CN113340525A - Method for acquiring working characteristic parameters of piezoelectric pressure sensor for implementing quasi-static calibration - Google Patents
Method for acquiring working characteristic parameters of piezoelectric pressure sensor for implementing quasi-static calibration Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L25/00—Testing or calibrating of apparatus for measuring force, torque, work, mechanical power, or mechanical efficiency
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- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L27/00—Testing or calibrating of apparatus for measuring fluid pressure
- G01L27/002—Calibrating, i.e. establishing true relation between transducer output value and value to be measured, zeroing, linearising or span error determination
Abstract
The invention discloses a method for acquiring working characteristic parameters of a piezoelectric pressure sensor for implementing quasi-static calibration, and belongs to the technical field of measurement and calibration of pressure sensors. The method for acquiring the working characteristic parameters of the piezoelectric pressure sensor for implementing quasi-static calibration fully utilizes all information of the half-sine pressure pulse, wherein the rising edge of the half-sine pressure pulse is utilized to simulate the continuous pressurization operation (positive stroke) of the static calibration, and the falling edge of the half-sine pressure pulse is utilized to simulate the continuous decompression operation (reverse stroke) of the static calibration, so that not only can the sensitivity and the linearity of the piezoelectric pressure sensor be acquired, but also the repeatability, the hysteresis and the basic error of the piezoelectric pressure sensor can be evaluated.
Description
Technical Field
The invention belongs to the technical field of pressure sensor measurement calibration, and particularly relates to a method for acquiring working characteristic parameters of a piezoelectric pressure sensor for implementing quasi-static calibration.
Background
When the piezoelectric pressure sensor bears static pressure, a charge leakage phenomenon occurs, so that static calibration cannot be implemented to accurately acquire working characteristic parameters such as sensitivity, linearity, repeatability, hysteresis, basic error and the like of the piezoelectric pressure sensor. At present, quasi-static calibration is generally adopted internationally to obtain the amplitude characteristic of the piezoelectric pressure sensor. Quasi-static calibration is to use a drop-weight or pendulum-type pulse generator to generate a pressure pulse similar to a semi-sinusoidal shape as a pressure source, and the effective bandwidth of the pressure source is within 1kHz and is far lower than the natural frequency of the pressure sensor (generally tens kHz to hundreds kHz).
The existing method for acquiring the working characteristic parameters based on the quasi-static calibration mainly comprises two methods: one method is that a plurality of pressure detection points are uniformly selected within the range of the calibrated piezoelectric pressure sensor, 3-5 independent repeated experiments are carried out on each pressure detection point, and fitting is carried out based on the pulse pressure amplitude to obtain the sensitivity and the linearity of the sensor. The other method is to refer to a direct comparison type quasi-static calibration principle, uniformly select a plurality of pressure detection points on the rising edge of the pressure pulse output by a standard pressure sensor, acquire calibration data corresponding to each pressure detection point on the rising edge of the output response curve of the calibrated pressure sensor, and obtain the sensitivity and the linearity of the calibrated piezoelectric pressure sensor through repeated experiments.
Through retrieval, the chinese patent application No. 2018111548520 discloses a piezoelectric pressure sensor calibration method and device, and the calibration method of the application includes the following steps: s1, applying continuous pressure to the standard sensor and the sensor to be calibrated; s2, acquiring a first pressure curve of the standard sensor and a second pressure curve of the sensor to be calibrated; s3, determining time points Ta and Tb corresponding to 10%. Pmax and 90%. Pmax in the first pressure curve according to the maximum value Pmax of the first pressure curve; s4, equally dividing the time period from Ta to Tb into n parts to obtain time points T1-Tn-1; s5, calculating the sensitivities Sca, Scb and Sc 1-Scn-1 of the sensor to be calibrated according to the first pressure curve pressure value, the corresponding sensitivity and the second pressure curve pressure value at the time points Ta, Tb and T1-Tn-1; s6, linearizing the sensitivities Sca, Scb and Sc 1-Scn-1 to obtain the linearity error of the sensor to be calibrated. By adopting the method of the application, calibration can be carried out according to the continuous pressure values, the sectional sensitivity and the linear error of the sensor to be calibrated can be obtained, and the calibration efficiency is improved. The method also makes full use of the rising edge information of the pressure pulse to develop calibration, so that the repeatability, the delay and the basic error of the sensor to be calibrated cannot be evaluated.
Disclosure of Invention
1. Problems to be solved
The invention aims to overcome the defect that the repeatability, the delay and the basic error of a sensor cannot be evaluated by adopting the conventional method for acquiring the working characteristic parameters of the piezoelectric pressure sensor, and provides the method for acquiring the working characteristic parameters of the piezoelectric pressure sensor for implementing quasi-static calibration. By adopting the technical scheme of the invention, not only can the sensitivity and the linearity of the sensor be effectively obtained, but also the repeatability, the hysteresis and the basic error of the piezoelectric pressure sensor can be evaluated.
2. Technical scheme
In order to solve the problems, the technical scheme adopted by the invention is as follows:
the invention discloses a method for acquiring working characteristic parameters of a piezoelectric pressure sensor for implementing quasi-static calibration, which comprises the following steps of:
the method comprises the following steps: carrying out a quasi-static calibration experiment on the upper limit of the measuring range of the calibrated piezoelectric pressure sensor to obtain a reference pressure response curve detected by the standard pressure sensor and a response curve detected by the calibrated piezoelectric pressure sensor;
step two: translating the response curve of the calibrated piezoelectric pressure sensor on a time axis to enable the response curve of the calibrated piezoelectric pressure sensor to correspond to the peak value of the reference pressure response curve, and eliminating the phase difference between the two response curves;
step three: uniformly selecting m pressure detection points on the rising edge of a reference pressure response curve, namely the positive stroke, and acquiring data corresponding to the m pressure detection points on the rising edge of the response curve of the calibrated piezoelectric pressure sensor;
step four: selecting m pressure detection points which are the same as the step three on the falling edge of the reference pressure response curve, namely the reverse stroke, and acquiring data corresponding to the m pressure detection points on the falling edge of the response curve of the calibrated piezoelectric pressure sensor;
step five: repeating the first step to the fourth step, carrying out n independent repeated experiments on the upper limit of the measuring range of the calibrated piezoelectric pressure sensor, and calculating to obtain the arithmetic mean value of the response voltage values output by each pressure detection point
Step six: using least square method to form data set by m pressure detection point data and the data set obtained in step five
Fitting the formed data set to obtain a working linear equation y of the calibrated piezoelectric pressure sensorLSAnd a sensitivity b;
step seven: acquiring full-scale output value y of calibrated piezoelectric pressure sensorFSSpecifically, the calculation is performed according to the following formula:
yFS＝｜b(pmax-pmin)｜
wherein p ismaxAnd pminRespectively an upper limit pressure value and a lower limit pressure value of a measurement range;
step eight: calculating the linearity epsilon of the piezoelectric pressure sensor to be calibrated according to the following formulaLComprises the following steps:
in the above formula,. DELTA.yLmaxArithmetic mean of output values for individual pressure sensing points
Calculating the value y at each pressure verification point by using the working linear equation of the calibrated piezoelectric pressure sensoriDeviation Δ y therebetweenLiMaximum of medium absolute value;
step nine:calculating the repeatability epsilon of the calibrated piezoelectric pressure sensor by using the following formulaR：
Wherein s is the standard deviation of the calibrated piezoelectric pressure sensor in the whole measuring range;
step ten: the hysteresis ε of a calibrated piezoelectric pressure sensor is calculated using the following equationH：
In the formula: | Δ yH｜maxFor the arithmetic mean of the positive stroke output values of the same pressure calibration point in each pressure calibration point
Arithmetic mean of the inverse of the stroke output
Difference Δ y ofHiMaximum of medium absolute value;
step eleven: the basic error a of the calibrated piezoelectric pressure sensor is calculated using the following formula:
A＝±(εR+εLH)
in the formula: epsilonLHIs the systematic error of the calibrated piezoelectric pressure sensor.
Further, the arithmetic mean of the response voltage values output from the respective pressure verification points in step five
Calculated from the following equation:
wherein the content of the first and second substances,
is the arithmetic mean of the positive stroke verification output values of each pressure verification point in n independent repeated experiments,
the arithmetic mean value of the reverse stroke verification output value of each pressure verification point is calculated by the following formula respectively:
yIijfor the jth verification output value, y, of the ith pressure verification point of the positive stroke of the calibrated piezoelectric pressure sensorDijThe jth verification output value is the jth verification output value of the ith pressure verification point of the reverse stroke of the calibrated piezoelectric pressure sensor.
Further, the standard deviation s of the calibrated piezoelectric pressure sensor over the entire measurement range is calculated according to the following formula:
wherein the standard deviation s of the positive stroke subsample at each pressure detection pointIiAnd inverse run subsample standard deviation sDiThe calculation is performed according to the following formula:
furthermore, the working linear equation y of the piezoelectric pressure sensor is calibrated in the sixth stepLSComprises the following steps:
yLS＝a+bp
in the formula, the intercept a and the slope b are respectively calculated according to the following formula:
wherein p isiThe sensitivity of the calibrated piezoelectric pressure sensor is the slope b of the working linear equation of the calibrated piezoelectric pressure sensor, which is the pressure value of the ith pressure detection point.
Further, the system error ε of the piezoelectric pressure sensor being calibratedLHCalculated according to the following formula:
in the above formula, | Δ yLH｜maxFor arithmetic mean of positive stroke output values of individual verification points
And arithmetic mean of inverse run-length output values
Calculating the value y at each pressure verification point by using the working linear equation of the calibrated piezoelectric pressure sensoriDifference of difference (Δ y)LH)Ii、(ΔyLH)DiMaximum of absolute values, wherein:
further, in step nine, the repeatability ε of the piezoelectric pressure transducer is calibratedRThe calculation can also be made using the following formula:
wherein s ismaxFor each pressure measurement point the standard deviation s of the positive stroke subsampleIiAnd inverse run subsample standard deviation sDiMaximum value of (1), t0.95Inclusion factor for 95% confidence under t distribution;
furthermore, in the eleventh step, the basic error a can also be calculated by using the following formula;
furthermore, in the third step and the fourth step, the number m of the pressure detection points is more than or equal to 6, and in the fifth step, the repeated experiment times n are more than or equal to 3.
Furthermore, in the first step, the reference pressure response curve is obtained indirectly by combining a mathematical model between the force of the hammer head of the heavy hammer and the pressure in the pressure making oil cylinder, wherein the reference pressure response curve is measured by a standard pressure sensor arranged on the wall surface of the pressure making oil cylinder of the semi-sinusoidal pressure pulse generator, or a force curve monitored by a high-precision force sensor arranged on the heavy hammer head of the semi-sinusoidal pressure pulse generator; or an acceleration curve obtained by monitoring by a high-precision acceleration sensor arranged on the heavy hammer is indirectly obtained by combining a mathematical model between the acceleration of the heavy hammer and the pressure in the pressure generating oil cylinder; or an acceleration curve obtained by monitoring by a laser speed interferometer arranged above the heavy hammer in the vertical direction is indirectly obtained by combining a mathematical model between the acceleration of the heavy hammer and the pressure in the pressure generating oil cylinder; or the laser interferometer is used for monitoring the change curve of part of the optical path of the pressure transmission medium in the pressure generating oil cylinder and is indirectly obtained by combining a mathematical model between the part of the optical path of the pressure transmission medium and the pressure applied to the pressure transmission medium.
Furthermore, in the sixth step, a fitting method of a working linear equation of the calibrated piezoelectric pressure sensor is obtained by adopting a tangent method or an endpoint translation method.
Further, after the basic error of the calibrated piezoelectric pressure sensor is obtained in the eleventh step, the accuracy grade of the calibrated piezoelectric pressure sensor can be determined according to the corresponding relationship between the basic error and the accuracy grade of the pressure sensor given by the (static) verification rule of the pressure sensor of the people's republic of china (jjjg 860-2015).
3. Advantageous effects
Compared with the prior art, the invention has the beneficial effects that:
(1) according to the method for acquiring the working characteristic parameters of the piezoelectric pressure sensor for implementing the quasi-static calibration, continuous pressurization and depressurization operation of the static calibration are simulated by utilizing the rising edge and the falling edge of the semi-sinusoidal pressure pulse respectively, so that the continuous increase and continuous decrease of the quasi-static calibration excitation can be realized, the sensitivity and the linearity of the piezoelectric pressure sensor can be acquired, and the repeatability, the hysteresis and the basic error of the piezoelectric pressure sensor can be evaluated.
(2) According to the method for acquiring the working characteristic parameters of the piezoelectric pressure sensor for implementing quasi-static calibration, disclosed by the invention, the accuracy grade of the piezoelectric pressure sensor can be further determined according to the corresponding relation between the basic error and the accuracy grade of the pressure sensor given by the (static) calibration procedure (JJJG 860-2015) of the pressure sensor in the people's republic of China.
Drawings
Fig. 1 is a schematic diagram of the working principle of the ground drop hammer type hydraulic calibration device.
FIG. 2 is a typical response curve for a quasi-static calibrated pressure sensor.
Reference numerals: 1-calibrated piezoelectric pressure sensor, 2-standard pressure sensor 1, 3-standard pressure sensor 2, 4-pressure transmission medium, 5-pressure making oil cylinder, 6-precision piston rod, 7-weight dropper, 8-voltage response curve of calibrated piezoelectric pressure sensor 1, 9-reference pressure response curve.
Detailed Description
The invention provides a method for acquiring the operating characteristic parameters of a piezoelectric pressure sensor for implementing quasi-static calibration, which fully utilizes all information of half-sine pressure pulses, wherein the rising edge of the half-sine pressure pulse is used for simulating continuous pressurization operation (positive stroke) of the static calibration, and the falling edge of the half-sine pressure pulse is used for simulating continuous decompression operation (reverse stroke) of the static calibration. The invention is further described with reference to specific examples.
Example 1
With reference to fig. 1 and fig. 2, a method for obtaining operating characteristic parameters of a piezoelectric pressure sensor for performing quasi-static calibration according to this embodiment includes the following steps:
the method comprises the following steps: a drop hammer hydraulic calibration device is used as a half-sine pressure pulse generator, as shown in figure 1, a 211M0160 type piezoelectric pressure sensor produced by Kistler company is used as a calibrated pressure sensor 1, and the upper limit of the measuring range of the calibrated pressure sensor 1 is 6.90 MPa. The standard pressure sensors 2 and 3 are piezoresistive pressure sensors of the type 4045a100 manufactured by Kistler, switzerland. The calibrated pressure sensor 1, the standard pressure sensor 2 and the standard pressure sensor 3 are all installed on the same height of the wall surface of the pressure making oil cylinder 5. The primary impact test is carried out on the upper range limit of the calibrated piezoelectric pressure sensor 1, the heavy hammer 7 impacts the precision piston rod 6 in a free falling mode, then the precision piston rod 6 extrudes the pressure transmission medium 4, when the kinetic energy of the heavy hammer 7 is completely converted into the elastic potential energy of the pressure transmission medium 4, the pressure borne by the pressure transmission medium 4 reaches the maximum, then the heavy hammer 7 and the precision piston rod 6 begin to rebound until the elastic potential energy of the pressure transmission medium 4 returns to zero, and in the process from the impact beginning to the elastic potential energy of the pressure transmission medium 4 returning to zero, the pressure pulse similar to the half sine shape shown in fig. 2 can be generated in the pressure making cylinder 5. In fig. 2, curve 8 is the voltage response curve detected by the calibrated piezoelectric pressure sensor 1; curve 9 is a reference pressure response curve that is the average of the pressure versus time curves sensed by standard pressure sensor 2 and standard pressure sensor 3.
Step two: translating the voltage response curve 8 of the calibrated piezoelectric pressure sensor 1 on a time axis to enable the voltage response curve 8 of the calibrated piezoelectric pressure sensor 1 to correspond to the peak value of the reference pressure response curve 9, and eliminating the phase difference between the two response curves;
step three: uniformly selecting 11 pressure detection points on the rising edge of a reference pressure response curve 9, wherein the 11 pressure detection points are respectively 0MPa, 0.69MPa, 1.37MPa, 2.08MPa, 2.77MPa, 3.44MPa, 4.12MPa, 4.83MPa, 5.52, 6.21MPa and 6.90MPa, and obtaining voltage values corresponding to the 11 pressure detection points on the rising edge of a voltage response curve 8 of the calibrated piezoelectric pressure sensor 1;
step four: selecting 11 pressure detection points which are completely the same as the step three on the falling edge of the reference pressure response curve 9, and acquiring voltage values of the 11 pressure detection points corresponding to the falling edge of the voltage response curve 8 of the calibrated piezoelectric pressure sensor;
step five: and repeating the first step to the fourth step, wherein 4 independent repeated tests are carried out on the upper limit of the measuring range of the calibrated piezoelectric pressure sensor 1, and the response voltage values of the calibrated piezoelectric pressure sensor 1 at 11 pressure detection points on the rising edge (positive stroke) and the falling edge (reverse stroke) obtained by the 4 tests are shown in table 1.
Arithmetic mean of 11 pressure verification point positive stroke verification output values
And arithmetic mean of inverse run verification output values
Respectively according to the formulas (1) and (2):
yIijthe method comprises the steps that an output value is verified for the jth time of the ith pressure verification point of the positive stroke of a calibrated piezoelectric pressure sensor 1;
yDijthe output value is verified for the jth pressure verification point of the reverse stroke of the calibrated piezoelectric pressure sensor 1.
TABLE 1 Voltage response data for positive and negative strokes of a calibrated piezoelectric pressure transducer 1
Arithmetic mean value of output values of individual pressure detection points
Can be calculated from equation (3):
step six: combining the calibration data in Table 1, the least square method is adopted to carry out the data set consisting of 11 pressure detection point data and the data set consisting of
Fitting the formed data set to obtain the least square linear equation y of the calibrated piezoelectric pressure sensor 1LSAs shown in equation (4):
yLS＝0.7372p+0.0107 (4)
the sensitivity b of the calibrated piezoelectric pressure sensor 1 is 0.7372V/MPa, the correlation coefficient is 1.0000, and the remaining standard deviation is 0.0055V.
Step seven: acquiring the full-scale output value of the calibrated piezoelectric pressure sensor 1 and acquiring the full-scale output value y of the calibrated piezoelectric pressure sensor 1FSCalculating according to the formula (5):
yFS＝｜b(pmax-pmin)｜ (5)
upper limit pressure value p of measuring rangemax6.9MPa, the lower limit pressure value p of the measurement rangeminThe full-scale output of the calibrated piezoelectric pressure sensor 1, which is 0MPa, can be calculated from equation (22) in combination with the calculated sensitivity of the calibrated piezoelectric pressure sensor 1, which is 5.09V.
Step eight: according to the data in Table 1 and equation (4), the arithmetic mean of the output values of the pressure detection points can be calculated according to equation (6)
Calculating the value y at each pressure verification point by using the working linear equation of the calibrated piezoelectric pressure sensoriDifference value of (a) yLi：
Difference value deltayLiMaximum value of medium absolute value Δ yLmax＝0.0107V。
The linearity epsilon of the calibrated piezoelectric pressure sensor 1 can be calculated according to the formula (7)L：
Step nine: calculating the repeatability epsilon of the calibrated piezoelectric pressure sensor 1R。
And calculating the standard deviation s of the positive stroke sample of the calibrated piezoelectric pressure sensor 1 at each detection point according to the formulas (8) and (9) respectively by combining the data in the table 1IiAnd inverse run subsample standard deviation sDi。
The standard deviation s of the calibrated piezoelectric pressure sensor 1 in the whole measuring range is calculated according to the formula (10):
repeatability epsilon of calibrated piezoelectric pressure sensor 1RThe calculation can be made according to equation (11):
step ten: calculating the arithmetic mean value of the positive stroke output values of the same pressure verification point in all the verification points according to the formula (12)
Arithmetic mean of the inverse of the stroke output
Difference Δ y ofHi：
Substituting the relevant data in Table 1 into equation (12), the difference Δ y can be calculatedHiMaximum value | Δ y of medium absolute valueH｜max0.03V. The hysteresis ε of the calibrated piezoelectric pressure transducer 1 can be calculated according to equation (13)H：
Step eleven: the arithmetic mean of the positive stroke output values of the respective verification points was calculated according to equation (14) in combination with the data shown in Table 1
Calculating the value y at each pressure verification point by using the working linear equation of the calibrated piezoelectric pressure sensori(calculated according to equation (4)) of the difference (Δ y)LH)Ii：
Calculating the arithmetic mean of the reverse stroke output values of the respective detection points according to the formula (15)
Calculating the value y at each pressure verification point by using the working linear equation of the calibrated piezoelectric pressure sensoriDifference of difference (Δ y)LH)Di：
(14) And (15) the maximum | Δ y of absolute values in the data of the two-equation calculation resultLH｜max0.018V, systematic error εLHCan be calculated according to equation (16):
the fundamental error a of the calibrated piezoelectric pressure sensor 1 can be calculated using equation (17):
A＝±(εR+εLH)＝±(0.09％+0.35％)＝±0.44％ (17)
further, according to the corresponding relationship between the basic error and the accuracy grade of the pressure sensor given by the pressure sensor (static) verification regulation (jjjg 860-2015) of the people's republic of china, the accuracy grade of the calibrated piezoelectric pressure sensor of type 211M0160 of Kistler corporation in this embodiment can be determined to be 0.5.
Claims (10)
1. A method for acquiring the working characteristic parameters of a piezoelectric pressure sensor for implementing quasi-static calibration is characterized by comprising the following steps:
the method comprises the following steps: carrying out a quasi-static calibration experiment on the upper limit of the measuring range of the calibrated piezoelectric pressure sensor to obtain a reference pressure response curve detected by the standard pressure sensor and a response curve detected by the calibrated piezoelectric pressure sensor;
step two: translating the response curve of the calibrated piezoelectric pressure sensor on a time axis to enable the response curve of the calibrated piezoelectric pressure sensor to correspond to the peak value of the reference pressure response curve, and eliminating the phase difference between the two response curves;
step three: uniformly selecting m pressure detection points on the rising edge of a reference pressure response curve, namely the positive stroke, and acquiring data corresponding to the m pressure detection points on the rising edge of the response curve of the calibrated piezoelectric pressure sensor;
step four: selecting m pressure detection points which are the same as the step three on the falling edge of the reference pressure response curve, namely the reverse stroke, and acquiring data corresponding to the m pressure detection points on the falling edge of the response curve of the calibrated piezoelectric pressure sensor;
step five: repeating the first step to the fourth step, carrying out n independent repeated experiments on the upper limit of the measuring range of the calibrated piezoelectric pressure sensor, and calculating to obtain the arithmetic mean value of the response voltage values output by each pressure detection point
Step six: using least square method to form data set by m pressure detection point data and the data set obtained in step five
Fitting the formed data set to obtain a working linear equation y of the calibrated piezoelectric pressure sensorLSAnd a sensitivity b;
step seven: acquiring full-scale output value y of calibrated piezoelectric pressure sensorFSSpecifically, the calculation is performed according to the following formula:
yFS＝|b(pmax-pmin)|
wherein p ismaxAnd pminRespectively an upper limit pressure value and a lower limit pressure value of a measurement range;
step eight: calculating the linearity epsilon of the piezoelectric pressure sensor to be calibrated according to the following formulaLComprises the following steps:
in the above formula,. DELTA.yLmaxArithmetic mean of output values for individual pressure sensing points
Calculating the value y at each pressure verification point by using the working linear equation of the calibrated piezoelectric pressure sensoriDeviation Δ y therebetweenLiMaximum of medium absolute value;
step nine: calculating the repeatability epsilon of the calibrated piezoelectric pressure sensor by using the following formulaR：
Wherein s is the standard deviation of the calibrated piezoelectric pressure sensor in the whole measuring range;
step ten: the hysteresis ε of a calibrated piezoelectric pressure sensor is calculated using the following equationH：
In the formula: | Δ yH|maxFor the arithmetic mean of the positive stroke output values of the same pressure calibration point in each pressure calibration point
Arithmetic mean of the inverse of the stroke output
Difference Δ y ofHiMaximum of medium absolute value;
step eleven: the basic error a of the calibrated piezoelectric pressure sensor is calculated using the following formula:
A＝±(εR+εLH)
in the formula: epsilonLHIs the systematic error of the calibrated piezoelectric pressure sensor.
2. The method as claimed in claim 1, wherein the response voltage values outputted from each pressure verification point in step five are arithmetically averaged
Calculated from the following equation:
wherein the content of the first and second substances,
is the arithmetic mean of the positive stroke verification output values of each pressure verification point in n independent repeated experiments,
the arithmetic mean value of the reverse stroke verification output value of each pressure verification point is calculated by the following formula respectively:
yIijfor the jth verification output value, y, of the ith pressure verification point of the positive stroke of the calibrated piezoelectric pressure sensorDijThe jth verification output value is the jth verification output value of the ith pressure verification point of the reverse stroke of the calibrated piezoelectric pressure sensor.
3. The method of claim 2, wherein the standard deviation s of the calibrated piezoelectric pressure sensor over the entire measurement range is calculated according to the following formula:
wherein the standard deviation s of the positive stroke subsample at each pressure detection pointIiAnd inverse run subsample standard deviation sDiThe calculation is performed according to the following formula:
4. the method for obtaining the operating characteristic parameters of the piezoelectric pressure sensor with quasi-static calibration as claimed in claim 1, wherein the equation y of the operating line of the piezoelectric pressure sensor to be calibrated in step six isLSComprises the following steps:
yLS＝a+bp
in the formula, the intercept a and the slope b are respectively calculated according to the following formula:
wherein p isiThe sensitivity of the calibrated piezoelectric pressure sensor is the slope b of the working linear equation of the calibrated piezoelectric pressure sensor, which is the pressure value of the ith pressure detection point.
5. The method for obtaining the operating parameters of a piezoelectric pressure transducer with quasi-static calibration according to any of claims 1-4, wherein the system error ε of the calibrated piezoelectric pressure transducerLHCalculated according to the following formula:
in the above formula, | Δ yLH|maxFor arithmetic mean of positive stroke output values of individual verification points
And arithmetic mean of inverse run-length output values
Calculating the value y at each pressure verification point by using the working linear equation of the calibrated piezoelectric pressure sensoriDifference of difference (Δ y)LH)Ii、(ΔyLH)DiMaximum of absolute values, wherein:
6. the method for obtaining the operating characteristic parameters of the piezoelectric pressure sensor for performing the quasi-static calibration according to any one of claims 1 to 4, wherein in the ninth step, the repeatability epsilon of the piezoelectric pressure sensor to be calibrated isRThe calculation can also be made using the following formula:
wherein s ismaxFor each pressure measurement point the standard deviation s of the positive stroke subsampleIiAnd inverse run subsample standard deviation sDiMaximum value of (1), t0.95Is the inclusion factor at 95% confidence under the t distribution.
7. The method for acquiring the operating characteristic parameters of the piezoelectric pressure sensor for performing the quasi-static calibration according to any one of claims 1 to 4, wherein in the eleventh step, the basic error A can also be calculated by using the following formula;
8. the method for acquiring the operating characteristic parameters of the piezoelectric pressure sensor for performing quasi-static calibration as claimed in claim 5, wherein in the third step and the fourth step, the number m of pressure detection points is greater than or equal to 6, and in the fifth step, the number n of repeated experiments is greater than or equal to 3.
9. The method for obtaining the operating characteristic parameters of the piezoelectric pressure sensor for performing quasi-static calibration according to any one of claims 1 to 4, wherein in the first step, the reference pressure response curve is obtained indirectly by combining a mathematical model between the hammer head force and the pressure in the pressure generating cylinder, wherein the force response curve is obtained by a standard pressure sensor installed on the wall surface of the pressure generating cylinder of the semi-sinusoidal pressure pulse generator, or a force curve monitored by a high-precision force sensor installed on the heavy hammer head of the semi-sinusoidal pressure pulse generator; or an acceleration curve obtained by monitoring by a high-precision acceleration sensor arranged on the heavy hammer is indirectly obtained by combining a mathematical model between the acceleration of the heavy hammer and the pressure in the pressure generating oil cylinder; or an acceleration curve obtained by monitoring by a laser speed interferometer arranged above the heavy hammer in the vertical direction is indirectly obtained by combining a mathematical model between the acceleration of the heavy hammer and the pressure in the pressure generating oil cylinder; or the laser interferometer is used for monitoring the change curve of part of the optical path of the pressure transmission medium in the pressure generating oil cylinder and is indirectly obtained by combining a mathematical model between the part of the optical path of the pressure transmission medium and the pressure applied to the pressure transmission medium.
10. The method for acquiring the operating characteristic parameters of the piezoelectric pressure sensor for performing the quasi-static calibration according to any one of claims 1 to 4, wherein in the sixth step, a method for fitting an operating linear equation of the piezoelectric pressure sensor to be calibrated is acquired by using a tangent method or an endpoint translation method.
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