the order, constant coefficient and zero output of the pulse pressure sensor at other m-1 pressure calibration points; S7, calculating a system error curve p of the pulse pressure sensor si and a residual standard deviation s of the pressure prediction i ; S8, calculating a dynamic test error curve Δp ij (t); S9, calculating a random error curve p rij (t); S10, repeating S8-S9 to obtain the random error curves of other C-1 experiments; S11, repeating S7-S10 to obtain the corresponding residual standard deviation and overall standard deviation data at other m-1 pressure calibration points.

2. The method of claim 1, wherein: The pressure source is a drop hammer type hydraulic pulse generator or a pendulum type hydraulic pulse generator.

3. The method of claim 1, wherein: the reference pressure curve p measured in S3 at the i-th pressure calibration point i the voltage response curve y i (t) can be calculated by the following equations (1) and (2), respectively; In the above two equations, p ij (t) and y ij (t) are the pressure curve and the voltage curve measured in the jth calibration experiment at the ith pressure calibration point, respectively.

4. The method of claim 3, wherein: The n-order constant coefficient differential equation with zero output in S4 is expressed as equation (3): In the above formula, a n , a n-1 1, a0 are all constant coefficients, b0 is zero position output, d n y i (t) / dt n is the n-th order differential of y i (t) with respect to time t, d n-1 y i (t) / dt n-1 is the n-1-th order differential of y i (t) with respect to time t, dy i (t) / dt is the 1st order differential of y i (t) with respect to time t.

5. The method of claim 4, wherein: In S7, take the ith pressure calibration point as an example, suppose the data set {d n y i (t) / dt n ,d n-1 y i (t) / dt n-1 ,...,y i (t)} is substituted into equation (3) to obtain the pressure prediction curve p′ i (t), then the system error curve of the pulse pressure sensor is p si : p si (t) = p i (t) - p' i (t) (4) If the number of sampling points of the pressure prediction curve is N, the residual standard deviation s of the pressure prediction using the equation (3) quantitative model is i is: 。 6. The method of claim 5, wherein: In S8, the dataset {d} obtained from the j-th repeated experiment... n y ij (t) / dt n ,d n-1 y ij (t) / dt n-1 ,...,y ij Substituting (t) into equation (3), we can obtain the pressure measurement curve p′ based on the mathematical model of the nth-order constant coefficient differential equation with zero-position output. ij (t), and thus the dynamic test error curve Δp can be obtained. ij (t) is: Δp ij (t) = p ij (t) - p' ij (t) (6).

7. The method of claim 6, wherein: S9 Dynamic test error curve Δp ij (t) Subtract system error curve p si The random error curve p rij (t) for the jth experiment can be obtained p rij (t) = Δp ij (t) - p si (t) (7).

8. The method of claim 7, wherein: The random error curve of other C-1 experiments is calculated in S10, at which time the population standard deviation q representing the size of random error i This can be calculated from equation (8): In the above formula, p rijl (t) is the random error curve p rij (t) at the lth sampling point. is the average value of the random error data measured at the lth sampling point in C repeated experiments.

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